Finite Group Databasebeta

← #29718249

Subgroups — #29718249

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455440C211yesmaximal, characteristic, complemented
2C2×#16839935C211yesmaximal, characteristic, complemented
3#21455071C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21451581C211yesmaximal, characteristic, complemented
6#21447040C211yesmaximal, characteristic, complemented
7#21447033C211yesmaximal, characteristic, complemented
8#21446861C211yesmaximal, characteristic, complemented
9#21446839C211yesmaximal, characteristic, complemented
10#21446288C211yesmaximal, characteristic, complemented
11#21446268C211yesmaximal, characteristic, complemented
12#21446195C211yesmaximal, characteristic, complemented
13#21446045C211yesmaximal, characteristic, complemented
14#21445778C211yesmaximal, characteristic, complemented
15C61×#3489C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic
18C2×#14519802C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20C2×#14519766C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16840013—21no—
24#16840010—21no—
25#16839996—21no—
26#16839993—21no—
27#16839935—24no—
28#16839907—21no—
29#16839907—21no—
30#16839901—21no—
31#16839896—21no—
32#16839805C2211yescharacteristic, complemented
33#16839779—24no—
34C2×#14519704C2211yescharacteristic
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40#16839766C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44C2×#14519696C2211yescharacteristic, complemented
45C2×#14519696C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic
47#16839684—22no—
48#16839677—22no—
49#16839669C2211yescharacteristic, complemented
50#16839663C2211yescharacteristic, complemented
51#16839631C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×2−1+4×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58D4×Q8×C61—21no—
59C61×#548—21no—
60C61×#547—21no—
61C61×#547—22no—
62C61×#546—21no—
63C61×#546—22no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#536—21no—
67C61×#536C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75#14519802—22no—
76#14519802—22no—
77#14519802—22no—
78#14519802—41no—
79#14519802—41no—
80#14519802—41no—
81C2×#11758201—21no—
82C2×#11758201—21no—
83C2×#11758201—21no—
84C2×#11758199—21no—
85C2×#11758199—21no—
86C2×#11758199—21no—
87C2×#11758194—21no—
88C2×#11758194—22no—
89C2×#11758194—41no—
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C22×#92418—21no—
95#14519766—22no—
96#14519766—41no—
97#14519751—21no—
98#14519751—21no—
99#14519751—21no—
100#14519751—21no—
101#14519736—22no—
102#14519736—41no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—22no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519710—21no—
113#14519708—21no—
114#14519704—22no—
115#14519704—22no—
116#14519704—22no—
117#14519704—22no—
118#14519704—41no—
119#14519704D414yescomplemented
120#14519701—21no—
121#14519701—21no—
122#14519701—21no—
123#14519698—21no—
124#14519698—21no—
125#14519698—21no—
126#14519697—21no—
127#14519697—21no—
128#14519696—22no—
129#14519696—41no—
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519684—22no—
1332−1+4×C61—22no—
1342−1+4×C61—22no—
1352−1+4×C61—41no—
1362−1+4×C61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—22no—
141C2×#41×C61—21no—
142C2×#41×C61—22no—
143C2×#41×C61—22no—
144C2×#41×C61—41no—
145C2×#41×C61—41no—
146C2×#41×C61D411yescharacteristic
147C2×#41×C61D411yescharacteristic
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151C22×Q8×C61—21no—
152C22×Q8×C61—21no—
153C22×Q8×C61D411yescharacteristic
154C22×Q8×C61C2311yescharacteristic
155C22×D4×C61—21no—
156C22×D4×C61D411yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C4⋊Q8×C61—22no—
160C4⋊Q8×C61—21no—
161#124×C61—22no—
162#124×C61—21no—
163#123×C61—22no—
164#123×C61—22no—
165#123×C61—22no—
166#123×C61—22no—
167#123×C61—21no—
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61—21no—
172C22⋊Q8×C61—21no—
173C22⋊Q8×C61—21no—
174C22⋊Q8×C61—21no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177C22⋊Q8×C61—21no—
178C22⋊Q8×C61—21no—
179C22⋊Q8×C61D411yescharacteristic
180C22⋊Q8×C61D411yescharacteristic
181#121×C61—22no—
182#121×C61—22no—
183#121×C61—22no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61—22no—
187#121×C61D411yescharacteristic
188#121×C61D411yescharacteristic
189#120×C61—22no—
190#120×C61—21no—
191C4×Q8×C61—21no—
192C4×D4×C61—22no—
193C4×D4×C61—22no—
194C4×D4×C61—21no—
195C4×D4×C61—22no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61—21no—
199#117×C61C2311yescharacteristic
200C2×C4⋊C4×C61—22no—
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61D412yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61D412yes—
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—22no—
212#41×C61—22no—
213#41×C61—21no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—42no—
222#41×C61—42no—
223#41×C61—41no—
224#41×C61—41no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—44no—
230#41×C61—44no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61C2×D412yes—
234#41×C61#4112yes—
235C2×Q8×C61—22no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—21no—
243C2×Q8×C61—22no—
244C2×Q8×C61—41no—
245C2×Q8×C61—42no—
246C2×Q8×C61—42no—
247C2×Q8×C61—42no—
248C2×Q8×C61—42no—
249C2×Q8×C61C2×D411yescharacteristic
250C2×Q8×C61C2×D411yescharacteristic
251C2×Q8×C61C2×D411yescharacteristic
252C2×D4×C61—21no—
253C2×D4×C61—22no—
254C2×D4×C61—22no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—22no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—41no—
264C2×D4×C61—42no—
265C2×D4×C61—42no—
266C2×D4×C61C2×D411yescharacteristic
267C2×D4×C61C2×D411yescharacteristic
268C2×D4×C61C2×D411yescharacteristic
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—22no—
275C22×C4×C61—22no—
276C22×C4×C61—21no—
277C22×C4×C61—22no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—42no—
283C22×C4×C61—42no—
284C22×C4×C61C2×D412yes—
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D412yes—
291C22×C4×C61C2411yescharacteristic
292C2×C22⋊D61—41no—
293C2×C22⋊D61—41no—
294C2×C22⋊D61—82no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C2×D244—21no—
299C2×D244—21no—
300C2×D244—21no—
301C2×D244—21no—
302C2×D244—21no—
303C2×D244—21no—
304C4⋊C4×C61—22no—
305C4⋊C4×C61—22no—
306C4⋊C4×C61—22no—
307C4⋊C4×C61—22no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—22no—
310C4⋊C4×C61—22no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61C2×D411yescharacteristic
315C4⋊C4×C61C2×D411yescharacteristic
316C22⋊C4×C61—22no—
317C22⋊C4×C61—22no—
318C22⋊C4×C61—22no—
319C22⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—22no—
323C22⋊C4×C61—22no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C42×C61—22no—
329C42×C61—21no—
330C22⋊Dic61—42no—
331#11758201—42no—
332#11758201—42no—
333#11758201—42no—
334#11758199—42no—
335#11758199—42no—
336#11758199—42no—
337#11758198—44no—
338#11758198—41no—
339#11758198—41no—
340#11758198—82no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—42no—
344#11758196—82no—
345C4×Dic61—21no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61C2×D412yes—
349#11758194—21no—
350#11758194—21no—
351#11758194—21no—
352#11758194—21no—
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—42no—
357#11758194C2×D412yes—
358C2×#92418—21no—
359C2×#92418—21no—
360C2×#92418—21no—
361C2×#92418—21no—
362C2×#92418—42no—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—42no—
371C23×C61—42no—
372C23×C61—81no—
373C23×C61#12011yescharacteristic
374C23×C61#12011yescharacteristic
375C23×C61C22×D411yescharacteristic
376C22×D61—42no—
377C22×D61—42no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381Q8×C61—21no—
382Q8×C61—21no—
383Q8×C61—21no—
384Q8×C61—21no—
385Q8×C61—21no—
386Q8×C61—42no—
387Q8×C61—44no—
388Q8×C61—41no—
389Q8×C61—41no—
390Q8×C61—41no—
391Q8×C61—41no—
392Q8×C61#12112yes—
393D4×C61—22no—
394D4×C61—22no—
395D4×C61—21no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—42no—
403D4×C61—42no—
404D4×C61—44no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—81no—
410D4×C61—82no—
411D4×C61#12112yes—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—21no—
418C2×C4×C61—21no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—22no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—22no—
425C2×C4×C61—21no—
426C2×C4×C61—22no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—22no—
430C2×C4×C61—21no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—42no—
434C2×C4×C61—42no—
435C2×C4×C61—42no—
436C2×C4×C61—44no—
437C2×C4×C61—44no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—42no—
443C2×C4×C61—82no—
444C2×C4×C61#12011yescharacteristic
445C2×C4×C61#12011yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C22×D411yescharacteristic
448C2×C4×C61C22×D411yescharacteristic
449C2×C4×C61C2×#4111yescharacteristic
450C2×C4×C61H(5,𝔽2)11yescharacteristic
451C2×C4×C61H(5,𝔽2)11yescharacteristic
452C22⋊D61—82no—
453C22⋊D61—82no—
454C2×Dic61—22no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—42no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462D244—41no—
463D244—41no—
464D244—41no—
465D244—41no—
466#92418—22no—
467#92418—41no—
468#92418—41no—
469#92418—41no—
470#24469—611nomaximal, Sylow
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—22no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—81no—
489C22×C61—81no—
490C22×C61—84no—
491C22×C61C2×#12011yescharacteristic
492C22×C61D4211yescharacteristic
493C22×C61#54611yescharacteristic
494C2×D61—82no—
495C2×D61—82no—
496C2×D61—81no—
497C2×D61—81no—
498C2×D61—81no—
499C4×C61—21no—
500C4×C61—21no—
501C4×C61—22no—
502C4×C61—42no—
503C4×C61—41no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—42no—
507C4×C61—41no—
508C4×C61C2×#12111yescharacteristic
509C4×C61#53411yescharacteristic
510C4×C61D4211yescharacteristic
511C4×C61#54611yescharacteristic
512Dic61—42no—
513Dic61—81no—
514Dic61—81no—
515#3489D6111yescharacteristic, complemented
516#3055—611no—
517C2×#454—611no—
518#3006—611no—
519C2×#421—611no—
520#2620—611no—
521#2039—611no—
522#2038—611no—
523#2006—611no—
524#2003—611no—
525#1901—611no—
526#1897—611no—
527#1883—611no—
528#1859—611no—
529#1793—611no—
530C2×C61—21no—
531C2×C61—21no—
532C2×C61—41no—
533C2×C61—41no—
534C2×C61—42no—
535C2×C61—81no—
536C2×C61—81no—
537C2×C61#241011yescharacteristic
538C2×C61#302011yescharacteristic
539C2×C61#302111yescharacteristic
540D61—161no—
541C2×2−1+4C2×D6111yescharacteristic
542C22×#41C2×D6111yescharacteristic
543C2×AGL(1,ℤ/8)—611no—
544C2×AGL(1,ℤ/8)—611no—
545C2×AGL(1,ℤ/8)—611no—
546C22×M16—611no—
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C2×D6111yescharacteristic
555#536—21no—
556#536C2×D6111yescharacteristic
557C2×#124—611no—
558#525—21no—
559#525C2×D6111yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C2×D6111yescharacteristic
562C2×#121—611no—
563#520C2×D6111yescharacteristic
564C2×#117—611no—
565#469—1221no—
566#468—1221no—
567#466—1221no—
568#465—1221no—
569#454—1224no—
570#449—1221no—
571#449—1221no—
572#448—1221no—
573#447—1221no—
574#428—611no—
575#421—1224no—
576C2×#104—611no—
577C2×#104—611no—
578C2×#104—611no—
579C2×#104—611no—
580C2×#104—611no—
581C2×#104—611no—
582#418—611no—
583#417—611no—
584#417—611no—
585#417—611no—
586C2×#101—611no—
587C2×#101—611no—
588#407—611no—
589#396—1222no—
590#394—1222no—
591#391—611no—
592#390—611no—
593#384—611no—
594#343—611no—
595#343—611no—
596#339—611no—
597#339—611no—
598C61#2446911yescharacteristic, complemented, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41C22⋊D6111yescharacteristic
613C2×#41C22⋊D6111yescharacteristic
614C2×#41C22×D6111yescharacteristic
615C2×#41C22×D6111yescharacteristic
616C2×#41C22×D6111yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8C22⋊D6111yescharacteristic
620C22×Q8C22×D6111yescharacteristic
621C22×D4—21no—
622C22×D4—611no—
623C22×D4—1221no—
624C22×D4C22⋊D6111yescharacteristic
625C23×C4—21no—
626C23×C4C22×D6111yescharacteristic
627AGL(1,ℤ/8)—1222no—
628AGL(1,ℤ/8)—1222no—
629AGL(1,ℤ/8)—1222no—
630AGL(1,ℤ/8)—2441no—
631AGL(1,ℤ/8)—2441no—
632AGL(1,ℤ/8)—2441no—
633C2×SD16—1221no—
634C2×SD16—1221no—
635C2×SD16—1221no—
636C2×D8—1221no—
637C2×D8—1221no—
638C2×D8—1221no—
639C2×M16—611no—
640C2×M16—611no—
641C2×M16—611no—
642C2×M16—611no—
643C2×M16—1221no—
644C2×M16—1222no—
645C2×M16—2441no—
646C22×C8—1221no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—1222no—
652#124—2441no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8C22⋊D6111yescharacteristic
670C22⋊Q8C22⋊D6111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—1221no—
678#121—1221no—
679#121—1221no—
680#121—1221no—
681#121C22⋊D6111yescharacteristic
682#121C22⋊D6111yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—1222no—
694#117—2441no—
695#117C22×D6111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—611no—
699C2×C4⋊C4—1222no—
700C2×C4⋊C4—1221no—
701C2×C4⋊C4C22⋊D6112yes—
702C2×C4⋊C4C22×D6111yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4C22⋊D6112yes—
709C2×C42—611no—
710C2×C42—611no—
711#107—1221no—
712#106—1221no—
713#104—614no—
714#104—1222no—
715#104—1222no—
716#104—1222no—
717#104—1222no—
718#104—2441no—
719#103—1221no—
720#103—1221no—
721#103—1221no—
722#102—1221no—
723#102—1221no—
724#102—1221no—
725#102—1221no—
726#102—1221no—
727#101—1222no—
728#101—2441no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731#95—1222no—
732C24—21no—
733C24—1221no—
734C24C2×C22⋊D6111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41D4×D6112yes—
760#41#1175822412yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×C22⋊D6111yescharacteristic
776C2×Q8C2×C22⋊D6111yescharacteristic
777C2×Q8C2×C22⋊D6111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—1221no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—4882no—
799C2×D4—2441no—
800C2×D4—2441no—
801C2×D4C2×C22⋊D6111yescharacteristic
802C2×D4C2×C22⋊D6111yescharacteristic
803C2×D4C2×C22⋊D6111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4C2×C22⋊D6112yes—
823C22×C4C2×C22⋊D6111yescharacteristic
824C22×C4C2×C22⋊D6111yescharacteristic
825C22×C4C2×C22⋊D6111yescharacteristic
826C22×C4C2×C22⋊D6111yescharacteristic
827C22×C4C2×C22⋊D6111yescharacteristic
828C22×C4C2×C22⋊D6112yes—
829C22×C4C23×D6111yescharacteristic
830SD16—2442no—
831SD16—2442no—
832SD16—2442no—
833D8—2442no—
834D8—2442no—
835D8—2442no—
836M16—612no—
837M16—1221no—
838M16—1221no—
839M16—1221no—
840M16—1221no—
841M16—1221no—
842M16—1221no—
843M16—1221no—
844M16—2442no—
845C2×C8—1221no—
846C2×C8—1221no—
847C2×C8—1221no—
848C2×C8—1221no—
849C2×C8—2442no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—4882no—
863C4⋊C4—2442no—
864C4⋊C4C2×C22⋊D6111yescharacteristic
865C4⋊C4C2×C22⋊D6111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—4882no—
879C22⋊C4—2444no—
880C22⋊C4—2442no—
881C22⋊C4—2441no—
882C22⋊C4—2441no—
883C42—22no—
884C42—21no—
885C42—612no—
886C42—1221no—
887C42—1221no—
888C42—1221no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—81no—
899C23—2442no—
900C23—2442no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23#1451974611yescharacteristic
905C23#1451974611yescharacteristic
906C23C22×C22⋊D6111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#1451974912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—81no—
936D4—82no—
937D4—4882no—
938D4—4882no—
939D4—2441no—
940D4—2441no—
941D4—2441no—
942D4—2441no—
943D4#1451974912yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—42no—
975C2×C4—82no—
976C2×C4—1222no—
977C2×C4—2441no—
978C2×C4—2442no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4#1451974611yescharacteristic
985C2×C4#1451974611yescharacteristic
986C2×C4C2×D4×D6111yescharacteristic
987C2×C4C22×C22⋊D6111yescharacteristic
988C2×C4C22×C22⋊D6111yescharacteristic
989C2×C4C2×#1175822411yescharacteristic
990C2×C4#1451982211yescharacteristic
991C2×C4#1451982211yescharacteristic
992C8—1222no—
993C8—2441no—
994C8—2441no—
995C8—2441no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—84no—
1016C22—4882no—
1017C22—4882no—
1018C22—4881no—
1019C22—4881no—
1020C22—4881no—
1021C22C2×#1451974611yescharacteristic
1022C22D4×C22⋊D6111yescharacteristic
1023C22#1684040611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—41no—
1028C4—42no—
1029C4—41no—
1030C4—42no—
1031C4—41no—
1032C4—41no—
1033C4—4881no—
1034C4—4881no—
1035C4—2442no—
1036C4C2×#1451974911yescharacteristic
1037C4#1684032111yescharacteristic
1038C4D4×C22⋊D6111yescharacteristic
1039C4#1684040611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—9761no—
1048C2#2144919311yescharacteristic
1049C2#2145518311yescharacteristic
1050C2#2145519111yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3489C2
socleC22×C61C2×#120
hypercenter#3489D61
hypocenterC61#24469
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #21455440C2semidirect
2. C2×#16839935C2semidirect
3. #21455071C2semidirect
4. C2×#16839779C2semidirect
5. #21451581C2semidirect
6. #21447040C2semidirect
7. #21447033C2semidirect
8. #21446861C2semidirect
9. #21446839C2semidirect
10. #21446288C2semidirect
11. #21446268C2semidirect
12. #21446195C2semidirect
13. #21446045C2semidirect
14. #21445778C2semidirect
15. C61×#3489C2semidirect
18. C2×#14519802C22semidirect
20. C2×#14519766C22semidirect
32. #16839805C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. #16839766C22semidirect
43. #16839763C22semidirect
44. C2×#14519696C22semidirect
45. C2×#14519696C22semidirect
49. #16839669C22semidirect
50. #16839663C22semidirect
51. #16839631C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
119. #14519704D4semidirect
515. #3489D61semidirect
598. C61#24469semidirect

Maximal subgroups

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

subgroupindex
#214554402
C2×#168399352
#214550712
C2×#168397792
#214515812
#214470402
#214470332
#214468612
#214468392
#214462882
#214462682
#214461952
#214460452
#214457782
C61×#34892
#2446961