Finite Group Databasebeta

← #26379769

Subgroups — #26379769

Order 12032.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689700C211yesmaximal, characteristic
2#20246555C211yesmaximal, characteristic, complemented
3#20246550C211yesmaximal, characteristic, complemented
4#20246542C211yesmaximal, characteristic, complemented
5#20246539C211yesmaximal, characteristic, complemented
6#20246472C211yesmaximal, characteristic, complemented
7#20246469C211yesmaximal, characteristic, complemented
8#20246429C211yesmaximal, characteristic, complemented
9#20246426C211yesmaximal, characteristic, complemented
10#20246421C211yesmaximal, characteristic, complemented
11#20246416C211yesmaximal, characteristic, complemented
12#20246407C211yesmaximal, characteristic, complemented
13#20246390C211yesmaximal, characteristic, complemented
14#20246260C211yesmaximal, characteristic, complemented
15#20246258C211yesmaximal, characteristic, complemented
16#20246227C211yesmaximal, characteristic, complemented
17#20246214C211yesmaximal, characteristic, complemented
18#20246155C211yesmaximal, characteristic, complemented
19#20246151C211yesmaximal, characteristic, complemented
20#20246147C211yesmaximal, characteristic, complemented
21#20246147C211yesmaximal, characteristic, complemented
22#20246086C211yesmaximal, characteristic, complemented
23#20246085C211yesmaximal, characteristic, complemented
24#20246078C211yesmaximal, characteristic, complemented
25#20246074C211yesmaximal, characteristic, complemented
26#20246067C211yesmaximal, characteristic, complemented
27#20245978C211yesmaximal, characteristic, complemented
28#20245920C211yesmaximal, characteristic, complemented
29C4×#13093996C211yesmaximal, characteristic, complemented
30#20245873C211yesmaximal, characteristic, complemented
31C47×#2324C211yesmaximal, characteristic, complemented
32C22×#10625352C2211yescharacteristic
33C22×#10625352C2211yescharacteristic
34#15689700C4116yescomplemented
35C2×#13094002C2211yescharacteristic
36C2×#13094002C2211yescharacteristic
37C2×#13094001C2211yescharacteristic
38C2×#13094001C2211yescharacteristic
39C2×#13093998C2211yescharacteristic
40C2×#13093997C2211yescharacteristic
41C2×#13093997C2211yescharacteristic
42C2×#13093996C2211yescharacteristic
43C2×#13093996C2211yescharacteristic
44C2×#13093996C2211yescharacteristic
45C2×#13093996C2211yescharacteristic
46C2×C4×Dic94C2211yescharacteristic
47C2×#13093989C2211yescharacteristic
48C2×#13093986C2211yescharacteristic
49C2×C4×C22⋊D47C2211yescharacteristic
50C2×C4×C22⋊D47C2211yescharacteristic
51C2×C4×C22⋊D47C2211yescharacteristic
52C2×(C22⋊D47)⋊C4C2211yescharacteristic
53C2×#13093981C2211yescharacteristic
54C2×#13093980C2211yescharacteristic
55C2×#13093980C2211yescharacteristic
56C22×Dic47⋊C4C2211yescharacteristic
57C2×C4⋊C4×D47C2211yescharacteristic
58C22×C4×Dic47C2211yescharacteristic
59#15689029C2211yescharacteristic
60#15689028C2211yescharacteristic
61#15689027C2211yescharacteristic
62#15689027C2211yescharacteristic
63#15689027C2211yescharacteristic
64#15689027C2211yescharacteristic
65#15689026C2211yescharacteristic
66#15689026C2211yescharacteristic
67#15689024C2211yescharacteristic
68#15689023C2211yescharacteristic
69#15689023C2211yescharacteristic
70#15689023C2211yescharacteristic
71#15689023C2211yescharacteristic
72#15689023C2211yescharacteristic
73#15689023C2211yescharacteristic
74#15689023C2211yescharacteristic
75#15689023C2211yescharacteristic
76#15689020C2211yescharacteristic
77#15689020C2211yescharacteristic
78#15689019C2211yescharacteristic
79#15689018C2211yescharacteristic
80#15689018C2211yescharacteristic
81#15689018C2211yescharacteristic
82#15689018C2211yescharacteristic
83#15689017C2211yescharacteristic
84#15689017C2211yescharacteristic
85#15689016C2211yescharacteristic
86#15689016C2211yescharacteristic
87#15689015C2211yescharacteristic
88#15689014C2211yescharacteristic
89#15689014C2211yescharacteristic
90#15689014C2211yescharacteristic
91#15689013C2211yescharacteristic
92#15689013C2211yescharacteristic
93#15689013C2211yescharacteristic
94#15689012C2211yescharacteristic
95#15689011C2211yescharacteristic
96#15689011C2211yescharacteristic
97#15689009C2211yescharacteristic
98#15689009C2211yescharacteristic
99#15689008C2211yescharacteristic
100#15689008C2211yescharacteristic
101#15689007C2211yescharacteristic
102#15689007C2211yescharacteristic
103#15689007C2211yescharacteristic
104#15689007C2211yescharacteristic
105#15689005C2211yescharacteristic
106#15689005C2211yescharacteristic
107#15689004C2211yescharacteristic
108#15689004C2211yescharacteristic
109#15689004C2211yescharacteristic
110#15689004C2211yescharacteristic
111#15689004C2211yescharacteristic
112#15689004C2211yescharacteristic
113#15689003C2211yescharacteristic
114#15689003C2211yescharacteristic
115#15689003C2211yescharacteristic
116#15689003C2211yescharacteristic
117#15689002C2211yescharacteristic
118#15689001C2211yescharacteristic
119#15689001C2211yescharacteristic
120#15689000C2211yescharacteristic
121#15689000C2211yescharacteristic
122#15689000C2211yescharacteristic
123#15688999C2211yescharacteristic
124#15688999C2211yescharacteristic
125#15688999C2211yescharacteristic
126#15688999C2211yescharacteristic
127#15688999C2211yescharacteristic
128#15688999C2211yescharacteristic
129#15688999C2211yescharacteristic
130#15688999C2211yescharacteristic
131#15688997C2211yescharacteristic
132#15688996C2211yescharacteristic
133#15688995C2211yescharacteristic
134#15688994C2211yescharacteristic
135#15688994C2211yescharacteristic
136#15688994C2211yescharacteristic
137#15688986C2211yescharacteristic
138#15688985C2211yescharacteristic
139#15688984C2211yescharacteristic
140#15688984C2211yescharacteristic
141#15688981C2211yescharacteristic
142#15688981C2211yescharacteristic
143#15688981C2211yescharacteristic
144#15688981C2211yescharacteristic
145#15688981C2211yescharacteristic
146#15688981C2211yescharacteristic
147#15688980C2211yescharacteristic
148C4⋊C4×Dic47C2211yescharacteristic
149C4×Dic47⋊C4C2211yescharacteristic
150C4×Dic47⋊C4C2211yescharacteristic
151#15688974C2211yescharacteristic
152#15688974C2211yescharacteristic
153#15688974C2211yescharacteristic
154#15688974C2211yescharacteristic
155C22⋊C4×Dic47C2211yescharacteristic
156C22⋊C4×Dic47C2211yescharacteristic
157C22⋊C4×Dic47C2211yescharacteristic
158C22⋊C4×Dic47C2211yescharacteristic
159C22⋊C4×Dic47C2211yescharacteristic
160C22⋊C4×Dic47C2211yescharacteristic
161C22⋊C4×Dic47C2211yescharacteristic
162C4×(C2×D47)⋊C4C2211yescharacteristic
163C4×(C2×D47)⋊C4C2211yescharacteristic
164C4×(C2×D47)⋊C4C2211yescharacteristic
165C4×(C2×D47)⋊C4C2211yescharacteristic
166C4×C22⋊Dic47C2211yescharacteristic
167C4×C22⋊Dic47C2211yescharacteristic
168#15688970C2211yescharacteristic
169#15688970C2211yescharacteristic
170#15688970C2211yescharacteristic
171C2×C47⋊#95C2211yescharacteristic
172#95×D47C2211yescharacteristic
173C2×#121×C47C2211yescharacteristic
174C2×C4×D4×C47C2211yescharacteristic
175C2×#117×C47C2211yescharacteristic
176C47×#390C2211yescharacteristic
177C47×#390C2211yescharacteristic
178C47×#390C2211yescharacteristic
179C47×#389C2211yescharacteristic
180C47×#388C2211yescharacteristic
181C47×#388C2211yescharacteristic
182C47×#386C2211yescharacteristic
183C47×#386C2211yescharacteristic
184C47×#385C2211yescharacteristic
185C47×#385C2211yescharacteristic
186C47×#380C2211yescharacteristic
187C4×C4⋊C4×C47C2211yescharacteristic
188C2×#10625352—42no—
189C2×#10625352—42no—
190C2×#10625352—42no—
191C2×#10625352—42no—
192C2×#10625352C2×C418yescomplemented
193C2×#10625352C2×C418yescomplemented
194C22×Dic94C2311yescharacteristic
195C22×Dic94C2311yescharacteristic
196C22×D188C2311yescharacteristic
197C22×C22⋊D47C2311yescharacteristic
198C22×C22⋊D47C2311yescharacteristic
199C22×C22⋊D47C2311yescharacteristic
200C22×C22⋊D47C2311yescharacteristic
201C22×C22⋊D47C2311yescharacteristic
202C22×C22⋊D47C2311yescharacteristic
203C23×Dic47C2311yescharacteristic
204C23×Dic47C2311yescharacteristic
205C23×Dic47C2311yescharacteristic
206C23×Dic47C2311yescharacteristic
207C23×Dic47C2311yescharacteristic
208C23×Dic47C2311yescharacteristic
209C22×C4×D47C2311yescharacteristic
210C22×C4×D47C2311yescharacteristic
211C22×C4×D47C2311yescharacteristic
212C22×C4×D47C2311yescharacteristic
213C22×C4×D47C2311yescharacteristic
214C22×C4×D47C2311yescharacteristic
215#13094002C2×C418yescomplemented
216#13094002C2×C418yescomplemented
217#13094001C2×C418yescomplemented
218#13094001C2×C418yescomplemented
219#13093998C2×C418yescomplemented
220#13093997C2×C418yescomplemented
221#13093997C2×C418yescomplemented
222#13093996C2×C418yescomplemented
223#13093996C2×C418yescomplemented
224#13093996C2×C418yescomplemented
225#13093996C2×C418yescomplemented
226C4×Dic94—42no—
227#13093989—42no—
228#13093986—42no—
229C4×C22⋊D47—42no—
230C4×C22⋊D47—42no—
231C4×C22⋊D47—42no—
232(C22⋊D47)⋊C4—42no—
233#13093981—42no—
234#13093980—42no—
235#13093980—42no—
236C2×C4⋊Dic47C2311yescharacteristic
237C2×C4⋊Dic47C2311yescharacteristic
238C2×C4⋊Dic47C2311yescharacteristic
239C2×Dic47⋊C4C2×C418yescomplemented
240C2×Dic47⋊C4C2311yescharacteristic
241C2×Dic47⋊C4C2311yescharacteristic
242C2×Dic47⋊C4C2311yescharacteristic
243C2×Dic47⋊C4C2311yescharacteristic
244C2×Dic47⋊C4C2311yescharacteristic
245C2×Dic47⋊C4C2311yescharacteristic
246C2×Dic47⋊C4C2311yescharacteristic
247C2×Dic47⋊C4C2311yescharacteristic
248C2×Dic47⋊C4C2311yescharacteristic
249C2×Dic47⋊C4C2311yescharacteristic
250C2×Dic47⋊C4C2311yescharacteristic
251C2×Dic47⋊C4C2311yescharacteristic
252C2×Dic47⋊C4C2311yescharacteristic
253C2×Dic47⋊C4C2311yescharacteristic
254C2×Dic47⋊C4C2311yescharacteristic
255C2×Dic47⋊C4C2311yescharacteristic
256C2×Dic47⋊C4C2311yescharacteristic
257C2×Dic47⋊C4C2311yescharacteristic
258C4⋊C4×D47—42no—
259C2×C22⋊Dic47C2311yescharacteristic
260C2×C22⋊Dic47C2311yescharacteristic
261C2×C22⋊Dic47C2311yescharacteristic
262C2×C22⋊Dic47C2311yescharacteristic
263C2×C22⋊Dic47C2311yescharacteristic
264C2×C22⋊Dic47C2311yescharacteristic
265C2×C22⋊Dic47C2311yescharacteristic
266C2×C22⋊Dic47C2311yescharacteristic
267C2×C22⋊Dic47C2311yescharacteristic
268C2×C22⋊Dic47C2311yescharacteristic
269C2×C22⋊Dic47C2311yescharacteristic
270C2×C22⋊Dic47C2311yescharacteristic
271C2×(C2×D47)⋊C4C2311yescharacteristic
272C2×(C2×D47)⋊C4C2311yescharacteristic
273C2×(C2×D47)⋊C4C2311yescharacteristic
274C2×(C2×D47)⋊C4C2311yescharacteristic
275C2×(C2×D47)⋊C4C2311yescharacteristic
276C2×(C2×D47)⋊C4C2311yescharacteristic
277C2×(C2×D47)⋊C4C2311yescharacteristic
278C2×(C2×D47)⋊C4C2311yescharacteristic
279C2×(C2×D47)⋊C4C2311yescharacteristic
280C2×(C2×D47)⋊C4C2311yescharacteristic
281C2×(C2×D47)⋊C4C2311yescharacteristic
282C2×(C2×D47)⋊C4C2311yescharacteristic
283C2×(C2×D47)⋊C4C2311yescharacteristic
284C2×(C2×D47)⋊C4C2311yescharacteristic
285C2×(C2×D47)⋊C4C2311yescharacteristic
286C2×(C2×D47)⋊C4C2311yescharacteristic
287C2×C4×Dic47—42no—
288C2×C4×Dic47C2311yescharacteristic
289C2×C4×Dic47C2311yescharacteristic
290C2×C4×Dic47C2311yescharacteristic
291C2×C4×Dic47C2311yescharacteristic
292C2×C4×Dic47C2311yescharacteristic
293C2×C4×Dic47C2311yescharacteristic
294C2×C4×Dic47C2311yescharacteristic
295C2×C4×Dic47C2311yescharacteristic
296C2×C4×Dic47C2311yescharacteristic
297C2×C4×Dic47C2311yescharacteristic
298C2×C4×Dic47C2311yescharacteristic
299C2×C4×Dic47C2311yescharacteristic
300C2×C4×Dic47C2311yescharacteristic
301C2×C4×Dic47C2311yescharacteristic
302C2×C4×Dic47C2311yescharacteristic
303C2×C4×Dic47C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C47⋊#95C2311yescharacteristic
315C47⋊#95C2311yescharacteristic
316C47⋊#95C2311yescharacteristic
317C47⋊#95C2311yescharacteristic
318C47⋊#95C2311yescharacteristic
319C47⋊#95C2311yescharacteristic
320C47⋊#95C2311yescharacteristic
321C47⋊#95C2311yescharacteristic
322C47⋊#95C2311yescharacteristic
323C47⋊#95C2311yescharacteristic
324C47⋊#95C2311yescharacteristic
325C47⋊#95C2311yescharacteristic
326C47⋊#95C2311yescharacteristic
327C47⋊#95C2311yescharacteristic
328C47⋊#95C2311yescharacteristic
329C47⋊#95C2311yescharacteristic
330C47⋊#95C2311yescharacteristic
331C47⋊#95C2311yescharacteristic
332C47⋊#95C2311yescharacteristic
333C47⋊#95C2311yescharacteristic
334C47⋊#95C2311yescharacteristic
335C47⋊#95C2311yescharacteristic
336C47⋊#95C2311yescharacteristic
337C47⋊#95C2311yescharacteristic
338C22×D4×C47C2311yescharacteristic
339C22×D4×C47C2311yescharacteristic
340C22×D4×C47C2311yescharacteristic
341C23×C4×C47C2311yescharacteristic
342C23×C4×C47C2311yescharacteristic
343C23×C4×C47C2311yescharacteristic
344#121×C47C2×C418yescomplemented
345C4×D4×C47—42no—
346#117×C47—42no—
347C2×C4⋊C4×C47C2311yescharacteristic
348C2×C4⋊C4×C47C2311yescharacteristic
349C2×C4⋊C4×C47C2311yescharacteristic
350C2×C4⋊C4×C47C2311yescharacteristic
351C2×C4⋊C4×C47C2311yescharacteristic
352C2×C4⋊C4×C47C2311yescharacteristic
353C2×C4⋊C4×C47C2311yescharacteristic
354C2×C22⋊C4×C47C2311yescharacteristic
355C2×C22⋊C4×C47C2311yescharacteristic
356C2×C22⋊C4×C47C2311yescharacteristic
357C2×C22⋊C4×C47C2311yescharacteristic
358C2×C22⋊C4×C47C2311yescharacteristic
359C2×C22⋊C4×C47C2311yescharacteristic
360C2×C22⋊C4×C47C2311yescharacteristic
361C2×C22⋊C4×C47C2311yescharacteristic
362C2×C22⋊C4×C47C2311yescharacteristic
363C2×C22⋊C4×C47C2311yescharacteristic
364C2×C22⋊C4×C47C2311yescharacteristic
365C2×C22⋊C4×C47C2311yescharacteristic
366C2×C42×C47C2311yescharacteristic
367C2×C42×C47C2311yescharacteristic
368C2×C42×C47C2311yescharacteristic
369C2×C42×C47C2311yescharacteristic
370#95×C47C2311yescharacteristic
371#95×C47C2311yescharacteristic
372#95×C47C2311yescharacteristic
373#95×C47C2311yescharacteristic
374#95×C47C2311yescharacteristic
375#95×C47C2311yescharacteristic
376C24×C47C2411yescharacteristic
377C24×C47C2411yescharacteristic
378C24×C47C2411yescharacteristic
379C23×D47C2411yescharacteristic
380C23×D47C2411yescharacteristic
381C2×D4×C47—41no—
382C2×D4×C47—41no—
383C2×D4×C47—41no—
384C2×D4×C47—41no—
385C2×D4×C47—41no—
386C2×D4×C47—41no—
387C2×D4×C47C22×C414yes—
388C2×D4×C47C22×C414yes—
389C2×D4×C47C22×C414yes—
390C22×C4×C47—22no—
391C22×C4×C47—22no—
392C22×C4×C47—41no—
393C22×C4×C47—41no—
394C22×C4×C47—41no—
395C22×C4×C47—41no—
396C22×C4×C47—41no—
397C22×C4×C47—41no—
398C22×C4×C47C22×C414yes—
399C22×C4×C47C2411yescharacteristic
400C22×C4×C47C2411yescharacteristic
401C22×C4×C47C2411yescharacteristic
402C22×C4×C47C2411yescharacteristic
403C22×C4×C47C2411yescharacteristic
404C22×C4×C47C2411yescharacteristic
405C22×C4×C47C2411yescharacteristic
406C22×C4×C47C2411yescharacteristic
407C22×C4×C47C2411yescharacteristic
408C22×C4×C47C2411yescharacteristic
409C22×C4×C47C2411yescharacteristic
410C22×C4×C47C2411yescharacteristic
411C2×C22⋊D47—22no—
412C2×C22⋊D47—22no—
413C2×C22⋊D47—41no—
414C2×C22⋊D47—41no—
415C2×C22⋊D47—41no—
416C2×C22⋊D47—41no—
417C2×C22⋊D47—41no—
418C2×C22⋊D47—41no—
419C2×C22⋊D47—41no—
420C2×C22⋊D47—41no—
421C2×C22⋊D47—41no—
422C2×C22⋊D47—41no—
423C2×C22⋊D47C22×C414yes—
424C2×C22⋊D47C22×C414yes—
425C2×C22⋊D47C22×C414yes—
426C2×C22⋊D47C22×C414yes—
427C2×C22⋊D47C22×C414yes—
428C2×C22⋊D47C22×C414yes—
429C22×Dic47—22no—
430C22×Dic47—22no—
431C22×Dic47—22no—
432C22×Dic47—22no—
433C22×Dic47—22no—
434C22×Dic47—41no—
435C22×Dic47—41no—
436C22×Dic47—41no—
437C22×Dic47—41no—
438C22×Dic47—41no—
439C22×Dic47—41no—
440C22×Dic47—41no—
441C22×Dic47—41no—
442C22×Dic47—41no—
443C22×Dic47C22×C414yes—
444C22×Dic47C22×C414yes—
445C22×Dic47C22×C414yes—
446C22×Dic47C22×C414yes—
447C22×Dic47C2411yescharacteristic
448C22×Dic47C2411yescharacteristic
449C22×Dic47C2411yescharacteristic
450C22×Dic47C2411yescharacteristic
451C22×Dic47C2411yescharacteristic
452C22×Dic47C2411yescharacteristic
453C22×Dic47C2411yescharacteristic
454C22×Dic47C2411yescharacteristic
455C22×Dic47C2411yescharacteristic
456C22×Dic47C2411yescharacteristic
457C22×Dic47C2411yescharacteristic
458C22×Dic47C2411yescharacteristic
459C22×Dic47C2411yescharacteristic
460C22×Dic47C2411yescharacteristic
461#10625352—416no—
462#10625352—416no—
463C2×D188—41no—
464C2×D188—41no—
465C2×D188C22×C414yes—
466C2×C4×D47—22no—
467C2×C4×D47—22no—
468C2×C4×D47—22no—
469C2×C4×D47—41no—
470C2×C4×D47—41no—
471C2×C4×D47—41no—
472C2×C4×D47—41no—
473C2×C4×D47—41no—
474C2×C4×D47—41no—
475C2×C4×D47—41no—
476C2×C4×D47—41no—
477C2×C4×D47—41no—
478C2×C4×D47—41no—
479C2×C4×D47—41no—
480C2×C4×D47—41no—
481C2×C4×D47—41no—
482C2×C4×D47C22×C414yes—
483C2×C4×D47C22×C414yes—
484C2×Dic94—22no—
485C2×Dic94—22no—
486C2×Dic94—41no—
487C2×Dic94—41no—
488C2×Dic94C22×C414yes—
489C2×Dic94C22×C414yes—
490C4⋊C4×C47—22no—
491C4⋊C4×C47—41no—
492C4⋊C4×C47—41no—
493C4⋊C4×C47—41no—
494C4⋊C4×C47—41no—
495C4⋊C4×C47—41no—
496C4⋊C4×C47C22×C414yes—
497C22⋊C4×C47—22no—
498C22⋊C4×C47—41no—
499C22⋊C4×C47—41no—
500C22⋊C4×C47—41no—
501C22⋊C4×C47—41no—
502C22⋊C4×C47—41no—
503C22⋊C4×C47—41no—
504C22⋊C4×C47—41no—
505C22⋊C4×C47—41no—
506C22⋊C4×C47—41no—
507C22⋊C4×C47C22×C414yes—
508C22⋊C4×C47C22×C414yes—
509C42×C47—22no—
510C42×C47—41no—
511C42×C47—41no—
512C42×C47—41no—
513C22⋊Dic47—22no—
514C22⋊Dic47—22no—
515C22⋊Dic47—41no—
516C22⋊Dic47—41no—
517C22⋊Dic47—41no—
518C22⋊Dic47—41no—
519C22⋊Dic47—41no—
520C22⋊Dic47—41no—
521C22⋊Dic47—41no—
522C22⋊Dic47—41no—
523C22⋊Dic47C22×C414yes—
524C22⋊Dic47C22×C414yes—
525(C2×D47)⋊C4—22no—
526(C2×D47)⋊C4—22no—
527(C2×D47)⋊C4—22no—
528(C2×D47)⋊C4—41no—
529(C2×D47)⋊C4—41no—
530(C2×D47)⋊C4—41no—
531(C2×D47)⋊C4—41no—
532(C2×D47)⋊C4—41no—
533(C2×D47)⋊C4—41no—
534(C2×D47)⋊C4—41no—
535(C2×D47)⋊C4—41no—
536(C2×D47)⋊C4—41no—
537(C2×D47)⋊C4C22×C414yes—
538(C2×D47)⋊C4C22×C414yes—
539(C2×D47)⋊C4C22×C414yes—
540(C2×D47)⋊C4C22×C414yes—
541C4⋊Dic47—41no—
542C4⋊Dic47—41no—
543C4⋊Dic47C22×C414yes—
544Dic47⋊C4—22no—
545Dic47⋊C4—22no—
546Dic47⋊C4—22no—
547Dic47⋊C4—22no—
548Dic47⋊C4—22no—
549Dic47⋊C4—41no—
550Dic47⋊C4—41no—
551Dic47⋊C4—41no—
552Dic47⋊C4—41no—
553Dic47⋊C4—41no—
554Dic47⋊C4—41no—
555Dic47⋊C4—41no—
556Dic47⋊C4C22×C414yes—
557Dic47⋊C4C22×C414yes—
558Dic47⋊C4C22×C414yes—
559Dic47⋊C4C22×C414yes—
560Dic47⋊C4C22×C414yes—
561Dic47⋊C4C22×C414yes—
562C4×Dic47—22no—
563C4×Dic47—22no—
564C4×Dic47—22no—
565C4×Dic47—22no—
566C4×Dic47—22no—
567C4×Dic47—41no—
568C4×Dic47—41no—
569C4×Dic47—41no—
570C4×Dic47—41no—
571C4×Dic47—41no—
572C4×Dic47—41no—
573C4×Dic47—41no—
574C4×Dic47—41no—
575C4×Dic47—41no—
576C4×Dic47—41no—
577C4×Dic47—41no—
578C23×C47—21no—
579C23×C47—21no—
580C23×C47—21no—
581C23×C47—21no—
582C23×C47—21no—
583C23×C47—21no—
584C23×C47—21no—
585C23×C47—21no—
586C23×C47—21no—
587C23×C47—21no—
588C23×C47—21no—
589C23×C47—21no—
590C23×C47—21no—
591C23×C47—21no—
592C23×C47—21no—
593C23×C47—21no—
594C23×C47—21no—
595C23×C47—21no—
596C23×C47C23×C412yes—
597C23×C47C23×C412yes—
598C23×C47C23×C412yes—
599C23×C47C2511yescharacteristic
600C22×D47—21no—
601C22×D47—21no—
602C22×D47—21no—
603C22×D47—21no—
604C22×D47—21no—
605C22×D47—21no—
606C22×D47—21no—
607C22×D47—21no—
608C22×D47—21no—
609C22×D47—21no—
610C22×D47—21no—
611C22×D47—21no—
612C22×D47C23×C412yes—
613C22×D47C23×C412yes—
614D4×C47—44no—
615D4×C47—44no—
616D4×C47—44no—
617C2×C4×C47—21no—
618C2×C4×C47—21no—
619C2×C4×C47—21no—
620C2×C4×C47—21no—
621C2×C4×C47—21no—
622C2×C4×C47—21no—
623C2×C4×C47—21no—
624C2×C4×C47—21no—
625C2×C4×C47—21no—
626C2×C4×C47—21no—
627C2×C4×C47—21no—
628C2×C4×C47—21no—
629C2×C4×C47—21no—
630C2×C4×C47—21no—
631C2×C4×C47—21no—
632C2×C4×C47—21no—
633C2×C4×C47—21no—
634C2×C4×C47—21no—
635C2×C4×C47—21no—
636C2×C4×C47—21no—
637C2×C4×C47—21no—
638C2×C4×C47—21no—
639C2×C4×C47—21no—
640C2×C4×C47—21no—
641C2×C4×C47—21no—
642C2×C4×C47—21no—
643C2×C4×C47—21no—
644C2×C4×C47—21no—
645C2×C4×C47—21no—
646C2×C4×C47—21no—
647C2×C4×C47—21no—
648C2×C4×C47—44no—
649C2×C4×C47—44no—
650C2×C4×C47—82no—
651C2×C4×C47C23×C412yes—
652C2×C4×C47C23×C412yes—
653C2×C4×C47C23×C412yes—
654C2×C4×C47C23×C412yes—
655C2×C4×C47H(5,𝔽2)12yes—
656C22⋊D47—28no—
657C22⋊D47—44no—
658C22⋊D47—44no—
659C22⋊D47—44no—
660C22⋊D47—44no—
661C22⋊D47—44no—
662C2×Dic47—21no—
663C2×Dic47—21no—
664C2×Dic47—21no—
665C2×Dic47—21no—
666C2×Dic47—21no—
667C2×Dic47—21no—
668C2×Dic47—21no—
669C2×Dic47—21no—
670C2×Dic47—21no—
671C2×Dic47—21no—
672C2×Dic47—21no—
673C2×Dic47—21no—
674C2×Dic47—28no—
675C2×Dic47—28no—
676C2×Dic47—21no—
677C2×Dic47—21no—
678C2×Dic47—21no—
679C2×Dic47—21no—
680C2×Dic47—21no—
681C2×Dic47—21no—
682C2×Dic47—21no—
683C2×Dic47—21no—
684C2×Dic47—21no—
685C2×Dic47—21no—
686C2×Dic47—21no—
687C2×Dic47—21no—
688C2×Dic47—21no—
689C2×Dic47—21no—
690C2×Dic47—21no—
691C2×Dic47—21no—
692C2×Dic47—21no—
693C2×Dic47—21no—
694C2×Dic47—21no—
695C2×Dic47—21no—
696C2×Dic47—21no—
697C2×Dic47—44no—
698C2×Dic47—44no—
699C2×Dic47—44no—
700C2×Dic47—82no—
701C2×Dic47C23×C412yes—
702C2×Dic47C23×C412yes—
703C2×Dic47C23×C412yes—
704C2×Dic47C23×C412yes—
705C2×Dic47C23×C412yes—
706C2×Dic47C23×C412yes—
707C2×Dic47H(5,𝔽2)12yes—
708C2×Dic47H(5,𝔽2)12yes—
709C2×Dic472−1+412yes—
710D188—44no—
711C4×D47—28no—
712C4×D47—44no—
713C4×D47—82no—
714C4×D47—82no—
715C4×D47—82no—
716C4×D47—82no—
717Dic94—28no—
718Dic94—44no—
719#34414—471nomaximal, Sylow
720C22×C47—22no—
721C22×C47—22no—
722C22×C47—22no—
723C22×C47—22no—
724C22×C47—22no—
725C22×C47—22no—
726C22×C47—22no—
727C22×C47—22no—
728C22×C47—22no—
729C22×C47—41no—
730C22×C47—41no—
731C22×C47—41no—
732C22×C47—41no—
733C22×C47—41no—
734C22×C47—41no—
735C22×C47—41no—
736C22×C47—41no—
737C22×C47—41no—
738C22×C47—41no—
739C22×C47—41no—
740C22×C47—41no—
741C22×C47C24×C411yescharacteristic
742C22×C47C2×H(5,𝔽2)11yescharacteristic
743C22×C47C2×H(5,𝔽2)11yescharacteristic
744C22×C47C2×H(5,𝔽2)11yescharacteristic
745C22×C47C2×2−1+411yescharacteristic
746C22×C47#58511yescharacteristic
747C22×C47#58511yescharacteristic
748C2×D47—22no—
749C2×D47—22no—
750C2×D47—22no—
751C2×D47—22no—
752C2×D47—22no—
753C2×D47—22no—
754C2×D47—41no—
755C2×D47—41no—
756C2×D47—41no—
757C2×D47—41no—
758C2×D47—41no—
759C2×D47—41no—
760C2×D47—41no—
761C2×D47—41no—
762C4×C47—22no—
763C4×C47—22no—
764C4×C47—22no—
765C4×C47—22no—
766C4×C47—22no—
767C4×C47—41no—
768C4×C47—41no—
769C4×C47—41no—
770C4×C47—41no—
771C4×C47—41no—
772C4×C47—41no—
773C4×C47—41no—
774Dic47—22no—
775Dic47—22no—
776Dic47—22no—
777Dic47—22no—
778Dic47—22no—
779Dic47—22no—
780Dic47—41no—
781Dic47—41no—
782Dic47—41no—
783Dic47—41no—
784Dic47—41no—
785Dic47—41no—
786Dic47—41no—
787Dic47#51814yes—
788C2×#537—471no—
789#2378—471no—
790#2378—471no—
791#2377—471no—
792#2377—471no—
793#2368—471no—
794#2368—471no—
795#2363—471no—
796#2363—471no—
797#2363—471no—
798#2362—471no—
799#2361—471no—
800#2360—471no—
801#2345—471no—
802#2344—471no—
803#2341—471no—
804#2339—471no—
805#2333—471no—
806#2333—471no—
807#2333—471no—
808#2333—471no—
809#2325—471no—
810#2325—471no—
811#2324—471no—
812#2324—471no—
813#2324D4711yescharacteristic, complemented
814#2323—471no—
815#2311—471no—
816C4×C22⋊Q8—471no—
817C4×#121—471no—
818#2297—471no—
819C2×C47—42no—
820C2×C47—42no—
821C2×C47—42no—
822C2×C47C2×#51811yescharacteristic
823C2×C47C4×H(5,𝔽2)11yescharacteristic
824C2×C47C4×2−1+411yescharacteristic
825C2×C47#354111yescharacteristic
826C2×C47#354211yescharacteristic
827C2×C47#354811yescharacteristic
828C2×C47#355111yescharacteristic
829D47—42no—
830D47—42no—
831C22×#41—471no—
832C22×#41—471no—
833#537—4716no—
834C2×C22⋊Q8—471no—
835C2×C22⋊Q8—471no—
836C2×C22⋊Q8—471no—
837C2×C22⋊Q8—471no—
838C2×#121—471no—
839C2×#121—471no—
840C2×#121—471no—
841C2×#121—471no—
842C2×#121—471no—
843C2×#121—471no—
844C2×#121—471no—
845C2×#121C2×D4711yescharacteristic
846C2×C4×Q8—471no—
847C2×C4×Q8—471no—
848C2×C4×D4—471no—
849C2×C4×D4—471no—
850C2×C4×D4—471no—
851C2×C4×D4—471no—
852C2×C4×D4—471no—
853C2×C4×D4C2×D4711yescharacteristic
854C2×#117—471no—
855C2×#117—471no—
856C2×#117—471no—
857C2×#117C2×D4711yescharacteristic
858C22×C4⋊C4—471no—
859C22×C4⋊C4—471no—
860C22×C42—471no—
861#391—471no—
862#391—471no—
863#391—471no—
864#391—471no—
865#391—471no—
866#391—471no—
867#390—471no—
868#390—471no—
869#390—471no—
870#390—471no—
871#390—471no—
872#390—471no—
873#390—471no—
874#390—471no—
875#390—471no—
876#390—471no—
877#390—471no—
878#390C2×D4711yescharacteristic
879#390C2×D4711yescharacteristic
880#390C2×D4711yescharacteristic
881#389—471no—
882#389—471no—
883#389—471no—
884#389—471no—
885#389—471no—
886#389—471no—
887#389—471no—
888#389C2×D4711yescharacteristic
889#388—471no—
890#388—471no—
891#388—471no—
892#388—471no—
893#388—471no—
894#388—471no—
895#388—471no—
896#388—471no—
897#388—471no—
898#388—471no—
899#388—471no—
900#388—471no—
901#388—471no—
902#388—471no—
903#388C2×D4711yescharacteristic
904#388C2×D4711yescharacteristic
905#387—471no—
906#387—471no—
907#387—471no—
908#387—471no—
909#387—471no—
910#387—471no—
911#387—471no—
912#387—471no—
913#387—471no—
914#387—471no—
915#387—471no—
916#387—471no—
917#387—471no—
918#387—471no—
919#387—471no—
920#387—471no—
921#386—471no—
922#386—471no—
923#386—471no—
924#386—471no—
925#386—471no—
926#386—471no—
927#386—471no—
928#386—471no—
929#386—471no—
930#386—471no—
931#386—471no—
932#386—471no—
933#386—471no—
934#386—471no—
935#386—471no—
936#386—471no—
937#386—471no—
938#386—471no—
939#386C2×D4711yescharacteristic
940#386C2×D4711yescharacteristic
941#385—471no—
942#385—471no—
943#385—471no—
944#385—471no—
945#385—471no—
946#385—471no—
947#385C2×D4711yescharacteristic
948#385C2×D4711yescharacteristic
949#381—471no—
950#381—471no—
951#381—471no—
952#381—471no—
953#380—471no—
954#380—471no—
955#380—471no—
956#380—471no—
957#380—471no—
958#380—471no—
959#380—471no—
960#380C2×D4711yescharacteristic
961C4×C4⋊C4—471no—
962C4×C4⋊C4—471no—
963C4×C4⋊C4—471no—
964C4×C4⋊C4—471no—
965C4×C4⋊C4—471no—
966C4×C4⋊C4—471no—
967C4×C4⋊C4—471no—
968C4×C4⋊C4C2×D4711yescharacteristic
969C4×C22⋊C4—471no—
970C4×C22⋊C4—471no—
971C4×C22⋊C4—471no—
972C4×C22⋊C4—471no—
973C4×C22⋊C4—471no—
974C4×C22⋊C4—471no—
975C4×C22⋊C4—471no—
976C4×C22⋊C4—471no—
977C4×C22⋊C4—471no—
978C4×C22⋊C4—471no—
979C4×C22⋊C4—471no—
980C4×C22⋊C4—471no—
981C4×C22⋊C4—471no—
982C4×C22⋊C4—471no—
983C4×C22⋊C4—471no—
984C4×C22⋊C4—471no—
985C2×#95—471no—
986C2×#95—471no—
987C47#3441411yescharacteristic, complemented, Sylow
988C2×#41—478no—
989C2×#41—478no—
990C2×#41—1882no—
991C2×#41—1882no—
992C2×#41—1882no—
993C2×#41—1882no—
994C22×Q8—471no—
995C22×Q8—471no—
996C22×D4—471no—
997C22×D4—471no—
998C22×D4—471no—
999C22×D4—471no—
1000C22×D4—471no—
1001C22×D4—471no—
1002C22×D4—471no—
1003C22×D4C22×D4711yescharacteristic
1004C22×D4C22×D4711yescharacteristic
1005C22×D4C22×D4711yescharacteristic
1006C23×C4—471no—
1007C23×C4—471no—
1008C23×C4—471no—
1009C23×C4—471no—
1010C23×C4—471no—
1011C23×C4—471no—
1012C23×C4—471no—
1013C23×C4—471no—
1014C23×C4—471no—
1015C23×C4—471no—
1016C23×C4—471no—
1017C23×C4—471no—
1018C23×C4C22×D4711yescharacteristic
1019C23×C4C22×D4711yescharacteristic
1020C23×C4C22×D4711yescharacteristic
1021C22⋊Q8—478no—
1022C22⋊Q8—478no—
1023C22⋊Q8—478no—
1024C22⋊Q8—478no—
1025#121—478no—
1026#121—478no—
1027#121—478no—
1028#121—478no—
1029#121—478no—
1030#121—478no—
1031#121—478no—
1032#121C4×D4718yescomplemented
1033C4×Q8—1882no—
1034C4×Q8—1882no—
1035C4×D4—42no—
1036C4×D4—1882no—
1037C4×D4—1882no—
1038C4×D4—1882no—
1039C4×D4—1882no—
1040C4×D4—1882no—
1041#117—42no—
1042#117—1882no—
1043#117—1882no—
1044#117—1882no—
1045C2×C4⋊C4—478no—
1046C2×C4⋊C4—471no—
1047C2×C4⋊C4—471no—
1048C2×C4⋊C4—471no—
1049C2×C4⋊C4—471no—
1050C2×C4⋊C4—471no—
1051C2×C4⋊C4—471no—
1052C2×C4⋊C4—471no—
1053C2×C4⋊C4—471no—
1054C2×C4⋊C4—471no—
1055C2×C4⋊C4—471no—
1056C2×C4⋊C4—471no—
1057C2×C4⋊C4—471no—
1058C2×C4⋊C4—471no—
1059C2×C4⋊C4—471no—
1060C2×C4⋊C4—471no—
1061C2×C4⋊C4—471no—
1062C2×C4⋊C4—471no—
1063C2×C4⋊C4—471no—
1064C2×C4⋊C4—471no—
1065C2×C4⋊C4—471no—
1066C2×C4⋊C4—471no—
1067C2×C4⋊C4—1882no—
1068C2×C4⋊C4C22×D4711yescharacteristic
1069C2×C4⋊C4C22×D4711yescharacteristic
1070C2×C4⋊C4C22×D4711yescharacteristic
1071C2×C4⋊C4C22×D4711yescharacteristic
1072C2×C4⋊C4C22×D4711yescharacteristic
1073C2×C4⋊C4C22×D4711yescharacteristic
1074C2×C4⋊C4C22×D4711yescharacteristic
1075C2×C22⋊C4—471no—
1076C2×C22⋊C4—471no—
1077C2×C22⋊C4—471no—
1078C2×C22⋊C4—471no—
1079C2×C22⋊C4—471no—
1080C2×C22⋊C4—471no—
1081C2×C22⋊C4—471no—
1082C2×C22⋊C4—471no—
1083C2×C22⋊C4—471no—
1084C2×C22⋊C4—471no—
1085C2×C22⋊C4—471no—
1086C2×C22⋊C4—471no—
1087C2×C22⋊C4—471no—
1088C2×C22⋊C4—471no—
1089C2×C22⋊C4—471no—
1090C2×C22⋊C4—471no—
1091C2×C22⋊C4—471no—
1092C2×C22⋊C4—471no—
1093C2×C22⋊C4—471no—
1094C2×C22⋊C4—471no—
1095C2×C22⋊C4—471no—
1096C2×C22⋊C4—471no—
1097C2×C22⋊C4—471no—
1098C2×C22⋊C4—471no—
1099C2×C22⋊C4—471no—
1100C2×C22⋊C4—471no—
1101C2×C22⋊C4—471no—
1102C2×C22⋊C4—471no—
1103C2×C22⋊C4C22×D4711yescharacteristic
1104C2×C22⋊C4C22×D4711yescharacteristic
1105C2×C22⋊C4C22×D4711yescharacteristic
1106C2×C22⋊C4C22×D4711yescharacteristic
1107C2×C22⋊C4C22×D4711yescharacteristic
1108C2×C22⋊C4C22×D4711yescharacteristic
1109C2×C22⋊C4C22×D4711yescharacteristic
1110C2×C22⋊C4C22×D4711yescharacteristic
1111C2×C22⋊C4C22×D4711yescharacteristic
1112C2×C22⋊C4C22×D4711yescharacteristic
1113C2×C22⋊C4C22×D4711yescharacteristic
1114C2×C22⋊C4C22×D4711yescharacteristic
1115C2×C42—471no—
1116C2×C42—471no—
1117C2×C42—471no—
1118C2×C42—471no—
1119C2×C42—471no—
1120C2×C42—471no—
1121C2×C42—471no—
1122C2×C42—471no—
1123C2×C42—471no—
1124C2×C42—471no—
1125C2×C42—471no—
1126C2×C42—471no—
1127C2×C42—471no—
1128C2×C42—471no—
1129C2×C42—471no—
1130C2×C42—471no—
1131C2×C42—1882no—
1132C2×C42C22×D4711yescharacteristic
1133C2×C42C22×D4711yescharacteristic
1134C2×C42C22×D4711yescharacteristic
1135C2×C42C22×D4711yescharacteristic
1136#95—471no—
1137#95—471no—
1138#95—471no—
1139#95—471no—
1140#95—471no—
1141#95—471no—
1142#95—471no—
1143#95—471no—
1144#95—471no—
1145#95—471no—
1146#95—471no—
1147#95—471no—
1148#95—471no—
1149#95—471no—
1150#95—471no—
1151#95—471no—
1152#95—471no—
1153#95—471no—
1154#95—471no—
1155#95—471no—
1156#95—471no—
1157#95—471no—
1158#95—471no—
1159#95—471no—
1160#95—471no—
1161#95—471no—
1162#95—471no—
1163#95—471no—
1164#95—471no—
1165#95—471no—
1166#95—471no—
1167#95—471no—
1168#95—471no—
1169#95—471no—
1170#95C22×D4711yescharacteristic
1171#95C22×D4711yescharacteristic
1172#95C22×D4711yescharacteristic
1173#95C22×D4711yescharacteristic
1174#95C22×D4711yescharacteristic
1175#95C22×D4711yescharacteristic
1176C24—471no—
1177C24—471no—
1178C24C23×D4711yescharacteristic
1179C24C23×D4711yescharacteristic
1180C24C23×D4711yescharacteristic
1181#41—18816no—
1182#41—18816no—
1183C2×Q8—474no—
1184C2×Q8—474no—
1185C2×Q8—942no—
1186C2×Q8—942no—
1187C2×Q8—1881no—
1188C2×Q8—1881no—
1189C2×D4—41no—
1190C2×D4—41no—
1191C2×D4—41no—
1192C2×D4—41no—
1193C2×D4—41no—
1194C2×D4—41no—
1195C2×D4—474no—
1196C2×D4—474no—
1197C2×D4—474no—
1198C2×D4—474no—
1199C2×D4—474no—
1200C2×D4—474no—
1201C2×D4—474no—
1202C2×D4—942no—
1203C2×D4—942no—
1204C2×D4—1881no—
1205C2×D4—1881no—
1206C2×D4—1881no—
1207C2×D4—1881no—
1208C2×D4—1881no—
1209C2×D4—1881no—
1210C2×D4—1881no—
1211C2×D4—1881no—
1212C2×D4—1881no—
1213C2×D4—1881no—
1214C2×D4—1881no—
1215C2×D4—1881no—
1216C2×D4C2×C4×D4714yes—
1217C2×D4C2×C4×D4714yes—
1218C2×D4C2×C4×D4714yes—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—471no—
1228C22×C4—474no—
1229C22×C4—474no—
1230C22×C4—471no—
1231C22×C4—471no—
1232C22×C4—471no—
1233C22×C4—471no—
1234C22×C4—471no—
1235C22×C4—471no—
1236C22×C4—474no—
1237C22×C4—474no—
1238C22×C4—474no—
1239C22×C4—474no—
1240C22×C4—471no—
1241C22×C4—471no—
1242C22×C4—471no—
1243C22×C4—471no—
1244C22×C4—471no—
1245C22×C4—471no—
1246C22×C4—471no—
1247C22×C4—942no—
1248C22×C4—942no—
1249C22×C4—942no—
1250C22×C4—942no—
1251C22×C4—942no—
1252C22×C4—942no—
1253C22×C4—942no—
1254C22×C4—942no—
1255C22×C4—1881no—
1256C22×C4—1881no—
1257C22×C4—1881no—
1258C22×C4—1881no—
1259C22×C4—1881no—
1260C22×C4—1881no—
1261C22×C4—1881no—
1262C22×C4—1881no—
1263C22×C4—1881no—
1264C22×C4—1881no—
1265C22×C4—1881no—
1266C22×C4—1881no—
1267C22×C4—1881no—
1268C22×C4—1881no—
1269C22×C4—1881no—
1270C22×C4—1881no—
1271C22×C4—1881no—
1272C22×C4—1881no—
1273C22×C4—1881no—
1274C22×C4—1881no—
1275C22×C4—1881no—
1276C22×C4—1881no—
1277C22×C4C2×C4×D4714yes—
1278C22×C4C23×D4711yescharacteristic
1279C22×C4C23×D4711yescharacteristic
1280C22×C4C23×D4711yescharacteristic
1281C22×C4C23×D4711yescharacteristic
1282C22×C4C23×D4711yescharacteristic
1283C22×C4C23×D4711yescharacteristic
1284C22×C4C23×D4711yescharacteristic
1285C22×C4C23×D4711yescharacteristic
1286C22×C4C23×D4711yescharacteristic
1287C22×C4C23×D4711yescharacteristic
1288C22×C4C23×D4711yescharacteristic
1289C22×C4C23×D4711yescharacteristic
1290C4⋊C4—22no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—474no—
1297C4⋊C4—474no—
1298C4⋊C4—474no—
1299C4⋊C4—474no—
1300C4⋊C4—474no—
1301C4⋊C4—474no—
1302C4⋊C4—474no—
1303C4⋊C4—942no—
1304C4⋊C4—942no—
1305C4⋊C4—942no—
1306C4⋊C4—942no—
1307C4⋊C4—942no—
1308C4⋊C4—1881no—
1309C4⋊C4—1881no—
1310C4⋊C4—1881no—
1311C4⋊C4—1881no—
1312C4⋊C4—1881no—
1313C4⋊C4—1881no—
1314C4⋊C4—1881no—
1315C4⋊C4—1881no—
1316C4⋊C4—1881no—
1317C4⋊C4C2×C4×D4714yes—
1318C22⋊C4—22no—
1319C22⋊C4—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—474no—
1329C22⋊C4—474no—
1330C22⋊C4—474no—
1331C22⋊C4—474no—
1332C22⋊C4—474no—
1333C22⋊C4—474no—
1334C22⋊C4—942no—
1335C22⋊C4—942no—
1336C22⋊C4—942no—
1337C22⋊C4—942no—
1338C22⋊C4—942no—
1339C22⋊C4—1881no—
1340C22⋊C4—1881no—
1341C22⋊C4—1881no—
1342C22⋊C4—1881no—
1343C22⋊C4—1881no—
1344C22⋊C4—1881no—
1345C22⋊C4—1881no—
1346C22⋊C4—1881no—
1347C22⋊C4—1881no—
1348C22⋊C4—1881no—
1349C22⋊C4—1881no—
1350C22⋊C4—1881no—
1351C22⋊C4—1881no—
1352C22⋊C4—1881no—
1353C22⋊C4—1881no—
1354C22⋊C4—1881no—
1355C22⋊C4—1881no—
1356C22⋊C4C2×C4×D4714yes—
1357C22⋊C4C2×C4×D4714yes—
1358C42—22no—
1359C42—41no—
1360C42—41no—
1361C42—41no—
1362C42—942no—
1363C42—942no—
1364C42—942no—
1365C42—942no—
1366C42—942no—
1367C42—1881no—
1368C42—1881no—
1369C42—1881no—
1370C42—1881no—
1371C42—1881no—
1372C42—1881no—
1373C42—1881no—
1374C42—1881no—
1375C42—1881no—
1376C42—1881no—
1377C42—1881no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—472no—
1397C23—472no—
1398C23—941no—
1399C23—941no—
1400C23—941no—
1401C23—941no—
1402C23—941no—
1403C23—941no—
1404C23—941no—
1405C23—941no—
1406C23—941no—
1407C23—941no—
1408C23—941no—
1409C23—941no—
1410C23C22×C4×D4712yes—
1411C23C22×C4×D4712yes—
1412C23C22×C4×D4712yes—
1413C23C24×D4711yescharacteristic
1414Q8—948no—
1415Q8—1884no—
1416D4—44no—
1417D4—44no—
1418D4—44no—
1419D4—948no—
1420D4—1884no—
1421D4—1884no—
1422D4—1884no—
1423D4—1884no—
1424D4—1884no—
1425D4—1884no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—44no—
1458C2×C4—44no—
1459C2×C4—82no—
1460C2×C4—472no—
1461C2×C4—472no—
1462C2×C4—472no—
1463C2×C4—472no—
1464C2×C4—472no—
1465C2×C4—472no—
1466C2×C4—472no—
1467C2×C4—472no—
1468C2×C4—472no—
1469C2×C4—948no—
1470C2×C4—948no—
1471C2×C4—948no—
1472C2×C4—941no—
1473C2×C4—941no—
1474C2×C4—941no—
1475C2×C4—941no—
1476C2×C4—941no—
1477C2×C4—941no—
1478C2×C4—941no—
1479C2×C4—941no—
1480C2×C4—941no—
1481C2×C4—941no—
1482C2×C4—941no—
1483C2×C4—941no—
1484C2×C4—941no—
1485C2×C4—941no—
1486C2×C4—941no—
1487C2×C4—941no—
1488C2×C4—941no—
1489C2×C4—941no—
1490C2×C4—941no—
1491C2×C4—941no—
1492C2×C4—941no—
1493C2×C4—941no—
1494C2×C4—941no—
1495C2×C4—941no—
1496C2×C4—941no—
1497C2×C4—941no—
1498C2×C4—941no—
1499C2×C4—941no—
1500C2×C4—941no—
1501C2×C4—941no—
1502C2×C4—941no—
1503C2×C4—941no—
1504C2×C4—941no—
1505C2×C4—3762no—
1506C2×C4—3762no—
1507C2×C4—3762no—
1508C2×C4—3762no—
1509C2×C4—3762no—
1510C2×C4—1884no—
1511C2×C4—1884no—
1512C2×C4—1884no—
1513C2×C4—1884no—
1514C2×C4C22×C4×D4712yes—
1515C2×C4C22×C4×D4712yes—
1516C2×C4C22×C4×D4712yes—
1517C2×C4C22×C4×D4712yes—
1518C2×C4#1309406912yes—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—22no—
1523C22—22no—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—942no—
1541C22—942no—
1542C22—942no—
1543C22—942no—
1544C22—942no—
1545C22—942no—
1546C22—1881no—
1547C22—1881no—
1548C22—1881no—
1549C22—1881no—
1550C22—1881no—
1551C22—1881no—
1552C22—1881no—
1553C22—1881no—
1554C22C23×C4×D4711yescharacteristic
1555C22H(5,𝔽2)×D4711yescharacteristic
1556C22H(5,𝔽2)×D4711yescharacteristic
1557C22C2×#1309406911yescharacteristic
1558C222−1+4×D4711yescharacteristic
1559C22#1568995811yescharacteristic
1560C22#1568995911yescharacteristic
1561C4—22no—
1562C4—22no—
1563C4—22no—
1564C4—22no—
1565C4—22no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—474no—
1574C4—942no—
1575C4—942no—
1576C4—942no—
1577C4—942no—
1578C4—942no—
1579C4—942no—
1580C4—1881no—
1581C4—1881no—
1582C4—1881no—
1583C4—1881no—
1584C4—1881no—
1585C4—1881no—
1586C4—1881no—
1587C2—42no—
1588C2—42no—
1589C2—42no—
1590C2—1882no—
1591C2—1882no—
1592C2#518×D4711yescharacteristic
1593C2C4×#1309406911yescharacteristic
1594C2#2025659911yescharacteristic
1595C2#2025767211yescharacteristic
1596C2#2025769111yescharacteristic
1597C2#2025778311yescharacteristic
1598C2#2025780911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2324C2
socle, cosocleC23×C47C25
prime radicalC2×#15689700C2
hypercenter#2324D47
hypocenterC47#34414
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2324

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20246555C2semidirect
3. #20246550C2semidirect
4. #20246542C2semidirect
5. #20246539C2semidirect
6. #20246472C2semidirect
7. #20246469C2semidirect
8. #20246429C2semidirect
9. #20246426C2semidirect
10. #20246421C2semidirect
11. #20246416C2semidirect
12. #20246407C2semidirect
13. #20246390C2semidirect
14. #20246260C2semidirect
15. #20246258C2semidirect
16. #20246227C2semidirect
17. #20246214C2semidirect
18. #20246155C2semidirect
19. #20246151C2semidirect
20. #20246147C2semidirect
21. #20246147C2semidirect
22. #20246086C2semidirect
23. #20246085C2semidirect
24. #20246078C2semidirect
25. #20246074C2semidirect
26. #20246067C2semidirect
27. #20245978C2semidirect
28. #20245920C2semidirect
29. C4×#13093996C2semidirect
30. #20245873C2semidirect
31. C47×#2324C2semidirect
34. #15689700C4semidirect
192. C2×#10625352C2×C4semidirect
193. C2×#10625352C2×C4semidirect
215. #13094002C2×C4semidirect
216. #13094002C2×C4semidirect
217. #13094001C2×C4semidirect
218. #13094001C2×C4semidirect
219. #13093998C2×C4semidirect
220. #13093997C2×C4semidirect
221. #13093997C2×C4semidirect
222. #13093996C2×C4semidirect
223. #13093996C2×C4semidirect
224. #13093996C2×C4semidirect
225. #13093996C2×C4semidirect
239. C2×Dic47⋊C4C2×C4semidirect
344. #121×C47C2×C4semidirect
813. #2324D47semidirect
987. C47#34414semidirect
1032. #121C4×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156897002
#202465552
#202465502
#202465422
#202465392
#202464722
#202464692
#202464292
#202464262
#202464212
#202464162
#202464072
#202463902
#202462602
#202462582
#202462272
#202462142
#202461552
#202461512
#202461472
#202460862
#202460852
#202460782
#202460742
#202460672
#202459782
#202459202
C4×#130939962
#202458732
C47×#23242
#3441447