Finite Group Databasebeta

← #29647549

Subgroups — #29647549

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459868C211yesmaximal, characteristic
2#21454854C211yesmaximal, characteristic, complemented
3#21444394C211yesmaximal, characteristic, complemented
4#21444390C211yesmaximal, characteristic, complemented
5#21444382C211yesmaximal, characteristic, complemented
6#21444373C211yesmaximal, characteristic, complemented
7#21444369C211yesmaximal, characteristic, complemented
8#21444360C211yesmaximal, characteristic, complemented
9#21444355C211yesmaximal, characteristic, complemented
10#21444351C211yesmaximal, characteristic, complemented
11#21444338C211yesmaximal, characteristic, complemented
12#21444321C211yesmaximal, characteristic, complemented
13#21444308C211yesmaximal, characteristic, complemented
14C2×#16839498C211yesmaximal, characteristic, complemented
15C61×#2318C211yesmaximal, characteristic, complemented
16#16840482C411yescharacteristic, complemented
17#16840467—21no—
18#16840452C411yescharacteristic, complemented
19#16840452C411yescharacteristic, complemented
20#16840438—21no—
21#16840438—21no—
22D4×Dic122C411yescharacteristic, complemented
23#16840421C411yescharacteristic, complemented
24#16840421C411yescharacteristic, complemented
25#16840417C411yescharacteristic, complemented
26#16840416C411yescharacteristic, complemented
27#16840406—21no—
28#16840377—21no—
29#16840354—21no—
30#16840354—21no—
31#16840319C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840273C2211yescharacteristic
34#16840273C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519756C2211yescharacteristic
37#16840241—21no—
38#16839840—21no—
39#16839834—21no—
40#16839834—21no—
41D4×#92418—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839726C2211yescharacteristic
45#16839726C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48#16839498C2211yescharacteristic
49#16839498C2211yescharacteristic
50#16839498C2211yescharacteristic
51#16839498C2211yescharacteristic
52#16839498C2211yescharacteristic
53#16839498C2211yescharacteristic
54#16839498C2211yescharacteristic
55#16839498C2211yescharacteristic
56#16839498C2211yescharacteristic
57#16839498C2211yescharacteristic
58#16839498C2211yescharacteristic
59#16839498C2211yescharacteristic
60#16839495C2211yescharacteristic
61#16839495C2211yescharacteristic
62#16839495C2211yescharacteristic
63#16839495C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C61×#388—21no—
66C61×#387—21no—
67C61×#386—21no—
68C61×#385—21no—
69C61×#383C2211yescharacteristic
70C61×#382C2211yescharacteristic
71C61×#381C2211yescharacteristic
72C61×#380C2211yescharacteristic
73C4×C22⋊C4×C61C2211yescharacteristic
74C2×#95×C61C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic, complemented
77C2×#11758224—21no—
78C22×Dic122C2×C411yescharacteristic
79C22×Dic122C2×C411yescharacteristic, complemented
80C2×#11758194—21no—
81C2×#11758194—21no—
82C22×#92418—21no—
83C22×#92418—21no—
84#14519777C2×C411yescharacteristic, complemented
85#14519777C2×C411yescharacteristic, complemented
86#14519776—21no—
87#14519771—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519769—21no—
93#14519769C2×C411yescharacteristic, complemented
94#14519767—21no—
95#14519767—21no—
96#14519765C2×C411yescharacteristic, complemented
97#14519764—21no—
98#14519763—21no—
99#14519763—21no—
100#14519761—21no—
101#14519761—21no—
102#14519760—21no—
103#14519760—21no—
104#14519760—21no—
105#14519759—21no—
106#14519759—21no—
107#14519758—21no—
108#14519758—21no—
109#14519757—21no—
110#14519756—21no—
111#14519756—21no—
112#14519756—21no—
113#14519756—21no—
114#14519756—21no—
115#14519756C2×C411yescharacteristic
116#14519756C2×C411yescharacteristic
117#14519756C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic, complemented
119#14519756C2×C411yescharacteristic, complemented
120#14519756C2×C411yescharacteristic, complemented
121#14519756C2311yescharacteristic
122#14519756C2311yescharacteristic
123#14519756C2311yescharacteristic
124#14519755—21no—
125#14519755—21no—
126#14519754—21no—
127#14519754—21no—
128#14519751C2×C411yescharacteristic
129#14519751C2×C411yescharacteristic, complemented
130#14519751C2311yescharacteristic
131#14519749—21no—
132#14519749—21no—
133#14519748—21no—
134#14519746—21no—
135#14519746—21no—
136C4×Dic122—21no—
137C4×Dic122C2×C411yescharacteristic, complemented
138C4×Dic122C2×C411yescharacteristic, complemented
139C4×Dic122C2×C411yescharacteristic, complemented
140#14519742—21no—
141C4×D244C2×C411yescharacteristic, complemented
142D4×Dic61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148#14519737—21no—
149#14519737—21no—
150#14519736—21no—
151#14519736C2×C411yescharacteristic
152#14519736C2×C411yescharacteristic, complemented
153#14519734—21no—
154#14519733—21no—
155#14519733—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×C4⋊Dic61C2×C411yescharacteristic, complemented
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168C22⋊#92418—21no—
169C22⋊#92418C2311yescharacteristic
170C22⋊#92418C2311yescharacteristic
171C22⋊#92418C2311yescharacteristic
172C22⋊#92418C2311yescharacteristic
173#14519688—21no—
174C4×#92418—21no—
175C22×D4×C61D411yescharacteristic
176C23×C4×C61—21no—
177C23×C4×C61C2311yescharacteristic
178C23×C4×C61C2311yescharacteristic
179C4×D4×C61C2×C411yescharacteristic
180C4×D4×C61C2×C411yescharacteristic
181C4×D4×C61C2×C411yescharacteristic
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61D411yescharacteristic
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61D411yescharacteristic
194C2×C22⋊C4×C61D411yescharacteristic
195C2×C42×C61—21no—
196C2×C42×C61C2311yescharacteristic
197#95×C61—21no—
198#95×C61—21no—
199#95×C61—21no—
200#95×C61—21no—
201#95×C61—21no—
202#95×C61C2311yescharacteristic
203#95×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C24×C61C2×D411yescharacteristic
208C2×D4×C61—42no—
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C2×D4×C61C22⋊C411yescharacteristic
212C2×D4×C61C22⋊C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—42no—
218C22×C4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61—81no—
221C22×C4×C61—81no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244#11758224—44no—
245#11758222—81no—
246#11758222—81no—
247C2×D244C22×C411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×Dic122—21no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122—81no—
255C2×Dic122—81no—
256C2×Dic122C22×C411yescharacteristic
257C2×Dic122C22×C411yescharacteristic
258C2×Dic122C22×C411yescharacteristic
259C4⋊C4×C61—81no—
260C4⋊C4×C61—81no—
261C4⋊C4×C61C22⋊C411yescharacteristic
262C4⋊C4×C61C22⋊C411yescharacteristic
263C4⋊C4×C61C22⋊C411yescharacteristic
264C4⋊C4×C61C22⋊C411yescharacteristic
265C22⋊C4×C61—42no—
266C22⋊C4×C61—81no—
267C22⋊C4×C61—81no—
268C22⋊C4×C61C22⋊C411yescharacteristic
269C22⋊C4×C61C22⋊C411yescharacteristic
270C22⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C22⋊C4×C61C22⋊C411yescharacteristic
273C22⋊C4×C61C22⋊C411yescharacteristic
274C22⋊C4×C61C22⋊C411yescharacteristic
275C22⋊C4×C61C22⋊C411yescharacteristic
276C42×C61—81no—
277C42×C61C22×C411yescharacteristic
278C42×C61C22×C411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305C4⋊Dic61C22×C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326#11758194—81no—
327#11758194—81no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—21no—
332C2×#92418—81no—
333C2×#92418—81no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—22no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C2×C22⋊C411yescharacteristic
344C23×C61C2×C22⋊C411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C22×D61—21no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—41no—
351D4×C61—41no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
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—84no—
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C23×C411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C22⋊D61—42no—
390C22⋊D61—41no—
391C22⋊D61—41no—
392C22⋊D61—42no—
393C22⋊D61—81no—
394C22⋊D61—81no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—81no—
405C2×Dic61—81no—
406D244—41no—
407C4×D61—42no—
408C4×D61—81no—
409C4×D61—81no—
410Dic122—42no—
411Dic122—41no—
412Dic122—41no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#17598—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61#42112yes—
439C22×C61C22×C22⋊C411yescharacteristic
440C22×C61#57711yescharacteristic
441C22×C61#57811yescharacteristic
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—81no—
456C4×C61—81no—
457C4×C61—81no—
458C4×C61—81no—
459Dic61—41no—
460Dic61—41no—
461Dic61—41no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61—41no—
466#3520—611no—
467#2974—611no—
468#2318D6111yescharacteristic, complemented
469#1521—611no—
470#1520—611no—
471#1518—611no—
472#1516—611no—
473#1515—611no—
474#1513—611no—
475#1512—611no—
476#1511—611no—
477#1508—611no—
478#1504—611no—
479#1501—611no—
480C2×#328—611no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—22no—
484C2×C61—41no—
485C2×C61—41no—
486C2×C61—41no—
487C2×C61#288311yescharacteristic
488C2×C61#289811yescharacteristic
489C2×C61C2×#42111yescharacteristic
490D61—81no—
491#556—611no—
492#554—1221no—
493#552—611no—
494#552—611no—
495#551—1221no—
496#551—1221no—
497D4×Q8—611no—
498#548—611no—
499#548—611no—
500#547—611no—
501#547—611no—
502#546—1221no—
503#542—1221no—
504#539—1221no—
505#539—1221no—
506#533—611no—
507#529—611no—
508#525—611no—
509#525—611no—
510C2×C22⋊Q8—611no—
511C2×C22⋊Q8—611no—
512#520—1221no—
513C2×C4×D4C2×D6111yescharacteristic
514#436—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#431—611no—
520#407—611no—
521#407—611no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8—611no—
524#388—21no—
525#387—21no—
526#386—21no—
527#385—21no—
528#383C2×D6111yescharacteristic
529#382C2×D6111yescharacteristic
530#381C2×D6111yescharacteristic
531#380C2×D6111yescharacteristic
532C4×C22⋊C4C2×D6111yescharacteristic
533C2×#95C2×D6111yescharacteristic
534#328—611no—
535#328—611no—
536#328—611no—
537#328—611no—
538#328—611no—
539#328—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328—611no—
545#328—611no—
546#327—611no—
547#327—611no—
548#327—611no—
549#327—611no—
550C61#1759811yescharacteristic, complemented, Sylow
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—1221no—
554C22×Q8—611no—
555C22×Q8—611no—
556C22×D4C22⋊D6111yescharacteristic
557C23×C4—21no—
558C23×C4C22×D6111yescharacteristic
559C23×C4C22×D6111yescharacteristic
560C2×M16—1221no—
561C2×M16—1221no—
562C22×C8—1221no—
563C22×C8—1221no—
564C4⋊Q8—611no—
565C4⋊Q8—611no—
566C4⋊Q8—1221no—
567#126—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#125—611no—
573#125—1221no—
574#125—1221no—
575#125—1221no—
576#124—611no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592C22⋊Q8—611no—
593C22⋊Q8—611no—
594C22⋊Q8—611no—
595C22⋊Q8—611no—
596C22⋊Q8—611no—
597C22⋊Q8—611no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608#121—611no—
609#121—611no—
610#121—611no—
611#121—1221no—
612#121—1221no—
613#121—1221no—
614#120—1221no—
615#120—1221no—
616C4×Q8—611no—
617C4×Q8—611no—
618C4×Q8—611no—
619C4×Q8—1221no—
620C4×Q8—1221no—
621C4×D4—611no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4C4×D6111yescharacteristic
631C4×D4C4×D6111yescharacteristic
632C4×D4C4×D6111yescharacteristic
633C4×D4C4×D6111yescharacteristic
634C4×D4D24411yescharacteristic
635C4×D4D24411yescharacteristic
636C4×D4D24411yescharacteristic
637C4×D4D24411yescharacteristic
638#117—611no—
639#117—611no—
640#117—1221no—
641#117—1221no—
642#117—1221no—
643#117—1221no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4C22⋊D6111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4C22⋊D6111yescharacteristic
658C2×C22⋊C4C22⋊D6111yescharacteristic
659C2×C42—21no—
660C2×C42C22×D6111yescharacteristic
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—611no—
666C22⋊C8—611no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8—1221no—
670C22⋊C8—1221no—
671#97—1221no—
672C4×C8—1221no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95C22×D6111yescharacteristic
679#95C22×D6111yescharacteristic
680#95C22×D6111yescharacteristic
681#95C22×D6111yescharacteristic
682C24C2×C22⋊D6111yescharacteristic
683C24C2×C22⋊D6111yescharacteristic
684#41—4881no—
685#41—4881no—
686#41—2444no—
687C2×Q8—611no—
688C2×Q8—611no—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—1221no—
693C2×Q8—4881no—
694C2×Q8—4881no—
695C2×D4—42no—
696C2×D4—611no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4#1175819811yescharacteristic
703C2×D4#1175819811yescharacteristic
704C2×D4#1175819811yescharacteristic
705C2×D4#1175819811yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4C2×C4×D6111yescharacteristic
723C22×C4C2×C4×D6111yescharacteristic
724C22×C4C2×C4×D6111yescharacteristic
725C22×C4C2×C4×D6111yescharacteristic
726C22×C4C2×D24411yescharacteristic
727C22×C4C2×D24411yescharacteristic
728C22×C4C2×D24411yescharacteristic
729C22×C4C2×D24411yescharacteristic
730C22×C4C2×C22⋊D6111yescharacteristic
731C22×C4C2×C22⋊D6111yescharacteristic
732C22×C4C2×C22⋊D6111yescharacteristic
733C22×C4C2×C22⋊D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—4881no—
736M16—4881no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—4881no—
742C2×C8—4881no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4#1175819811yescharacteristic
769C4⋊C4#1175819811yescharacteristic
770C4⋊C4#1175819811yescharacteristic
771C4⋊C4#1175819811yescharacteristic
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4#1175819811yescharacteristic
793C22⋊C4#1175819811yescharacteristic
794C22⋊C4#1175819811yescharacteristic
795C22⋊C4#1175819811yescharacteristic
796C22⋊C4#1175819811yescharacteristic
797C22⋊C4#1175819811yescharacteristic
798C22⋊C4#1175819811yescharacteristic
799C22⋊C4#1175819811yescharacteristic
800C42—81no—
801C42—1221no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—1221no—
806C42C2×C4×D6111yescharacteristic
807C42C2×C4×D6111yescharacteristic
808C42C2×D24411yescharacteristic
809C42C2×D24411yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—1221no—
819C23C2×#1175819811yescharacteristic
820C23C2×#1175819811yescharacteristic
821C23C2×#1175819811yescharacteristic
822C23C2×#1175819811yescharacteristic
823C23C22×C22⋊D6111yescharacteristic
824Q8—4881no—
825Q8—4881no—
826Q8—2441no—
827Q8—2441no—
828Q8—2441no—
829Q8—2442no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—4881no—
835D4—4881no—
836D4—2441no—
837D4—2442no—
838D4—2442no—
839D4—2441no—
840D4—2441no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—84no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4881no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4C2×#1175819811yescharacteristic
883C2×C4C2×#1175819811yescharacteristic
884C2×C4C2×#1175819811yescharacteristic
885C2×C4C2×#1175819811yescharacteristic
886C2×C4C2×#1175819811yescharacteristic
887C2×C4C2×#1175819811yescharacteristic
888C2×C4C2×#1175819811yescharacteristic
889C2×C4C2×#1175819811yescharacteristic
890C2×C4C22×C4×D6111yescharacteristic
891C2×C4C22×D24411yescharacteristic
892C8—2441no—
893C8—2441no—
894C8—2441no—
895C8—2441no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—2441no—
914C22—2441no—
915C22—2441no—
916C22#1683978012yes—
917C22C22×#1175819811yescharacteristic
918C22#1684057311yescharacteristic
919C22#1684057711yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—2441no—
935C4—2441no—
936C4—2441no—
937C4—2441no—
938C4—2441no—
939C4—2441no—
940C4—2441no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—4881no—
948C2#2145427911yescharacteristic
949C2#2145434911yescharacteristic
950C2C2×#1683978011yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2318C2
socleC22×C61C22×C22⋊C4
prime radical#21459868C2
cosocleC22×C4×C61C24
hypercenter#2318D61
hypocenterC61#17598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #21454854C2semidirect
3. #21444394C2semidirect
4. #21444390C2semidirect
5. #21444382C2semidirect
6. #21444373C2semidirect
7. #21444369C2semidirect
8. #21444360C2semidirect
9. #21444355C2semidirect
10. #21444351C2semidirect
11. #21444338C2semidirect
12. #21444321C2semidirect
13. #21444308C2semidirect
14. C2×#16839498C2semidirect
15. C61×#2318C2semidirect
16. #16840482C4semidirect
18. #16840452C4semidirect
19. #16840452C4semidirect
22. D4×Dic122C4semidirect
23. #16840421C4semidirect
24. #16840421C4semidirect
25. #16840417C4semidirect
26. #16840416C4semidirect
76. C2×#11758222C2×C4semidirect
79. C22×Dic122C2×C4semidirect
84. #14519777C2×C4semidirect
85. #14519777C2×C4semidirect
93. #14519769C2×C4semidirect
96. #14519765C2×C4semidirect
118. #14519756C2×C4semidirect
119. #14519756C2×C4semidirect
120. #14519756C2×C4semidirect
129. #14519751C2×C4semidirect
137. C4×Dic122C2×C4semidirect
138. C4×Dic122C2×C4semidirect
139. C4×Dic122C2×C4semidirect
141. C4×D244C2×C4semidirect
152. #14519736C2×C4semidirect
157. C2×C4⋊Dic61C2×C4semidirect
468. #2318D61semidirect
550. C61#17598semidirect

Maximal subgroups

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

subgroupindex
#214598682
#214548542
#214443942
#214443902
#214443822
#214443732
#214443692
#214443602
#214443552
#214443512
#214443382
#214443212
#214443082
C2×#168394982
C61×#23182
#1759861