Finite Group Databasebeta

← #26381549

Subgroups — #26381549

Order 12032.

1940 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689850C211yesmaximal, characteristic
2#20246572C211yesmaximal, characteristic
3#20246571C211yesmaximal, characteristic
4#20246570C211yesmaximal, characteristic
5#20246481C211yesmaximal, characteristic
6#20246479C211yesmaximal, characteristic
7#20246443C211yesmaximal, characteristic
8#20246443C211yesmaximal, characteristic
9#20246441C211yesmaximal, characteristic
10#20246342C211yesmaximal, characteristic
11#20246342C211yesmaximal, characteristic
12#20246340C211yesmaximal, characteristic
13#20246307C211yesmaximal, characteristic
14#20246305C211yesmaximal, characteristic
15#20246302C211yesmaximal, characteristic
16#20246194C211yesmaximal, characteristic
17#20246190C211yesmaximal, characteristic
18#20246188C211yesmaximal, characteristic
19#20246186C211yesmaximal, characteristic
20#20246126C211yesmaximal, characteristic
21#20246126C211yesmaximal, characteristic
22#20246103C211yesmaximal, characteristic
23#20246103C211yesmaximal, characteristic
24#20246037C211yesmaximal, characteristic
25#20246037C211yesmaximal, characteristic
26#20246036C211yesmaximal, characteristic
27#20246036C211yesmaximal, characteristic
28#20245959C211yesmaximal, characteristic
29#20245861C211yesmaximal, characteristic
30#20245861C211yesmaximal, characteristic
31C47×#2382C211yesmaximal, characteristic
32#15689850C4116yescomplemented
33C2×#13094023C2211yescharacteristic
34C2×#13094023C2211yescharacteristic
35C2×#13094023C2211yescharacteristic
36C2×#13094015C2211yescharacteristic
37C2×#13094014C2211yescharacteristic
38C2×#13094014C2211yescharacteristic
39C2×#13094014C2211yescharacteristic
40C2×#13094014C2211yescharacteristic
41C2×C4×Dic94C2211yescharacteristic
42C2×C4×Dic94C2211yescharacteristic
43C2×C4×Dic94C2211yescharacteristic
44C2×C4×Dic94C2211yescharacteristic
45C2×#13093989C2211yescharacteristic
46C2×#13093989C2211yescharacteristic
47C2×#13093989C2211yescharacteristic
48C2×#13093989C2211yescharacteristic
49C2×#13093989C2211yescharacteristic
50C2×#13093989C2211yescharacteristic
51C2×#13093989C2211yescharacteristic
52C2×#13093989C2211yescharacteristic
53#15689027C2211yescharacteristic
54#15689027C2211yescharacteristic
55#15689027C2211yescharacteristic
56#15689027C2211yescharacteristic
57#15689027C2211yescharacteristic
58#15689027C2211yescharacteristic
59#15689027C2211yescharacteristic
60#15689027C2211yescharacteristic
61#15689027C2211yescharacteristic
62#15689027C2211yescharacteristic
63#15689022C2211yescharacteristic
64#15689022C2211yescharacteristic
65#15689021C2211yescharacteristic
66#15689020C2211yescharacteristic
67#15689020C2211yescharacteristic
68#15689020C2211yescharacteristic
69#15689020C2211yescharacteristic
70#15689020C2211yescharacteristic
71#15689020C2211yescharacteristic
72#15689020C2211yescharacteristic
73#15689020C2211yescharacteristic
74#15689020C2211yescharacteristic
75#15689019C2211yescharacteristic
76#15689019C2211yescharacteristic
77#15689019C2211yescharacteristic
78#15689018C2211yescharacteristic
79#15689018C2211yescharacteristic
80#15689018C2211yescharacteristic
81#15689018C2211yescharacteristic
82#15689018C2211yescharacteristic
83#15689018C2211yescharacteristic
84#15689018C2211yescharacteristic
85#15689018C2211yescharacteristic
86#15689018C2211yescharacteristic
87#15689010C2211yescharacteristic
88#15689010C2211yescharacteristic
89#15689010C2211yescharacteristic
90#15689009C2211yescharacteristic
91#15689009C2211yescharacteristic
92#15689009C2211yescharacteristic
93#15689009C2211yescharacteristic
94#15689009C2211yescharacteristic
95#15689009C2211yescharacteristic
96#15689009C2211yescharacteristic
97#15689009C2211yescharacteristic
98#15689008C2211yescharacteristic
99#15689008C2211yescharacteristic
100#15689008C2211yescharacteristic
101#15689008C2211yescharacteristic
102#15689007C2211yescharacteristic
103#15689007C2211yescharacteristic
104#15689007C2211yescharacteristic
105#15689007C2211yescharacteristic
106#15689007C2211yescharacteristic
107#15689006C2211yescharacteristic
108#15689006C2211yescharacteristic
109#15689006C2211yescharacteristic
110#15689006C2211yescharacteristic
111#15689006C2211yescharacteristic
112#15689006C2211yescharacteristic
113#15689005C2211yescharacteristic
114#15689005C2211yescharacteristic
115#15689005C2211yescharacteristic
116#15689005C2211yescharacteristic
117#15689005C2211yescharacteristic
118#15689005C2211yescharacteristic
119#15689005C2211yescharacteristic
120#15689004C2211yescharacteristic
121#15689004C2211yescharacteristic
122#15689004C2211yescharacteristic
123#15689004C2211yescharacteristic
124#15689004C2211yescharacteristic
125#15689004C2211yescharacteristic
126#15689004C2211yescharacteristic
127#15688992C2211yescharacteristic
128#15688992C2211yescharacteristic
129#15688992C2211yescharacteristic
130#15688991C2211yescharacteristic
131#15688990C2211yescharacteristic
132#15688990C2211yescharacteristic
133#15688990C2211yescharacteristic
134#15688988C2211yescharacteristic
135#15688988C2211yescharacteristic
136#15688987C2211yescharacteristic
137#15688987C2211yescharacteristic
138#15688987C2211yescharacteristic
139#15688987C2211yescharacteristic
140#15688987C2211yescharacteristic
141#15688987C2211yescharacteristic
142C4⋊C4×Dic47C2211yescharacteristic
143C4⋊C4×Dic47C2211yescharacteristic
144C4⋊C4×Dic47C2211yescharacteristic
145C4⋊C4×Dic47C2211yescharacteristic
146C4⋊C4×Dic47C2211yescharacteristic
147C4⋊C4×Dic47C2211yescharacteristic
148C4×Dic47⋊C4C2211yescharacteristic
149C4×Dic47⋊C4C2211yescharacteristic
150C4×Dic47⋊C4C2211yescharacteristic
151C4×Dic47⋊C4C2211yescharacteristic
152C4×Dic47⋊C4C2211yescharacteristic
153C4×Dic47⋊C4C2211yescharacteristic
154C4×C4⋊Dic47C2211yescharacteristic
155C4×C4⋊Dic47C2211yescharacteristic
156#15688974C2211yescharacteristic
157#15688974C2211yescharacteristic
158#15688974C2211yescharacteristic
159#15688974C2211yescharacteristic
160#15688974C2211yescharacteristic
161#15688974C2211yescharacteristic
162#15688974C2211yescharacteristic
163#15688974C2211yescharacteristic
164#15688974C2211yescharacteristic
165#15688974C2211yescharacteristic
166#15688974C2211yescharacteristic
167#15688974C2211yescharacteristic
168#15688968C2211yescharacteristic
169#15688968C2211yescharacteristic
170#15688968C2211yescharacteristic
171#15688968C2211yescharacteristic
172C42×Dic47C2211yescharacteristic
173C2×#125×C47C2211yescharacteristic
174C47×#389C2211yescharacteristic
175C47×#389C2211yescharacteristic
176C47×#389C2211yescharacteristic
177C47×#389C2211yescharacteristic
178C47×#387C2211yescharacteristic
179C47×#387C2211yescharacteristic
180C47×#387C2211yescharacteristic
181C47×#387C2211yescharacteristic
182C47×#387C2211yescharacteristic
183C47×#387C2211yescharacteristic
184C47×#387C2211yescharacteristic
185C47×#387C2211yescharacteristic
186C47×#382C2211yescharacteristic
187C47×#382C2211yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×Dic94C2311yescharacteristic
190C22×Dic94C2311yescharacteristic
191C22×Dic94C2311yescharacteristic
192#13094023C2×C418yes—
193#13094023C2×C418yes—
194#13094023C2×C418yes—
195#13094015C2×C418yes—
196#13094014C2×C418yes—
197#13094014C2×C418yes—
198#13094014C2×C418yes—
199#13094014C2×C418yes—
200C4×Dic94—42no—
201C4×Dic94—42no—
202C4×Dic94C2×C418yes—
203C4×Dic94C2×C418yes—
204#13093989—42no—
205#13093989—42no—
206#13093989—42no—
207#13093989—42no—
208#13093989C2×C418yes—
209#13093989C2×C418yes—
210#13093989C2×C418yes—
211#13093989C2×C418yes—
212C2×C4⋊Dic47C2311yescharacteristic
213C2×C4⋊Dic47C2311yescharacteristic
214C2×C4⋊Dic47C2311yescharacteristic
215C2×C4⋊Dic47C2311yescharacteristic
216C2×C4⋊Dic47C2311yescharacteristic
217C2×C4⋊Dic47C2311yescharacteristic
218C2×C4⋊Dic47C2311yescharacteristic
219C2×C4⋊Dic47C2311yescharacteristic
220C2×C4⋊Dic47C2311yescharacteristic
221C2×C4⋊Dic47C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊C4C2311yescharacteristic
235C2×Dic47⋊C4C2311yescharacteristic
236C2×Dic47⋊C4C2311yescharacteristic
237C2×Dic47⋊C4C2311yescharacteristic
238C2×Dic47⋊C4C2311yescharacteristic
239C2×Dic47⋊C4C2311yescharacteristic
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×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C2×C4×Dic47C2311yescharacteristic
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C2×C4×Dic47C2311yescharacteristic
265C2×C4×Dic47C2311yescharacteristic
266C2×C4×Dic47C2311yescharacteristic
267C2×C4×Dic47C2311yescharacteristic
268C2×C4×Dic47C2311yescharacteristic
269C2×C4×Dic47C2311yescharacteristic
270C2×C4×Dic47C2311yescharacteristic
271C2×C4×Dic47C2311yescharacteristic
272C2×C4×Dic47C2311yescharacteristic
273C2×C4×Dic47C2311yescharacteristic
274C2×C4×Dic47C2311yescharacteristic
275C2×C4×Dic47C2311yescharacteristic
276C2×C4×Dic47C2311yescharacteristic
277C2×C4×Dic47C2311yescharacteristic
278C2×C4×Dic47C2311yescharacteristic
279C2×C4×Dic47C2311yescharacteristic
280C2×C4×Dic47C2311yescharacteristic
281C2×C4×Dic47C2311yescharacteristic
282C2×C4×Dic47C2311yescharacteristic
283C2×C4×Dic47C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
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
328#125×C47C2×C418yes—
329C2×C4⋊C4×C47C2311yescharacteristic
330C2×C4⋊C4×C47C2311yescharacteristic
331C2×C4⋊C4×C47C2311yescharacteristic
332C2×C4⋊C4×C47C2311yescharacteristic
333C2×C4⋊C4×C47C2311yescharacteristic
334C2×C4⋊C4×C47C2311yescharacteristic
335C2×C4⋊C4×C47C2311yescharacteristic
336C2×C4⋊C4×C47C2311yescharacteristic
337C2×C4⋊C4×C47C2311yescharacteristic
338C2×C4⋊C4×C47C2311yescharacteristic
339C2×C4⋊C4×C47C2311yescharacteristic
340C2×C4⋊C4×C47C2311yescharacteristic
341C2×C4⋊C4×C47C2311yescharacteristic
342C2×C4⋊C4×C47C2311yescharacteristic
343C2×C42×C47C2311yescharacteristic
344C2×C42×C47C2311yescharacteristic
345C2×C42×C47C2311yescharacteristic
346C2×C42×C47C2311yescharacteristic
347C2×C42×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351#95×C47C2311yescharacteristic
352#95×C47C2311yescharacteristic
353#95×C47C2311yescharacteristic
354#95×C47C2311yescharacteristic
355#95×C47C2311yescharacteristic
356#95×C47C2311yescharacteristic
357#95×C47C2311yescharacteristic
358#95×C47C2311yescharacteristic
359#95×C47C2311yescharacteristic
360#95×C47C2311yescharacteristic
361#95×C47C2311yescharacteristic
362#95×C47C2311yescharacteristic
363#95×C47C2311yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×C4×C47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2411yescharacteristic
390C22×Dic47C2411yescharacteristic
391C22×Dic47C2411yescharacteristic
392C22×Dic47C2411yescharacteristic
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C2×Dic94—22no—
396C2×Dic94—22no—
397C2×Dic94—22no—
398C2×Dic94—22no—
399C2×Dic94—22no—
400C2×Dic94—22no—
401C2×Dic94—22no—
402C2×Dic94—22no—
403C2×Dic94C22×C414yes—
404C2×Dic94C22×C414yes—
405C2×Dic94C22×C414yes—
406C2×Dic94C22×C414yes—
407C4⋊C4×C47—41no—
408C4⋊C4×C47—41no—
409C4⋊C4×C47—41no—
410C4⋊C4×C47—41no—
411C4⋊C4×C47—41no—
412C4⋊C4×C47—41no—
413C4⋊C4×C47—41no—
414C4⋊C4×C47—41no—
415C4⋊C4×C47C22×C414yes—
416C4⋊C4×C47C22×C414yes—
417C4⋊C4×C47C22×C414yes—
418C4⋊C4×C47C22×C414yes—
419C4⋊C4×C47C22×C414yes—
420C4⋊C4×C47C22×C414yes—
421C42×C47—41no—
422C42×C47—41no—
423C42×C47—41no—
424C42×C47—41no—
425C42×C47C22×C414yes—
426C4⋊Dic47—22no—
427C4⋊Dic47—22no—
428C4⋊Dic47—41no—
429C4⋊Dic47—41no—
430C4⋊Dic47—41no—
431C4⋊Dic47—41no—
432C4⋊Dic47C22×C414yes—
433C4⋊Dic47C22×C414yes—
434C4⋊Dic47C22×C414yes—
435C4⋊Dic47C22×C414yes—
436Dic47⋊C4—22no—
437Dic47⋊C4—22no—
438Dic47⋊C4—22no—
439Dic47⋊C4—22no—
440Dic47⋊C4—22no—
441Dic47⋊C4—22no—
442Dic47⋊C4—22no—
443Dic47⋊C4—22no—
444Dic47⋊C4—22no—
445Dic47⋊C4—22no—
446Dic47⋊C4—41no—
447Dic47⋊C4—41no—
448Dic47⋊C4—41no—
449Dic47⋊C4—41no—
450Dic47⋊C4—41no—
451Dic47⋊C4—41no—
452Dic47⋊C4—41no—
453Dic47⋊C4—41no—
454Dic47⋊C4—41no—
455Dic47⋊C4—41no—
456Dic47⋊C4C22×C414yes—
457Dic47⋊C4C22×C414yes—
458Dic47⋊C4C22×C414yes—
459Dic47⋊C4C22×C414yes—
460Dic47⋊C4C22×C414yes—
461Dic47⋊C4C22×C414yes—
462Dic47⋊C4C22×C414yes—
463Dic47⋊C4C22×C414yes—
464Dic47⋊C4C22×C414yes—
465Dic47⋊C4C22×C414yes—
466Dic47⋊C4C22×C414yes—
467Dic47⋊C4C22×C414yes—
468C4×Dic47—22no—
469C4×Dic47—22no—
470C4×Dic47—22no—
471C4×Dic47—22no—
472C4×Dic47—22no—
473C4×Dic47—22no—
474C4×Dic47—22no—
475C4×Dic47—22no—
476C4×Dic47—22no—
477C4×Dic47—41no—
478C4×Dic47—41no—
479C4×Dic47—41no—
480C4×Dic47—41no—
481C4×Dic47—41no—
482C4×Dic47—41no—
483C4×Dic47—41no—
484C4×Dic47—41no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47—41no—
489C4×Dic47—41no—
490C4×Dic47C22×C414yes—
491C4×Dic47C22×C414yes—
492C4×Dic47C22×C414yes—
493C4×Dic47C22×C414yes—
494C4×Dic47C22×C414yes—
495C4×Dic47C22×C414yes—
496C4×Dic47C22×C414yes—
497C4×Dic47C22×C414yes—
498C23×C47C2511yescharacteristic
499C2×C4×C47—21no—
500C2×C4×C47—21no—
501C2×C4×C47—21no—
502C2×C4×C47—21no—
503C2×C4×C47—21no—
504C2×C4×C47—21no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47C23×C412yes—
538C2×C4×C47C23×C412yes—
539C2×C4×C47C23×C412yes—
540C2×C4×C47C23×C412yes—
541C2×C4×C47C23×C412yes—
542C2×C4×C47C23×C412yes—
543C2×C4×C47C23×C412yes—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47—21no—
548C2×Dic47—21no—
549C2×Dic47—21no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47C23×C412yes—
580C2×Dic47C23×C412yes—
581C2×Dic47C23×C412yes—
582C2×Dic47C23×C412yes—
583C2×Dic47C23×C412yes—
584C2×Dic47C23×C412yes—
585C2×Dic47C23×C412yes—
586C2×Dic47C23×C412yes—
587C2×Dic47H(5,𝔽2)12yes—
588C2×Dic472−1+412yes—
589C2×Dic472−1+412yes—
590C2×Dic472−1+412yes—
591C2×Dic472−1+412yes—
592Dic94—28no—
593Dic94—28no—
594Dic94—28no—
595Dic94—28no—
596#34488—471nomaximal, Sylow
597C22×C47C24×C411yescharacteristic
598C22×C47C2×H(5,𝔽2)11yescharacteristic
599C22×C47C2×2−1+411yescharacteristic
600C22×C47C2×2−1+411yescharacteristic
601C22×C47C2×2−1+411yescharacteristic
602C22×C47C2×2−1+411yescharacteristic
603C22×C47#58511yescharacteristic
604C4×C47—22no—
605C4×C47—22no—
606C4×C47—22no—
607C4×C47—22no—
608C4×C47—22no—
609C4×C47—22no—
610C4×C47—22no—
611C4×C47—41no—
612C4×C47—41no—
613C4×C47—41no—
614C4×C47—41no—
615C4×C47—41no—
616C4×C47—41no—
617C4×C47—41no—
618C4×C47—41no—
619Dic47—22no—
620Dic47—22no—
621Dic47—22no—
622Dic47—22no—
623Dic47—22no—
624Dic47—22no—
625Dic47—22no—
626Dic47—41no—
627Dic47—41no—
628Dic47—41no—
629Dic47—41no—
630Dic47—41no—
631Dic47—41no—
632Dic47—41no—
633Dic47#51914yes—
634Dic47#52014yes—
635C2×#557—471no—
636#2382—471no—
637#2382—471no—
638#2382—471no—
639#2382D4711yescharacteristic
640#2370—471no—
641#2370—471no—
642#2365—471no—
643#2365—471no—
644#2365—471no—
645#2355—471no—
646#2355—471no—
647#2355—471no—
648#2351—471no—
649#2351—471no—
650Q8×C4⋊C4—471no—
651#2336—471no—
652#2336—471no—
653#2336—471no—
654#2336—471no—
655#2330—471no—
656#2330—471no—
657#2327—471no—
658#2327—471no—
659#2320—471no—
660#2320—471no—
661#2320—471no—
662#2320—471no—
663C4×C4⋊Q8—471no—
664#2295—471no—
665#2295—471no—
666C2×C47C2×#51911yescharacteristic
667C2×C47C2×#52011yescharacteristic
668C2×C47C4×2−1+411yescharacteristic
669C2×C47#355211yescharacteristic
670C2×C47#355411yescharacteristic
671C2×C47#355511yescharacteristic
672C2×C47#355611yescharacteristic
673#557—4716no—
674C2×C4⋊Q8—471no—
675C2×C4⋊Q8—471no—
676C2×C4⋊Q8—471no—
677C2×#125—471no—
678C2×#125—471no—
679C2×#125—471no—
680C2×#125—471no—
681C2×#125—471no—
682C2×#125C2×D4711yescharacteristic
683C2×C4×Q8—471no—
684C2×C4×Q8—471no—
685C2×C4×Q8—471no—
686C2×C4×Q8—471no—
687C2×C4×Q8—471no—
688C2×C4×Q8—471no—
689C2×C4×Q8—471no—
690C2×C4×Q8—471no—
691C2×C4×Q8—471no—
692C2×C4×Q8—471no—
693C2×C4×Q8—471no—
694C2×C4×Q8—471no—
695#391—471no—
696#391—471no—
697#391—471no—
698#391—471no—
699#391—471no—
700#391—471no—
701#391—471no—
702#391—471no—
703#391—471no—
704#391—471no—
705#389—471no—
706#389—471no—
707#389—471no—
708#389—471no—
709#389—471no—
710#389—471no—
711#389—471no—
712#389—471no—
713#389—471no—
714#389—471no—
715#389—471no—
716#389—471no—
717#389—471no—
718#389—471no—
719#389—471no—
720#389—471no—
721#389—471no—
722#389—471no—
723#389—471no—
724#389—471no—
725#389—471no—
726#389—471no—
727#389—471no—
728#389—471no—
729#389C2×D4711yescharacteristic
730#389C2×D4711yescharacteristic
731#389C2×D4711yescharacteristic
732#389C2×D4711yescharacteristic
733#387—471no—
734#387—471no—
735#387—471no—
736#387—471no—
737#387—471no—
738#387—471no—
739#387—471no—
740#387—471no—
741#387—471no—
742#387—471no—
743#387—471no—
744#387—471no—
745#387—471no—
746#387—471no—
747#387—471no—
748#387—471no—
749#387—471no—
750#387—471no—
751#387—471no—
752#387—471no—
753#387—471no—
754#387—471no—
755#387—471no—
756#387—471no—
757#387—471no—
758#387—471no—
759#387—471no—
760#387—471no—
761#387—471no—
762#387—471no—
763#387—471no—
764#387—471no—
765#387—471no—
766#387—471no—
767#387—471no—
768#387—471no—
769#387—471no—
770#387—471no—
771#387—471no—
772#387—471no—
773#387C2×D4711yescharacteristic
774#387C2×D4711yescharacteristic
775#387C2×D4711yescharacteristic
776#387C2×D4711yescharacteristic
777#387C2×D4711yescharacteristic
778#387C2×D4711yescharacteristic
779#387C2×D4711yescharacteristic
780#387C2×D4711yescharacteristic
781#384—471no—
782#384—471no—
783#384—471no—
784#383—471no—
785#383—471no—
786#383—471no—
787#383—471no—
788#382—471no—
789#382—471no—
790#382—471no—
791#382—471no—
792#382—471no—
793#382—471no—
794#382—471no—
795#382—471no—
796#382C2×D4711yescharacteristic
797#382C2×D4711yescharacteristic
798C4×C4⋊C4—471no—
799C4×C4⋊C4—471no—
800C4×C4⋊C4—471no—
801C4×C4⋊C4—471no—
802C4×C4⋊C4—471no—
803C4×C4⋊C4—471no—
804C4×C4⋊C4—471no—
805C4×C4⋊C4—471no—
806C4×C4⋊C4—471no—
807C4×C4⋊C4—471no—
808C4×C4⋊C4—471no—
809C4×C4⋊C4—471no—
810C4×C4⋊C4—471no—
811C4×C4⋊C4—471no—
812C4×C4⋊C4—471no—
813C4×C4⋊C4—471no—
814C4×C4⋊C4—471no—
815C4×C4⋊C4—471no—
816C4×C4⋊C4—471no—
817C4×C4⋊C4—471no—
818C4×C4⋊C4—471no—
819C4×C4⋊C4—471no—
820C4×C4⋊C4—471no—
821C4×C4⋊C4—471no—
822C4×C4⋊C4—471no—
823C4×C4⋊C4—471no—
824#376—471no—
825#376—471no—
826#376—471no—
827#376—471no—
828C43—471no—
829C47#3448811yescharacteristic, complemented, Sylow
830C22×Q8—471no—
831C22×Q8—471no—
832C22×Q8—471no—
833C22×Q8—471no—
834C4⋊Q8—478no—
835C4⋊Q8—478no—
836C4⋊Q8—478no—
837#125—478no—
838#125—478no—
839#125—478no—
840#125—478no—
841#125—478no—
842#125C4×D4718yes—
843C4×Q8—478no—
844C4×Q8—478no—
845C4×Q8—478no—
846C4×Q8—478no—
847C4×Q8—478no—
848C4×Q8—478no—
849C4×Q8—1882no—
850C4×Q8—1882no—
851C4×Q8—1882no—
852C4×Q8—1882no—
853C4×Q8—1882no—
854C4×Q8—1882no—
855C2×C4⋊C4—471no—
856C2×C4⋊C4—471no—
857C2×C4⋊C4—471no—
858C2×C4⋊C4—471no—
859C2×C4⋊C4—471no—
860C2×C4⋊C4—471no—
861C2×C4⋊C4—471no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4—471no—
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C4⋊C4C22×D4711yescharacteristic
906C2×C4⋊C4C22×D4711yescharacteristic
907C2×C4⋊C4C22×D4711yescharacteristic
908C2×C4⋊C4C22×D4711yescharacteristic
909C2×C4⋊C4C22×D4711yescharacteristic
910C2×C4⋊C4C22×D4711yescharacteristic
911C2×C42—471no—
912C2×C42—471no—
913C2×C42—471no—
914C2×C42—471no—
915C2×C42—471no—
916C2×C42—471no—
917C2×C42—471no—
918C2×C42—471no—
919C2×C42—471no—
920C2×C42—471no—
921C2×C42—471no—
922C2×C42—471no—
923C2×C42—471no—
924C2×C42—471no—
925C2×C42—471no—
926C2×C42—471no—
927C2×C42—471no—
928C2×C42—471no—
929C2×C42—471no—
930C2×C42—471no—
931C2×C42—471no—
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42C22×D4711yescharacteristic
942C2×C42C22×D4711yescharacteristic
943C2×C42C22×D4711yescharacteristic
944C2×C42C22×D4711yescharacteristic
945C2×C42C22×D4711yescharacteristic
946#95—471no—
947#95—471no—
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95—471no—
967#95—471no—
968#95—471no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95C22×D4711yescharacteristic
991#95C22×D4711yescharacteristic
992#95C22×D4711yescharacteristic
993#95C22×D4711yescharacteristic
994#95C22×D4711yescharacteristic
995#95C22×D4711yescharacteristic
996#95C22×D4711yescharacteristic
997#95C22×D4711yescharacteristic
998#95C22×D4711yescharacteristic
999#95C22×D4711yescharacteristic
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006C2×Q8—474no—
1007C2×Q8—474no—
1008C2×Q8—474no—
1009C2×Q8—474no—
1010C2×Q8—942no—
1011C2×Q8—942no—
1012C2×Q8—942no—
1013C2×Q8—942no—
1014C2×Q8—942no—
1015C2×Q8—942no—
1016C2×Q8—942no—
1017C2×Q8—942no—
1018C22×C4—471no—
1019C22×C4—471no—
1020C22×C4—471no—
1021C22×C4—471no—
1022C22×C4—471no—
1023C22×C4—471no—
1024C22×C4—471no—
1025C22×C4—471no—
1026C22×C4—471no—
1027C22×C4—471no—
1028C22×C4—471no—
1029C22×C4—471no—
1030C22×C4—471no—
1031C22×C4—471no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4C23×D4711yescharacteristic
1035C22×C4C23×D4711yescharacteristic
1036C22×C4C23×D4711yescharacteristic
1037C22×C4C23×D4711yescharacteristic
1038C22×C4C23×D4711yescharacteristic
1039C22×C4C23×D4711yescharacteristic
1040C22×C4C23×D4711yescharacteristic
1041C22×C4C23×D4711yescharacteristic
1042C22×C4C23×D4711yescharacteristic
1043C22×C4C23×D4711yescharacteristic
1044C22×C4C23×D4711yescharacteristic
1045C22×C4C23×D4711yescharacteristic
1046C22×C4C23×D4711yescharacteristic
1047C22×C4C23×D4711yescharacteristic
1048C22×C4C23×D4711yescharacteristic
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—474no—
1058C4⋊C4—474no—
1059C4⋊C4—474no—
1060C4⋊C4—474no—
1061C4⋊C4—474no—
1062C4⋊C4—474no—
1063C4⋊C4—474no—
1064C4⋊C4—474no—
1065C4⋊C4—474no—
1066C4⋊C4—474no—
1067C4⋊C4—474no—
1068C4⋊C4—474no—
1069C4⋊C4—474no—
1070C4⋊C4—474no—
1071C4⋊C4—474no—
1072C4⋊C4—474no—
1073C4⋊C4—942no—
1074C4⋊C4—942no—
1075C4⋊C4—942no—
1076C4⋊C4—942no—
1077C4⋊C4—942no—
1078C4⋊C4—942no—
1079C4⋊C4—942no—
1080C4⋊C4—942no—
1081C4⋊C4—942no—
1082C4⋊C4—942no—
1083C4⋊C4—942no—
1084C4⋊C4—942no—
1085C4⋊C4—1881no—
1086C4⋊C4—1881no—
1087C4⋊C4—1881no—
1088C4⋊C4—1881no—
1089C4⋊C4—1881no—
1090C4⋊C4—1881no—
1091C4⋊C4—1881no—
1092C4⋊C4—1881no—
1093C4⋊C4—1881no—
1094C4⋊C4—1881no—
1095C4⋊C4—1881no—
1096C4⋊C4—1881no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4C2×C4×D4714yes—
1100C4⋊C4C2×C4×D4714yes—
1101C4⋊C4C2×C4×D4714yes—
1102C4⋊C4C2×C4×D4714yes—
1103C4⋊C4C2×C4×D4714yes—
1104C4⋊C4C2×C4×D4714yes—
1105C42—41no—
1106C42—41no—
1107C42—41no—
1108C42—41no—
1109C42—474no—
1110C42—474no—
1111C42—474no—
1112C42—474no—
1113C42—474no—
1114C42—474no—
1115C42—474no—
1116C42—474no—
1117C42—942no—
1118C42—942no—
1119C42—942no—
1120C42—942no—
1121C42—942no—
1122C42—942no—
1123C42—942no—
1124C42—942no—
1125C42—942no—
1126C42—1881no—
1127C42—1881no—
1128C42—1881no—
1129C42—1881no—
1130C42—1881no—
1131C42—1881no—
1132C42—1881no—
1133C42—1881no—
1134C42—1881no—
1135C42—1881no—
1136C42—1881no—
1137C42—1881no—
1138C42—1881no—
1139C42C2×C4×D4714yes—
1140C23C24×D4711yescharacteristic
1141Q8—948no—
1142Q8—948no—
1143Q8—948no—
1144Q8—948no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—472no—
1184C2×C4—472no—
1185C2×C4—472no—
1186C2×C4—472no—
1187C2×C4—472no—
1188C2×C4—472no—
1189C2×C4—472no—
1190C2×C4—472no—
1191C2×C4—472no—
1192C2×C4—472no—
1193C2×C4—472no—
1194C2×C4—472no—
1195C2×C4—472no—
1196C2×C4—941no—
1197C2×C4—941no—
1198C2×C4—941no—
1199C2×C4—941no—
1200C2×C4—941no—
1201C2×C4—941no—
1202C2×C4—941no—
1203C2×C4—941no—
1204C2×C4—941no—
1205C2×C4—941no—
1206C2×C4—941no—
1207C2×C4—941no—
1208C2×C4—941no—
1209C2×C4—941no—
1210C2×C4—941no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—941no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4C22×C4×D4712yes—
1232C2×C4C22×C4×D4712yes—
1233C2×C4C22×C4×D4712yes—
1234C2×C4C22×C4×D4712yes—
1235C2×C4C22×C4×D4712yes—
1236C2×C4C22×C4×D4712yes—
1237C2×C4C22×C4×D4712yes—
1238C22C23×C4×D4711yescharacteristic
1239C22H(5,𝔽2)×D4711yescharacteristic
1240C222−1+4×D4711yescharacteristic
1241C222−1+4×D4711yescharacteristic
1242C222−1+4×D4711yescharacteristic
1243C222−1+4×D4711yescharacteristic
1244C22#1568995811yescharacteristic
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—474no—
1261C4—474no—
1262C4—942no—
1263C4—942no—
1264C4—942no—
1265C4—942no—
1266C4—942no—
1267C4—942no—
1268C4—942no—
1269C4—1881no—
1270C4—1881no—
1271C4—1881no—
1272C4—1881no—
1273C4—1881no—
1274C4—1881no—
1275C4—1881no—
1276C2#519×D4711yescharacteristic
1277C2#520×D4711yescharacteristic
1278C2#2025659911yescharacteristic
1279C2#2025782211yescharacteristic
1280C2#2025785011yescharacteristic
1281C2#2025786711yescharacteristic
1282C2#2025788211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2382C2
socle, prime radical, cosocleC23×C47C25
hypercenter#2382D47
hypocenterC47#34488
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
32. #15689850C4semidirect
829. C47#34488semidirect

Maximal subgroups

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

subgroupindex
C2×#156898502
#202465722
#202465712
#202465702
#202464812
#202464792
#202464432
#202464412
#202463422
#202463402
#202463072
#202463052
#202463022
#202461942
#202461902
#202461882
#202461862
#202461262
#202461032
#202460372
#202460362
#202459592
#202458612
C47×#23822
#3448847