Finite Group Databasebeta

← #29695703

Subgroups — #29695703

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×D244C211yesmaximal, characteristic
2M16×D244C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21448263C211yesmaximal, characteristic, complemented
6#21446738C211yesmaximal, characteristic, complemented
7#21446651C211yesmaximal, characteristic, complemented
8#21446266C211yesmaximal, characteristic, complemented
9#21446261C211yesmaximal, characteristic, complemented
10#21446120C211yesmaximal, characteristic, complemented
11#21446120C211yesmaximal, characteristic, complemented
12#21445839C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445761C211yesmaximal, characteristic, complemented
15C61×#1759C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic, complemented
19C2×M16×D61C2211yescharacteristic, complemented
20#16840434C411yescharacteristic, complemented
21Q8×D244C411yescharacteristic, complemented
22#16840424C411yescharacteristic, complemented
23#16840424C411yescharacteristic, complemented
24#16840416—21no—
25#16840416C411yescharacteristic, complemented
26#16840407—21no—
27#16840407—21no—
28#16840407C411yescharacteristic, complemented
29#16840407C411yescharacteristic, complemented
30D4×D244—21no—
31D4×D244C411yescharacteristic, complemented
32#16840312—21no—
33#16840312C2211yescharacteristic
34#16840274—21no—
35#16840274—21no—
36#16840274C2211yescharacteristic
37#16840274C2211yescharacteristic
38C2×C4×D244—21no—
39C2×C4×D244C2211yescharacteristic
40C2×#14519734C2211yescharacteristic, complemented
41C2×C42×D61C2211yescharacteristic, complemented
42#16839841—21no—
43#16839835—21no—
44#16839835—21no—
45C8×D244—21no—
46#16839786C2211yescharacteristic, complemented
47#16839777—24no—
48C2×#14519705C2211yescharacteristic, complemented
49C2×#14519705C2211yescharacteristic, complemented
50C2×#14519705C2211yescharacteristic, complemented
51C2×#14519705C2211yescharacteristic, complemented
52C2×#14519704C2211yescharacteristic
53C2×#14519704C2211yescharacteristic
54C2×#14519703C2211yescharacteristic, complemented
55C2×#14519703C2211yescharacteristic, complemented
56C2×#14519703C2211yescharacteristic, complemented
57C2×#14519703C2211yescharacteristic, complemented
58#104×D61—24no—
59#16839725C2211yescharacteristic, complemented
60#16839725C2211yescharacteristic, complemented
61#16839654—21no—
62#16839647—21no—
63#16839640—21no—
64#16839636—21no—
65C4×C4⋊Dic61C2211yescharacteristic, complemented
66C4×#11758198C2211yescharacteristic, complemented
67C4×#11758198C2211yescharacteristic, complemented
68#16839521C2211yescharacteristic, complemented
69#16839521C2211yescharacteristic, complemented
70C4×#41×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C2×#104×C61C2211yescharacteristic
73C4×M16×C61C2211yescharacteristic, complemented
74C61×#376C2211yescharacteristic, complemented
75C61×#339C2211yescharacteristic, complemented
76C61×#339C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic
78C2×#11758226C2×C411yescharacteristic, complemented
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222C2311yescharacteristic
82C2×#11758222C2311yescharacteristic
83C2×#11758224—21no—
84C2×#11758224—21no—
85C2×#11758224C2×C411yescharacteristic
86C2×#11758224C2×C411yescharacteristic, complemented
87#41×D61—22no—
88#41×D61—22no—
89#41×D61—22no—
90#41×D61—22no—
91#41×D61—41no—
92#41×D61—41no—
93#41×D61—41no—
94#41×D61—41no—
95C2×Q8×D61C2×C411yescharacteristic
96C2×Q8×D61C2×C411yescharacteristic, complemented
97C22×D244—21no—
98C22×D244D411yescharacteristic
99C2×D4×D61—21no—
100C2×D4×D61—21no—
101C2×D4×D61C2×C411yescharacteristic
102C2×D4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C2×#11758194C2311yescharacteristic
109C2×#11758194C2311yescharacteristic
110C2×#11758189—21no—
111C2×#11758189—21no—
112M16×D61—22no—
113M16×D61—22no—
114M16×D61—41no—
115M16×D61—41no—
116C2×C8×D61—21no—
117C2×C8×D61—21no—
118#14519777—21no—
119#14519777C2×C411yescharacteristic, complemented
120#14519774—21no—
121#14519774C2×C411yescharacteristic, complemented
122#14519765—21no—
123#14519765—21no—
124#14519765C2×C411yescharacteristic, complemented
125#14519765C2×C411yescharacteristic, complemented
126#14519761—21no—
127#14519761—21no—
128#14519761—21no—
129#14519761—21no—
130#14519761—21no—
131#14519761—21no—
132#14519757—21no—
133#14519757—21no—
134#14519757—21no—
135#14519757—21no—
136#14519757C2×C411yescharacteristic
137#14519757C2×C411yescharacteristic
138#14519757C2×C411yescharacteristic, complemented
139#14519757C2×C411yescharacteristic, complemented
140#14519752—21no—
141#14519752—21no—
142#14519752—21no—
143#14519752—21no—
144#14519752C2×C411yescharacteristic
145#14519752C2×C411yescharacteristic
146#14519752C2×C411yescharacteristic, complemented
147#14519752C2×C411yescharacteristic, complemented
148#14519751—21no—
149#14519751—21no—
150#14519751—21no—
151#14519751—21no—
152#14519751—21no—
153#14519751—21no—
154#14519747—21no—
155#14519747—21no—
156#14519747—21no—
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160C4×D244—21no—
161C4×D244—21no—
162C4×D244—21no—
163C4×D244—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244—21no—
168C4×D244—21no—
169C4×D244—21no—
170C4×D244C2×C411yescharacteristic
171C4×D244C2×C411yescharacteristic
172C4×D244C2×C411yescharacteristic
173C4×D244C2×C411yescharacteristic
174C4×D244D411yescharacteristic
175C4×D244D411yescharacteristic
176C4×D244D411yescharacteristic
177C4×D244D411yescharacteristic
178#14519734—22no—
179#14519734—41no—
180C2×C4⋊Dic61—21no—
181C2×C4⋊Dic61—21no—
182C2×C4⋊Dic61D411yescharacteristic
183C2×#11758196—21no—
184C2×#11758198—21no—
185C2×#11758198—21no—
186C2×#11758198—21no—
187C2×#11758198—21no—
188C2×#11758198—21no—
189C2×#11758198D411yescharacteristic
190C2×#11758198D411yescharacteristic
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61—22no—
195C42×D61—41no—
196C4⋊#92418—21no—
197C4⋊#92418—21no—
198#14519705—22no—
199#14519705—22no—
200#14519705—41no—
201#14519705—41no—
202#14519704—22no—
203#14519704—22no—
204#14519703—22no—
205#14519703—22no—
206#14519703—41no—
207#14519703—41no—
208#14519689—21no—
209#14519689—21no—
210#14519689—21no—
211#14519689—21no—
212#14519684—21no—
213#14519684—21no—
214#14519684—21no—
215C2×#41×C61C2311yescharacteristic
216C2×M16×C61C2311yescharacteristic
217C2×M16×C61C2311yescharacteristic
218C4×Q8×C61C2×C411yescharacteristic, complemented
219C4×Q8×C61C2×C411yescharacteristic, complemented
220C4×D4×C61—21no—
221C4×D4×C61—21no—
222C4×D4×C61C2×C411yescharacteristic, complemented
223C4×D4×C61C2×C411yescharacteristic, complemented
224#117×C61—21no—
225#117×C61C2311yescharacteristic
226C2×C42×C61—21no—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2311yescharacteristic
229C2×C42×C61C2311yescharacteristic
230#104×C61—22no—
231#104×C61D414yescomplemented
232#97×C61—21no—
233C4×C8×C61—21no—
234#95×C61—21no—
235#95×C61—21no—
236C23×D61—21no—
237C23×D61—21no—
238C23×D61C2×D411yescharacteristic
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61C2×D412yes—
243#41×C61#4112yes—
244C2×Q8×C61C22×C411yescharacteristic
245C2×D4×C61—21no—
246C2×D4×C61C22×C411yescharacteristic
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2411yescharacteristic
255C2×C22⋊D61—21no—
256C2×C22⋊D61—21no—
257C2×C22⋊D61—21no—
258C2×C22⋊D61—21no—
259C2×C22⋊D61—21no—
260C2×C22⋊D61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61C2×D411yescharacteristic
266C22×Dic61C2×D411yescharacteristic
267#11758226—22no—
268#11758226—22no—
269#11758226—41no—
270#11758226—41no—
271Q8×D61—22no—
272Q8×D61—22no—
273Q8×D61—41no—
274Q8×D61—41no—
275#11758224—22no—
276#11758224—22no—
277#11758224—41no—
278#11758224—41no—
279#11758224—42no—
280#11758224—42no—
281#11758224—42no—
282#11758224—42no—
283D4×D61—22no—
284D4×D61—22no—
285D4×D61—41no—
286D4×D61—41no—
287D4×D61—42no—
288D4×D61—42no—
289D4×D61—42no—
290D4×D61—42no—
291#11758222—21no—
292#11758222—21no—
293#11758222—21no—
294#11758222—21no—
295#11758222—21no—
296#11758222—21no—
297#11758222—21no—
298#11758222—21no—
299#11758222—42no—
300#11758222—42no—
301#11758222—42no—
302#11758222—42no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—21no—
311C2×D244—42no—
312C2×D244—44no—
313C2×D244C22⋊C411yescharacteristic
314C2×D244C22⋊C411yescharacteristic
315C2×D244C22⋊C411yescharacteristic
316C2×D244C22⋊C411yescharacteristic
317C2×D244C22×C411yescharacteristic
318C2×D244C22×C411yescharacteristic
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—42no—
334C2×C4×D61—42no—
335C2×C4×D61—42no—
336C2×C4×D61—42no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61C22×C411yescharacteristic
341C2×C4×D61C22×C411yescharacteristic
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×Dic122—21no—
349C2×Dic122—21no—
350C2×Dic122C22×C411yescharacteristic
351C2×Dic122C22×C411yescharacteristic
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61C2×D412yescomplemented
356C2×C8×C61—21no—
357C2×C8×C61—21no—
358C4⋊C4×C61—21no—
359C4⋊C4×C61—21no—
360C4⋊C4×C61C22×C411yescharacteristic
361C4⋊C4×C61C22×C411yescharacteristic
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C22⋊C4×C61—21no—
365C42×C61—21no—
366C42×C61—21no—
367C42×C61—21no—
368C42×C61—21no—
369C42×C61—21no—
370C42×C61—21no—
371C42×C61C22×C411yescharacteristic
372C42×C61C22×C411yescharacteristic
373C42×C61C2×D411yescharacteristic
374C42×C61C2×D411yescharacteristic
375C42×C61C2×D412yescomplemented
376#11758198—21no—
377#11758198—21no—
378#11758198—21no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—21no—
387#11758198—21no—
388#11758198—42no—
389#11758198—42no—
390#11758198—42no—
391#11758198C22⋊C411yescharacteristic
392#11758198C22⋊C411yescharacteristic
393#11758198C22⋊C411yescharacteristic
394#11758198C22⋊C411yescharacteristic
395#11758198C22⋊C411yescharacteristic
396#11758198C22⋊C411yescharacteristic
397#11758198C22⋊C411yescharacteristic
398#11758198C22⋊C411yescharacteristic
399C4⋊Dic61—21no—
400C4⋊Dic61—21no—
401C4⋊Dic61—21no—
402C4⋊Dic61—21no—
403C4⋊Dic61—21no—
404C4⋊Dic61—21no—
405C4⋊Dic61—42no—
406C4⋊Dic61C22⋊C411yescharacteristic
407C4⋊Dic61C22⋊C411yescharacteristic
408C4⋊Dic61C22⋊C411yescharacteristic
409C4⋊Dic61C22⋊C411yescharacteristic
410#11758196—42no—
411C4×Dic61—21no—
412C4×Dic61—21no—
413C4×Dic61—21no—
414C4×Dic61—21no—
415C4×Dic61—42no—
416#11758194—21no—
417#11758194—21no—
418#11758194—21no—
419#11758194—21no—
420C2×#92418—21no—
421C2×#92418—21no—
422#11758189—42no—
423#11758189—42no—
424C8×D61—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61C22×D411yescharacteristic
428C22×D61—21no—
429C22×D61—21no—
430C22×D61—21no—
431C22×D61—21no—
432C22×D61—22no—
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—42no—
439C22×D61—42no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—81no—
443C22×D61—81no—
444C22×D61C2×C22⋊C411yescharacteristic
445C22×D61C2×C22⋊C411yescharacteristic
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61C4×D412yes—
450D4×C61—22no—
451D4×C61—22no—
452D4×C61—21no—
453D4×C61C4×D412yes—
454C2×C4×C61—21no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—22no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—42no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—81no—
469C2×C4×C61C2×C22⋊C411yescharacteristic
470C2×C4×C61C2×C22⋊C411yescharacteristic
471C2×C4×C61C2×C22⋊C411yescharacteristic
472C2×C4×C61C2×C22⋊C411yescharacteristic
473C2×C4×C61C23×C411yescharacteristic
474C2×C4×C61C22×D411yescharacteristic
475C2×C4×C61C22×D411yescharacteristic
476C2×C4×C61C2×#4111yescharacteristic
477C2×C4×C61H(5,𝔽2)11yescharacteristic
478C2×C4×C61H(5,𝔽2)11yescharacteristic
479C22⋊D61—42no—
480C22⋊D61—42no—
481C22⋊D61—42no—
482C22⋊D61—42no—
483C22⋊D61—41no—
484C22⋊D61—41no—
485C22⋊D61—41no—
486C22⋊D61—41no—
487C2×Dic61—21no—
488C2×Dic61—21no—
489C2×Dic61—21no—
490C2×Dic61—21no—
491C2×Dic61—22no—
492C2×Dic61—21no—
493C2×Dic61—21no—
494C2×Dic61—42no—
495C2×Dic61—42no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61C2×C22⋊C411yescharacteristic
502C2×Dic61C2×C22⋊C411yescharacteristic
503C2×Dic61C2×C22⋊C411yescharacteristic
504C2×Dic61C2×C22⋊C411yescharacteristic
505D244—22no—
506D244—22no—
507D244—21no—
508D244—21no—
509D244—21no—
510D244—21no—
511D244—41no—
512D244—41no—
513D244—42no—
514D244—42no—
515D244—42no—
516D244—42no—
517D244—42no—
518D244—81no—
519D244—81no—
520D244—81no—
521C4×D61—21no—
522C4×D61—21no—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—21no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—48no—
542C4×D61—41no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—41no—
546Dic122—21no—
547Dic122—21no—
548Dic122—21no—
549Dic122—21no—
550Dic122—42no—
551Dic122—42no—
552C8×C61—22no—
553C8×C61—41no—
554#92418—41no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—22no—
560C22×C61—41no—
561C22×C61—41no—
562C22×C61C22×C22⋊C411yescharacteristic
563C22×C61D4211yescharacteristic
564C22×C61#54611yescharacteristic
565C2×D61—21no—
566C2×D61—21no—
567C2×D61—21no—
568C2×D61—21no—
569C2×D61—21no—
570C2×D61—21no—
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—21no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—41no—
579C2×D61—41no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—84no—
585C2×D61—81no—
586C2×D61—81no—
587C2×D61—84no—
588C2×D61#42112yescomplemented
589C4×C61—22no—
590C4×C61—21no—
591C4×C61—21no—
592C4×C61—21no—
593C4×C61—21no—
594C4×C61—42no—
595C4×C61—41no—
596C4×C61—41no—
597C4×C61—81no—
598C4×C61C2×C4×D411yescharacteristic
599C4×C61#51811yescharacteristic
600C4×C61D4211yescharacteristic
601C4×C61#54611yescharacteristic
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—42no—
607Dic61—41no—
608Dic61—41no—
609Dic61—81no—
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#1789—611no—
624#1759D6111yescharacteristic, complemented
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—42no—
628C2×C61D4×C22⋊C411yescharacteristic
629C2×C61C2×#42111yescharacteristic
630C2×C61#290111yescharacteristic
631D61—22no—
632D61—41no—
633D61—41no—
634D61—41no—
635D61—81no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
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×#41C2×D6111yescharacteristic
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—611no—
679C2×#104—611no—
680C2×#104—1224no—
681C2×#104C2×D6111yescharacteristic
682C2×#104C2×D6111yescharacteristic
683#407—611no—
684#407—611no—
685C4×M16C2×D6111yescharacteristic, complemented
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376C2×D6111yescharacteristic, complemented
694#339—611no—
695#339—611no—
696#339C2×D6111yescharacteristic, complemented
697#339C2×D6111yescharacteristic, complemented
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—611no—
705C2×#41—1221no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—1222no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41—2441no—
717C2×#41C22×D6111yescharacteristic
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4—1221no—
726C23×C4—611no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4—1221no—
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×Q8C4×D6111yescharacteristic, complemented
786C4×Q8C4×D6111yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—21no—
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×D4C4×D6111yescharacteristic, complemented
808C4×D4C4×D6111yescharacteristic, complemented
809#117—21no—
810#117—1222no—
811#117—2441no—
812#117C22×D6111yescharacteristic
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—21no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—1222no—
828C2×C42—1221no—
829C2×C42—2441no—
830C2×C42C22×D6111yescharacteristic
831C2×C42C22×D6111yescharacteristic
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—22no—
836#104—1222no—
837#104—1222no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—2441no—
843#104—2441no—
844#104—2441no—
845#104—2441no—
846#104D24414yescomplemented
847C22⋊C8—1221no—
848C22⋊C8—1221no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—21no—
852C4×C8—21no—
853#95—21no—
854#95—21no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—611no—
859C24—611no—
860C24—1221no—
861C24—1221no—
862#41—21no—
863#41—21no—
864#41—1222no—
865#41—1222no—
866#41—1222no—
867#41—1222no—
868#41—1221no—
869#41—1221no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—2442no—
877#41—2442no—
878#41—2442no—
879#41—2442no—
880#41—2441no—
881#41—2441no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2442no—
886#41—2441no—
887#41—2441no—
888#41C2×D24412yes—
889#41#1175822212yes—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—1221no—
893C2×Q8—1221no—
894C2×Q8—1222no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8—2441no—
898C2×Q8C2×C4×D6111yescharacteristic
899C2×D4—21no—
900C2×D4—611no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—1221no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1222no—
915C2×D4—1222no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—2442no—
923C2×D4—2444no—
924C2×D4—2441no—
925C2×D4—2441no—
926C2×D4—2442no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4—2442no—
930C2×D4C2×C4×D6111yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—611no—
937C22×C4—611no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
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—1221no—
964C22×C4—2442no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4—2442no—
969C22×C4—2442no—
970C22×C4—2442no—
971C22×C4D4×D6111yescharacteristic
972C22×C4D4×D6111yescharacteristic
973C22×C4C23×D6111yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—1221no—
978M16—1221no—
979M16—1221no—
980M16—1221no—
981M16—2442no—
982M16—2442no—
983M16C2×D24412yescomplemented
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—21no—
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—2442no—
1003C4⋊C4—2442no—
1004C4⋊C4C2×C4×D6111yescharacteristic
1005C4⋊C4C2×C4×D6111yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
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—2442no—
1030C22⋊C4—2442no—
1031C22⋊C4—2442no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—2442no—
1043C42C2×C4×D6111yescharacteristic
1044C42C2×C4×D6111yescharacteristic
1045C42C2×D24412yescomplemented
1046C42D4×D6111yescharacteristic
1047C42D4×D6111yescharacteristic
1048C23—21no—
1049C23—611no—
1050C23—611no—
1051C23—611no—
1052C23—611no—
1053C23—1222no—
1054C23—1221no—
1055C23—1221no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—1221no—
1060C23—4881no—
1061C23—4881no—
1062C23—2441no—
1063C23—2441no—
1064C23—2441no—
1065C23—2442no—
1066C23—2442no—
1067C23—2442no—
1068C23—2442no—
1069C23C2×D4×D6111yescharacteristic
1070Q8—21no—
1071Q8—1221no—
1072Q8—1221no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—2442no—
1076Q8—2442no—
1077Q8C4×D24412yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—1222no—
1082D4—1222no—
1083D4—1221no—
1084D4—1221no—
1085D4—1221no—
1086D4—1221no—
1087D4—4881no—
1088D4—4881no—
1089D4—4881no—
1090D4—2441no—
1091D4—2441no—
1092D4—2442no—
1093D4—2442no—
1094D4—2442no—
1095D4—2442no—
1096D4—2442no—
1097D4—2442no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2441no—
1102D4—2441no—
1103D4—2441no—
1104D4—2441no—
1105D4C4×D24412yes—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—81no—
1121C2×C4—611no—
1122C2×C4—611no—
1123C2×C4—611no—
1124C2×C4—611no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
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—1222no—
1146C2×C4—1221no—
1147C2×C4—1221no—
1148C2×C4—2442no—
1149C2×C4—2442no—
1150C2×C4—2442no—
1151C2×C4—2442no—
1152C2×C4—2448no—
1153C2×C4—2442no—
1154C2×C4—2442no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2441no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4C22⋊C4×D6111yescharacteristic
1165C2×C4C22⋊C4×D6111yescharacteristic
1166C2×C4C22⋊C4×D6111yescharacteristic
1167C2×C4C22⋊C4×D6111yescharacteristic
1168C2×C4C22×C4×D6111yescharacteristic
1169C2×C4C2×D4×D6111yescharacteristic
1170C2×C4C22×D24411yescharacteristic
1171C2×C4C2×#1175822211yescharacteristic
1172C2×C4#1451982311yescharacteristic
1173C2×C4#1451982311yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—2441no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—22no—
1181C22—41no—
1182C22—41no—
1183C22—612no—
1184C22—1221no—
1185C22—1221no—
1186C22—1221no—
1187C22—1221no—
1188C22—1221no—
1189C22—1221no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—4881no—
1196C22—4881no—
1197C22—4884no—
1198C22—4884no—
1199C22—2442no—
1200C22—2442no—
1201C22—2441no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22—2441no—
1207C22C2×C22⋊C4×D6111yescharacteristic
1208C22D4×D24411yescharacteristic
1209C22#1684040811yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—42no—
1216C4—41no—
1217C4—41no—
1218C4—81no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—1221no—
1223C4—4881no—
1224C4—2442no—
1225C4—2441no—
1226C4—2441no—
1227C4C2×C4×D24411yescharacteristic
1228C4#1684023611yescharacteristic
1229C4D4×D24411yescharacteristic
1230C4#1684040811yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—42no—
1234C2—1222no—
1235C2—4881no—
1236C2—4881no—
1237C2—2441no—
1238C2—2441no—
1239C2—2441no—
1240C2C22⋊C4×D24411yescharacteristic
1241C2#421×D6111yescharacteristic
1242C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C22×C22⋊C4
prime radical#41×D244C2
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. M16×D244C2semidirect
3. C2×#16839777C2semidirect
4. C2×#104×D61C2semidirect
5. #21448263C2semidirect
6. #21446738C2semidirect
7. #21446651C2semidirect
8. #21446266C2semidirect
9. #21446261C2semidirect
10. #21446120C2semidirect
11. #21446120C2semidirect
12. #21445839C2semidirect
13. #21445761C2semidirect
14. #21445761C2semidirect
15. C61×#1759C2semidirect
18. C2×M16×D61C22semidirect
19. C2×M16×D61C22semidirect
20. #16840434C4semidirect
21. Q8×D244C4semidirect
22. #16840424C4semidirect
23. #16840424C4semidirect
25. #16840416C4semidirect
28. #16840407C4semidirect
29. #16840407C4semidirect
31. D4×D244C4semidirect
40. C2×#14519734C22semidirect
41. C2×C42×D61C22semidirect
46. #16839786C22semidirect
48. C2×#14519705C22semidirect
49. C2×#14519705C22semidirect
50. C2×#14519705C22semidirect
51. C2×#14519705C22semidirect
54. C2×#14519703C22semidirect
55. C2×#14519703C22semidirect
56. C2×#14519703C22semidirect
57. C2×#14519703C22semidirect
59. #16839725C22semidirect
60. #16839725C22semidirect
65. C4×C4⋊Dic61C22semidirect
66. C4×#11758198C22semidirect
67. C4×#11758198C22semidirect
68. #16839521C22semidirect
69. #16839521C22semidirect
73. C4×M16×C61C22semidirect
74. C61×#376C22semidirect
75. C61×#339C22semidirect
76. C61×#339C22semidirect
78. C2×#11758226C2×C4semidirect
86. C2×#11758224C2×C4semidirect
96. C2×Q8×D61C2×C4semidirect
102. C2×D4×D61C2×C4semidirect
119. #14519777C2×C4semidirect
121. #14519774C2×C4semidirect
124. #14519765C2×C4semidirect
125. #14519765C2×C4semidirect
138. #14519757C2×C4semidirect
139. #14519757C2×C4semidirect
146. #14519752C2×C4semidirect
147. #14519752C2×C4semidirect
218. C4×Q8×C61C2×C4semidirect
219. C4×Q8×C61C2×C4semidirect
222. C4×D4×C61C2×C4semidirect
223. C4×D4×C61C2×C4semidirect
231. #104×C61D4semidirect
355. M16×C61C2×D4semidirect
375. C42×C61C2×D4semidirect
588. C2×D61#421semidirect
624. #1759D61semidirect
685. C4×M16C2×D61semidirect
693. #376C2×D61semidirect
696. #339C2×D61semidirect
697. #339C2×D61semidirect
698. C61#22434semidirect
785. C4×Q8C4×D61semidirect
786. C4×Q8C4×D61semidirect
807. C4×D4C4×D61semidirect
808. C4×D4C4×D61semidirect
846. #104D244semidirect
983. M16C2×D244semidirect
1045. C42C2×D244semidirect

Maximal subgroups

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

subgroupindex
#41×D2442
M16×D2442
C2×#168397772
C2×#104×D612
#214482632
#214467382
#214466512
#214462662
#214462612
#214461202
#214458392
#214457612
C61×#17592
#2243461