Finite Group Databasebeta

← #26379083

Subgroups — #26379083

Order 12032.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093997C211yesmaximal, characteristic
2#20246544C212yesmaximal, complemented
3#20246541C212yesmaximal, complemented
4#20246427C212yesmaximal, complemented
5#20246421C212yesmaximal, complemented
6#20246258C211yesmaximal, characteristic, complemented
7#20246252C211yesmaximal, characteristic, complemented
8#20246240C211yesmaximal, characteristic, complemented
9#20246237C211yesmaximal, characteristic, complemented
10#20246234C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D47C211yesmaximal, characteristic, complemented
12#20246204C211yesmaximal, characteristic, complemented
13#20246151C212yesmaximal, complemented
14#20246148C212yesmaximal, complemented
15#20246080C212yesmaximal, complemented
16#20246076C212yesmaximal, complemented
17#20245969C211yesmaximal, characteristic, complemented
18#20245968C211yesmaximal, characteristic, complemented
19#20245965C211yesmaximal, characteristic, complemented
20#20245963C211yesmaximal, characteristic, complemented
21#20245770C211yesmaximal, characteristic, complemented
22#20245769C211yesmaximal, characteristic, complemented
23C47×#2342C211yesmaximal, characteristic, complemented
24C23×D188C2211yescharacteristic
25C23×C22⋊D47C2211yescharacteristic
26C23×C22⋊D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28C2×#13093997C4116yescomplemented
29C2×#13093997C2211yescharacteristic
30C2×#13093997C2211yescharacteristic
31C2×#13093997C2211yescharacteristic
32C2×#13093997C2211yescharacteristic
33C2×#13093997C2211yescharacteristic
34C2×#13093997C2211yescharacteristic
35C2×#13093997C2211yescharacteristic
36C2×#13093997C2211yescharacteristic
37C2×C4×C22⋊D47C2212yescomplemented
38C2×(C22⋊D47)⋊C4C2212yescomplemented
39C2×#13093983C2211yescharacteristic
40C2×#13093982C2212yescomplemented
41C2×#13093981C2212yescomplemented
42C2×#13093980C2211yescharacteristic
43C2×#13093980C2211yescharacteristic
44C22×Dic47⋊C4C2211yescharacteristic
45C22×C22⋊Dic47C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D47C2211yescharacteristic
48C2×C22⋊C4×D47C2211yescharacteristic
49#15689025C2212yescomplemented
50#15689025C2212yescomplemented
51#15689024C2212yescomplemented
52#15689024C2212yescomplemented
53#15689023C2212yescomplemented
54#15689023C2212yescomplemented
55#15689023C2212yescomplemented
56#15689023C2212yescomplemented
57#15689023C2212yescomplemented
58#15689023C2212yescomplemented
59#15689020C2212yescomplemented
60#15689018C2212yescomplemented
61#15689016C2212yescomplemented
62#15689016C2212yescomplemented
63#15689015C2212yescomplemented
64#15689014C2212yescomplemented
65#15689013C2212yescomplemented
66#15689012C2212yescomplemented
67#15689010C2212yescomplemented
68#15689007C2212yescomplemented
69#15689005C2212yescomplemented
70#15689004C2212yescomplemented
71#15689002C2212yescomplemented
72#15689002C2212yescomplemented
73#15689002C2212yescomplemented
74#15689001C2212yescomplemented
75#15689001C2212yescomplemented
76#15689001C2212yescomplemented
77#15689001C2212yescomplemented
78#15689000C2212yescomplemented
79#15689000C2212yescomplemented
80#15689000C2212yescomplemented
81#15688999C2212yescomplemented
82#15688999C2212yescomplemented
83#15688998C2212yescomplemented
84#15688997C2212yescomplemented
85#15688994C2212yescomplemented
86#15688986C2211yescharacteristic
87#15688985C2212yescomplemented
88#15688985C2212yescomplemented
89#15688984C2211yescharacteristic
90#15688984C2211yescharacteristic
91#15688983C2211yescharacteristic
92#15688982C2212yescomplemented
93#15688981C2211yescharacteristic
94#15688981C2211yescharacteristic
95#15688980C2212yescomplemented
96#15688979C2211yescharacteristic
97#15688978C2211yescharacteristic
98#15688978C2211yescharacteristic
99#15688978C2211yescharacteristic
100#15688978C2211yescharacteristic
101#15688978C2211yescharacteristic
102#15688978C2211yescharacteristic
103C4×Dic47⋊C4C2212yescomplemented
104#15688974C2212yescomplemented
105C22⋊C4×Dic47C2211yescharacteristic
106C22⋊C4×Dic47C2211yescharacteristic
107C22⋊C4×Dic47C2212yescomplemented
108C4×(C2×D47)⋊C4C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×C22⋊Dic47C2211yescharacteristic
111#15688970C2212yescomplemented
112#15688970C2212yescomplemented
113C2×#117×C47C2211yescharacteristic
114C22×C22⋊C4×C47C2211yescharacteristic
115C22×C22⋊C4×C47C2211yescharacteristic
116C47×#388C2212yescomplemented
117C47×#388C2212yescomplemented
118C47×#385C2212yescomplemented
119C47×#381C2211yescharacteristic
120C47×#380C2211yescharacteristic
121C47×#379C2211yescharacteristic
122C4×C22⋊C4×C47C2211yescharacteristic
123C4×C22⋊C4×C47C2212yescomplemented
124C24×D47C2311yescharacteristic
125C24×D47C2311yescharacteristic
126C22×D188—42no—
127C22×D188—42no—
128C22×D188C2×C418yescomplemented
129C22×D188C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×D188C2311yescharacteristic
132C22×D188C2311yescharacteristic
133C22×C22⋊D47—44no—
134C22×C22⋊D47—42no—
135C22×C22⋊D47—42no—
136C22×C22⋊D47C2×C418yes—
137C22×C22⋊D47C2×C418yescomplemented
138C22×C22⋊D47C2311yescharacteristic
139C22×C22⋊D47C2311yescharacteristic
140C22×C22⋊D47C2311yescharacteristic
141C22×C22⋊D47C2311yescharacteristic
142C22×C22⋊D47C2311yescharacteristic
143C22×C22⋊D47C2311yescharacteristic
144C22×C22⋊D47C2311yescharacteristic
145C22×C22⋊D47C2311yescharacteristic
146C23×Dic47C2311yescharacteristic
147C23×Dic47C2311yescharacteristic
148C23×Dic47C2312yes—
149C22×C4×D47—44no—
150C22×C4×D47C2×C418yescomplemented
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2312yes—
154C22×C4×D47C2312yes—
155C22×C4×D47C2311yescharacteristic
156C22×C4×D47C2311yescharacteristic
157#13093997C2×C418yescomplemented
158#13093997C2×C418yescomplemented
159#13093997C2×C418yescomplemented
160#13093997C2×C418yescomplemented
161#13093997C2×C418yescomplemented
162#13093997C2×C418yescomplemented
163#13093997C2×C418yescomplemented
164#13093997C2×C418yescomplemented
165C4×C22⋊D47—44no—
166(C22⋊D47)⋊C4—44no—
167#13093983—42no—
168#13093982—44no—
169#13093981—44no—
170#13093980—42no—
171#13093980—42no—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2312yes—
174C2×Dic47⋊C4C2×C418yescomplemented
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2311yescharacteristic
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×C22⋊Dic47—42no—
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2×C418yescomplemented
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2311yescharacteristic
209C2×(C2×D47)⋊C4C2311yescharacteristic
210C22⋊C4×D47—42no—
211C22⋊C4×D47—42no—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C25×C47C2311yescharacteristic
231C23×C4×C47C2311yescharacteristic
232C23×C4×C47C2312yes—
233C23×C4×C47C2311yescharacteristic
234#117×C47—42no—
235C2×C4⋊C4×C47C2312yes—
236C2×C4⋊C4×C47C2312yes—
237C2×C22⋊C4×C47—42no—
238C2×C22⋊C4×C47C2×C418yescomplemented
239C2×C22⋊C4×C47C2311yescharacteristic
240C2×C22⋊C4×C47C2311yescharacteristic
241C2×C22⋊C4×C47C2311yescharacteristic
242C2×C22⋊C4×C47C2311yescharacteristic
243C2×C22⋊C4×C47C2312yes—
244C2×C22⋊C4×C47C2312yes—
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2311yescharacteristic
247C2×C22⋊C4×C47C2311yescharacteristic
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C42×C47C2312yes—
251C2×C42×C47C2312yes—
252#95×C47C2312yes—
253#95×C47C2312yes—
254#95×C47C2312yes—
255#95×C47C2312yes—
256C24×C47—22no—
257C24×C47—22no—
258C24×C47—42no—
259C24×C47—42no—
260C24×C47C22×C414yes—
261C24×C47C2411yescharacteristic
262C24×C47C2411yescharacteristic
263C24×C47C2411yescharacteristic
264C23×D47—22no—
265C23×D47—22no—
266C23×D47—22no—
267C23×D47—22no—
268C23×D47—42no—
269C23×D47—42no—
270C23×D47—42no—
271C23×D47—42no—
272C23×D47C22×C414yes—
273C23×D47C22×C414yes—
274C23×D47C2411yescharacteristic
275C23×D47C2411yescharacteristic
276C23×D47C2411yescharacteristic
277C23×D47C2411yescharacteristic
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—42no—
281C22×C4×C47—42no—
282C22×C4×C47—42no—
283C22×C4×C47—42no—
284C22×C4×C47C22×C414yes—
285C22×C4×C47C22×C414yes—
286C22×C4×C47C2412yes—
287C22×C4×C47C2412yes—
288C22×C4×C47C2412yes—
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C2×C22⋊D47—24no—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—416no—
297C2×C22⋊D47—416no—
298C2×C22⋊D47—41no—
299C2×C22⋊D47—41no—
300C2×C22⋊D47—41no—
301C2×C22⋊D47—41no—
302C2×C22⋊D47—41no—
303C2×C22⋊D47—41no—
304C2×C22⋊D47—41no—
305C2×C22⋊D47—41no—
306C2×C22⋊D47—42no—
307C2×C22⋊D47—42no—
308C2×C22⋊D47C22×C414yes—
309C2×C22⋊D47C22×C414yes—
310C2×C22⋊D47C22×C414yes—
311C2×C22⋊D47C22×C414yes—
312C2×C22⋊D47C22×C414yes—
313C2×C22⋊D47C22×C414yes—
314C2×C22⋊D47C22×C414yes—
315C2×C22⋊D47C22×C414yes—
316C22×Dic47—22no—
317C22×Dic47—22no—
318C22×Dic47—24no—
319C22×Dic47—42no—
320C22×Dic47—42no—
321C22×Dic47—42no—
322C22×Dic47C22×C414yes—
323C22×Dic47C22×C414yes—
324C22×Dic47C2412yes—
325C22×Dic47C2412yes—
326C22×Dic47C2412yes—
327C22×Dic47C2412yes—
328C22×Dic47C2411yescharacteristic
329C22×Dic47C2411yescharacteristic
330C22×Dic47C2411yescharacteristic
331C22×Dic47C2411yescharacteristic
332C2×D188—416no—
333C2×D188—41no—
334C2×D188—41no—
335C2×D188—41no—
336C2×D188—41no—
337C2×D188—41no—
338C2×D188—41no—
339C2×D188—41no—
340C2×D188—41no—
341C2×D188C22×C414yes—
342C2×D188C22×C414yes—
343C2×D188C22×C414yes—
344C2×D188C22×C414yes—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—416no—
348C2×C4×D47—42no—
349C2×C4×D47—42no—
350C2×C4×D47—42no—
351C2×C4×D47—42no—
352C2×C4×D47—42no—
353C2×C4×D47—42no—
354C2×C4×D47—42no—
355C2×C4×D47—42no—
356C2×C4×D47C22×C414yes—
357C2×C4×D47C22×C414yes—
358C2×C4×D47C22×C414yes—
359C2×C4×D47C22×C414yes—
360C4⋊C4×C47—42no—
361C4⋊C4×C47—42no—
362C22⋊C4×C47—22no—
363C22⋊C4×C47—22no—
364C22⋊C4×C47—22no—
365C22⋊C4×C47—22no—
366C22⋊C4×C47—42no—
367C22⋊C4×C47—42no—
368C22⋊C4×C47—42no—
369C22⋊C4×C47C22×C414yes—
370C22⋊C4×C47C22×C414yes—
371C22⋊C4×C47C22×C414yes—
372C22⋊C4×C47C22×C414yes—
373C42×C47—42no—
374C42×C47—42no—
375C22⋊Dic47—22no—
376C22⋊Dic47—22no—
377C22⋊Dic47—22no—
378C22⋊Dic47—22no—
379C22⋊Dic47—42no—
380C22⋊Dic47—42no—
381C22⋊Dic47—42no—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4—42no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388(C2×D47)⋊C4—42no—
389(C2×D47)⋊C4—42no—
390(C2×D47)⋊C4—42no—
391(C2×D47)⋊C4—42no—
392(C2×D47)⋊C4—42no—
393(C2×D47)⋊C4—42no—
394(C2×D47)⋊C4—42no—
395(C2×D47)⋊C4—42no—
396(C2×D47)⋊C4C22×C414yes—
397(C2×D47)⋊C4C22×C414yes—
398(C2×D47)⋊C4C22×C414yes—
399(C2×D47)⋊C4C22×C414yes—
400C4⋊Dic47—42no—
401C4⋊Dic47—42no—
402Dic47⋊C4—24no—
403Dic47⋊C4—24no—
404Dic47⋊C4—42no—
405Dic47⋊C4—42no—
406Dic47⋊C4C22×C414yes—
407Dic47⋊C4C22×C414yes—
408Dic47⋊C4C22×C414yes—
409Dic47⋊C4C22×C414yes—
410C4×Dic47—24no—
411C4×Dic47—24no—
412C4×Dic47—42no—
413C4×Dic47—42no—
414C4×Dic47—42no—
415C4×Dic47—42no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—21no—
421C23×C47—22no—
422C23×C47—21no—
423C23×C47—21no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—28no—
427C23×C47—44no—
428C23×C47—44no—
429C23×C47—84no—
430C23×C47—84no—
431C23×C47C23×C412yes—
432C23×C47C23×C412yes—
433C23×C47C23×C412yes—
434C23×C47H(5,𝔽2)12yes—
435C23×C47H(5,𝔽2)12yes—
436C23×C47C2511yescharacteristic
437C22×D47—28no—
438C22×D47—22no—
439C22×D47—22no—
440C22×D47—21no—
441C22×D47—21no—
442C22×D47—22no—
443C22×D47—22no—
444C22×D47—21no—
445C22×D47—21no—
446C22×D47—21no—
447C22×D47—21no—
448C22×D47—21no—
449C22×D47—21no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—22no—
453C22×D47—22no—
454C22×D47—28no—
455C22×D47—44no—
456C22×D47—44no—
457C22×D47—44no—
458C22×D47—44no—
459C22×D47—48no—
460C22×D47—48no—
461C22×D47—84no—
462C22×D47—84no—
463C22×D47C23×C412yes—
464C22×D47C23×C412yes—
465C22×D47C23×C412yes—
466C22×D47C23×C412yes—
467C2×C4×C47—28no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—21no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—21no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—44no—
487C2×C4×C47—84no—
488C2×C4×C47C23×C412yes—
489C2×C4×C47C23×C412yes—
490C2×C4×C47C23×C412yes—
491C2×C4×C47C23×C412yes—
492C22⋊D47—28no—
493C22⋊D47—28no—
494C22⋊D47—44no—
495C22⋊D47—44no—
496C22⋊D47—44no—
497C22⋊D47—44no—
498C22⋊D47—44no—
499C22⋊D47—44no—
500C2×Dic47—28no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—21no—
505C2×Dic47—22no—
506C2×Dic47—28no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—22no—
514C2×Dic47—22no—
515C2×Dic47—22no—
516C2×Dic47—22no—
517C2×Dic47—22no—
518C2×Dic47—22no—
519C2×Dic47—84no—
520C2×Dic47C23×C412yes—
521C2×Dic47C23×C412yes—
522C2×Dic47C23×C412yes—
523C2×Dic47C23×C412yes—
524C2×Dic47H(5,𝔽2)14yes—
525D188—44no—
526D188—44no—
527D188—44no—
528D188—44no—
529C4×D47—28no—
530C4×D47—28no—
531C4×D47—44no—
532C4×D47—44no—
533C4×D47—84no—
534C4×D47—84no—
535#34363—471nomaximal, Sylow
536C22×C47—22no—
537C22×C47—22no—
538C22×C47—24no—
539C22×C47—24no—
540C22×C47—22no—
541C22×C47—22no—
542C22×C47—22no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47—22no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47—88no—
551C22×C47#51814yes—
552C22×C47C24×C411yescharacteristic
553C22×C47C2×H(5,𝔽2)12yes—
554C22×C47C2×H(5,𝔽2)11yescharacteristic
555C22×C47C2×H(5,𝔽2)11yescharacteristic
556C22×C47#58512yes—
557C2×D47—22no—
558C2×D47—22no—
559C2×D47—22no—
560C2×D47—22no—
561C2×D47—22no—
562C2×D47—22no—
563C2×D47—22no—
564C2×D47—22no—
565C2×D47—22no—
566C2×D47—22no—
567C2×D47—22no—
568C2×D47—22no—
569C2×D47—416no—
570C2×D47—42no—
571C2×D47—42no—
572C2×D47—42no—
573C2×D47—42no—
574C2×D47—42no—
575C2×D47—42no—
576C2×D47—42no—
577C2×D47—42no—
578C2×D47—88no—
579C4×C47—22no—
580C4×C47—22no—
581C4×C47—22no—
582C4×C47—22no—
583C4×C47—42no—
584C4×C47—42no—
585C4×C47—42no—
586C4×C47—42no—
587Dic47—22no—
588Dic47—22no—
589Dic47—22no—
590Dic47—42no—
591Dic47—42no—
592Dic47—42no—
593Dic47—42no—
594Dic47#51814yes—
595C22×#121—471no—
596#2377—472no—
597#2377—472no—
598#2363—472no—
599#2363—472no—
600#2344—471no—
601#2344—471no—
602#2342—471no—
603#2342—471no—
604#2342—471no—
605#2342D4711yescharacteristic, complemented
606D4×C22⋊C4—471no—
607D4×C22⋊C4—471no—
608#2333—472no—
609#2333—472no—
610#2324—472no—
611#2324—472no—
612#2309—471no—
613#2309—471no—
614#2308—471no—
615#2308—471no—
616#2280—471no—
617#2280—471no—
618C2×C47—24no—
619C2×C47—42no—
620C2×C47—42no—
621C2×C47C2×#51811yescharacteristic
622C2×C47C2×#51811yescharacteristic
623C2×C47#342811yescharacteristic
624C2×C47#354212yes—
625C2×C47#354212yes—
626D47—42no—
627D47—42no—
628D47—42no—
629D47—42no—
630C23×D4—471no—
631C23×D4—471no—
632C23×D4—471no—
633C24×C4—471no—
634C2×#121—4716no—
635C2×#121—471no—
636C2×#121—471no—
637C2×#121—471no—
638C2×#121—471no—
639C2×#121—471no—
640C2×#121—471no—
641C2×#121—471no—
642C2×#121—471no—
643C2×C4×D4—472no—
644C2×C4×D4—472no—
645C2×#117—471no—
646C2×#117—472no—
647C2×#117—471no—
648C2×#117—471no—
649C2×#117—472no—
650C2×#117C2×D4711yescharacteristic
651C22×C4⋊C4—471no—
652C22×C22⋊C4—471no—
653C22×C22⋊C4—471no—
654C22×C22⋊C4—471no—
655C22×C22⋊C4—471no—
656C22×C22⋊C4C2×D4711yescharacteristic
657C22×C22⋊C4C2×D4711yescharacteristic
658#390—472no—
659#390—472no—
660#390—472no—
661#390—472no—
662#390—472no—
663#390—472no—
664#390—472no—
665#390—472no—
666#390—472no—
667#390—472no—
668#389—472no—
669#389—472no—
670#388—472no—
671#388—472no—
672#388—472no—
673#388—472no—
674#388—472no—
675#388—472no—
676#388C2×D4712yescomplemented
677#388C2×D4712yescomplemented
678#387—472no—
679#387—472no—
680#387—472no—
681#387—472no—
682#386—472no—
683#386—472no—
684#386—472no—
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386—472no—
690#386—472no—
691#386—472no—
692#386—472no—
693#386—472no—
694#385—472no—
695#385—472no—
696#385—472no—
697#385C2×D4712yescomplemented
698#381—471no—
699#381—471no—
700#381—471no—
701#381—472no—
702#381—472no—
703#381C2×D4711yescharacteristic
704#380—471no—
705#380—472no—
706#380—471no—
707#380—471no—
708#380—472no—
709#380C2×D4711yescharacteristic
710#379—471no—
711#379—471no—
712#379—471no—
713#379—471no—
714#379—471no—
715#379—471no—
716#379—471no—
717#379C2×D4711yescharacteristic
718C4×C4⋊C4—472no—
719C4×C4⋊C4—472no—
720C4×C22⋊C4—471no—
721C4×C22⋊C4—471no—
722C4×C22⋊C4—471no—
723C4×C22⋊C4—472no—
724C4×C22⋊C4—472no—
725C4×C22⋊C4—472no—
726C4×C22⋊C4—472no—
727C4×C22⋊C4—472no—
728C4×C22⋊C4C2×D4711yescharacteristic
729C4×C22⋊C4C2×D4712yescomplemented
730C47#3436311yescharacteristic, complemented, Sylow
731C25—471no—
732C25—471no—
733C25C22×D4711yescharacteristic
734C22×D4—471no—
735C22×D4—471no—
736C22×D4—478no—
737C22×D4—478no—
738C22×D4—471no—
739C22×D4—471no—
740C22×D4—471no—
741C22×D4—471no—
742C22×D4—471no—
743C22×D4—471no—
744C22×D4—478no—
745C22×D4—471no—
746C22×D4—471no—
747C22×D4—471no—
748C22×D4—471no—
749C22×D4—1882no—
750C22×D4—1882no—
751C22×D4—1884no—
752C22×D4—1882no—
753C22×D4—1882no—
754C23×C4—471no—
755C23×C4—471no—
756C23×C4—471no—
757C23×C4—471no—
758C23×C4—478no—
759C23×C4—471no—
760C23×C4—471no—
761C23×C4—472no—
762C23×C4—472no—
763C23×C4—472no—
764C23×C4—1884no—
765C23×C4C22×D4711yescharacteristic
766C23×C4C22×D4712yes—
767C23×C4C22×D4711yescharacteristic
768#121—478no—
769#121—478no—
770#121—478no—
771#121—478no—
772#121—478no—
773#121—478no—
774#121—478no—
775#121—478no—
776C4×D4—1884no—
777C4×D4—1884no—
778#117—42no—
779#117—1884no—
780#117—1884no—
781#117—1882no—
782#117—1882no—
783#117—1882no—
784C2×C4⋊C4—478no—
785C2×C4⋊C4—471no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—471no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—472no—
792C2×C4⋊C4—472no—
793C2×C4⋊C4—472no—
794C2×C4⋊C4—472no—
795C2×C4⋊C4C22×D4712yes—
796C2×C4⋊C4C22×D4712yes—
797C2×C22⋊C4—42no—
798C2×C22⋊C4—478no—
799C2×C22⋊C4—471no—
800C2×C22⋊C4—471no—
801C2×C22⋊C4—471no—
802C2×C22⋊C4—471no—
803C2×C22⋊C4—471no—
804C2×C22⋊C4—471no—
805C2×C22⋊C4—471no—
806C2×C22⋊C4—471no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—472no—
820C2×C22⋊C4—472no—
821C2×C22⋊C4—472no—
822C2×C22⋊C4—472no—
823C2×C22⋊C4—472no—
824C2×C22⋊C4—1882no—
825C2×C22⋊C4—1882no—
826C2×C22⋊C4—1882no—
827C2×C22⋊C4C4×D4718yescomplemented
828C2×C22⋊C4C22×D4711yescharacteristic
829C2×C22⋊C4C22×D4711yescharacteristic
830C2×C22⋊C4C22×D4711yescharacteristic
831C2×C22⋊C4C22×D4711yescharacteristic
832C2×C22⋊C4C22×D4712yes—
833C2×C22⋊C4C22×D4712yes—
834C2×C22⋊C4C22×D4712yes—
835C2×C22⋊C4C22×D4711yescharacteristic
836C2×C22⋊C4C22×D4711yescharacteristic
837C2×C22⋊C4C22×D4711yescharacteristic
838C2×C22⋊C4C22×D4711yescharacteristic
839C2×C42—472no—
840C2×C42—472no—
841C2×C42—472no—
842C2×C42—472no—
843C2×C42—472no—
844C2×C42—472no—
845C2×C42C22×D4712yes—
846C2×C42C22×D4712yes—
847#95—472no—
848#95—472no—
849#95—472no—
850#95—472no—
851#95—472no—
852#95—472no—
853#95—472no—
854#95—472no—
855#95—472no—
856#95—472no—
857#95—472no—
858#95—472no—
859#95C22×D4712yes—
860#95C22×D4712yes—
861#95C22×D4712yes—
862#95C22×D4712yes—
863C24—22no—
864C24—22no—
865C24—42no—
866C24—42no—
867C24—471no—
868C24—471no—
869C24—471no—
870C24—471no—
871C24—474no—
872C24—474no—
873C24—942no—
874C24—942no—
875C24—942no—
876C24—942no—
877C24—1882no—
878C24—1882no—
879C24—1882no—
880C24—1882no—
881C24C2×C4×D4714yes—
882C24C23×D4711yescharacteristic
883C24C23×D4711yescharacteristic
884C24C23×D4711yescharacteristic
885C2×D4—474no—
886C2×D4—474no—
887C2×D4—474no—
888C2×D4—474no—
889C2×D4—474no—
890C2×D4—474no—
891C2×D4—474no—
892C2×D4—474no—
893C2×D4—474no—
894C2×D4—474no—
895C2×D4—474no—
896C2×D4—474no—
897C2×D4—944no—
898C2×D4—944no—
899C2×D4—18816no—
900C2×D4—1881no—
901C2×D4—1881no—
902C2×D4—1881no—
903C2×D4—1881no—
904C2×D4—1881no—
905C2×D4—1881no—
906C2×D4—1881no—
907C2×D4—1881no—
908C2×D4—18816no—
909C2×D4—18816no—
910C2×D4—1882no—
911C2×D4—1882no—
912C2×D4—1881no—
913C2×D4—1881no—
914C2×D4—1881no—
915C2×D4—1881no—
916C2×D4—1881no—
917C2×D4—1881no—
918C2×D4—1881no—
919C2×D4—1881no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—471no—
927C22×C4—474no—
928C22×C4—474no—
929C22×C4—471no—
930C22×C4—471no—
931C22×C4—471no—
932C22×C4—474no—
933C22×C4—474no—
934C22×C4—474no—
935C22×C4—474no—
936C22×C4—472no—
937C22×C4—472no—
938C22×C4—472no—
939C22×C4—472no—
940C22×C4—944no—
941C22×C4—944no—
942C22×C4—944no—
943C22×C4—942no—
944C22×C4—942no—
945C22×C4—1882no—
946C22×C4—1882no—
947C22×C4—1882no—
948C22×C4—1882no—
949C22×C4—1882no—
950C22×C4—1882no—
951C22×C4—1882no—
952C22×C4—1882no—
953C22×C4—18816no—
954C22×C4—1882no—
955C22×C4—1882no—
956C22×C4—1882no—
957C22×C4C2×C4×D4714yes—
958C22×C4C2×C4×D4714yes—
959C22×C4C23×D4712yes—
960C22×C4C23×D4712yes—
961C22×C4C23×D4712yes—
962C22×C4C23×D4712yes—
963C22×C4C23×D4711yescharacteristic
964C22×C4C23×D4711yescharacteristic
965C22×C4C23×D4711yescharacteristic
966C22×C4C23×D4711yescharacteristic
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—474no—
970C4⋊C4—474no—
971C4⋊C4—474no—
972C4⋊C4—474no—
973C4⋊C4—944no—
974C4⋊C4—944no—
975C4⋊C4—1882no—
976C4⋊C4—1882no—
977C4⋊C4—1882no—
978C4⋊C4—1882no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—474no—
987C22⋊C4—474no—
988C22⋊C4—474no—
989C22⋊C4—474no—
990C22⋊C4—942no—
991C22⋊C4—942no—
992C22⋊C4—942no—
993C22⋊C4—942no—
994C22⋊C4—1882no—
995C22⋊C4—1882no—
996C22⋊C4—1882no—
997C22⋊C4—1882no—
998C22⋊C4—1882no—
999C22⋊C4—1882no—
1000C22⋊C4—1882no—
1001C22⋊C4—1882no—
1002C22⋊C4—1882no—
1003C22⋊C4—1882no—
1004C22⋊C4—1882no—
1005C22⋊C4—1882no—
1006C22⋊C4—1882no—
1007C22⋊C4—1882no—
1008C22⋊C4—1882no—
1009C22⋊C4—1882no—
1010C22⋊C4—1882no—
1011C22⋊C4C2×C4×D4714yes—
1012C22⋊C4C2×C4×D4714yes—
1013C22⋊C4C2×C4×D4714yes—
1014C22⋊C4C2×C4×D4714yes—
1015C42—42no—
1016C42—42no—
1017C42—944no—
1018C42—944no—
1019C42—1882no—
1020C42—1882no—
1021C42—1882no—
1022C42—1882no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—28no—
1034C23—44no—
1035C23—44no—
1036C23—84no—
1037C23—84no—
1038C23—472no—
1039C23—472no—
1040C23—472no—
1041C23—472no—
1042C23—948no—
1043C23—948no—
1044C23—942no—
1045C23—942no—
1046C23—942no—
1047C23—942no—
1048C23—941no—
1049C23—941no—
1050C23—941no—
1051C23—941no—
1052C23—941no—
1053C23—941no—
1054C23—941no—
1055C23—941no—
1056C23—942no—
1057C23—942no—
1058C23—942no—
1059C23—942no—
1060C23—3764no—
1061C23—3764no—
1062C23—1884no—
1063C23—1884no—
1064C23—1884no—
1065C23—1884no—
1066C23—1888no—
1067C23—1888no—
1068C23C22×C4×D4712yes—
1069C23C22×C4×D4712yes—
1070C23C22×C4×D4712yes—
1071C23#1309406912yes—
1072C23#1309407012yes—
1073C23C24×D4711yescharacteristic
1074D4—948no—
1075D4—948no—
1076D4—1884no—
1077D4—1884no—
1078D4—1884no—
1079D4—1884no—
1080D4—1884no—
1081D4—1884no—
1082D4—1884no—
1083D4—1884no—
1084D4—1884no—
1085D4—1884no—
1086C2×C4—28no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—44no—
1106C2×C4—84no—
1107C2×C4—472no—
1108C2×C4—474no—
1109C2×C4—472no—
1110C2×C4—472no—
1111C2×C4—472no—
1112C2×C4—948no—
1113C2×C4—948no—
1114C2×C4—948no—
1115C2×C4—948no—
1116C2×C4—942no—
1117C2×C4—941no—
1118C2×C4—941no—
1119C2×C4—941no—
1120C2×C4—941no—
1121C2×C4—942no—
1122C2×C4—942no—
1123C2×C4—942no—
1124C2×C4—942no—
1125C2×C4—942no—
1126C2×C4—942no—
1127C2×C4—942no—
1128C2×C4—942no—
1129C2×C4—942no—
1130C2×C4—942no—
1131C2×C4—942no—
1132C2×C4—942no—
1133C2×C4—3764no—
1134C2×C4—3764no—
1135C2×C4—3764no—
1136C2×C4—1884no—
1137C2×C4—1884no—
1138C2×C4C22×C4×D4712yes—
1139C2×C4C22×C4×D4712yes—
1140C2×C4C22×C4×D4712yes—
1141C2×C4C22×C4×D4712yes—
1142C22—22no—
1143C22—22no—
1144C22—24no—
1145C22—24no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—88no—
1157C22—942no—
1158C22—942no—
1159C22—942no—
1160C22—942no—
1161C22—942no—
1162C22—942no—
1163C22—942no—
1164C22—942no—
1165C22—942no—
1166C22—942no—
1167C22—942no—
1168C22—942no—
1169C22—3768no—
1170C22—18816no—
1171C22—1882no—
1172C22—1882no—
1173C22—1882no—
1174C22—1882no—
1175C22—1882no—
1176C22—1882no—
1177C22—1882no—
1178C22—1882no—
1179C22#1568959514yes—
1180C22C23×C4×D4711yescharacteristic
1181C22H(5,𝔽2)×D4712yes—
1182C22C2×#1309406911yescharacteristic
1183C22C2×#1309407011yescharacteristic
1184C22#1568995912yes—
1185C4—22no—
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—474no—
1194C4—942no—
1195C4—942no—
1196C4—942no—
1197C4—1882no—
1198C4—1882no—
1199C4—1882no—
1200C4—1882no—
1201C2—24no—
1202C2—42no—
1203C2—42no—
1204C2—1882no—
1205C2—1882no—
1206C2—1882no—
1207C2—1882no—
1208C2#518×D4711yescharacteristic
1209C2C2×#1568959511yescharacteristic
1210C2#2025658911yescharacteristic
1211C2#2025768912yes—
1212C2#2025769712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2342C2
socle, cosocleC23×C47C25
prime radicalC22×#13093997C2
hypercenter#2342D47
hypocenterC47#34363
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #20246544C2semidirect
3. #20246541C2semidirect
4. #20246427C2semidirect
5. #20246421C2semidirect
6. #20246258C2semidirect
7. #20246252C2semidirect
8. #20246240C2semidirect
9. #20246237C2semidirect
10. #20246234C2semidirect
11. C22⋊C4×C22⋊D47C2semidirect
12. #20246204C2semidirect
13. #20246151C2semidirect
14. #20246148C2semidirect
15. #20246080C2semidirect
16. #20246076C2semidirect
17. #20245969C2semidirect
18. #20245968C2semidirect
19. #20245965C2semidirect
20. #20245963C2semidirect
21. #20245770C2semidirect
22. #20245769C2semidirect
23. C47×#2342C2semidirect
28. C2×#13093997C4semidirect
37. C2×C4×C22⋊D47C22semidirect
38. C2×(C22⋊D47)⋊C4C22semidirect
40. C2×#13093982C22semidirect
41. C2×#13093981C22semidirect
49. #15689025C22semidirect
50. #15689025C22semidirect
51. #15689024C22semidirect
52. #15689024C22semidirect
53. #15689023C22semidirect
54. #15689023C22semidirect
55. #15689023C22semidirect
56. #15689023C22semidirect
57. #15689023C22semidirect
58. #15689023C22semidirect
59. #15689020C22semidirect
60. #15689018C22semidirect
61. #15689016C22semidirect
62. #15689016C22semidirect
63. #15689015C22semidirect
64. #15689014C22semidirect
65. #15689013C22semidirect
66. #15689012C22semidirect
67. #15689010C22semidirect
68. #15689007C22semidirect
69. #15689005C22semidirect
70. #15689004C22semidirect
71. #15689002C22semidirect
72. #15689002C22semidirect
73. #15689002C22semidirect
74. #15689001C22semidirect
75. #15689001C22semidirect
76. #15689001C22semidirect
77. #15689001C22semidirect
78. #15689000C22semidirect
79. #15689000C22semidirect
80. #15689000C22semidirect
81. #15688999C22semidirect
82. #15688999C22semidirect
83. #15688998C22semidirect
84. #15688997C22semidirect
85. #15688994C22semidirect
87. #15688985C22semidirect
88. #15688985C22semidirect
92. #15688982C22semidirect
95. #15688980C22semidirect
103. C4×Dic47⋊C4C22semidirect
104. #15688974C22semidirect
107. C22⋊C4×Dic47C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
111. #15688970C22semidirect
112. #15688970C22semidirect
116. C47×#388C22semidirect
117. C47×#388C22semidirect
118. C47×#385C22semidirect
123. C4×C22⋊C4×C47C22semidirect
128. C22×D188C2×C4semidirect
137. C22×C22⋊D47C2×C4semidirect
150. C22×C4×D47C2×C4semidirect
157. #13093997C2×C4semidirect
158. #13093997C2×C4semidirect
159. #13093997C2×C4semidirect
160. #13093997C2×C4semidirect
161. #13093997C2×C4semidirect
162. #13093997C2×C4semidirect
163. #13093997C2×C4semidirect
164. #13093997C2×C4semidirect
174. C2×Dic47⋊C4C2×C4semidirect
191. C2×(C2×D47)⋊C4C2×C4semidirect
238. C2×C22⋊C4×C47C2×C4semidirect
605. #2342D47semidirect
676. #388C2×D47semidirect
677. #388C2×D47semidirect
697. #385C2×D47semidirect
729. C4×C22⋊C4C2×D47semidirect
730. C47#34363semidirect
827. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939972
#202465442
#202465412
#202464272
#202464212
#202462582
#202462522
#202462402
#202462372
#202462342
C22⋊C4×C22⋊D472
#202462042
#202461512
#202461482
#202460802
#202460762
#202459692
#202459682
#202459652
#202459632
#202457702
#202457692
C47×#23422
#3436347