Finite Group Databasebeta

← #28556354

Subgroups — #28556354

Order 15104.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432754C211yesmaximal, characteristic, complemented
2#21426956C211yesmaximal, characteristic, complemented
3#21422673C211yesmaximal, characteristic, complemented
4#21422660C211yesmaximal, characteristic, complemented
5#21422652C211yesmaximal, characteristic
6#21422647C211yesmaximal, characteristic, complemented
7#21422634C211yesmaximal, characteristic, complemented
8#21422629C211yesmaximal, characteristic, complemented
9#21422621C211yesmaximal, characteristic, complemented
10#21422608C211yesmaximal, characteristic, complemented
11#21422600C211yesmaximal, characteristic
12#21422595C211yesmaximal, characteristic, complemented
13#21422582C211yesmaximal, characteristic, complemented
14C2×#16837139C211yesmaximal, characteristic, complemented
15C59×#3495C211yesmaximal, characteristic
16#16837463—21no—
17#16837463—21no—
18#16837459C2211yescharacteristic
19#16837459C2211yescharacteristic
20#16837455C2211yescharacteristic
21#16837455C2211yescharacteristic
22#16837429—21no—
23#16837366C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25#16837358—21no—
26#16837288—21no—
27#16837288—21no—
28#16837277—21no—
29#16837270C2211yescharacteristic
30#16837268C2211yescharacteristic
31#16837265C2211yescharacteristic
32C4×C4⋊Dic59C2211yescharacteristic
33C22⋊C4×Dic59—21no—
34#16837248C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36#16837139C2211yescharacteristic
37#16837139C2211yescharacteristic
38#16837139C2211yescharacteristic
39#16837139C2211yescharacteristic
40#16837139C2211yescharacteristic
41#16837139C2211yescharacteristic
42#16837139C2211yescharacteristic
43#16837139C2211yescharacteristic
44#16837139C2211yescharacteristic
45#16837139C2211yescharacteristic
46#16837139C2211yescharacteristic
47#16837139C2211yescharacteristic
48#16837136C2211yescharacteristic
49#16837136C2211yescharacteristic
50#16837136C2211yescharacteristic
51#16837136C2211yescharacteristic
52C59×#556—21no—
53C59×#554—21no—
54C59×#552—21no—
55C59×#552—21no—
56C59×#552—21no—
57C59×#552—21no—
58C59×#551—21no—
59C59×#551—21no—
60C59×#544C411yescharacteristic, complemented
61C59×#542C411yescharacteristic, complemented
62C59×#542C411yescharacteristic, complemented
63C59×#541C411yescharacteristic, complemented
64C59×#541C411yescharacteristic, complemented
65C59×#536C411yescharacteristic, complemented
66C59×#533C2211yescharacteristic
67C59×#533C2211yescharacteristic
68C59×#529C2211yescharacteristic
69C59×#529C2211yescharacteristic
70C59×#525C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C59×#520C411yescharacteristic, complemented
73C59×#519C411yescharacteristic, complemented
74C2×#117×C59C2211yescharacteristic
75C23×Dic59—21no—
76C2×#11745664—21no—
77C22×C59⋊C8—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C4×Dic59—21no—
82C2×C4×Dic59—21no—
83C4⋊(C59⋊C8)—21no—
84C4⋊(C59⋊C8)—21no—
85C4⋊(C59⋊C8)—21no—
86C4⋊(C59⋊C8)—21no—
87C22⋊(C59⋊C8)—21no—
88C22⋊(C59⋊C8)—21no—
89C22⋊(C59⋊C8)C2311yescharacteristic
90C22⋊(C59⋊C8)C2311yescharacteristic
91C22⋊(C59⋊C8)C2311yescharacteristic
92C22⋊(C59⋊C8)C2311yescharacteristic
93#14273638—21no—
94#14273638—21no—
95C4×C59⋊C8—21no—
96C4×C59⋊C8—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95C2311yescharacteristic
104C59⋊#95C2311yescharacteristic
105C59⋊#95C2311yescharacteristic
106C59⋊#95C2311yescharacteristic
107C2×#41×C59C2×C411yescharacteristic
108C22×Q8×C59C2×C411yescharacteristic
109C23×C4×C59C2311yescharacteristic
110C4⋊Q8×C59—21no—
111C4⋊Q8×C59C2×C411yescharacteristic, complemented
112C4⋊Q8×C59C2×C411yescharacteristic, complemented
113C4⋊Q8×C59C2×C411yescharacteristic, complemented
114C4⋊Q8×C59C2×C411yescharacteristic, complemented
115#126×C59—21no—
116#126×C59—21no—
117#126×C59—21no—
118#126×C59—21no—
119#126×C59—21no—
120#126×C59—21no—
121#126×C59—21no—
122#126×C59—21no—
123#125×C59—21no—
124#125×C59—21no—
125#125×C59—21no—
126#125×C59—21no—
127#125×C59—21no—
128#125×C59—21no—
129#125×C59—21no—
130#125×C59C2×C411yescharacteristic, complemented
131#125×C59C2×C411yescharacteristic, complemented
132#124×C59—21no—
133#124×C59—21no—
134#124×C59C2×C411yescharacteristic, complemented
135#124×C59C2×C411yescharacteristic, complemented
136#123×C59—21no—
137#123×C59—21no—
138#123×C59—21no—
139#123×C59—21no—
140#123×C59—21no—
141#123×C59—21no—
142#123×C59—21no—
143C22⋊Q8×C59—21no—
144C22⋊Q8×C59—21no—
145C22⋊Q8×C59—21no—
146C22⋊Q8×C59—21no—
147C22⋊Q8×C59—21no—
148C22⋊Q8×C59—21no—
149C22⋊Q8×C59—21no—
150C22⋊Q8×C59—21no—
151C22⋊Q8×C59—21no—
152C22⋊Q8×C59—21no—
153C22⋊Q8×C59C2×C411yescharacteristic
154C22⋊Q8×C59C2×C411yescharacteristic
155C22⋊Q8×C59C2×C411yescharacteristic
156C22⋊Q8×C59C2311yescharacteristic
157C22⋊Q8×C59C2311yescharacteristic
158C22⋊Q8×C59C2311yescharacteristic
159#121×C59C2×C411yescharacteristic
160#121×C59C2311yescharacteristic
161#120×C59—21no—
162C4×Q8×C59—21no—
163C4×Q8×C59—21no—
164C4×Q8×C59—21no—
165C4×Q8×C59—21no—
166C4×Q8×C59C2×C411yescharacteristic, complemented
167C4×Q8×C59C2×C411yescharacteristic, complemented
168C4×Q8×C59C2×C411yescharacteristic, complemented
169C4×Q8×C59C2×C411yescharacteristic, complemented
170C4×Q8×C59C2×C411yescharacteristic, complemented
171C4×Q8×C59C2×C411yescharacteristic, complemented
172C4×D4×C59—21no—
173C4×D4×C59—21no—
174C4×D4×C59—21no—
175C4×D4×C59—21no—
176C4×D4×C59—21no—
177C4×D4×C59—21no—
178C4×D4×C59C2×C411yescharacteristic, complemented
179C4×D4×C59C2×C411yescharacteristic, complemented
180#117×C59—21no—
181#117×C59—21no—
182#117×C59—21no—
183#117×C59—21no—
184#117×C59—21no—
185#117×C59—21no—
186#117×C59—21no—
187#117×C59C2×C411yescharacteristic
188#117×C59C2×C411yescharacteristic
189#117×C59C2×C411yescharacteristic
190#117×C59C2×C411yescharacteristic
191#117×C59C2×C411yescharacteristic
192#117×C59D411yescharacteristic
193#117×C59D411yescharacteristic
194#117×C59D411yescharacteristic
195#117×C59D411yescharacteristic
196C2×C4⋊C4×C59—21no—
197C2×C4⋊C4×C59—21no—
198C2×C4⋊C4×C59C2×C411yescharacteristic
199C2×C4⋊C4×C59D411yescharacteristic
200C2×C4⋊C4×C59D411yescharacteristic
201C2×C22⋊C4×C59—21no—
202C2×C22⋊C4×C59D411yescharacteristic
203C2×C22⋊C4×C59D411yescharacteristic
204C2×C42×C59C2311yescharacteristic
205C2×C42×C59C2311yescharacteristic
206C24×C59C2×D411yescharacteristic
207#41×C59—42no—
208C2×Q8×C59—21no—
209C2×Q8×C59—21no—
210C2×Q8×C59—21no—
211C2×Q8×C59—42no—
212C2×Q8×C59C22×C411yescharacteristic
213C2×Q8×C59C22×C411yescharacteristic
214C2×Q8×C59C22×C411yescharacteristic
215C2×D4×C59—21no—
216C2×D4×C59—21no—
217C2×D4×C59—21no—
218C2×D4×C59C22×C411yescharacteristic
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—42no—
225C22×C4×C59C22×C411yescharacteristic
226C22×C4×C59C22×C411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59C2×D411yescharacteristic
234C22×C4×C59C2411yescharacteristic
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—42no—
240C22×Dic59—42no—
241C22×Dic59—81no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59C22⋊C411yescharacteristic
266C4⋊C4×C59C22⋊C411yescharacteristic
267C4⋊C4×C59C22⋊C411yescharacteristic
268C4⋊C4×C59C22⋊C411yescharacteristic
269C4⋊C4×C59C22⋊C411yescharacteristic
270C4⋊C4×C59C22⋊C411yescharacteristic
271C4⋊C4×C59C22⋊C411yescharacteristic
272C4⋊C4×C59C22⋊C411yescharacteristic
273C4⋊C4×C59C22×C411yescharacteristic
274C4⋊C4×C59C22×C411yescharacteristic
275C4⋊C4×C59C22×C411yescharacteristic
276C4⋊C4×C59C22×C411yescharacteristic
277C22⋊C4×C59—21no—
278C22⋊C4×C59—21no—
279C22⋊C4×C59—21no—
280C22⋊C4×C59—21no—
281C22⋊C4×C59—21no—
282C22⋊C4×C59—21no—
283C22⋊C4×C59—21no—
284C22⋊C4×C59—21no—
285C22⋊C4×C59—21no—
286C22⋊C4×C59—21no—
287C22⋊C4×C59—21no—
288C22⋊C4×C59—21no—
289C22⋊C4×C59—21no—
290C22⋊C4×C59—21no—
291C22⋊C4×C59—21no—
292C22⋊C4×C59C22⋊C411yescharacteristic
293C22⋊C4×C59C22⋊C411yescharacteristic
294C22⋊C4×C59C22⋊C411yescharacteristic
295C22⋊C4×C59C22⋊C411yescharacteristic
296C22⋊C4×C59C22⋊C411yescharacteristic
297C22⋊C4×C59C22⋊C411yescharacteristic
298C22⋊C4×C59C22⋊C411yescharacteristic
299C22⋊C4×C59C22⋊C411yescharacteristic
300C42×C59—21no—
301C42×C59—21no—
302C42×C59—21no—
303C42×C59—21no—
304C42×C59—21no—
305C42×C59—21no—
306C42×C59—21no—
307C42×C59C22×C411yescharacteristic
308C42×C59C22×C411yescharacteristic
309C42×C59C22×C411yescharacteristic
310C42×C59C22×C411yescharacteristic
311C42×C59C2×D411yescharacteristic
312C42×C59C2×D411yescharacteristic
313C42×C59C2×D411yescharacteristic
314C42×C59C2×D411yescharacteristic
315C22⋊Dic59—42no—
316C4⋊Dic59—42no—
317C4⋊Dic59—81no—
318C4×Dic59—42no—
319C4×Dic59—81no—
320#11745664—42no—
321C2×C59⋊C8—21no—
322C2×C59⋊C8—21no—
323C2×C59⋊C8—21no—
324C2×C59⋊C8—21no—
325C2×C59⋊C8—42no—
326C23×C59—21no—
327C23×C59—21no—
328C23×C59—22no—
329C23×C59—21no—
330C23×C59—41no—
331C23×C59C2×C22⋊C411yescharacteristic
332C23×C59C2×C22⋊C411yescharacteristic
333C23×C59C22×D411yescharacteristic
334Q8×C59—41no—
335Q8×C59—41no—
336Q8×C59—41no—
337Q8×C59—42no—
338Q8×C59—81no—
339Q8×C59—81no—
340D4×C59—41no—
341D4×C59—41no—
342D4×C59—41no—
343D4×C59—42no—
344D4×C59—81no—
345C2×C4×C59—21no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—21no—
352C2×C4×C59—21no—
353C2×C4×C59—21no—
354C2×C4×C59—21no—
355C2×C4×C59—21no—
356C2×C4×C59—21no—
357C2×C4×C59—21no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—42no—
365C2×C4×C59—42no—
366C2×C4×C59—81no—
367C2×C4×C59—81no—
368C2×C4×C59—81no—
369C2×C4×C59C2×C22⋊C411yescharacteristic
370C2×C4×C59C2×C22⋊C411yescharacteristic
371C2×C4×C59C2×C22⋊C411yescharacteristic
372C2×C4×C59C2×C22⋊C411yescharacteristic
373C2×C4×C59C2×C22⋊C411yescharacteristic
374C2×C4×C59C2×C22⋊C411yescharacteristic
375C2×C4×C59C2×C22⋊C411yescharacteristic
376C2×C4×C59C2×C22⋊C411yescharacteristic
377C2×C4×C59C2×C22⋊C411yescharacteristic
378C2×C4×C59C2×C22⋊C411yescharacteristic
379C2×C4×C59C23×C411yescharacteristic
380C2×C4×C59C22×D411yescharacteristic
381C2×Dic59—22no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—41no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—84no—
394C59⋊C8—41no—
395C59⋊C8—41no—
396C59⋊C8—41no—
397C59⋊C8—41no—
398#17609—591nomaximal, Sylow
399C22×C59—21no—
400C22×C59—21no—
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—21no—
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59—41no—
409C22×C59—41no—
410C22×C59—41no—
411C22×C59#41012yes—
412C22×C59C22×C22⋊C411yescharacteristic
413C22×C59#57711yescharacteristic
414C22×C59#57811yescharacteristic
415C4×C59—21no—
416C4×C59—21no—
417C4×C59—21no—
418C4×C59—21no—
419C4×C59—21no—
420C4×C59—21no—
421C4×C59—21no—
422C4×C59—21no—
423C4×C59—21no—
424C4×C59—21no—
425C4×C59—21no—
426C4×C59—21no—
427C4×C59—41no—
428C4×C59—41no—
429C4×C59—41no—
430C4×C59—41no—
431C4×C59—41no—
432C4×C59—41no—
433C4×C59—41no—
434Dic59—42no—
435Dic59—81no—
436Dic59—81no—
437Dic59—81no—
438#3495D5911yescharacteristic
439#2924—591no—
440#2343—591no—
441#1521—591no—
442#1518—591no—
443#1516—591no—
444#1515—591no—
445#1512—591no—
446#1511—591no—
447#1509—591no—
448#1506—591no—
449#1504—591no—
450#1503—591no—
451#1500—591no—
452C2×#328—591no—
453C2×C59—21no—
454C2×C59—21no—
455C2×C59—22no—
456C2×C59—41no—
457C2×C59—81no—
458C2×C59C2×#41011yescharacteristic
459C2×C59#289811yescharacteristic
460C2×C59#290111yescharacteristic
461#556—21no—
462#554—21no—
463#552—21no—
464#552—21no—
465#552—21no—
466#552—21no—
467#551—21no—
468#551—21no—
469#544Dic5911yescharacteristic, complemented
470#542Dic5911yescharacteristic, complemented
471#542Dic5911yescharacteristic, complemented
472#541Dic5911yescharacteristic, complemented
473#541Dic5911yescharacteristic, complemented
474#536Dic5911yescharacteristic, complemented
475#533C2×D5911yescharacteristic
476#533C2×D5911yescharacteristic
477#529C2×D5911yescharacteristic
478#529C2×D5911yescharacteristic
479#525C2×D5911yescharacteristic
480C2×C22⋊Q8C2×D5911yescharacteristic
481#520Dic5911yescharacteristic, complemented
482#519Dic5911yescharacteristic, complemented
483C2×#117C2×D5911yescharacteristic
484#433—1181no—
485#433—1181no—
486#432—591no—
487#432—591no—
488#431—591no—
489#431—591no—
490#424—1181no—
491#407—591no—
492C2×C22⋊C8—591no—
493#405—1181no—
494#387—1181no—
495#387—1181no—
496#385—1181no—
497#383—591no—
498#382—591no—
499#381—591no—
500C4×C4⋊C4—591no—
501C4×C22⋊C4—1181no—
502#376—591no—
503C2×#95—591no—
504#328—591no—
505#328—591no—
506#328—591no—
507#328—591no—
508#328—591no—
509#328—591no—
510#328—591no—
511#328—591no—
512#328—591no—
513#328—591no—
514#328—591no—
515#328—591no—
516#327—591no—
517#327—591no—
518#327—591no—
519#327—591no—
520C59#1760911yescharacteristic, complemented, Sylow
521C2×#41C2×Dic5911yescharacteristic
522C22×Q8C2×Dic5911yescharacteristic
523C23×C4—1181no—
524C23×C4C22×D5911yescharacteristic
525C2×M16—1181no—
526C22×C8—1181no—
527C4⋊Q8—21no—
528C4⋊Q8C2×Dic5911yescharacteristic, complemented
529C4⋊Q8C2×Dic5911yescharacteristic, complemented
530C4⋊Q8C2×Dic5911yescharacteristic, complemented
531C4⋊Q8C2×Dic5911yescharacteristic, complemented
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×Dic5911yescharacteristic, complemented
548#125C2×Dic5911yescharacteristic, complemented
549#124—21no—
550#124—21no—
551#124C2×Dic5911yescharacteristic, complemented
552#124C2×Dic5911yescharacteristic, complemented
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8C2×Dic5911yescharacteristic
571C22⋊Q8C2×Dic5911yescharacteristic
572C22⋊Q8C2×Dic5911yescharacteristic
573C22⋊Q8C22×D5911yescharacteristic
574C22⋊Q8C22×D5911yescharacteristic
575C22⋊Q8C22×D5911yescharacteristic
576#121C2×Dic5911yescharacteristic
577#121C22×D5911yescharacteristic
578#120—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8C2×Dic5911yescharacteristic, complemented
584C4×Q8C2×Dic5911yescharacteristic, complemented
585C4×Q8C2×Dic5911yescharacteristic, complemented
586C4×Q8C2×Dic5911yescharacteristic, complemented
587C4×Q8C2×Dic5911yescharacteristic, complemented
588C4×Q8C2×Dic5911yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4C2×Dic5911yescharacteristic, complemented
596C4×D4C2×Dic5911yescharacteristic, complemented
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117C2×Dic5911yescharacteristic
605#117C2×Dic5911yescharacteristic
606#117C2×Dic5911yescharacteristic
607#117C2×Dic5911yescharacteristic
608#117C2×Dic5911yescharacteristic
609#117C22⋊D5911yescharacteristic
610#117C22⋊D5911yescharacteristic
611#117C22⋊D5911yescharacteristic
612#117C22⋊D5911yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—1181no—
616C2×C4⋊C4—1181no—
617C2×C4⋊C4C2×Dic5911yescharacteristic
618C2×C4⋊C4C22⋊D5911yescharacteristic
619C2×C4⋊C4C22⋊D5911yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1181no—
622C2×C22⋊C4C22⋊D5911yescharacteristic
623C2×C22⋊C4C22⋊D5911yescharacteristic
624C2×C42—1181no—
625C2×C42—1181no—
626C2×C42C22×D5911yescharacteristic
627C2×C42C22×D5911yescharacteristic
628C4⋊C8—1181no—
629C4⋊C8—1181no—
630C4⋊C8—1181no—
631C4⋊C8—1181no—
632C22⋊C8—591no—
633C22⋊C8—591no—
634C22⋊C8—591no—
635C22⋊C8—591no—
636C22⋊C8—1181no—
637C22⋊C8—1181no—
638#97—1181no—
639#97—1181no—
640C4×C8—1181no—
641C4×C8—1181no—
642#95—591no—
643#95—591no—
644#95—591no—
645#95—591no—
646#95—1181no—
647#95—1181no—
648#95—1181no—
649#95—1181no—
650#95—1181no—
651#95—1181no—
652C24C2×C22⋊D5911yescharacteristic
653#41—42no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—42no—
658C2×Q8C22×Dic5911yescharacteristic
659C2×Q8C22×Dic5911yescharacteristic
660C2×Q8C22×Dic5911yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22×Dic5911yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—1181no—
672C22×C4—1181no—
673C22×C4—1181no—
674C22×C4—1181no—
675C22×C4—4721no—
676C22×C4—2362no—
677C22×C4—2362no—
678C22×C4C22×Dic5911yescharacteristic
679C22×C4C22×Dic5911yescharacteristic
680C22×C4C2×C22⋊D5911yescharacteristic
681C22×C4C2×C22⋊D5911yescharacteristic
682C22×C4C2×C22⋊D5911yescharacteristic
683C22×C4C2×C22⋊D5911yescharacteristic
684C22×C4C2×C22⋊D5911yescharacteristic
685C22×C4C2×C22⋊D5911yescharacteristic
686C22×C4C2×C22⋊D5911yescharacteristic
687C22×C4C23×D5911yescharacteristic
688M16—2362no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—2362no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—4721no—
718C4⋊C4—2362no—
719C4⋊C4C22⋊Dic5911yescharacteristic
720C4⋊C4C22⋊Dic5911yescharacteristic
721C4⋊C4C22⋊Dic5911yescharacteristic
722C4⋊C4C22⋊Dic5911yescharacteristic
723C4⋊C4C22⋊Dic5911yescharacteristic
724C4⋊C4C22⋊Dic5911yescharacteristic
725C4⋊C4C22⋊Dic5911yescharacteristic
726C4⋊C4C22⋊Dic5911yescharacteristic
727C4⋊C4C22×Dic5911yescharacteristic
728C4⋊C4C22×Dic5911yescharacteristic
729C4⋊C4C22×Dic5911yescharacteristic
730C4⋊C4C22×Dic5911yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—2362no—
747C22⋊C4C22⋊Dic5911yescharacteristic
748C22⋊C4C22⋊Dic5911yescharacteristic
749C22⋊C4C22⋊Dic5911yescharacteristic
750C22⋊C4C22⋊Dic5911yescharacteristic
751C22⋊C4C22⋊Dic5911yescharacteristic
752C22⋊C4C22⋊Dic5911yescharacteristic
753C22⋊C4C22⋊Dic5911yescharacteristic
754C22⋊C4C22⋊Dic5911yescharacteristic
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—4721no—
763C42—2362no—
764C42C22×Dic5911yescharacteristic
765C42C22×Dic5911yescharacteristic
766C42C22×Dic5911yescharacteristic
767C42C22×Dic5911yescharacteristic
768C42C2×C22⋊D5911yescharacteristic
769C42C2×C22⋊D5911yescharacteristic
770C42C2×C22⋊D5911yescharacteristic
771C42C2×C22⋊D5911yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23C2×C22⋊Dic5911yescharacteristic
778C23C2×C22⋊Dic5911yescharacteristic
779C23C22×C22⋊D5911yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786D4—41no—
787D4—42no—
788D4—41no—
789D4—41no—
790D4—81no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—1182no—
816C2×C4—4724no—
817C2×C4—2361no—
818C2×C4—2361no—
819C2×C4—2361no—
820C2×C4—2361no—
821C2×C4—2361no—
822C2×C4—2361no—
823C2×C4—2361no—
824C2×C4—2361no—
825C2×C4—2361no—
826C2×C4—2361no—
827C2×C4—2361no—
828C2×C4C2×C22⋊Dic5911yescharacteristic
829C2×C4C2×C22⋊Dic5911yescharacteristic
830C2×C4C2×C22⋊Dic5911yescharacteristic
831C2×C4C2×C22⋊Dic5911yescharacteristic
832C2×C4C2×C22⋊Dic5911yescharacteristic
833C2×C4C2×C22⋊Dic5911yescharacteristic
834C2×C4C2×C22⋊Dic5911yescharacteristic
835C2×C4C2×C22⋊Dic5911yescharacteristic
836C2×C4C2×C22⋊Dic5911yescharacteristic
837C2×C4C2×C22⋊Dic5911yescharacteristic
838C2×C4C23×Dic5911yescharacteristic
839C2×C4C22×C22⋊D5911yescharacteristic
840C8—2361no—
841C8—2361no—
842C8—2361no—
843C8—2361no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#1683737612yes—
857C22C22×C22⋊Dic5911yescharacteristic
858C22#1683821011yescharacteristic
859C22#1683821711yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—4721no—
880C4—4721no—
881C4—4721no—
882C4—2362no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#1683737611yescharacteristic
889C2#2143262911yescharacteristic
890C2#2143264311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#3495C2
socleC22×C59C22×C22⋊C4
prime radicalC59×#525C22
cosocleC22×C4×C59C24
hypercenter#3495D59
hypocenterC59#17609
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #21432754C2semidirect
2. #21426956C2semidirect
3. #21422673C2semidirect
4. #21422660C2semidirect
6. #21422647C2semidirect
7. #21422634C2semidirect
8. #21422629C2semidirect
9. #21422621C2semidirect
10. #21422608C2semidirect
12. #21422595C2semidirect
13. #21422582C2semidirect
14. C2×#16837139C2semidirect
60. C59×#544C4semidirect
61. C59×#542C4semidirect
62. C59×#542C4semidirect
63. C59×#541C4semidirect
64. C59×#541C4semidirect
65. C59×#536C4semidirect
72. C59×#520C4semidirect
73. C59×#519C4semidirect
111. C4⋊Q8×C59C2×C4semidirect
112. C4⋊Q8×C59C2×C4semidirect
113. C4⋊Q8×C59C2×C4semidirect
114. C4⋊Q8×C59C2×C4semidirect
130. #125×C59C2×C4semidirect
131. #125×C59C2×C4semidirect
134. #124×C59C2×C4semidirect
135. #124×C59C2×C4semidirect
166. C4×Q8×C59C2×C4semidirect
167. C4×Q8×C59C2×C4semidirect
168. C4×Q8×C59C2×C4semidirect
169. C4×Q8×C59C2×C4semidirect
170. C4×Q8×C59C2×C4semidirect
171. C4×Q8×C59C2×C4semidirect
178. C4×D4×C59C2×C4semidirect
179. C4×D4×C59C2×C4semidirect
469. #544Dic59semidirect
470. #542Dic59semidirect
471. #542Dic59semidirect
472. #541Dic59semidirect
473. #541Dic59semidirect
474. #536Dic59semidirect
481. #520Dic59semidirect
482. #519Dic59semidirect
520. C59#17609semidirect
528. C4⋊Q8C2×Dic59semidirect
529. C4⋊Q8C2×Dic59semidirect
530. C4⋊Q8C2×Dic59semidirect
531. C4⋊Q8C2×Dic59semidirect
547. #125C2×Dic59semidirect
548. #125C2×Dic59semidirect
551. #124C2×Dic59semidirect
552. #124C2×Dic59semidirect
583. C4×Q8C2×Dic59semidirect
584. C4×Q8C2×Dic59semidirect
585. C4×Q8C2×Dic59semidirect
586. C4×Q8C2×Dic59semidirect
587. C4×Q8C2×Dic59semidirect
588. C4×Q8C2×Dic59semidirect
595. C4×D4C2×Dic59semidirect
596. C4×D4C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#214327542
#214269562
#214226732
#214226602
#214226522
#214226472
#214226342
#214226292
#214226212
#214226082
#214226002
#214225952
#214225822
C2×#168371392
C59×#34952
#1760959