Finite Group Databasebeta

← #29695701

Subgroups — #29695701

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#21459302C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21448265C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446649C211yesmaximal, characteristic, complemented
8#21446268C211yesmaximal, characteristic, complemented
9#21446261C211yesmaximal, characteristic, complemented
10#21446120C211yesmaximal, characteristic, complemented
11#21445838C211yesmaximal, characteristic, complemented
12#21445764C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445628C211yesmaximal, characteristic, complemented
15C61×#1871C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic, complemented
19#16840430C411yescharacteristic, complemented
20#16840425C411yescharacteristic, complemented
21#16840422C411yescharacteristic, complemented
22#16840418C411yescharacteristic, complemented
23#16840414C411yescharacteristic, complemented
24#16840410—21no—
25#16840409C411yescharacteristic, complemented
26#16840404—21no—
27#16840403C411yescharacteristic, complemented
28#16840399—21no—
29#16840396C411yescharacteristic, complemented
30#16840394—21no—
31#16840309—21no—
32#16840308C2211yescharacteristic
33#16840274C2211yescharacteristic
34#16840271—21no—
35#16840271—21no—
36#16840230C2211yescharacteristic
37C2×C4×C22⋊D61C2211yescharacteristic
38C4×D4×D61—21no—
39C2×#14519736C2211yescharacteristic, complemented
40C2×C42×D61C2211yescharacteristic, complemented
41#16839838—21no—
42#16839833—21no—
43#16839831—21no—
44C8×C22⋊D61—21no—
45#16839785C2211yescharacteristic, complemented
46#16839778—24no—
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49C2×#14519705C2211yescharacteristic, complemented
50C2×#14519705C2211yescharacteristic, complemented
51C2×#14519704C2211yescharacteristic, complemented
52C2×#14519704C2211yescharacteristic, complemented
53C2×#14519703C2211yescharacteristic
54C2×#14519703C2211yescharacteristic
55C2×#14519703C2211yescharacteristic, complemented
56C2×#14519703C2211yescharacteristic, complemented
57#104×D61—24no—
58#16839726C2211yescharacteristic, complemented
59#16839725C2211yescharacteristic, complemented
60M16×Dic61C2211yescharacteristic, complemented
61#16839656—21no—
62#16839649—21no—
63#16839638—21no—
64#16839636—21no—
65C4×#11758196C2211yescharacteristic, complemented
66C4×#11758198C2211yescharacteristic, complemented
67#16839608C2211yescharacteristic, complemented
68#16839521C2211yescharacteristic, complemented
69#16839521C2211yescharacteristic, complemented
70C22×M16×C61C2211yescharacteristic, complemented
71C61×#525C2211yescharacteristic
72C2×#104×C61C2211yescharacteristic, complemented
73C2×#104×C61C2211yescharacteristic, complemented
74C4×C22⋊C4×C61C2211yescharacteristic, complemented
75C61×#339C2211yescharacteristic, complemented
76C61×#339C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic
78C2×#11758222—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—41no—
84C2×#11758222—41no—
85C2×#11758222C2×C411yescharacteristic, complemented
86C2×#11758222C2×C411yescharacteristic, complemented
87C2×#11758222C2311yescharacteristic
88C2×#11758222C2311yescharacteristic
89C2×#11758224—21no—
90C2×#11758224C2×C411yescharacteristic
91#41×D61—22no—
92#41×D61—22no—
93#41×D61—41no—
94#41×D61—41no—
95C22×Dic122C2×C411yescharacteristic, complemented
96C2×Q8×D61C2×C411yescharacteristic
97C22×D244C2×C411yescharacteristic, complemented
98C22×C22⋊D61—21no—
99C22×C22⋊D61D411yescharacteristic
100C2×D4×D61—21no—
101C2×D4×D61—21no—
102C2×D4×D61C2×C411yescharacteristic
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C2×#11758194C2311yescharacteristic
108C2×#11758194C2311yescharacteristic
109C2×#11758189—21no—
110M16×D61—22no—
111M16×D61—41no—
112C2×C8×D61—21no—
113#14519776—21no—
114#14519775C2×C411yescharacteristic, complemented
115#14519773—21no—
116#14519773C2×C411yescharacteristic, complemented
117#14519766C2×C411yescharacteristic, complemented
118#14519764C2×C411yescharacteristic, complemented
119#14519763—21no—
120#14519763—21no—
121#14519762—21no—
122#14519762—21no—
123#14519761—21no—
124#14519759—21no—
125#14519759—21no—
126#14519757C2×C411yescharacteristic
127#14519757C2×C411yescharacteristic
128#14519755—21no—
129#14519755—21no—
130#14519754—21no—
131#14519754—21no—
132#14519752—21no—
133#14519752C2×C411yescharacteristic
134#14519752C2×C411yescharacteristic
135#14519750—21no—
136#14519750—21no—
137#14519750—21no—
138#14519750—21no—
139#14519749—21no—
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519748—21no—
144#14519747—21no—
145#14519747—21no—
146#14519747—21no—
147#14519745—21no—
148#14519745—21no—
149#14519742C2×C411yescharacteristic, complemented
150#14519742C2×C411yescharacteristic, complemented
151C4×D244—21no—
152C4×D244—21no—
153D4×Dic61—21no—
154#14519739—21no—
155#14519739C2×C411yescharacteristic, complemented
156#14519739C2×C411yescharacteristic, complemented
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61C2×C411yescharacteristic
160C4×C22⋊D61C2×C411yescharacteristic
161C4×C22⋊D61C2×C411yescharacteristic
162C4×C22⋊D61C2×C411yescharacteristic
163C4×C22⋊D61D411yescharacteristic
164C4×C22⋊D61D411yescharacteristic
165C4×C22⋊D61D411yescharacteristic
166C4×C22⋊D61D411yescharacteristic
167#14519737—21no—
168#14519737—21no—
169#14519737—21no—
170#14519737—21no—
171#14519736—22no—
172#14519736—41no—
173#14519734—21no—
174C2×C4⋊Dic61—21no—
175C2×#11758196—21no—
176C2×#11758196D411yescharacteristic
177C4⋊C4×D61—21no—
178C2×C22⋊Dic61—21no—
179C2×C22⋊Dic61D411yescharacteristic
180C2×#11758198—21no—
181C2×#11758198D411yescharacteristic
182C22⋊C4×D61—21no—
183C22⋊C4×D61—21no—
184C2×C4×Dic61—21no—
185C2×C4×Dic61C2311yescharacteristic
186C2×C4×Dic61C2311yescharacteristic
187C2×C4×Dic61C2311yescharacteristic
188C42×D61—21no—
189C42×D61—22no—
190C42×D61—41no—
191#14519706—21no—
192#14519706—21no—
193#14519705—22no—
194#14519705—22no—
195#14519705—41no—
196#14519705—41no—
197#14519704—22no—
198#14519704—41no—
199#14519703—22no—
200#14519703—22no—
201#14519703—22no—
202#14519703D414yescomplemented
203C22⋊#92418—21no—
204C22⋊#92418—21no—
205#14519689—21no—
206#14519689—21no—
207#14519687—21no—
208C8×Dic61—21no—
209#14519684—21no—
210#14519684—21no—
211#14519684—21no—
212#14519684—21no—
213C2×#41×C61C2311yescharacteristic
214C23×C4×C61C2311yescharacteristic
215C2×M16×C61—21no—
216C2×M16×C61—22no—
217C2×M16×C61—41no—
218C2×M16×C61C2311yescharacteristic
219C2×M16×C61C2311yescharacteristic
220C22×C8×C61—21no—
221#123×C61—21no—
222C22⋊Q8×C61C2×C411yescharacteristic, complemented
223C22⋊Q8×C61C2×C411yescharacteristic, complemented
224#121×C61C2×C411yescharacteristic, complemented
225#121×C61C2×C411yescharacteristic, complemented
226#120×C61—21no—
227C4×D4×C61—21no—
228C4×D4×C61—21no—
229#117×C61C2311yescharacteristic
230C2×C22⋊C4×C61—21no—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2311yescharacteristic
233#104×C61—22no—
234#104×C61—41no—
235#95×C61—21no—
236C24×C61C2×D411yescharacteristic
237C23×D61—21no—
238C23×D61—21no—
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—21no—
243#41×C61—21no—
244C2×Q8×C61C22×C411yescharacteristic
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61C22×C411yescharacteristic
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2411yescharacteristic
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61—21no—
270C2×C22⋊D61—42no—
271C2×C22⋊D61—42no—
272C2×C22⋊D61—42no—
273C2×C22⋊D61C22⋊C411yescharacteristic
274C2×C22⋊D61C22⋊C411yescharacteristic
275C2×C22⋊D61C22⋊C411yescharacteristic
276C2×C22⋊D61C22⋊C411yescharacteristic
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284#11758226—22no—
285#11758226—41no—
286Q8×D61—22no—
287Q8×D61—41no—
288#11758224—22no—
289#11758224—41no—
290#11758224—42no—
291#11758224—42no—
292D4×D61—22no—
293D4×D61—41no—
294D4×D61—42no—
295D4×D61—42no—
296D4×D61—44no—
297#11758222—21no—
298#11758222—21no—
299#11758222—21no—
300#11758222—21no—
301#11758222—21no—
302#11758222—21no—
303#11758222—22no—
304#11758222—22no—
305#11758222—41no—
306#11758222—41no—
307#11758222—42no—
308#11758222—42no—
309#11758222—42no—
310#11758222—42no—
311#11758222—42no—
312#11758222—42no—
313#11758222C2×D412yes—
314#11758222#4112yes—
315C2×D244—22no—
316C2×D244—21no—
317C2×D244—21no—
318C2×D244—21no—
319C2×D244—21no—
320C2×D244—41no—
321C2×D244C22×C411yescharacteristic
322C2×D244C22×C411yescharacteristic
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—21no—
334C2×C4×D61—21no—
335C2×C4×D61—42no—
336C2×C4×D61—42no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61—42no—
341C2×C4×D61—42no—
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×Dic122—22no—
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122—41no—
350C2×Dic122C22×C411yescharacteristic
351C2×Dic122C22×C411yescharacteristic
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61—42no—
356M16×C61C2×D412yescomplemented
357C2×C8×C61—21no—
358C2×C8×C61—21no—
359C2×C8×C61—42no—
360C4⋊C4×C61—21no—
361C4⋊C4×C61—21no—
362C4⋊C4×C61C22×C411yescharacteristic
363C4⋊C4×C61C22×C411yescharacteristic
364C22⋊C4×C61—21no—
365C22⋊C4×C61—21no—
366C22⋊C4×C61—21no—
367C22⋊C4×C61—21no—
368C22⋊C4×C61—21no—
369C22⋊C4×C61—42no—
370C42×C61—21no—
371C42×C61—21no—
372C42×C61—21no—
373C42×C61—21no—
374C42×C61—21no—
375C22⋊Dic61—21no—
376C22⋊Dic61—21no—
377C22⋊Dic61—42no—
378C22⋊Dic61C22⋊C411yescharacteristic
379C22⋊Dic61C22⋊C411yescharacteristic
380C22⋊Dic61C22⋊C411yescharacteristic
381C22⋊Dic61C22⋊C411yescharacteristic
382#11758198—21no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—21no—
387#11758198—21no—
388#11758198—21no—
389#11758198—21no—
390#11758198—42no—
391#11758198C22⋊C411yescharacteristic
392#11758198C22⋊C411yescharacteristic
393#11758198C22⋊C411yescharacteristic
394#11758198C22⋊C411yescharacteristic
395C4⋊Dic61—21no—
396C4⋊Dic61—21no—
397C4⋊Dic61—42no—
398#11758196—21no—
399#11758196—21no—
400#11758196—21no—
401#11758196—21no—
402#11758196—42no—
403#11758196C22⋊C411yescharacteristic
404#11758196C22⋊C411yescharacteristic
405#11758196C22⋊C411yescharacteristic
406#11758196C22⋊C411yescharacteristic
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—21no—
411C4×Dic61—21no—
412C4×Dic61—42no—
413C4×Dic61C22×C411yescharacteristic
414C4×Dic61C22×C411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416C4×Dic61C2×D411yescharacteristic
417C4×Dic61C2×D412yescomplemented
418#11758194—21no—
419#11758194—21no—
420#11758194—21no—
421#11758194—21no—
422C2×#92418—21no—
423C2×#92418—21no—
424#11758189—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—21no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61C2×C22⋊C411yescharacteristic
432C23×C61C2×C22⋊C411yescharacteristic
433C23×C61C22×D411yescharacteristic
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—22no—
438C22×D61—21no—
439C22×D61—41no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—42no—
443C22×D61—42no—
444C22×D61—81no—
445C22×D61—81no—
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450D4×C61—21no—
451D4×C61—21no—
452D4×C61—42no—
453D4×C61—41no—
454D4×C61—41no—
455D4×C61—81no—
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—22no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61C2×C22⋊C411yescharacteristic
478C2×C4×C61C2×C22⋊C411yescharacteristic
479C2×C4×C61C23×C411yescharacteristic
480C2×C4×C61C22×D411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C2×#4111yescharacteristic
483C2×C4×C61H(5,𝔽2)11yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C22⋊D61—22no—
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—22no—
489C22⋊D61—41no—
490C22⋊D61—41no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—42no—
495C22⋊D61—42no—
496C22⋊D61—41no—
497C22⋊D61—41no—
498C22⋊D61—81no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—22no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—42no—
507C2×Dic61—42no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61C2×C22⋊C411yescharacteristic
514C2×Dic61C2×C22⋊C411yescharacteristic
515C2×Dic61C2×C22⋊C411yescharacteristic
516C2×Dic61C2×C22⋊C411yescharacteristic
517C2×Dic61C2×C22⋊C411yescharacteristic
518C2×Dic61C2×C22⋊C411yescharacteristic
519D244—21no—
520D244—21no—
521D244—21no—
522D244—42no—
523D244—42no—
524D244—42no—
525D244—81no—
526D244C4×D412yes—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—22no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—22no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—42no—
542C4×D61—48no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—81no—
546Dic122—21no—
547Dic122—21no—
548Dic122—21no—
549Dic122—42no—
550Dic122—42no—
551Dic122C4×D412yes—
552C8×C61—22no—
553C8×C61—41no—
554#92418—41no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—21no—
565C22×C61—41no—
566C22×C61—41no—
567C22×C61—41no—
568C22×C61—81no—
569C22×C61—81no—
570C22×C61C22×C22⋊C411yescharacteristic
571C22×C61D4211yescharacteristic
572C22×C61#54611yescharacteristic
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—21no—
576C2×D61—22no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—41no—
586C2×D61—84no—
587C2×D61—84no—
588C2×D61#42112yescomplemented
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—42no—
592C4×C61—41no—
593C4×C61—41no—
594C4×C61—41no—
595C4×C61—81no—
596C4×C61C2×C4×D411yescharacteristic
597C4×C61#51811yescharacteristic
598C4×C61D4211yescharacteristic
599C4×C61#54611yescharacteristic
600Dic61—22no—
601Dic61—21no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—21no—
607Dic61—42no—
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#1871D6111yescharacteristic, complemented
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—41no—
628C2×C61—41no—
629C2×C61—81no—
630C2×C61D4×C22⋊C411yescharacteristic
631C2×C61C2×#42111yescharacteristic
632C2×C61#290111yescharacteristic
633D61—22no—
634D61—41no—
635D61—42no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16C2×D6111yescharacteristic, complemented
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—1221no—
657#525—1221no—
658#525C2×D6111yescharacteristic
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—611no—
679C2×#104—611no—
680C2×#104—1224no—
681C2×#104C2×D6111yescharacteristic, complemented
682C2×#104C2×D6111yescharacteristic, complemented
683#407—611no—
684#407—611no—
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#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—1222no—
707C2×#41—1222no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1221no—
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—1221no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4C22×D6111yescharacteristic
731C2×M16—21no—
732C2×M16—22no—
733C2×M16—41no—
734C2×M16—611no—
735C2×M16—611no—
736C2×M16—1221no—
737C2×M16—1222no—
738C2×M16—2441no—
739C2×M16C22×D6111yescharacteristic
740C2×M16C22×D6111yescharacteristic
741C22×C8—21no—
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—21no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8C4×D6111yescharacteristic, complemented
764C22⋊Q8C4×D6111yescharacteristic, complemented
765#121—611no—
766#121—611no—
767#121—1221no—
768#121—1221no—
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#121C4×D6111yescharacteristic, complemented
778#121C4×D6111yescharacteristic, complemented
779#120—21no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8—611no—
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—611no—
798C4×D4—611no—
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—1221no—
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—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—41no—
837#104—614no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—2441no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—1221no—
848C22⋊C8—1221no—
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—611no—
859C24—1221no—
860C24—1221no—
861C24D4×D6111yescharacteristic
862#41—21no—
863#41—21no—
864#41—21no—
865#41—21no—
866#41—612no—
867#41—612no—
868#41—1222no—
869#41—1222no—
870#41—1221no—
871#41—1221no—
872#41—1222no—
873#41—1222no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—1221no—
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—2442no—
888#41—2442no—
889#41—2441no—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—1221no—
893C2×Q8—1222no—
894C2×Q8—1221no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8—2441no—
898C2×Q8C2×C4×D6111yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—1222no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1222no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—2441no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2444no—
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—21no—
937C22×C4—21no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—1221no—
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—2442no—
962C22×C4—2442no—
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—42no—
978M16—1221no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16D4×D6112yescomplemented
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—42no—
987C2×C8—1221no—
988C2×C8—1221no—
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—21no—
1010C22⋊C4—21no—
1011C22⋊C4—42no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—611no—
1018C22⋊C4—611no—
1019C22⋊C4—611no—
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—21no—
1037C42—611no—
1038C42—611no—
1039C42—611no—
1040C42—611no—
1041C42—612no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—1221no—
1047C42—2442no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—611no—
1054C23—611no—
1055C23—1222no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—1221no—
1060C23—4881no—
1061C23—4881no—
1062C23—2441no—
1063C23—2442no—
1064C23—2442no—
1065C23—2442no—
1066C23—2442no—
1067C23C22⋊C4×D6111yescharacteristic
1068C23C22⋊C4×D6111yescharacteristic
1069C23C2×D4×D6111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—612no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—21no—
1079D4—21no—
1080D4—42no—
1081D4—41no—
1082D4—41no—
1083D4—81no—
1084D4—612no—
1085D4—1222no—
1086D4—1222no—
1087D4—1222no—
1088D4—1222no—
1089D4—1221no—
1090D4—1221no—
1091D4—1221no—
1092D4—4881no—
1093D4—4881no—
1094D4—2442no—
1095D4—2442no—
1096D4—2442no—
1097D4—2441no—
1098D4—2441no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2442no—
1103D4—2442no—
1104D4—2441no—
1105D4—2441no—
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—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—611no—
1128C2×C4—611no—
1129C2×C4—611no—
1130C2×C4—611no—
1131C2×C4—611no—
1132C2×C4—611no—
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—1222no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1222no—
1146C2×C4—1221no—
1147C2×C4—1222no—
1148C2×C4—4881no—
1149C2×C4—2442no—
1150C2×C4—2442no—
1151C2×C4—2442no—
1152C2×C4—2442no—
1153C2×C4—2442no—
1154C2×C4—2448no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2442no—
1158C2×C4—2442no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
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×C4#41×D6111yescharacteristic
1172C2×C4#1451982211yescharacteristic
1173C2×C4#1451982311yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—2441no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—81no—
1190C22—81no—
1191C22—612no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1222no—
1198C22—4884no—
1199C22—4884no—
1200C22—2442no—
1201C22—2442no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22—2441no—
1207C22C2×C22⋊C4×D6111yescharacteristic
1208C22#1684039611yescharacteristic
1209C22#1684040111yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—81no—
1217C4—1221no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—1221no—
1223C4—1222no—
1224C4—4881no—
1225C4—2442no—
1226C4—2441no—
1227C4C4×D4×D6111yescharacteristic
1228C4#1684023411yescharacteristic
1229C4#1684039411yescharacteristic
1230C4#1684040411yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—81no—
1236C2—1222no—
1237C2—4881no—
1238C2—2441no—
1239C2—2442no—
1240C2#2144863711yescharacteristic
1241C2#421×D6111yescharacteristic
1242C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#21459302C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. C2×#16839778C2semidirect
4. C2×#104×D61C2semidirect
5. #21448265C2semidirect
6. #21446736C2semidirect
7. #21446649C2semidirect
8. #21446268C2semidirect
9. #21446261C2semidirect
10. #21446120C2semidirect
11. #21445838C2semidirect
12. #21445764C2semidirect
13. #21445761C2semidirect
14. #21445628C2semidirect
15. C61×#1871C2semidirect
18. C2×M16×D61C22semidirect
19. #16840430C4semidirect
20. #16840425C4semidirect
21. #16840422C4semidirect
22. #16840418C4semidirect
23. #16840414C4semidirect
25. #16840409C4semidirect
27. #16840403C4semidirect
29. #16840396C4semidirect
39. C2×#14519736C22semidirect
40. C2×C42×D61C22semidirect
45. #16839785C22semidirect
49. C2×#14519705C22semidirect
50. C2×#14519705C22semidirect
51. C2×#14519704C22semidirect
52. C2×#14519704C22semidirect
55. C2×#14519703C22semidirect
56. C2×#14519703C22semidirect
58. #16839726C22semidirect
59. #16839725C22semidirect
60. M16×Dic61C22semidirect
65. C4×#11758196C22semidirect
66. C4×#11758198C22semidirect
67. #16839608C22semidirect
68. #16839521C22semidirect
69. #16839521C22semidirect
70. C22×M16×C61C22semidirect
72. C2×#104×C61C22semidirect
73. C2×#104×C61C22semidirect
74. C4×C22⋊C4×C61C22semidirect
75. C61×#339C22semidirect
76. C61×#339C22semidirect
85. C2×#11758222C2×C4semidirect
86. C2×#11758222C2×C4semidirect
95. C22×Dic122C2×C4semidirect
97. C22×D244C2×C4semidirect
114. #14519775C2×C4semidirect
116. #14519773C2×C4semidirect
117. #14519766C2×C4semidirect
118. #14519764C2×C4semidirect
149. #14519742C2×C4semidirect
150. #14519742C2×C4semidirect
155. #14519739C2×C4semidirect
156. #14519739C2×C4semidirect
202. #14519703D4semidirect
222. C22⋊Q8×C61C2×C4semidirect
223. C22⋊Q8×C61C2×C4semidirect
224. #121×C61C2×C4semidirect
225. #121×C61C2×C4semidirect
356. M16×C61C2×D4semidirect
417. C4×Dic61C2×D4semidirect
588. C2×D61#421semidirect
620. #1871D61semidirect
640. C22×M16C2×D61semidirect
681. C2×#104C2×D61semidirect
682. C2×#104C2×D61semidirect
692. C4×C22⋊C4C2×D61semidirect
696. #339C2×D61semidirect
697. #339C2×D61semidirect
698. C61#22434semidirect
763. C22⋊Q8C4×D61semidirect
764. C22⋊Q8C4×D61semidirect
777. #121C4×D61semidirect
778. #121C4×D61semidirect
983. M16D4×D61semidirect

Maximal subgroups

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

subgroupindex
#214593022
M16×C22⋊D612
C2×#168397782
C2×#104×D612
#214482652
#214467362
#214466492
#214462682
#214462612
#214461202
#214458382
#214457642
#214457612
#214456282
C61×#18712
#2243461