Finite Group Databasebeta

← #29647564

Subgroups — #29647564

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459839C211yesmaximal, characteristic
2#21454850C211yesmaximal, characteristic, complemented
3#21448459C211yesmaximal, characteristic, complemented
4#21444388C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444374C211yesmaximal, characteristic, complemented
7#21444362C211yesmaximal, characteristic, complemented
8#21444361C211yesmaximal, characteristic, complemented
9#21444347C211yesmaximal, characteristic, complemented
10#21444346C211yesmaximal, characteristic, complemented
11#21444343C211yesmaximal, characteristic, complemented
12#21444325C211yesmaximal, characteristic, complemented
13#21444312C211yesmaximal, characteristic, complemented
14#21444304C211yesmaximal, characteristic, complemented
15C61×#1516C211yesmaximal, characteristic, complemented
16#16840475C411yescharacteristic, complemented
17#16840470C411yescharacteristic, complemented
18#16840464C411yescharacteristic, complemented
19#16840461—21no—
20#16840456C411yescharacteristic, complemented
21#16840431C411yescharacteristic, complemented
22#16840407—21no—
23#16840403C411yescharacteristic, complemented
24#16840400C411yescharacteristic, complemented
25#16840399—21no—
26#16840396C411yescharacteristic, complemented
27#16840394—21no—
28#16840364—21no—
29#16840348—21no—
30#16840345—21no—
31#16840307C2211yescharacteristic
32#16840298C2211yescharacteristic
33#16840275C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41C8×C22⋊D61—21no—
42#16839816C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839662—21no—
48#16839659—21no—
49#16839656—21no—
50#16839654—21no—
51#16839624C2211yescharacteristic, complemented
52#16839622C2211yescharacteristic, complemented
53#16839621C2211yescharacteristic, complemented
54#16839613C2211yescharacteristic, complemented
55#16839607C2211yescharacteristic, complemented
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic, complemented
63#16839496C2211yescharacteristic, complemented
64#16839495C2211yescharacteristic
65#16839495C2211yescharacteristic
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C61×#381C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic
76C2×#11758224—21no—
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758194—21no—
85C2×#11758189—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic
88#14519773—21no—
89#14519773C2×C411yescharacteristic
90#14519772—21no—
91#14519771—21no—
92#14519770—21no—
93#14519768C2×C411yescharacteristic
94#14519767—21no—
95#14519766C2×C411yescharacteristic
96#14519765—21no—
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519761—21no—
102#14519761—21no—
103#14519760—21no—
104#14519759—21no—
105#14519757—21no—
106#14519754—21no—
107#14519753C2×C411yescharacteristic
108#14519752—21no—
109#14519752C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111#14519751—21no—
112#14519751—21no—
113#14519751—21no—
114#14519751C2×C411yescharacteristic
115#14519751C2×C411yescharacteristic
116#14519751C2311yescharacteristic
117#14519751C2311yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519749—21no—
124#14519749—21no—
125#14519749—21no—
126#14519748—21no—
127#14519748C2×C411yescharacteristic
128#14519747—21no—
129#14519747—21no—
130#14519747—21no—
131#14519745—21no—
132#14519745—21no—
133Q8×Dic61C2×C411yescharacteristic
134C4×D244—21no—
135D4×Dic61—21no—
136D4×Dic61C2×C411yescharacteristic
137#14519739—21no—
138#14519739C2×C411yescharacteristic
139#14519739C2×C411yescharacteristic
140C4×C22⋊D61—21no—
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519735—21no—
154#14519735C2×C411yescharacteristic
155#14519734—21no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61D411yescharacteristic
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174#14519706—21no—
175#14519706—21no—
176C22⋊#92418—21no—
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519689—21no—
180#14519689—21no—
181#14519687—21no—
182C8×Dic61—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210#41×C61—81no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61—81no—
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758226—81no—
249#11758224—81no—
250#11758224—81no—
251D4×D61—44no—
252D4×D61—81no—
253D4×D61—81no—
254D4×D61—81no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—81no—
260C2×D244C22×C411yescharacteristic
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—81no—
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×Dic122—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—81no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C22×C411yescharacteristic
278C4⋊C4×C61C22×C411yescharacteristic
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—81no—
285C42×C61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—81no—
289C22⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—81no—
306#11758198—81no—
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—81no—
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—42no—
322#11758196—81no—
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—42no—
330C4×Dic61—81no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335#11758194—81no—
336C2×#92418—21no—
337C2×#92418—21no—
338#11758189—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—42no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—81no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—81no—
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C23×C411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C22⋊D61—22no—
389C22⋊D61—22no—
390C22⋊D61—41no—
391C22⋊D61—41no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—42no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—22no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—81no—
415C2×Dic61—81no—
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422D244—41no—
423D244—41no—
424D244—42no—
425D244—81no—
426D244—81no—
427D244—81no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—42no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436Dic122—81no—
437C8×C61—41no—
438C8×C61—41no—
439#92418—41no—
440#92418—41no—
441#17599—611nomaximal, Sylow
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—81no—
454C22×C61—81no—
455C22×C61C22×C22⋊C411yescharacteristic
456C22×C61#57611yescharacteristic
457C22×C61#57711yescharacteristic
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61—162no—
473C2×D61—162no—
474C4×C61—21no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—41no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—81no—
482C4×C61—81no—
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—41no—
489Dic61—41no—
490Dic61—81no—
491Dic61—81no—
492Dic61#42112yes—
493#3519—611no—
494#2974—611no—
495#2319—611no—
496#1519—611no—
497#1519—611no—
498#1516—611no—
499#1516D6111yescharacteristic, complemented
500#1513—611no—
501#1513—611no—
502#1510—611no—
503#1510—611no—
504#1509—611no—
505#1505—611no—
506#1502—611no—
507#1500—611no—
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61—81no—
513C2×C61#288311yescharacteristic
514C2×C61#289711yescharacteristic
515C2×C61C2×#42111yescharacteristic
516D61—41no—
517D61—41no—
518D61—81no—
519D61—81no—
520#555—611no—
521#554—611no—
522#553—611no—
523#553—611no—
524#553—1221no—
525#550—611no—
526#546—611no—
527#546—611no—
528#546—1221no—
529#546—1221no—
530D42—611no—
531D42—1221no—
532#540—1221no—
533#538—1221no—
534#538—1221no—
535#532—611no—
536#529—611no—
537#525—611no—
538#525C2×D6111yescharacteristic
539C2×#121—611no—
540C2×#121—611no—
541#518—1221no—
542C2×C4×D4—611no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546C8×D4—1221no—
547#432—611no—
548#431—611no—
549#407—611no—
550#407—611no—
551C2×C22⋊C8—611no—
552C2×C22⋊C8C2×D6111yescharacteristic, complemented
553#390—1221no—
554#389—1221no—
555#388—1221no—
556#388—1221no—
557#381—611no—
558#381C2×D6111yescharacteristic, complemented
559#380—611no—
560#380—611no—
561C4×C4⋊C4—611no—
562#376—611no—
563#328—611no—
564#328—611no—
565#328C2×D6111yescharacteristic, complemented
566#328C2×D6111yescharacteristic, complemented
567#327—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327C2×D6111yescharacteristic, complemented
578#327C2×D6111yescharacteristic, complemented
579C61#1759911yescharacteristic, complemented, Sylow
580C2×#41—611no—
581C2×#41—1221no—
582C2×#41C4×D6111yescharacteristic
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C23×C4—611no—
590C23×C4C22×D6111yescharacteristic
591C2×M16—1221no—
592C2×M16—1221no—
593C22×C8—21no—
594C22×C8—1221no—
595C4⋊Q8—611no—
596#127—611no—
597#127—1221no—
598#126—1221no—
599#126—1221no—
600#126—1221no—
601#125—611no—
602#125—1221no—
603#124—611no—
604#124—1221no—
605#124—1221no—
606#124—1221no—
607#123—21no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614C22⋊Q8—611no—
615C22⋊Q8—1221no—
616C22⋊Q8—1221no—
617C22⋊Q8C4×D6111yescharacteristic
618C22⋊Q8C22×D6111yescharacteristic
619#121—611no—
620#121—611no—
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121C4×D6111yescharacteristic
640#121C22×D6111yescharacteristic
641#120—21no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647C4×Q8—611no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669#117—611no—
670#117—1221no—
671#117—1221no—
672#117C4×D6111yescharacteristic
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C2×C42—1221no—
692C4⋊C8—1221no—
693C4⋊C8—1221no—
694C22⋊C8—21no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8C22×D6111yescharacteristic
701C22⋊C8C22×D6111yescharacteristic
702#97—1221no—
703C4×C8—1221no—
704#95—21no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95C22×D6111yescharacteristic
710#95C22×D6111yescharacteristic
711C24—611no—
712C24—1221no—
713C24—1221no—
714C24D4×D6111yescharacteristic
715#41—81no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719C2×Q8—1221no—
720C2×Q8C2×C4×D6111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—611no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—611no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—2442no—
749C2×D4—2444no—
750C2×D4C2×C4×D6111yescharacteristic
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—81no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—4881no—
771C22×C4C2×C4×D6111yescharacteristic
772C22×C4C2×C4×D6111yescharacteristic
773C22×C4D4×D6111yescharacteristic
774C22×C4D4×D6111yescharacteristic
775C22×C4D4×D6111yescharacteristic
776C22×C4C23×D6111yescharacteristic
777M16—4881no—
778M16—4881no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—81no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—4881no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—4881no—
801C4⋊C4—4881no—
802C4⋊C4—2442no—
803C4⋊C4C2×C4×D6111yescharacteristic
804C4⋊C4C2×C4×D6111yescharacteristic
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—81no—
811C22⋊C4—611no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—4881no—
834C22⋊C4—4881no—
835C22⋊C4—4881no—
836C42—21no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—611no—
841C42—1221no—
842C42—1221no—
843C42—4881no—
844C42—2442no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—41no—
849C23—41no—
850C23—611no—
851C23—611no—
852C23—1221no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—4881no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—2441no—
861C23—2441no—
862C23—2442no—
863C23—2442no—
864C23C22⋊C4×D6111yescharacteristic
865C23C22⋊C4×D6111yescharacteristic
866C23C2×D4×D6111yescharacteristic
867Q8—41no—
868Q8—4881no—
869D4—41no—
870D4—42no—
871D4—41no—
872D4—41no—
873D4—81no—
874D4—1222no—
875D4—1222no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—2441no—
885D4—2441no—
886D4—2442no—
887D4—2442no—
888D4—2441no—
889D4—2441no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—81no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—1222no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—4881no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4881no—
925C2×C4—4881no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2442no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C22⋊C4×D6111yescharacteristic
939C2×C4C22⋊C4×D6111yescharacteristic
940C2×C4C22×C4×D6111yescharacteristic
941C2×C4C2×D4×D6111yescharacteristic
942C8—41no—
943C8—41no—
944C8—2441no—
945C8—2441no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—81no—
958C22—81no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—9762no—
966C22—9762no—
967C22—4881no—
968C22—4881no—
969C22—2441no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22C2×C22⋊C4×D6111yescharacteristic
976C22#1684056411yescharacteristic
977C22#1684056911yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—81no—
986C4—81no—
987C4—612no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—4881no—
994C4—4881no—
995C4—2441no—
996C4—2441no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—4881no—
1003C2—4881no—
1004C2—2441no—
1005C2—2441no—
1006C2#2145427711yescharacteristic
1007C2#2145434111yescharacteristic
1008C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#21459839C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17599
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448459C2semidirect
4. #21444388C2semidirect
5. #21444385C2semidirect
6. #21444374C2semidirect
7. #21444362C2semidirect
8. #21444361C2semidirect
9. #21444347C2semidirect
10. #21444346C2semidirect
11. #21444343C2semidirect
12. #21444325C2semidirect
13. #21444312C2semidirect
14. #21444304C2semidirect
15. C61×#1516C2semidirect
16. #16840475C4semidirect
17. #16840470C4semidirect
18. #16840464C4semidirect
20. #16840456C4semidirect
21. #16840431C4semidirect
23. #16840403C4semidirect
24. #16840400C4semidirect
26. #16840396C4semidirect
42. #16839816C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839624C22semidirect
52. #16839622C22semidirect
53. #16839621C22semidirect
54. #16839613C22semidirect
55. #16839607C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
62. #16839496C22semidirect
63. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C61×#381C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
499. #1516D61semidirect
552. C2×C22⋊C8C2×D61semidirect
558. #381C2×D61semidirect
565. #328C2×D61semidirect
566. #328C2×D61semidirect
577. #327C2×D61semidirect
578. #327C2×D61semidirect
579. C61#17599semidirect

Maximal subgroups

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

subgroupindex
#214598392
#214548502
#214484592
#214443882
#214443852
#214443742
#214443622
#214443612
#214443472
#214443462
#214443432
#214443252
#214443122
#214443042
C61×#15162
#1759961