Finite Group Databasebeta

← #29696206

Subgroups — #29696206

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3#21454551C211yesmaximal, characteristic, complemented
4#21446806C211yesmaximal, characteristic, complemented
5#21446806C211yesmaximal, characteristic, complemented
6#21446283C211yesmaximal, characteristic, complemented
7#21446279C211yesmaximal, characteristic, complemented
8#21446279C211yesmaximal, characteristic, complemented
9#21445901C211yesmaximal, characteristic, complemented
10#21445900C211yesmaximal, characteristic, complemented
11#21445809C211yesmaximal, characteristic, complemented
12#100×Dic61C211yesmaximal, characteristic, complemented
13#21445557C211yesmaximal, characteristic, complemented
14#21445556C211yesmaximal, characteristic, complemented
15C61×#1900C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19#16840476—21no—
20#16840476—21no—
21#16840476—21no—
22#16840476—21no—
23#16840476—21no—
24#16840476—21no—
25#16840476—21no—
26#16840476—21no—
27C2×#14519776C2211yescharacteristic
28C2×#14519764C412yes—
29C2×#14519763C412yes—
30C2×#14519749C412yes—
31C2×#14519748C2211yescharacteristic
32C2×D4×Dic61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519736C2211yescharacteristic
35C2×#14519735C2211yescharacteristic
36C2×#14519733C412yes—
37#16839838—21no—
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41#16839831—21no—
42#16839830—21no—
43C8×C22⋊D61—21no—
44#16839825—21no—
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519694C2211yescharacteristic
48C2×#14519694C2211yescharacteristic
49#16839726C2211yescharacteristic
50#16839725C2211yescharacteristic
51#16839725C2211yescharacteristic
52M16×Dic61C2211yescharacteristic
53M16×Dic61C2211yescharacteristic
54#16839531C2211yescharacteristic
55#16839531C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58#16839530C2211yescharacteristic
59#16839530C2211yescharacteristic
60#16839530C2211yescharacteristic
61#16839530C2211yescharacteristic
62#16839530C2211yescharacteristic
63#16839530C2211yescharacteristic
64C22×M16×C61C2211yescharacteristic
65C2×#121×C61C2211yescharacteristic
66C2×#100×C61C2211yescharacteristic
67C2×#100×C61C2211yescharacteristic
68C61×#407C2211yescharacteristic
69C61×#343C2211yescharacteristic
70C61×#343C2211yescharacteristic
71C22×Dic122C2×C412yes—
72C22×C22⋊D61C2×C412yes—
73C22×C22⋊D61C2×C411yescharacteristic
74C23×Dic61C2×C412yes—
75C22×C4×D61C2311yescharacteristic
76C2×#11758194—21no—
77C2×#11758194—22no—
78C2×#11758194—41no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85M16×D61—22no—
86M16×D61—22no—
87M16×D61—41no—
88M16×D61—41no—
89C22×#92418—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92#14519776—21no—
93#14519776—21no—
94#14519776—21no—
95#14519776—21no—
96#14519764—22no—
97#14519764—22no—
98#14519764—22no—
99#14519764—22no—
100#14519763—22no—
101#14519763—22no—
102#14519763—22no—
103#14519763—22no—
104#14519749—22no—
105#14519749—22no—
106#14519749—22no—
107#14519749—22no—
108#14519748—21no—
109#14519748—21no—
110#14519748—21no—
111#14519748—21no—
112D4×Dic61—21no—
113D4×Dic61—21no—
114D4×Dic61—21no—
115D4×Dic61—21no—
116C4×C22⋊D61D411yescharacteristic
117C4×C22⋊D61D411yescharacteristic
118C4×C22⋊D61D411yescharacteristic
119C4×C22⋊D61D411yescharacteristic
120C4×C22⋊D61D411yescharacteristic
121C4×C22⋊D61D411yescharacteristic
122C4×C22⋊D61D411yescharacteristic
123C4×C22⋊D61D411yescharacteristic
124#14519736—21no—
125#14519736—21no—
126#14519736—21no—
127#14519736—21no—
128#14519735—21no—
129#14519735—21no—
130#14519735—21no—
131#14519735—21no—
132#14519733—22no—
133#14519733—22no—
134#14519733—22no—
135#14519733—22no—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196C2×C412yes—
139C2×#11758196C2×C411yescharacteristic
140C2×C22⋊Dic61C2×C412yes—
141C2×C22⋊Dic61C2×C412yes—
142C2×C22⋊Dic61C2×C412yes—
143C2×C22⋊Dic61C2×C411yescharacteristic
144C2×#11758198C2×C412yes—
145C2×#11758198C2×C411yescharacteristic
146C2×C4×Dic61C2×C412yes—
147C2×C4×Dic61C2×C412yes—
148C2×C4×Dic61C2311yescharacteristic
149#14519706—21no—
150#14519706—21no—
151#14519706—21no—
152#14519706—21no—
153#14519694—22no—
154#14519694—41no—
155C22⋊#92418—21no—
156C22⋊#92418—21no—
157#14519689—21no—
158#14519689—21no—
159#14519689—21no—
160#14519689—21no—
161#14519687—21no—
162#14519687—21no—
163C8×Dic61—21no—
164C8×Dic61—21no—
165C22×D4×C61C2×C412yes—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×M16×C61—21no—
169C2×M16×C61—22no—
170C2×M16×C61—41no—
171C2×M16×C61C2311yescharacteristic
172C2×M16×C61C2311yescharacteristic
173C2×M16×C61C2311yescharacteristic
174C2×M16×C61C2311yescharacteristic
175C22×C8×C61—21no—
176#121×C61—21no—
177#121×C61—21no—
178#121×C61—21no—
179#121×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61C2×C412yes—
182#100×C61—22no—
183#100×C61—41no—
184C22⋊C8×C61—21no—
185C22⋊C8×C61—21no—
186C24×C61C22×C412yes—
187C24×C61C22×C411yescharacteristic
188C23×D61C22×C411yescharacteristic
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—82no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C412yes—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—82no—
213C2×C22⋊D61C22⋊C411yescharacteristic
214C2×C22⋊D61C22⋊C411yescharacteristic
215C2×C22⋊D61C22⋊C411yescharacteristic
216C2×C22⋊D61C22⋊C411yescharacteristic
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—44no—
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C412yes—
223C22×Dic61C22×C412yes—
224C22×Dic61C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—82no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—42no—
244M16×C61#4112yes—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—42no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61—22no—
257C22⋊Dic61—22no—
258C22⋊Dic61—22no—
259C22⋊Dic61—22no—
260C22⋊Dic61C22⋊C411yescharacteristic
261C22⋊Dic61C22⋊C411yescharacteristic
262C22⋊Dic61C22⋊C411yescharacteristic
263C22⋊Dic61C22⋊C411yescharacteristic
264#11758198—22no—
265#11758198—22no—
266#11758198C22⋊C411yescharacteristic
267#11758198C22⋊C411yescharacteristic
268#11758198C22⋊C411yescharacteristic
269#11758198C22⋊C411yescharacteristic
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274#11758196—22no—
275#11758196—22no—
276#11758196C22⋊C411yescharacteristic
277#11758196C22⋊C411yescharacteristic
278#11758196C22⋊C411yescharacteristic
279#11758196C22⋊C411yescharacteristic
280C4×Dic61—22no—
281C4×Dic61—22no—
282C4×Dic61—22no—
283C4×Dic61—22no—
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288#11758194—21no—
289#11758194—21no—
290#11758194—21no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194—21no—
295#11758194—42no—
296#11758194#4112yes—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—42no—
302#11758189—42no—
303#11758189—42no—
304C8×D61—42no—
305C8×D61—42no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61C2×C22⋊C411yescharacteristic
316C23×C61C2×C22⋊C411yescharacteristic
317C23×C61C23×C411yescharacteristic
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61C2×C22⋊C411yescharacteristic
323C22×D61C2×C22⋊C411yescharacteristic
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—82no—
329D4×C61—82no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—42no—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C2×C4×C612−1+411yescharacteristic
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—82no—
355C22⋊D61—82no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—41no—
362C2×Dic61—44no—
363C2×Dic61—44no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380Dic122—82no—
381Dic122—82no—
382C8×C61—22no—
383C8×C61—41no—
384C8×C61—41no—
385C8×C61—41no—
386#92418—22no—
387#92418—41no—
388#92418—41no—
389#92418—41no—
390#22483—611nomaximal, Sylow
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—82no—
405C22×C61—82no—
406C22×C61C22×C22⋊C411yescharacteristic
407C22×C61C4×#4111yescharacteristic
408C22×C61#52011yescharacteristic
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—81no—
416C2×D61—81no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—42no—
420C4×C61#54611yescharacteristic
421C4×C61#54611yescharacteristic
422C4×C61#54711yescharacteristic
423C4×C61#54711yescharacteristic
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—42no—
430Dic61—42no—
431Dic61#41312yes—
432C2×#555—611no—
433D4×M16—611no—
434D4×M16—611no—
435#1997—611no—
436#1997—611no—
437#1900—611no—
438#1900—611no—
439#1900—611no—
440#1900D6111yescharacteristic, complemented
441#1822—611no—
442#1822—611no—
443#1800—611no—
444C4×#100—611no—
445#1742—611no—
446#1742—611no—
447C2×C61—21no—
448C2×C61—21no—
449C2×C61—41no—
450C2×C61—41no—
451C2×C61—82no—
452C2×C61#233911yescharacteristic
453C2×C61C2×#41311yescharacteristic
454C2×C61#288811yescharacteristic
455D61—41no—
456D61—41no—
457C22×M16—611no—
458C22×M16—611no—
459C22×M16—611no—
460C22×M16C2×D6111yescharacteristic
461#555—1221no—
462#555—1221no—
463#555—1221no—
464#555—1221no—
465#555—1221no—
466#555—1221no—
467#555—1221no—
468#555—1221no—
469C2×C4⋊Q8—611no—
470C2×#124—612no—
471C2×#124—612no—
472C2×#121—612no—
473C2×#121—611no—
474C2×#121C2×D6111yescharacteristic
475C2×C4×D4—611no—
476C2×C4×D4—611no—
477C2×#117—611no—
478C2×#117—611no—
479C2×#117—612no—
480#436—1221no—
481#436—1221no—
482#435—1221no—
483#435—1221no—
484#435—1221no—
485#435—1221no—
486C8×D4—1221no—
487C8×D4—1221no—
488#423—611no—
489#423—611no—
490C2×#100—611no—
491C2×#100—611no—
492C2×#100C2×D6111yescharacteristic
493C2×#100C2×D6111yescharacteristic
494#407—611no—
495#407—611no—
496#407—611no—
497#407C2×D6111yescharacteristic
498C4×M16—611no—
499C4×M16—611no—
500#343—611no—
501#343—611no—
502#343—611no—
503#343—611no—
504#343—611no—
505#343—611no—
506#343—611no—
507#343—611no—
508#343—611no—
509#343—611no—
510#343C2×D6111yescharacteristic
511#343C2×D6111yescharacteristic
512C61#2248311yescharacteristic, complemented, Sylow
513C22×Q8—612no—
514C22×D4—611no—
515C22×D4—612no—
516C22×D4C4×D6112yes—
517C22×D4C22×D6111yescharacteristic
518C23×C4—611no—
519C23×C4—612no—
520C23×C4C22×D6111yescharacteristic
521C2×M16—21no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—611no—
525C2×M16—611no—
526C2×M16—611no—
527C2×M16—611no—
528C2×M16—1221no—
529C2×M16—1221no—
530C2×M16—1221no—
531C2×M16—1222no—
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C2×M16—2441no—
536C2×M16—2441no—
537C2×M16C22×D6111yescharacteristic
538C2×M16C22×D6111yescharacteristic
539C2×M16C22×D6111yescharacteristic
540C2×M16C22×D6111yescharacteristic
541C22×C8—21no—
542C22×C8—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C4⋊Q8—1221no—
546C4⋊Q8—1221no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549#124—1222no—
550#124—1222no—
551#124—1222no—
552#124—1222no—
553#124—1222no—
554#124—1222no—
555#124—1222no—
556#124—1222no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121—1221no—
562#121—1221no—
563#121—1221no—
564#121—1221no—
565#121—1222no—
566#121—1222no—
567#121—1222no—
568#121—1222no—
569C4×D4—611no—
570C4×D4—611no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—1221no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1221no—
581#117—1222no—
582#117—1222no—
583#117—1222no—
584#117—1222no—
585#117—1221no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—612no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4C22×D6111yescharacteristic
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—612no—
601C2×C22⋊C4—612no—
602C2×C22⋊C4—612no—
603C2×C22⋊C4—612no—
604C2×C22⋊C4C4×D6112yes—
605C2×C42—611no—
606C2×C42—612no—
607C2×C42—612no—
608C4⋊C8—1221no—
609C4⋊C8—1221no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612#100—22no—
613#100—41no—
614#100—1222no—
615#100—2441no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624#97—1221no—
625#97—1221no—
626C4×C8—1221no—
627C4×C8—1221no—
628C24—611no—
629C24C2×C4×D6112yes—
630C24C2×C4×D6111yescharacteristic
631C2×Q8—1222no—
632C2×Q8—1222no—
633C2×Q8—4882no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—82no—
643C2×D4—611no—
644C2×D4—611no—
645C2×D4—611no—
646C2×D4—611no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—4882no—
650C2×D4—2442no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2444no—
671C22×C4C2×C4×D6111yescharacteristic
672C22×C4C2×C4×D6112yes—
673C22×C4D4×D6111yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C22×C4D4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4C23×D6111yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—612no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—1221no—
692M16—1221no—
693M16—1221no—
694M16—2442no—
695M16—2442no—
696M16—2442no—
697M16#1175822412yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—2442no—
708C2×C8—2442no—
709C2×C8—2442no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—611no—
715C4⋊C4—611no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—611no—
725C22⋊C4—611no—
726C22⋊C4—611no—
727C22⋊C4—611no—
728C22⋊C4—611no—
729C22⋊C4—611no—
730C22⋊C4—611no—
731C22⋊C4—611no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—1222no—
745C42—1222no—
746C42—1222no—
747C42—1222no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—41no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—611no—
758C23—611no—
759C23—1221no—
760C23—1221no—
761C23—2441no—
762C23—2441no—
763C23C22⋊C4×D6111yescharacteristic
764C23C22⋊C4×D6111yescharacteristic
765C23C22×C4×D6111yescharacteristic
766Q8—4882no—
767Q8—4882no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—82no—
773D4—82no—
774D4—1222no—
775D4—1222no—
776D4—4882no—
777D4—4882no—
778D4—2441no—
779D4—2441no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—1222no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—2444no—
812C2×C4—2441no—
813C2×C4—2444no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4C22⋊C4×D6111yescharacteristic
817C2×C4C22⋊C4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4#41×D6111yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982411yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C8—2441no—
831C8—2441no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—82no—
846C22—82no—
847C22—1221no—
848C22—1221no—
849C22—1221no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—4881no—
854C22—4881no—
855C22C2×C22⋊C4×D6111yescharacteristic
856C22C4×#1175822411yescharacteristic
857C22#1684024111yescharacteristic
858C4—21no—
859C4—21no—
860C4—42no—
861C4—612no—
862C4—1221no—
863C4—1221no—
864C4—1221no—
865C4—1221no—
866C4—1221no—
867C4—2442no—
868C4—2442no—
869C4#1684039911yescharacteristic
870C4#1684040111yescharacteristic
871C4#1684041011yescharacteristic
872C4#1684041211yescharacteristic
873C2—21no—
874C2—21no—
875C2—41no—
876C2—41no—
877C2—82no—
878C2—2441no—
879C2—2441no—
880C2#2144864511yescharacteristic
881C2#413×D6111yescharacteristic
882C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1900C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840476C2
cosocleC22×C4×C61C24
hypercenter#1900D61
hypocenterC61#22483
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. #21454551C2semidirect
4. #21446806C2semidirect
5. #21446806C2semidirect
6. #21446283C2semidirect
7. #21446279C2semidirect
8. #21446279C2semidirect
9. #21445901C2semidirect
10. #21445900C2semidirect
11. #21445809C2semidirect
12. #100×Dic61C2semidirect
13. #21445557C2semidirect
14. #21445556C2semidirect
15. C61×#1900C2semidirect
440. #1900D61semidirect
512. C61#22483semidirect

Maximal subgroups

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

subgroupindex
C2×#168404762
M16×C22⋊D612
#214545512
#214468062
#214462832
#214462792
#214459012
#214459002
#214458092
#100×Dic612
#214455572
#214455562
C61×#19002
#2248361