Finite Group Databasebeta

← #29647557

Subgroups — #29647557

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#21448452C211yesmaximal, characteristic, complemented
3#21444397C211yesmaximal, characteristic, complemented
4#21444392C211yesmaximal, characteristic, complemented
5#21444384C211yesmaximal, characteristic, complemented
6#21444376C211yesmaximal, characteristic, complemented
7#21444371C211yesmaximal, characteristic, complemented
8#21444363C211yesmaximal, characteristic, complemented
9#21444358C211yesmaximal, characteristic, complemented
10#21444353C211yesmaximal, characteristic, complemented
11#21444340C211yesmaximal, characteristic, complemented
12#21444324C211yesmaximal, characteristic, complemented
13#21444311C211yesmaximal, characteristic, complemented
14C2×#16839500C211yesmaximal, characteristic, complemented
15C61×#2974C211yesmaximal, 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#16839655—21no—
39#16839648—21no—
40#16839642—21no—
41#16839637—21no—
42#16839630C2211yescharacteristic
43#16839628C2211yescharacteristic
44#16839625C2211yescharacteristic
45#16839622C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48#16839500C2211yescharacteristic
49#16839500C2211yescharacteristic
50#16839500C2211yescharacteristic
51#16839500C2211yescharacteristic
52#16839500C2211yescharacteristic
53#16839500C2211yescharacteristic
54#16839500C2211yescharacteristic
55#16839500C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839497C2211yescharacteristic
61#16839497C2211yescharacteristic
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C61×#436—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#407C2211yescharacteristic
72C61×#407C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic, complemented
77C2×#11758224—21no—
78C22×Dic122C2×C411yescharacteristic
79C22×Dic122C2×C411yescharacteristic, complemented
80C23×Dic61—21no—
81#14519777C2×C411yescharacteristic, complemented
82#14519777C2×C411yescharacteristic, complemented
83#14519776—21no—
84#14519771—21no—
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519769—21no—
90#14519769C2×C411yescharacteristic, complemented
91#14519767—21no—
92#14519767—21no—
93#14519765C2×C411yescharacteristic, complemented
94#14519764—21no—
95#14519763—21no—
96#14519763—21no—
97#14519761—21no—
98#14519761—21no—
99#14519760—21no—
100#14519760—21no—
101#14519760—21no—
102#14519759—21no—
103#14519759—21no—
104#14519758—21no—
105#14519758—21no—
106#14519757—21no—
107#14519756—21no—
108#14519756—21no—
109#14519756—21no—
110#14519756—21no—
111#14519756—21no—
112#14519756C2×C411yescharacteristic
113#14519756C2×C411yescharacteristic
114#14519756C2×C411yescharacteristic
115#14519756C2×C411yescharacteristic, complemented
116#14519756C2×C411yescharacteristic, complemented
117#14519756C2×C411yescharacteristic, complemented
118#14519756C2311yescharacteristic
119#14519756C2311yescharacteristic
120#14519756C2311yescharacteristic
121#14519755—21no—
122#14519755—21no—
123#14519754—21no—
124#14519754—21no—
125#14519751C2×C411yescharacteristic
126#14519751C2×C411yescharacteristic, complemented
127#14519751C2311yescharacteristic
128#14519749—21no—
129#14519749—21no—
130#14519748—21no—
131#14519746—21no—
132#14519746—21no—
133C4×Dic122—21no—
134C4×Dic122C2×C411yescharacteristic, complemented
135C4×Dic122C2×C411yescharacteristic, complemented
136C4×Dic122C2×C411yescharacteristic, complemented
137#14519742—21no—
138C4×D244C2×C411yescharacteristic, complemented
139D4×Dic61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145#14519737—21no—
146#14519737—21no—
147#14519736—21no—
148#14519736C2×C411yescharacteristic
149#14519736C2×C411yescharacteristic, complemented
150#14519734—21no—
151#14519733—21no—
152#14519733—21no—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61C2×C411yescharacteristic
156C2×C4⋊Dic61C2×C411yescharacteristic, complemented
157C2×#11758196—21no—
158C2×#11758196—21no—
159C4⋊C4×D61—21no—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61—21no—
165C2×C4×Dic61—21no—
166#14519684—21no—
167#14519684—21no—
168#14519684—21no—
169#14519684—21no—
170#14519684—21no—
171#14519684C2311yescharacteristic
172#14519684C2311yescharacteristic
173#14519684C2311yescharacteristic
174#14519684C2311yescharacteristic
175C22×D4×C61D411yescharacteristic
176C23×C4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C2×M16×C61—21no—
179C2×M16×C61—21no—
180C22×C8×C61—21no—
181C22×C8×C61—21no—
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61C2×C411yescharacteristic
184C4×D4×C61C2×C411yescharacteristic
185C4×D4×C61C2×C411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C4×D4×C61D411yescharacteristic
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C2×C4⋊C4×C61D411yescharacteristic
191C2×C22⋊C4×C61D411yescharacteristic
192C2×C22⋊C4×C61D411yescharacteristic
193C2×C42×C61C2311yescharacteristic
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
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—81no—
214C22×C4×C61—81no—
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—42no—
242C22×Dic61—81no—
243C22×Dic61—81no—
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
259M16×C61—81no—
260M16×C61—81no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—81no—
266C2×C8×C61—81no—
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C22⋊C4×C61C22⋊C411yescharacteristic
273C22⋊C4×C61C22⋊C411yescharacteristic
274C22⋊C4×C61C22⋊C411yescharacteristic
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C42×C61C22×C411yescharacteristic
280C42×C61C22×C411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
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—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—42no—
295C22⋊Dic61—81no—
296C22⋊Dic61—81no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—81no—
309C4⋊Dic61—81no—
310C4⋊Dic61C22×C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—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×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C23×C411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C22⋊D61—42no—
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—42no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—81no—
404C2×Dic61—81no—
405C2×Dic61—84no—
406D244—41no—
407C4×D61—42no—
408C4×D61—81no—
409C4×D61—81no—
410Dic122—42no—
411Dic122—41no—
412Dic122—41no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418C8×C61—41no—
419C8×C61—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—
455Dic61—41no—
456Dic61—41no—
457Dic61—41no—
458Dic61—41no—
459Dic61—41no—
460Dic61—41no—
461Dic61—41no—
462Dic61—81no—
463Dic61—81no—
464Dic61—81no—
465Dic61—81no—
466#3520—611no—
467#2974D6111yescharacteristic, complemented
468#2318—611no—
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—21no—
515#435—21no—
516#435—21no—
517C8×D4—21no—
518#432C2×D6111yescharacteristic
519#431C2×D6111yescharacteristic
520#407C2×D6111yescharacteristic
521#407C2×D6111yescharacteristic
522C2×C22⋊C8C2×D6111yescharacteristic
523C2×C22⋊C8C2×D6111yescharacteristic
524#388—1221no—
525#387—1221no—
526#386—1221no—
527#385—1221no—
528#383—611no—
529#382—611no—
530#381—611no—
531#380—611no—
532C4×C22⋊C4—611no—
533C2×#95—611no—
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×D4D24411yescharacteristic
557C23×C4—1221no—
558C23×C4C22×D6111yescharacteristic
559C23×C4C22×D6111yescharacteristic
560C2×M16—21no—
561C2×M16—21no—
562C22×C8—21no—
563C22×C8—21no—
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×D4C22⋊D6111yescharacteristic
635C4×D4C22⋊D6111yescharacteristic
636C4×D4C22⋊D6111yescharacteristic
637C4×D4C22⋊D6111yescharacteristic
638#117—611no—
639#117—611no—
640#117—1221no—
641#117—1221no—
642#117—1221no—
643#117—1221no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—1221no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4D24411yescharacteristic
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4D24411yescharacteristic
658C2×C22⋊C4D24411yescharacteristic
659C2×C42—1221no—
660C2×C42C22×D6111yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8C22×D6111yescharacteristic
668C22⋊C8C22×D6111yescharacteristic
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6111yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—611no—
674#95—611no—
675#95—611no—
676#95—611no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95—1221no—
681#95—1221no—
682C24C2×D24411yescharacteristic
683C24C2×D24411yescharacteristic
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—81no—
707C22×C4—81no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—4881no—
720C22×C4—4881no—
721C22×C4—2442no—
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—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—81no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
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—4881no—
767C4⋊C4—4881no—
768C4⋊C4#1175819811yescharacteristic
769C4⋊C4#1175819811yescharacteristic
770C4⋊C4#1175819811yescharacteristic
771C4⋊C4#1175819811yescharacteristic
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
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—4881no—
790C22⋊C4—4881no—
791C22⋊C4—2442no—
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—1221no—
801C42—1221no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—4881no—
806C42C2×C4×D6111yescharacteristic
807C42C2×C4×D6111yescharacteristic
808C42C2×C22⋊D6111yescharacteristic
809C42C2×C22⋊D6111yescharacteristic
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×D24411yescharacteristic
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—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4884no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—2442no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
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×C22⋊D6111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
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#1683977812yes—
917C22C22×#1175819811yescharacteristic
918C22#1684057411yescharacteristic
919C22#1684057911yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4881no—
931C4—4881no—
932C4—4881no—
933C4—4881no—
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#2145435311yescharacteristic
950C2C2×#1683977811yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2974C2
socleC22×C61C22×C22⋊C4
prime radical#21459868C2
cosocleC22×C4×C61C24
hypercenter#2974D61
hypocenterC61#17598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21448452C2semidirect
3. #21444397C2semidirect
4. #21444392C2semidirect
5. #21444384C2semidirect
6. #21444376C2semidirect
7. #21444371C2semidirect
8. #21444363C2semidirect
9. #21444358C2semidirect
10. #21444353C2semidirect
11. #21444340C2semidirect
12. #21444324C2semidirect
13. #21444311C2semidirect
14. C2×#16839500C2semidirect
15. C61×#2974C2semidirect
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
81. #14519777C2×C4semidirect
82. #14519777C2×C4semidirect
90. #14519769C2×C4semidirect
93. #14519765C2×C4semidirect
115. #14519756C2×C4semidirect
116. #14519756C2×C4semidirect
117. #14519756C2×C4semidirect
126. #14519751C2×C4semidirect
134. C4×Dic122C2×C4semidirect
135. C4×Dic122C2×C4semidirect
136. C4×Dic122C2×C4semidirect
138. C4×D244C2×C4semidirect
149. #14519736C2×C4semidirect
156. C2×C4⋊Dic61C2×C4semidirect
467. #2974D61semidirect
550. C61#17598semidirect

Maximal subgroups

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

subgroupindex
#214598682
#214484522
#214443972
#214443922
#214443842
#214443762
#214443712
#214443632
#214443582
#214443532
#214443402
#214443242
#214443112
C2×#168395002
C61×#29742
#1759861