Finite Group Databasebeta

← #29695702

Subgroups — #29695702

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D61C211yesmaximal, characteristic
2#21454551C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4C22×#14519704C211yesmaximal, characteristic, complemented
5#21448258C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446649C211yesmaximal, characteristic, complemented
8#21446264C211yesmaximal, characteristic, complemented
9#21446260C211yesmaximal, characteristic, complemented
10#21446119C211yesmaximal, characteristic, complemented
11#21446118C211yesmaximal, characteristic, complemented
12#21445837C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445631C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic, complemented
18C2×M16×D61C2211yescharacteristic, complemented
19#16840431C411yescharacteristic, complemented
20Q8×C22⋊D61C411yescharacteristic, complemented
21#16840423C411yescharacteristic, complemented
22#16840419C411yescharacteristic, complemented
23#16840411—21no—
24#16840411C411yescharacteristic, complemented
25#16840406—21no—
26#16840406C411yescharacteristic, complemented
27#16840400—21no—
28#16840400C411yescharacteristic, complemented
29D4×C22⋊D61—21no—
30D4×C22⋊D61C411yescharacteristic, complemented
31#16840308—21no—
32#16840308C2211yescharacteristic
33#16840273—21no—
34#16840273C2211yescharacteristic
35#16840269—21no—
36#16840269C2211yescharacteristic
37#41×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519734C2211yescharacteristic, complemented
41C22×C4×Dic61C2211yescharacteristic, complemented
42#16839837—21no—
43#16839836—21no—
44#16839830—21no—
45#16839825—21no—
46#16839785C2211yescharacteristic, complemented
47#16839777—24no—
48C2×#14519705C2211yescharacteristic, complemented
49C2×#14519705C2211yescharacteristic, complemented
50C2×#14519704—24no—
51C2×#14519704C2211yescharacteristic
52C2×#14519704C2211yescharacteristic
53C2×#14519704C2211yescharacteristic, complemented
54C2×#14519704C2211yescharacteristic, complemented
55C2×#14519703C2211yescharacteristic, complemented
56C2×#14519703C2211yescharacteristic, complemented
57#16839725C2211yescharacteristic, complemented
58M16×Dic61C2211yescharacteristic, complemented
59#16839651—21no—
60#16839644—21no—
61#16839639—21no—
62#16839634—21no—
63C4×#11758196C2211yescharacteristic, complemented
64C4×#11758198C2211yescharacteristic, complemented
65#16839608C2211yescharacteristic, complemented
66#16839523C2211yescharacteristic, complemented
67#16839523C2211yescharacteristic, complemented
68#16839522C2211yescharacteristic, complemented
69#16839522C2211yescharacteristic, complemented
70C22×#41×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C2×#104×C61C2211yescharacteristic
73C2×#104×C61C2211yescharacteristic, complemented
74C2×#104×C61C2211yescharacteristic, complemented
75C61×#407C2211yescharacteristic, complemented
76C4×C22⋊C4×C61C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic, complemented
78C2×#11758222—21no—
79C2×#11758222C2311yescharacteristic
80C2×#11758224—21no—
81C2×#11758224C2×C411yescharacteristic, complemented
82#41×D61—22no—
83#41×D61—22no—
84#41×D61—41no—
85#41×D61—41no—
86C2×Q8×D61C2×C411yescharacteristic, complemented
87C22×C22⋊D61—21no—
88C22×C22⋊D61D411yescharacteristic
89C2×D4×D61—21no—
90C2×D4×D61C2×C411yescharacteristic, complemented
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×#11758194—21no—
95C2×#11758194—22no—
96C2×#11758194—41no—
97C2×#11758194C2311yescharacteristic
98C2×#11758194C2311yescharacteristic
99C2×#11758189—21no—
100M16×D61—22no—
101M16×D61—41no—
102C22×#92418—21no—
103C2×C8×D61—21no—
104#14519775—21no—
105#14519775C2×C411yescharacteristic, complemented
106#14519773—21no—
107#14519773C2×C411yescharacteristic, complemented
108#14519766—21no—
109#14519766C2×C411yescharacteristic, complemented
110#14519764—21no—
111#14519764C2×C411yescharacteristic, complemented
112#14519760—21no—
113#14519760—21no—
114#14519760—21no—
115#14519758—21no—
116#14519758—21no—
117#14519758—21no—
118#14519756—21no—
119#14519756—21no—
120#14519756C2×C411yescharacteristic
121#14519756C2×C411yescharacteristic
122#14519753—21no—
123#14519753—21no—
124#14519753C2×C411yescharacteristic, complemented
125#14519753C2×C411yescharacteristic, complemented
126#14519751—21no—
127#14519751—21no—
128#14519751C2×C411yescharacteristic
129#14519751C2×C411yescharacteristic
130#14519749—21no—
131#14519749—21no—
132#14519749—21no—
133#14519749—21no—
134#14519749—21no—
135#14519749—21no—
136#14519748—21no—
137#14519748—21no—
138#14519748C2×C411yescharacteristic, complemented
139#14519748C2×C411yescharacteristic, complemented
140#14519746—21no—
141#14519746—21no—
142#14519746—21no—
143#14519745—21no—
144#14519745—21no—
145#14519745—21no—
146Q8×Dic61C2×C411yescharacteristic, complemented
147Q8×Dic61C2×C411yescharacteristic, complemented
148D4×Dic61—21no—
149D4×Dic61—21no—
150D4×Dic61C2×C411yescharacteristic, complemented
151D4×Dic61C2×C411yescharacteristic, complemented
152C4×C22⋊D61—21no—
153C4×C22⋊D61—21no—
154C4×C22⋊D61—21no—
155C4×C22⋊D61—21no—
156C4×C22⋊D61—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61—21no—
160C4×C22⋊D61—21no—
161C4×C22⋊D61—21no—
162C4×C22⋊D61C2×C411yescharacteristic
163C4×C22⋊D61C2×C411yescharacteristic
164C4×C22⋊D61C2×C411yescharacteristic
165C4×C22⋊D61C2×C411yescharacteristic
166C4×C22⋊D61D411yescharacteristic
167C4×C22⋊D61D411yescharacteristic
168C4×C22⋊D61D411yescharacteristic
169C4×C22⋊D61D411yescharacteristic
170#14519736—21no—
171#14519736C2311yescharacteristic
172#14519734—22no—
173#14519734—41no—
174C2×#11758196—21no—
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×#11758196D411yescharacteristic
178C2×C22⋊Dic61—21no—
179C2×C22⋊Dic61D411yescharacteristic
180C2×#11758198—21no—
181C2×#11758198—21no—
182C2×#11758198—21no—
183C2×#11758198D411yescharacteristic
184C2×C4×Dic61—21no—
185C2×C4×Dic61—22no—
186C2×C4×Dic61—21no—
187C2×C4×Dic61—41no—
188C2×C4×Dic61C2311yescharacteristic
189C2×C4×Dic61C2311yescharacteristic
190C2×C4×Dic61C2311yescharacteristic
191#14519706—21no—
192#14519706—21no—
193#14519705—22no—
194#14519705—41no—
195#14519704—22no—
196#14519704—22no—
197#14519704—22no—
198#14519704D414yescomplemented
199#14519703—22no—
200#14519703—41no—
201#14519689—21no—
202#14519689—21no—
203#14519687—21no—
204C8×Dic61—21no—
205#14519684—21no—
206#14519684—21no—
207#14519684—21no—
208#14519684—21no—
209C2×#41×C61—21no—
210C2×#41×C61—21no—
211C2×#41×C61—22no—
212C2×#41×C61—22no—
213C2×#41×C61—41no—
214C2×#41×C61—41no—
215C2×#41×C61C2×C411yescharacteristic
216C2×#41×C61C2×C411yescharacteristic
217C2×#41×C61C2311yescharacteristic
218C2×#41×C61C2311yescharacteristic
219C22×Q8×C61C2×C411yescharacteristic
220C22×D4×C61—21no—
221C22×D4×C61C2×C411yescharacteristic
222C23×C4×C61—21no—
223C23×C4×C61C2311yescharacteristic
224C2×M16×C61C2311yescharacteristic
225C2×M16×C61C2311yescharacteristic
226C2×C22⋊C4×C61—21no—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2311yescharacteristic
229#104×C61—22no—
230#104×C61—22no—
231#104×C61—41no—
232#104×C61—41no—
233C22⋊C8×C61—21no—
234C22⋊C8×C61—21no—
235#95×C61—21no—
236C24×C61—21no—
237C24×C61C2×D411yescharacteristic
238C23×D61—21no—
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—22no—
243#41×C61—22no—
244#41×C61—21no—
245#41×C61—21no—
246#41×C61—21no—
247#41×C61—21no—
248#41×C61—42no—
249#41×C61—42no—
250#41×C61—41no—
251#41×C61—41no—
252#41×C61—42no—
253#41×C61—42no—
254#41×C61C2×D412yes—
255#41×C61#4112yes—
256C2×Q8×C61—21no—
257C2×Q8×C61—22no—
258C2×Q8×C61—41no—
259C2×Q8×C61C22×C411yescharacteristic
260C2×Q8×C61C22×C411yescharacteristic
261C2×D4×C61—21no—
262C2×D4×C61—22no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—41no—
268C2×D4×C61—42no—
269C2×D4×C61—42no—
270C2×D4×C61C22×C411yescharacteristic
271C2×D4×C61C22×C411yescharacteristic
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—42no—
284C22×C4×C61—42no—
285C22×C4×C61C22×C411yescharacteristic
286C22×C4×C61C22×C411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291C2×C22⋊D61—21no—
292C2×C22⋊D61—21no—
293C2×C22⋊D61—21no—
294C2×C22⋊D61—21no—
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C2×C22⋊D61—21no—
298C2×C22⋊D61—21no—
299C2×C22⋊D61—21no—
300C2×C22⋊D61—42no—
301C2×C22⋊D61—44no—
302C2×C22⋊D61C22⋊C411yescharacteristic
303C2×C22⋊D61C22⋊C411yescharacteristic
304C2×C22⋊D61C22⋊C411yescharacteristic
305C2×C22⋊D61C22⋊C411yescharacteristic
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—42no—
312C22×Dic61—42no—
313C22×Dic61—42no—
314C22×Dic61C2×D411yescharacteristic
315C22×Dic61C2×D411yescharacteristic
316C22×Dic61C2×D411yescharacteristic
317#11758226—22no—
318#11758226—41no—
319Q8×D61—22no—
320Q8×D61—41no—
321#11758224—22no—
322#11758224—41no—
323#11758224—42no—
324#11758224—42no—
325D4×D61—22no—
326D4×D61—41no—
327D4×D61—42no—
328D4×D61—42no—
329#11758222—21no—
330#11758222—21no—
331#11758222—21no—
332#11758222—21no—
333#11758222—42no—
334#11758222—42no—
335C2×D244—21no—
336C2×D244C22×C411yescharacteristic
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—21no—
340C2×C4×D61—21no—
341C2×C4×D61—21no—
342C2×C4×D61—21no—
343C2×C4×D61—21no—
344C2×C4×D61—42no—
345C2×C4×D61—42no—
346C2×C4×D61C22×C411yescharacteristic
347C2×C4×D61C22×C411yescharacteristic
348C2×C4×D61C2×D411yescharacteristic
349C2×C4×D61C2×D411yescharacteristic
350C2×Dic122—21no—
351C2×Dic122C22×C411yescharacteristic
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61—21no—
356C2×C8×C61—21no—
357C2×C8×C61—21no—
358C22⋊C4×C61—42no—
359C42×C61—21no—
360C42×C61—21no—
361C42×C61—21no—
362C42×C61—21no—
363C22⋊Dic61—21no—
364C22⋊Dic61—21no—
365C22⋊Dic61—21no—
366C22⋊Dic61—21no—
367C22⋊Dic61—21no—
368C22⋊Dic61—21no—
369C22⋊Dic61—21no—
370C22⋊Dic61—21no—
371C22⋊Dic61—21no—
372C22⋊Dic61C22⋊C411yescharacteristic
373C22⋊Dic61C22⋊C411yescharacteristic
374C22⋊Dic61C22⋊C411yescharacteristic
375C22⋊Dic61C22⋊C411yescharacteristic
376#11758198—21no—
377#11758198—21no—
378#11758198—21no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—42no—
383#11758198—42no—
384#11758198C22⋊C411yescharacteristic
385#11758198C22⋊C411yescharacteristic
386#11758198C22⋊C411yescharacteristic
387#11758198C22⋊C411yescharacteristic
388C4⋊Dic61—21no—
389C4⋊Dic61—21no—
390C4⋊Dic61C22×C411yescharacteristic
391C4⋊Dic61C22×C411yescharacteristic
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—21no—
398#11758196—42no—
399#11758196—42no—
400#11758196C22⋊C411yescharacteristic
401#11758196C22⋊C411yescharacteristic
402#11758196C22⋊C411yescharacteristic
403#11758196C22⋊C411yescharacteristic
404C4×Dic61—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—42no—
411C4×Dic61C22×C411yescharacteristic
412C4×Dic61C22×C411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D412yescomplemented
416#11758194—21no—
417#11758194—21no—
418#11758194—21no—
419#11758194—42no—
420#11758194C2×D412yescomplemented
421C2×#92418—21no—
422C2×#92418—21no—
423C2×#92418—42no—
424#11758189—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—21no—
429C23×C61—22no—
430C23×C61—21no—
431C23×C61—41no—
432C23×C61—42no—
433C23×C61—42no—
434C23×C61—81no—
435C23×C61C2×C22⋊C411yescharacteristic
436C23×C61C2×C22⋊C411yescharacteristic
437C23×C61C22×D411yescharacteristic
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—21no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—42no—
444C22×D61—42no—
445C22×D61—81no—
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450Q8×C61—21no—
451Q8×C61—42no—
452Q8×C61C4×D412yes—
453D4×C61—22no—
454D4×C61—22no—
455D4×C61—21no—
456D4×C61—21no—
457D4×C61—21no—
458D4×C61—42no—
459D4×C61—42no—
460D4×C61—42no—
461D4×C61—41no—
462D4×C61—41no—
463D4×C61C4×D412yes—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—42no—
479C2×C4×C61—42no—
480C2×C4×C61—42no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61C2×C22⋊C411yescharacteristic
490C2×C4×C61C2×C22⋊C411yescharacteristic
491C2×C4×C61C23×C411yescharacteristic
492C2×C4×C61C22×D411yescharacteristic
493C2×C4×C61C22×D411yescharacteristic
494C2×C4×C61C2×#4111yescharacteristic
495C2×C4×C61H(5,𝔽2)11yescharacteristic
496C2×C4×C61H(5,𝔽2)11yescharacteristic
497C22⋊D61—22no—
498C22⋊D61—22no—
499C22⋊D61—41no—
500C22⋊D61—41no—
501C22⋊D61—42no—
502C22⋊D61—42no—
503C22⋊D61—42no—
504C22⋊D61—42no—
505C22⋊D61—41no—
506C22⋊D61—41no—
507C22⋊D61—42no—
508C22⋊D61—81no—
509C22⋊D61—81no—
510C22⋊D61—81no—
511C2×Dic61—21no—
512C2×Dic61—21no—
513C2×Dic61—22no—
514C2×Dic61—21no—
515C2×Dic61—21no—
516C2×Dic61—21no—
517C2×Dic61—22no—
518C2×Dic61—41no—
519C2×Dic61—41no—
520C2×Dic61—42no—
521C2×Dic61—42no—
522C2×Dic61—41no—
523C2×Dic61—41no—
524C2×Dic61—41no—
525C2×Dic61—48no—
526C2×Dic61—41no—
527C2×Dic61—81no—
528C2×Dic61C2×C22⋊C411yescharacteristic
529C2×Dic61C2×C22⋊C411yescharacteristic
530C2×Dic61C2×C22⋊C411yescharacteristic
531C2×Dic61C2×C22⋊C411yescharacteristic
532C2×Dic61C2×C22⋊C411yescharacteristic
533C2×Dic61C2×C22⋊C411yescharacteristic
534D244—21no—
535D244—21no—
536D244—42no—
537C4×D61—21no—
538C4×D61—21no—
539C4×D61—21no—
540C4×D61—21no—
541C4×D61—21no—
542C4×D61—21no—
543C4×D61—21no—
544C4×D61—21no—
545C4×D61—42no—
546C4×D61—42no—
547C4×D61—41no—
548C4×D61—41no—
549Dic122—21no—
550Dic122—21no—
551Dic122—42no—
552C8×C61—41no—
553C8×C61—41no—
554#92418—22no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—22no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—21no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—41no—
568C22×C61—41no—
569C22×C61—41no—
570C22×C61—41no—
571C22×C61—41no—
572C22×C61—84no—
573C22×C61#42112yescomplemented
574C22×C61C22×C22⋊C411yescharacteristic
575C22×C61D4211yescharacteristic
576C22×C61#54611yescharacteristic
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—21no—
581C2×D61—21no—
582C2×D61—21no—
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—41no—
586C2×D61—81no—
587C2×D61—81no—
588C2×D61—84no—
589C4×C61—22no—
590C4×C61—21no—
591C4×C61—21no—
592C4×C61—41no—
593C4×C61—81no—
594C4×C61—81no—
595C4×C61C2×C4×D411yescharacteristic
596C4×C61#51811yescharacteristic
597C4×C61D4211yescharacteristic
598C4×C61#54611yescharacteristic
599Dic61—21no—
600Dic61—21no—
601Dic61—21no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—42no—
606Dic61—42no—
607Dic61—41no—
608Dic61—41no—
609Dic61—41no—
610D4×#41—611no—
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963—611no—
617#1897—611no—
618#1896—611no—
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789D6111yescharacteristic, complemented
624#1759—611no—
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—22no—
628C2×C61—42no—
629C2×C61—41no—
630C2×C61—81no—
631C2×C61D4×C22⋊C411yescharacteristic
632C2×C61C2×#42111yescharacteristic
633C2×C61#290111yescharacteristic
634D61—41no—
635D61—41no—
636D61—81no—
637C22×#41—611no—
638C22×#41C2×D6111yescharacteristic
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—611no—
649#546—1221no—
650#546—1221no—
651D42—611no—
652D42—1221no—
653#532—611no—
654#532—1221no—
655#525—611no—
656#525—611no—
657#525—1221no—
658#525—1221no—
659C4×#41—611no—
660C2×C4×D4—611no—
661C2×C4×D4—1221no—
662C2×#117—611no—
663C22×C42—611no—
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423—611no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—1224no—
679C2×#104C2×D6111yescharacteristic
680C2×#104C2×D6111yescharacteristic
681C2×#104C2×D6111yescharacteristic, complemented
682C2×#104C2×D6111yescharacteristic, complemented
683#407—611no—
684#407C2×D6111yescharacteristic, complemented
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4C2×D6111yescharacteristic, complemented
693#376—611no—
694#339—611no—
695#339—611no—
696#339—611no—
697#339—611no—
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—22no—
702C2×#41—22no—
703C2×#41—41no—
704C2×#41—41no—
705C2×#41—611no—
706C2×#41—611no—
707C2×#41—611no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—2441no—
713C2×#41—2441no—
714C2×#41C4×D6111yescharacteristic
715C2×#41C4×D6111yescharacteristic
716C2×#41C22×D6111yescharacteristic
717C2×#41C22×D6111yescharacteristic
718C22×Q8—611no—
719C22×Q8C4×D6111yescharacteristic
720C22×D4—21no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4C4×D6111yescharacteristic
726C23×C4—21no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4C22×D6111yescharacteristic
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—1221no—
734C2×M16—1221no—
735C2×M16—1222no—
736C2×M16—1222no—
737C2×M16—2441no—
738C2×M16—2441no—
739C2×M16C22×D6111yescharacteristic
740C2×M16C22×D6111yescharacteristic
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—611no—
744C4⋊Q8—1221no—
745#127—611no—
746#127—1221no—
747#124—611no—
748#124—611no—
749#124—1221no—
750#124—1221no—
751#123—1221no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—611no—
760C22⋊Q8—611no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8—1221no—
764C22⋊Q8—1221no—
765#121—611no—
766#121—611no—
767#121—611no—
768#121—611no—
769#121—1221no—
770#121—1221no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121—1221no—
778#121—1221no—
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8—611no—
787C4×D4—611no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—611no—
796C4×D4—611no—
797C4×D4—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807C4×D4—1221no—
808C4×D4—1221no—
809#117—611no—
810#117—1222no—
811#117—1221no—
812#117—2441no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—611no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—1221no—
828C2×C42—1222no—
829C2×C42—1221no—
830C2×C42—2441no—
831C2×C42C22×D6111yescharacteristic
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—22no—
836#104—22no—
837#104—41no—
838#104—41no—
839#104—614no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—1222no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—21no—
848C22⋊C8—21no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—21no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—21no—
859C24—611no—
860C24—1221no—
861C24D4×D6111yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—42no—
871#41—42no—
872#41—41no—
873#41—41no—
874#41—42no—
875#41—42no—
876#41—1222no—
877#41—1222no—
878#41—1221no—
879#41—1221no—
880#41—1221no—
881#41—1221no—
882#41—2442no—
883#41—2442no—
884#41—2441no—
885#41—2442no—
886#41—2442no—
887#41—2441no—
888#41D4×D6112yes—
889#41#1175822412yes—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—41no—
893C2×Q8—611no—
894C2×Q8—1221no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8C2×C4×D6111yescharacteristic
898C2×Q8C2×C4×D6111yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—41no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—611no—
909C2×D4—611no—
910C2×D4—611no—
911C2×D4—611no—
912C2×D4—611no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1222no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—1221no—
923C2×D4—1221no—
924C2×D4—2441no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2442no—
928C2×D4—2444no—
929C2×D4C2×C4×D6111yescharacteristic
930C2×D4C2×C4×D6111yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—611no—
949C22×C4—611no—
950C22×C4—611no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—2442no—
964C22×C4—2442no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4C2×C4×D6111yescharacteristic
969C22×C4C2×C4×D6111yescharacteristic
970C22×C4D4×D6111yescharacteristic
971C22×C4D4×D6111yescharacteristic
972C22×C4D4×D6111yescharacteristic
973C22×C4C23×D6111yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—612no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—611no—
991C4⋊C4—611no—
992C4⋊C4—611no—
993C4⋊C4—611no—
994C4⋊C4—611no—
995C4⋊C4—611no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—1221no—
1003C4⋊C4—1221no—
1004C4⋊C4—2442no—
1005C4⋊C4—2442no—
1006C22⋊C4—42no—
1007C22⋊C4—611no—
1008C22⋊C4—611no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—1221no—
1016C22⋊C4—1221no—
1017C22⋊C4—1221no—
1018C22⋊C4—1221no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—1221no—
1028C22⋊C4—1221no—
1029C22⋊C4—1221no—
1030C22⋊C4—2442no—
1031C22⋊C4—2442no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—611no—
1037C42—611no—
1038C42—611no—
1039C42—611no—
1040C42—612no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—1221no—
1047C42—2442no—
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—81no—
1057C23—611no—
1058C23—611no—
1059C23—1221no—
1060C23—1221no—
1061C23—1221no—
1062C23—4881no—
1063C23—2441no—
1064C23—2441no—
1065C23—2442no—
1066C23—2442no—
1067C23C22⋊C4×D6111yescharacteristic
1068C23C22⋊C4×D6111yescharacteristic
1069C23C2×D4×D6111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—42no—
1074Q8—1221no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8#1451973712yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—21no—
1082D4—21no—
1083D4—42no—
1084D4—42no—
1085D4—42no—
1086D4—41no—
1087D4—41no—
1088D4—1222no—
1089D4—1222no—
1090D4—1221no—
1091D4—1221no—
1092D4—4881no—
1093D4—4881no—
1094D4—4881no—
1095D4—2442no—
1096D4—2441no—
1097D4—2441no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2442no—
1103D4—2441no—
1104D4—2441no—
1105D4#1451973712yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—611no—
1132C2×C4—611no—
1133C2×C4—611no—
1134C2×C4—611no—
1135C2×C4—611no—
1136C2×C4—611no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1221no—
1147C2×C4—1222no—
1148C2×C4—1221no—
1149C2×C4—1221no—
1150C2×C4—1221no—
1151C2×C4—1222no—
1152C2×C4—4881no—
1153C2×C4—2442no—
1154C2×C4—2442no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2442no—
1158C2×C4—2442no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2448no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4C22⋊C4×D6111yescharacteristic
1167C2×C4C22⋊C4×D6111yescharacteristic
1168C2×C4C22×C4×D6111yescharacteristic
1169C2×C4C2×D4×D6111yescharacteristic
1170C2×C4C2×D4×D6111yescharacteristic
1171C2×C4C2×#1175822411yescharacteristic
1172C2×C4#1451982211yescharacteristic
1173C2×C4#1451982211yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—1222no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—22no—
1186C22—42no—
1187C22—42no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—84no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1221no—
1198C22—1221no—
1199C22—1221no—
1200C22—4881no—
1201C22—4881no—
1202C22—4884no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22#1683977712yescomplemented
1207C22C2×C22⋊C4×D6111yescharacteristic
1208C22#1684039411yescharacteristic
1209C22#1684039911yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—41no—
1214C4—81no—
1215C4—81no—
1216C4—1221no—
1217C4—1221no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—2442no—
1223C4—2442no—
1224C4—2441no—
1225C4—2441no—
1226C4—2441no—
1227C4C2×#1451973711yescharacteristic
1228C4#1684023511yescharacteristic
1229C4#1684039411yescharacteristic
1230C4#1684039911yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—42no—
1236C2—81no—
1237C2—4881no—
1238C2—2441no—
1239C2—2441no—
1240C2#2144863511yescharacteristic
1241C2C2×#1683977711yescharacteristic
1242C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C22×C22⋊C4
prime radical#41×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21454551C2semidirect
3. C2×#16839777C2semidirect
4. C22×#14519704C2semidirect
5. #21448258C2semidirect
6. #21446736C2semidirect
7. #21446649C2semidirect
8. #21446264C2semidirect
9. #21446260C2semidirect
10. #21446119C2semidirect
11. #21446118C2semidirect
12. #21445837C2semidirect
13. #21445761C2semidirect
14. #21445631C2semidirect
15. C61×#1789C2semidirect
17. C22×#11758194C22semidirect
18. C2×M16×D61C22semidirect
19. #16840431C4semidirect
20. Q8×C22⋊D61C4semidirect
21. #16840423C4semidirect
22. #16840419C4semidirect
24. #16840411C4semidirect
26. #16840406C4semidirect
28. #16840400C4semidirect
30. D4×C22⋊D61C4semidirect
40. C2×#14519734C22semidirect
41. C22×C4×Dic61C22semidirect
46. #16839785C22semidirect
48. C2×#14519705C22semidirect
49. C2×#14519705C22semidirect
53. C2×#14519704C22semidirect
54. C2×#14519704C22semidirect
55. C2×#14519703C22semidirect
56. C2×#14519703C22semidirect
57. #16839725C22semidirect
58. M16×Dic61C22semidirect
63. C4×#11758196C22semidirect
64. C4×#11758198C22semidirect
65. #16839608C22semidirect
66. #16839523C22semidirect
67. #16839523C22semidirect
68. #16839522C22semidirect
69. #16839522C22semidirect
73. C2×#104×C61C22semidirect
74. C2×#104×C61C22semidirect
75. C61×#407C22semidirect
76. C4×C22⋊C4×C61C22semidirect
77. C2×#11758226C2×C4semidirect
81. C2×#11758224C2×C4semidirect
86. C2×Q8×D61C2×C4semidirect
90. C2×D4×D61C2×C4semidirect
105. #14519775C2×C4semidirect
107. #14519773C2×C4semidirect
109. #14519766C2×C4semidirect
111. #14519764C2×C4semidirect
124. #14519753C2×C4semidirect
125. #14519753C2×C4semidirect
138. #14519748C2×C4semidirect
139. #14519748C2×C4semidirect
146. Q8×Dic61C2×C4semidirect
147. Q8×Dic61C2×C4semidirect
150. D4×Dic61C2×C4semidirect
151. D4×Dic61C2×C4semidirect
198. #14519704D4semidirect
415. C4×Dic61C2×D4semidirect
420. #11758194C2×D4semidirect
573. C22×C61#421semidirect
623. #1789D61semidirect
681. C2×#104C2×D61semidirect
682. C2×#104C2×D61semidirect
684. #407C2×D61semidirect
692. C4×C22⋊C4C2×D61semidirect
698. C61#22434semidirect
1206. C22#16839777semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D612
#214545512
C2×#168397772
C22×#145197042
#214482582
#214467362
#214466492
#214462642
#214462602
#214461192
#214461182
#214458372
#214457612
#214456312
C61×#17892
#2243461