Finite Group Databasebeta

← #28556299

Subgroups — #28556299

Order 15104.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 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#21422656C211yesmaximal, characteristic, complemented
5#21422652C211yesmaximal, characteristic, complemented
6#21422643C211yesmaximal, characteristic, complemented
7#21422634C211yesmaximal, characteristic, complemented
8#21422625C211yesmaximal, characteristic, complemented
9#21422621C211yesmaximal, characteristic, complemented
10#21422604C211yesmaximal, characteristic, complemented
11#21422600C211yesmaximal, characteristic, complemented
12#21422591C211yesmaximal, characteristic, complemented
13#21422582C211yesmaximal, characteristic, complemented
14C2×#16837136C211yesmaximal, characteristic, complemented
15C59×#3494C211yesmaximal, characteristic
16#16837463—21no—
17#16837463—21no—
18#16837459C2211yescharacteristic, complemented
19#16837459C2211yescharacteristic, complemented
20#16837455C2211yescharacteristic, complemented
21#16837455C2211yescharacteristic, complemented
22#16837429—21no—
23#16837366C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25#16837358—21no—
26#16837288—21no—
27#16837288—21no—
28#16837277—21no—
29#16837270C2211yescharacteristic, complemented
30#16837268C2211yescharacteristic, complemented
31#16837265C2211yescharacteristic
32C4×C4⋊Dic59C2211yescharacteristic, complemented
33C22⋊C4×Dic59—21no—
34#16837248C2211yescharacteristic, complemented
35C2×C59⋊#95C2211yescharacteristic
36#16837139C2211yescharacteristic, complemented
37#16837139C2211yescharacteristic, complemented
38#16837139C2211yescharacteristic, complemented
39#16837139C2211yescharacteristic, complemented
40#16837136C2211yescharacteristic
41#16837136C2211yescharacteristic
42#16837136C2211yescharacteristic
43#16837136C2211yescharacteristic
44#16837136C2211yescharacteristic
45#16837136C2211yescharacteristic
46#16837136C2211yescharacteristic
47#16837136C2211yescharacteristic
48#16837136C2211yescharacteristic, complemented
49#16837136C2211yescharacteristic, complemented
50#16837136C2211yescharacteristic, complemented
51#16837136C2211yescharacteristic, complemented
52C59×#555—21no—
53C59×#553—21no—
54C59×#553—21no—
55C59×#551—21no—
56C59×#551—21no—
57C59×#547—21no—
58C59×#546—21no—
59C59×#546—21no—
60C59×#544C411yescharacteristic, complemented
61C59×#542C411yescharacteristic, complemented
62C59×#542C411yescharacteristic, complemented
63C59×#540C411yescharacteristic, complemented
64C59×#540C411yescharacteristic, complemented
65C59×#535C411yescharacteristic, complemented
66C59×#532C2211yescharacteristic
67C59×#532C2211yescharacteristic
68C59×#529C2211yescharacteristic
69C59×#529C2211yescharacteristic
70C59×#525C2211yescharacteristic
71C2×#121×C59C2211yescharacteristic
72C59×#520C411yescharacteristic, complemented
73C59×#518C411yescharacteristic, 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×C59—21no—
108C2×#41×C59—21no—
109C2×#41×C59C2×C411yescharacteristic
110C22×D4×C59—21no—
111C22×D4×C59C2×C411yescharacteristic
112C23×C4×C59C2311yescharacteristic
113C4⋊Q8×C59—21no—
114C4⋊Q8×C59C2×C411yescharacteristic, complemented
115C4⋊Q8×C59C2×C411yescharacteristic, complemented
116#127×C59C2×C411yescharacteristic, complemented
117#127×C59C2×C411yescharacteristic, complemented
118#126×C59—21no—
119#126×C59—21no—
120#126×C59—21no—
121#126×C59—21no—
122#125×C59—21no—
123#125×C59C2×C411yescharacteristic, complemented
124#125×C59C2×C411yescharacteristic, complemented
125#124×C59—21no—
126#124×C59—21no—
127#124×C59—21no—
128#124×C59—21no—
129#124×C59C2×C411yescharacteristic, complemented
130#124×C59C2×C411yescharacteristic, complemented
131#123×C59—21no—
132#123×C59—21no—
133#123×C59—21no—
134#123×C59—21no—
135#123×C59—21no—
136#123×C59—21no—
137#123×C59—21no—
138#123×C59—21no—
139#123×C59—21no—
140C22⋊Q8×C59—21no—
141C22⋊Q8×C59—21no—
142C22⋊Q8×C59—21no—
143C22⋊Q8×C59—21no—
144C22⋊Q8×C59C2×C411yescharacteristic
145C22⋊Q8×C59C2311yescharacteristic
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59—21no—
150#121×C59—21no—
151#121×C59—21no—
152#121×C59—21no—
153#121×C59—21no—
154#121×C59—21no—
155#121×C59—21no—
156#121×C59C2×C411yescharacteristic
157#121×C59C2×C411yescharacteristic
158#121×C59C2×C411yescharacteristic
159#121×C59C2311yescharacteristic
160#121×C59C2311yescharacteristic
161#121×C59C2311yescharacteristic
162#120×C59—21no—
163#120×C59—21no—
164#120×C59—21no—
165C4×Q8×C59C2×C411yescharacteristic, complemented
166C4×Q8×C59C2×C411yescharacteristic, complemented
167C4×D4×C59—21no—
168C4×D4×C59—21no—
169C4×D4×C59—21no—
170C4×D4×C59—21no—
171C4×D4×C59—21no—
172C4×D4×C59—21no—
173C4×D4×C59—21no—
174C4×D4×C59—21no—
175C4×D4×C59—21no—
176C4×D4×C59—21no—
177C4×D4×C59C2×C411yescharacteristic, complemented
178C4×D4×C59C2×C411yescharacteristic, complemented
179C4×D4×C59C2×C411yescharacteristic, complemented
180C4×D4×C59C2×C411yescharacteristic, complemented
181C4×D4×C59C2×C411yescharacteristic, complemented
182C4×D4×C59C2×C411yescharacteristic, complemented
183#117×C59—21no—
184#117×C59—21no—
185#117×C59—21no—
186#117×C59C2×C411yescharacteristic
187#117×C59C2×C411yescharacteristic
188#117×C59C2×C411yescharacteristic
189#117×C59C2×C411yescharacteristic
190#117×C59C2×C411yescharacteristic
191#117×C59D411yescharacteristic
192#117×C59D411yescharacteristic
193#117×C59D411yescharacteristic
194#117×C59D411yescharacteristic
195C2×C4⋊C4×C59—21no—
196C2×C4⋊C4×C59C2×C411yescharacteristic
197C2×C4⋊C4×C59D411yescharacteristic
198C2×C4⋊C4×C59D411yescharacteristic
199C2×C22⋊C4×C59—21no—
200C2×C22⋊C4×C59—21no—
201C2×C22⋊C4×C59—21no—
202C2×C22⋊C4×C59D411yescharacteristic
203C2×C22⋊C4×C59D411yescharacteristic
204C2×C42×C59C2311yescharacteristic
205C2×C42×C59C2311yescharacteristic
206C24×C59—21no—
207C24×C59C2×D411yescharacteristic
208#41×C59—42no—
209#41×C59—81no—
210#41×C59—81no—
211#41×C59—81no—
212#41×C59—81no—
213C2×Q8×C59—21no—
214C2×Q8×C59—21no—
215C2×Q8×C59C22×C411yescharacteristic
216C2×D4×C59—21no—
217C2×D4×C59—21no—
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—21no—
228C2×D4×C59—42no—
229C2×D4×C59—81no—
230C2×D4×C59—81no—
231C2×D4×C59C22×C411yescharacteristic
232C2×D4×C59C22×C411yescharacteristic
233C2×D4×C59C22×C411yescharacteristic
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—42no—
243C22×C4×C59C22×C411yescharacteristic
244C22×C4×C59C22×C411yescharacteristic
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D411yescharacteristic
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2×D411yescharacteristic
251C22×C4×C59C2×D411yescharacteristic
252C22×C4×C59C2411yescharacteristic
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—42no—
258C22×Dic59—42no—
259C22×Dic59—81no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—21no—
264C4⋊C4×C59—21no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59C22⋊C411yescharacteristic
272C4⋊C4×C59C22⋊C411yescharacteristic
273C4⋊C4×C59C22⋊C411yescharacteristic
274C4⋊C4×C59C22⋊C411yescharacteristic
275C4⋊C4×C59C22⋊C411yescharacteristic
276C4⋊C4×C59C22⋊C411yescharacteristic
277C4⋊C4×C59C22⋊C411yescharacteristic
278C4⋊C4×C59C22⋊C411yescharacteristic
279C4⋊C4×C59C22×C411yescharacteristic
280C4⋊C4×C59C22×C411yescharacteristic
281C4⋊C4×C59C22×C411yescharacteristic
282C4⋊C4×C59C22×C411yescharacteristic
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×C59—21no—
293C22⋊C4×C59—21no—
294C22⋊C4×C59—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—21no—
302C22⋊C4×C59C22⋊C411yescharacteristic
303C22⋊C4×C59C22⋊C411yescharacteristic
304C22⋊C4×C59C22⋊C411yescharacteristic
305C22⋊C4×C59C22⋊C411yescharacteristic
306C22⋊C4×C59C22⋊C411yescharacteristic
307C22⋊C4×C59C22⋊C411yescharacteristic
308C22⋊C4×C59C22⋊C411yescharacteristic
309C22⋊C4×C59C22⋊C411yescharacteristic
310C42×C59—21no—
311C42×C59—21no—
312C42×C59—21no—
313C42×C59C22×C411yescharacteristic
314C42×C59C22×C411yescharacteristic
315C42×C59C22×C411yescharacteristic
316C42×C59C22×C411yescharacteristic
317C42×C59C2×D411yescharacteristic
318C42×C59C2×D411yescharacteristic
319C42×C59C2×D411yescharacteristic
320C42×C59C2×D411yescharacteristic
321C22⋊Dic59—42no—
322C4⋊Dic59—42no—
323C4⋊Dic59—81no—
324C4×Dic59—42no—
325C4×Dic59—81no—
326#11745664—42no—
327C2×C59⋊C8—21no—
328C2×C59⋊C8—21no—
329C2×C59⋊C8—21no—
330C2×C59⋊C8—21no—
331C2×C59⋊C8—42no—
332C23×C59—21no—
333C23×C59—21no—
334C23×C59—22no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—41no—
339C23×C59—42no—
340C23×C59—81no—
341C23×C59—81no—
342C23×C59C2×C22⋊C411yescharacteristic
343C23×C59C2×C22⋊C411yescharacteristic
344C23×C59C22×D411yescharacteristic
345Q8×C59—41no—
346Q8×C59—81no—
347Q8×C59—81no—
348D4×C59—41no—
349D4×C59—41no—
350D4×C59—41no—
351D4×C59—42no—
352D4×C59—41no—
353D4×C59—41no—
354D4×C59—41no—
355D4×C59—41no—
356D4×C59—41no—
357D4×C59—41no—
358D4×C59—42no—
359D4×C59—81no—
360D4×C59—81no—
361D4×C59—81no—
362D4×C59—81no—
363D4×C59—81no—
364D4×C59—81no—
365D4×C59—81no—
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—21no—
369C2×C4×C59—21no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—21no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—21no—
376C2×C4×C59—21no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—42no—
384C2×C4×C59—81no—
385C2×C4×C59—81no—
386C2×C4×C59—81no—
387C2×C4×C59—81no—
388C2×C4×C59—81no—
389C2×C4×C59—81no—
390C2×C4×C59—81no—
391C2×C4×C59C2×C22⋊C411yescharacteristic
392C2×C4×C59C2×C22⋊C411yescharacteristic
393C2×C4×C59C2×C22⋊C411yescharacteristic
394C2×C4×C59C2×C22⋊C411yescharacteristic
395C2×C4×C59C2×C22⋊C411yescharacteristic
396C2×C4×C59C2×C22⋊C411yescharacteristic
397C2×C4×C59C2×C22⋊C411yescharacteristic
398C2×C4×C59C2×C22⋊C411yescharacteristic
399C2×C4×C59C2×C22⋊C411yescharacteristic
400C2×C4×C59C2×C22⋊C411yescharacteristic
401C2×C4×C59C23×C411yescharacteristic
402C2×C4×C59C22×D411yescharacteristic
403C2×Dic59—22no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—84no—
416C59⋊C8—41no—
417C59⋊C8—41no—
418C59⋊C8—41no—
419C59⋊C8—41no—
420#17604—591nomaximal, Sylow
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—42no—
429C22×C59—42no—
430C22×C59—41no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—41no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—162no—
440C22×C59#41012yes—
441C22×C59C22×C22⋊C411yescharacteristic
442C22×C59#57611yescharacteristic
443C22×C59#57711yescharacteristic
444C4×C59—21no—
445C4×C59—21no—
446C4×C59—21no—
447C4×C59—21no—
448C4×C59—21no—
449C4×C59—21no—
450C4×C59—21no—
451C4×C59—21no—
452C4×C59—21no—
453C4×C59—21no—
454C4×C59—21no—
455C4×C59—21no—
456C4×C59—41no—
457C4×C59—41no—
458C4×C59—41no—
459C4×C59—41no—
460C4×C59—41no—
461Dic59—42no—
462Dic59—81no—
463Dic59—81no—
464Dic59—81no—
465#3494D5911yescharacteristic
466#2924—591no—
467#2343—591no—
468#1521—591no—
469#1517—591no—
470#1516—591no—
471#1514—591no—
472#1512—591no—
473#1510—591no—
474#1509—591no—
475#1505—591no—
476#1504—591no—
477#1502—591no—
478#1500—591no—
479C2×#327—591no—
480C2×C59—21no—
481C2×C59—21no—
482C2×C59—22no—
483C2×C59—41no—
484C2×C59—81no—
485C2×C59—81no—
486C2×C59—81no—
487C2×C59C2×#41011yescharacteristic
488C2×C59#289711yescharacteristic
489C2×C59#290111yescharacteristic
490#555—21no—
491#553—21no—
492#553—21no—
493#551—21no—
494#551—21no—
495#547—21no—
496#546—21no—
497#546—21no—
498#544Dic5911yescharacteristic, complemented
499#542Dic5911yescharacteristic, complemented
500#542Dic5911yescharacteristic, complemented
501#540Dic5911yescharacteristic, complemented
502#540Dic5911yescharacteristic, complemented
503#535Dic5911yescharacteristic, complemented
504#532C2×D5911yescharacteristic
505#532C2×D5911yescharacteristic
506#529C2×D5911yescharacteristic
507#529C2×D5911yescharacteristic
508#525C2×D5911yescharacteristic
509C2×#121C2×D5911yescharacteristic
510#520Dic5911yescharacteristic, complemented
511#518Dic5911yescharacteristic, complemented
512C2×#117C2×D5911yescharacteristic
513#433—1181no—
514#433—1181no—
515#432—591no—
516#432—591no—
517#431—591no—
518#431—591no—
519#424—1181no—
520#407—591no—
521C2×C22⋊C8—591no—
522#405—1181no—
523#387—1181no—
524#387—1181no—
525#385—1181no—
526#383—591no—
527#382—591no—
528#381—591no—
529C4×C4⋊C4—591no—
530C4×C22⋊C4—1181no—
531#376—591no—
532C2×#95—591no—
533#328—591no—
534#328—591no—
535#328—591no—
536#328—591no—
537#327—591no—
538#327—591no—
539#327—591no—
540#327—591no—
541#327—591no—
542#327—591no—
543#327—591no—
544#327—591no—
545#327—591no—
546#327—591no—
547#327—591no—
548#327—591no—
549C59#1760411yescharacteristic, complemented, Sylow
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×Dic5911yescharacteristic
553C22×D4—21no—
554C22×D4C2×Dic5911yescharacteristic
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×M16—1181no—
558C22×C8—1181no—
559C4⋊Q8—21no—
560C4⋊Q8C2×Dic5911yescharacteristic, complemented
561C4⋊Q8C2×Dic5911yescharacteristic, complemented
562#127C2×Dic5911yescharacteristic, complemented
563#127C2×Dic5911yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×Dic5911yescharacteristic, complemented
570#125C2×Dic5911yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×Dic5911yescharacteristic, complemented
576#124C2×Dic5911yescharacteristic, complemented
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8C2×Dic5911yescharacteristic
591C22⋊Q8C22×D5911yescharacteristic
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C2×Dic5911yescharacteristic
603#121C2×Dic5911yescharacteristic
604#121C2×Dic5911yescharacteristic
605#121C22×D5911yescharacteristic
606#121C22×D5911yescharacteristic
607#121C22×D5911yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×Dic5911yescharacteristic, complemented
612C4×Q8C2×Dic5911yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4C2×Dic5911yescharacteristic, complemented
624C4×D4C2×Dic5911yescharacteristic, complemented
625C4×D4C2×Dic5911yescharacteristic, complemented
626C4×D4C2×Dic5911yescharacteristic, complemented
627C4×D4C2×Dic5911yescharacteristic, complemented
628C4×D4C2×Dic5911yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×Dic5911yescharacteristic
633#117C2×Dic5911yescharacteristic
634#117C2×Dic5911yescharacteristic
635#117C2×Dic5911yescharacteristic
636#117C2×Dic5911yescharacteristic
637#117C22⋊D5911yescharacteristic
638#117C22⋊D5911yescharacteristic
639#117C22⋊D5911yescharacteristic
640#117C22⋊D5911yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—1181no—
643C2×C4⋊C4—1181no—
644C2×C4⋊C4C2×Dic5911yescharacteristic
645C2×C4⋊C4C22⋊D5911yescharacteristic
646C2×C4⋊C4C22⋊D5911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—1181no—
651C2×C22⋊C4C22⋊D5911yescharacteristic
652C2×C22⋊C4C22⋊D5911yescharacteristic
653C2×C42—1181no—
654C2×C42—1181no—
655C2×C42C22×D5911yescharacteristic
656C2×C42C22×D5911yescharacteristic
657C4⋊C8—1181no—
658C4⋊C8—1181no—
659C4⋊C8—1181no—
660C4⋊C8—1181no—
661C22⋊C8—591no—
662C22⋊C8—591no—
663C22⋊C8—591no—
664C22⋊C8—591no—
665C22⋊C8—1181no—
666C22⋊C8—1181no—
667#97—1181no—
668#97—1181no—
669C4×C8—1181no—
670C4×C8—1181no—
671#95—591no—
672#95—591no—
673#95—591no—
674#95—591no—
675#95—1181no—
676#95—1181no—
677#95—1181no—
678#95—1181no—
679#95—1181no—
680#95—1181no—
681C24—21no—
682C24C2×C22⋊D5911yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×Dic5911yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×Dic5911yescharacteristic
707C2×D4C22×Dic5911yescharacteristic
708C2×D4C22×Dic5911yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—42no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—4721no—
723C22×C4—2362no—
724C22×C4—2362no—
725C22×C4C22×Dic5911yescharacteristic
726C22×C4C22×Dic5911yescharacteristic
727C22×C4C2×C22⋊D5911yescharacteristic
728C22×C4C2×C22⋊D5911yescharacteristic
729C22×C4C2×C22⋊D5911yescharacteristic
730C22×C4C2×C22⋊D5911yescharacteristic
731C22×C4C2×C22⋊D5911yescharacteristic
732C22×C4C2×C22⋊D5911yescharacteristic
733C22×C4C2×C22⋊D5911yescharacteristic
734C22×C4C23×D5911yescharacteristic
735M16—2362no—
736C2×C8—1181no—
737C2×C8—1181no—
738C2×C8—1181no—
739C2×C8—1181no—
740C2×C8—2362no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—4721no—
753C4⋊C4—2362no—
754C4⋊C4C22⋊Dic5911yescharacteristic
755C4⋊C4C22⋊Dic5911yescharacteristic
756C4⋊C4C22⋊Dic5911yescharacteristic
757C4⋊C4C22⋊Dic5911yescharacteristic
758C4⋊C4C22⋊Dic5911yescharacteristic
759C4⋊C4C22⋊Dic5911yescharacteristic
760C4⋊C4C22⋊Dic5911yescharacteristic
761C4⋊C4C22⋊Dic5911yescharacteristic
762C4⋊C4C22×Dic5911yescharacteristic
763C4⋊C4C22×Dic5911yescharacteristic
764C4⋊C4C22×Dic5911yescharacteristic
765C4⋊C4C22×Dic5911yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—2362no—
786C22⋊C4C22⋊Dic5911yescharacteristic
787C22⋊C4C22⋊Dic5911yescharacteristic
788C22⋊C4C22⋊Dic5911yescharacteristic
789C22⋊C4C22⋊Dic5911yescharacteristic
790C22⋊C4C22⋊Dic5911yescharacteristic
791C22⋊C4C22⋊Dic5911yescharacteristic
792C22⋊C4C22⋊Dic5911yescharacteristic
793C22⋊C4C22⋊Dic5911yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—4721no—
798C42—2362no—
799C42C22×Dic5911yescharacteristic
800C42C22×Dic5911yescharacteristic
801C42C22×Dic5911yescharacteristic
802C42C22×Dic5911yescharacteristic
803C42C2×C22⋊D5911yescharacteristic
804C42C2×C22⋊D5911yescharacteristic
805C42C2×C22⋊D5911yescharacteristic
806C42C2×C22⋊D5911yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊Dic5911yescharacteristic
818C23C2×C22⋊Dic5911yescharacteristic
819C23C22×C22⋊D5911yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—1182no—
867C2×C4—4724no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4—2361no—
871C2×C4—2361no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4C2×C22⋊Dic5911yescharacteristic
880C2×C4C2×C22⋊Dic5911yescharacteristic
881C2×C4C2×C22⋊Dic5911yescharacteristic
882C2×C4C2×C22⋊Dic5911yescharacteristic
883C2×C4C2×C22⋊Dic5911yescharacteristic
884C2×C4C2×C22⋊Dic5911yescharacteristic
885C2×C4C2×C22⋊Dic5911yescharacteristic
886C2×C4C2×C22⋊Dic5911yescharacteristic
887C2×C4C2×C22⋊Dic5911yescharacteristic
888C2×C4C2×C22⋊Dic5911yescharacteristic
889C2×C4C23×Dic5911yescharacteristic
890C2×C4C22×C22⋊D5911yescharacteristic
891C8—2361no—
892C8—2361no—
893C8—2361no—
894C8—2361no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22#1683737612yes—
915C22C22×C22⋊Dic5911yescharacteristic
916C22#1683820511yescharacteristic
917C22#1683821311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—4721no—
936C4—4721no—
937C4—4721no—
938C4—2362no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#1683737611yescharacteristic
947C2#2143262211yescharacteristic
948C2#2143264311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#3494C2
socleC22×C59C22×C22⋊C4
cosocleC22×C4×C59C24
hypercenter#3494D59
hypocenterC59#17604
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #21432754C2semidirect
2. #21426956C2semidirect
3. #21422673C2semidirect
4. #21422656C2semidirect
5. #21422652C2semidirect
6. #21422643C2semidirect
7. #21422634C2semidirect
8. #21422625C2semidirect
9. #21422621C2semidirect
10. #21422604C2semidirect
11. #21422600C2semidirect
12. #21422591C2semidirect
13. #21422582C2semidirect
14. C2×#16837136C2semidirect
18. #16837459C22semidirect
19. #16837459C22semidirect
20. #16837455C22semidirect
21. #16837455C22semidirect
29. #16837270C22semidirect
30. #16837268C22semidirect
32. C4×C4⋊Dic59C22semidirect
34. #16837248C22semidirect
36. #16837139C22semidirect
37. #16837139C22semidirect
38. #16837139C22semidirect
39. #16837139C22semidirect
48. #16837136C22semidirect
49. #16837136C22semidirect
50. #16837136C22semidirect
51. #16837136C22semidirect
60. C59×#544C4semidirect
61. C59×#542C4semidirect
62. C59×#542C4semidirect
63. C59×#540C4semidirect
64. C59×#540C4semidirect
65. C59×#535C4semidirect
72. C59×#520C4semidirect
73. C59×#518C4semidirect
114. C4⋊Q8×C59C2×C4semidirect
115. C4⋊Q8×C59C2×C4semidirect
116. #127×C59C2×C4semidirect
117. #127×C59C2×C4semidirect
123. #125×C59C2×C4semidirect
124. #125×C59C2×C4semidirect
129. #124×C59C2×C4semidirect
130. #124×C59C2×C4semidirect
165. C4×Q8×C59C2×C4semidirect
166. C4×Q8×C59C2×C4semidirect
177. C4×D4×C59C2×C4semidirect
178. C4×D4×C59C2×C4semidirect
179. C4×D4×C59C2×C4semidirect
180. C4×D4×C59C2×C4semidirect
181. C4×D4×C59C2×C4semidirect
182. C4×D4×C59C2×C4semidirect
498. #544Dic59semidirect
499. #542Dic59semidirect
500. #542Dic59semidirect
501. #540Dic59semidirect
502. #540Dic59semidirect
503. #535Dic59semidirect
510. #520Dic59semidirect
511. #518Dic59semidirect
549. C59#17604semidirect
560. C4⋊Q8C2×Dic59semidirect
561. C4⋊Q8C2×Dic59semidirect
562. #127C2×Dic59semidirect
563. #127C2×Dic59semidirect
569. #125C2×Dic59semidirect
570. #125C2×Dic59semidirect
575. #124C2×Dic59semidirect
576. #124C2×Dic59semidirect
611. C4×Q8C2×Dic59semidirect
612. C4×Q8C2×Dic59semidirect
623. C4×D4C2×Dic59semidirect
624. C4×D4C2×Dic59semidirect
625. C4×D4C2×Dic59semidirect
626. C4×D4C2×Dic59semidirect
627. C4×D4C2×Dic59semidirect
628. 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
#214226562
#214226522
#214226432
#214226342
#214226252
#214226212
#214226042
#214226002
#214225912
#214225822
C2×#168371362
C59×#34942
#1760459