Finite Group Databasebeta

← #29718234

Subgroups — #29718234

Order 15616.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455440C211yesmaximal, characteristic, complemented
2C2×#16839930C211yesmaximal, characteristic, complemented
3#21455071C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21451573C211yesmaximal, characteristic, complemented
6#21447045C211yesmaximal, characteristic, complemented
7#21447026C211yesmaximal, characteristic, complemented
8#21446861C211yesmaximal, characteristic, complemented
9#21446832C211yesmaximal, characteristic, complemented
10#21446283C211yesmaximal, characteristic, complemented
11#21446268C211yesmaximal, characteristic, complemented
12#21446195C211yesmaximal, characteristic, complemented
13#21446052C211yesmaximal, characteristic, complemented
14#21445773C211yesmaximal, characteristic, complemented
15C61×#3488C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic, complemented
18C2×#14519802C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic, complemented
20C2×#14519773C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic, complemented
22C2×#14519736C2211yescharacteristic, complemented
23#16840013—21no—
24#16840010—21no—
25#16839996—21no—
26#16839993—21no—
27#16839930—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, complemented
37C2×#14519704C2211yescharacteristic, complemented
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40#16839766C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic, complemented
43#16839763C2211yescharacteristic, complemented
44C2×#14519694C2211yescharacteristic, complemented
45C2×#14519694C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic, complemented
47#16839678—22no—
48#16839670—22no—
49#16839665C2211yescharacteristic, complemented
50#16839663C2211yescharacteristic, complemented
51#16839627C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×H(5,𝔽2)×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C61×#550—21no—
59C61×#548—21no—
60C61×#546—21no—
61C61×#546—22no—
62D42×C61—22no—
63D42×C61—21no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#535—21no—
67C61×#535C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×#121×C61—21no—
71C2×#121×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—22no—
76#14519802—22no—
77#14519802—22no—
78#14519802—22no—
79#14519802—41no—
80#14519802—41no—
81#14519802—41no—
82C2×#11758201—21no—
83C2×#11758201—21no—
84C2×#11758201—21no—
85C2×#11758199—21no—
86C2×#11758199—21no—
87C2×#11758199—21no—
88C2×#11758194—21no—
89C2×#11758194—22no—
90C2×#11758194—41no—
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C22×#92418—21no—
96#14519773—22no—
97#14519773—41no—
98#14519751—21no—
99#14519751—21no—
100#14519751—21no—
101#14519751—21no—
102#14519736—22no—
103#14519736—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—22no—
108C2×#11758198—21no—
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#14519694—22no—
129#14519694—41no—
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519684—22no—
133H(5,𝔽2)×C61—22no—
134H(5,𝔽2)×C61—22no—
135H(5,𝔽2)×C61—41no—
136H(5,𝔽2)×C61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—22no—
142C2×#41×C61—22no—
143C2×#41×C61—41no—
144C2×#41×C61—41no—
145C2×#41×C61D411yescharacteristic, complemented
146C2×#41×C61D411yescharacteristic, complemented
147C2×#41×C61C2311yescharacteristic
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C22×Q8×C61D411yescharacteristic, complemented
151C22×D4×C61—21no—
152C22×D4×C61—22no—
153C22×D4×C61—22no—
154C22×D4×C61—21no—
155C22×D4×C61—21no—
156C22×D4×C61D412yes—
157C22×D4×C61D411yescharacteristic, complemented
158C22×D4×C61C2311yescharacteristic
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161#127×C61—22no—
162#127×C61—21no—
163#124×C61—22no—
164#124×C61—21no—
165#123×C61—22no—
166#123×C61—21no—
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61—21no—
169C22⋊Q8×C61—21no—
170C22⋊Q8×C61D411yescharacteristic, complemented
171C22⋊Q8×C61D411yescharacteristic, complemented
172#121×C61—22no—
173#121×C61—22no—
174#121×C61—22no—
175#121×C61—22no—
176#121×C61—22no—
177#121×C61—21no—
178#121×C61—21no—
179#121×C61—21no—
180#121×C61—22no—
181#121×C61—21no—
182#121×C61—21no—
183#121×C61—21no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61D411yescharacteristic, complemented
187#121×C61D411yescharacteristic, complemented
188#120×C61—22no—
189#120×C61—22no—
190#120×C61—22no—
191#120×C61—22no—
192#120×C61—21no—
193C4×Q8×C61—21no—
194C4×D4×C61—22no—
195C4×D4×C61—22no—
196C4×D4×C61—21no—
197C4×D4×C61—22no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200#117×C61—21no—
201#117×C61C2311yescharacteristic
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61D412yes—
206C24×C61—22no—
207C24×C61—21no—
208C24×C61C2×D412yes—
209C24×C61C2×D411yescharacteristic
210C23×D61—21no—
211#41×C61—21no—
212#41×C61—21no—
213#41×C61—22no—
214#41×C61—22no—
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—21no—
222#41×C61—21no—
223#41×C61—42no—
224#41×C61—42no—
225#41×C61—41no—
226#41×C61—41no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61C2×D412yes—
234#41×C61#4112yes—
235C2×Q8×C61—21no—
236C2×Q8×C61—22no—
237C2×Q8×C61—41no—
238C2×Q8×C61C2×D411yescharacteristic
239C2×Q8×C61C2×D411yescharacteristic
240C2×Q8×C61C2×D411yescharacteristic
241C2×D4×C61—21no—
242C2×D4×C61—22no—
243C2×D4×C61—22no—
244C2×D4×C61—22no—
245C2×D4×C61—22no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—22no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—21no—
255C2×D4×C61—22no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—41no—
264C2×D4×C61—42no—
265C2×D4×C61—42no—
266C2×D4×C61—42no—
267C2×D4×C61—42no—
268C2×D4×C61—44no—
269C2×D4×C61—44no—
270C2×D4×C61—42no—
271C2×D4×C61—42no—
272C2×D4×C61—82no—
273C2×D4×C61—84no—
274C2×D4×C61C2×D411yescharacteristic
275C2×D4×C61C2×D411yescharacteristic
276C2×D4×C61C2×D411yescharacteristic
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—22no—
283C22×C4×C61—21no—
284C22×C4×C61—22no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—42no—
290C22×C4×C61—42no—
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D411yescharacteristic
296C22×C4×C61C2×D412yes—
297C22×C4×C61C2411yescharacteristic
298C2×C22⋊D61—44no—
299C2×C22⋊D61—41no—
300C2×C22⋊D61—41no—
301C2×C22⋊D61—82no—
302C2×C22⋊D61—82no—
303C2×C22⋊D61—82no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—21no—
311C2×D244—21no—
312C2×D244—21no—
313C4⋊C4×C61—22no—
314C4⋊C4×C61—22no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—21no—
318C4⋊C4×C61—21no—
319C4⋊C4×C61C2×D411yescharacteristic
320C4⋊C4×C61C2×D411yescharacteristic
321C22⋊C4×C61—22no—
322C22⋊C4×C61—22no—
323C22⋊C4×C61—22no—
324C22⋊C4×C61—22no—
325C22⋊C4×C61—22no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—22no—
331C22⋊C4×C61—22no—
332C22⋊C4×C61—21no—
333C42×C61—22no—
334C42×C61—21no—
335C22⋊Dic61—42no—
336C22⋊Dic61—82no—
337#11758201—42no—
338#11758201—42no—
339#11758201—42no—
340#11758199—42no—
341#11758199—42no—
342#11758199—42no—
343#11758198—41no—
344#11758198—41no—
345#11758198—82no—
346C4⋊Dic61—21no—
347C4⋊Dic61—21no—
348C4⋊Dic61—42no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61C2×D412yescomplemented
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357#11758194—21no—
358#11758194—21no—
359#11758194—21no—
360#11758194—42no—
361#11758194C2×D412yescomplemented
362C2×#92418—21no—
363C2×#92418—21no—
364C2×#92418—21no—
365C2×#92418—21no—
366C2×#92418—42no—
367C23×C61—21no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—22no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—44no—
380C23×C61—42no—
381C23×C61—42no—
382C23×C61—81no—
383C23×C61—82no—
384C23×C61—82no—
385C23×C61#12011yescharacteristic
386C23×C61#12011yescharacteristic
387C23×C61C22×D411yescharacteristic
388C22×D61—42no—
389C22×D61—42no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393Q8×C61—21no—
394Q8×C61—21no—
395Q8×C61—21no—
396Q8×C61—21no—
397Q8×C61—21no—
398Q8×C61—42no—
399Q8×C61#12112yes—
400D4×C61—22no—
401D4×C61—22no—
402D4×C61—21no—
403D4×C61—21no—
404D4×C61—21no—
405D4×C61—21no—
406D4×C61—21no—
407D4×C61—42no—
408D4×C61—42no—
409D4×C61—44no—
410D4×C61—42no—
411D4×C61—44no—
412D4×C61—44no—
413D4×C61—42no—
414D4×C61—41no—
415D4×C61—41no—
416D4×C61—41no—
417D4×C61—41no—
418D4×C61—41no—
419D4×C61—41no—
420D4×C61—41no—
421D4×C61—41no—
422D4×C61—81no—
423D4×C61—82no—
424D4×C61—82no—
425D4×C61—82no—
426D4×C61—82no—
427D4×C61#12112yes—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—22no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—22no—
441C2×C4×C61—21no—
442C2×C4×C61—22no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—42no—
447C2×C4×C61—42no—
448C2×C4×C61—42no—
449C2×C4×C61—44no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—42no—
455C2×C4×C61—82no—
456C2×C4×C61#12011yescharacteristic
457C2×C4×C61#12011yescharacteristic
458C2×C4×C61C22×D411yescharacteristic
459C2×C4×C61C22×D411yescharacteristic
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C2×#4111yescharacteristic
462C2×C4×C61H(5,𝔽2)11yescharacteristic
463C2×C4×C61H(5,𝔽2)11yescharacteristic
464C22⋊D61—88no—
465C22⋊D61—82no—
466C22⋊D61—82no—
467C2×Dic61—22no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—42no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475D244—41no—
476D244—41no—
477D244—41no—
478D244—41no—
479#92418—22no—
480#92418—41no—
481#92418—41no—
482#92418—41no—
483#24468—611nomaximal, Sylow
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—22no—
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—41no—
494C22×C61—41no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—42no—
503C22×C61—41no—
504C22×C61—81no—
505C22×C61—81no—
506C22×C61—82no—
507C22×C61—82no—
508C22×C61—84no—
509C22×C61—164no—
510C22×C61C2×#12011yescharacteristic
511C22×C61D4211yescharacteristic
512C22×C61#54611yescharacteristic
513C2×D61—82no—
514C2×D61—82no—
515C2×D61—81no—
516C2×D61—81no—
517C2×D61—81no—
518C4×C61—21no—
519C4×C61—21no—
520C4×C61—22no—
521C4×C61—41no—
522C4×C61—41no—
523C4×C61—42no—
524C4×C61—41no—
525C4×C61—41no—
526C4×C61C2×#12111yescharacteristic
527C4×C61#53411yescharacteristic
528C4×C61D4211yescharacteristic
529C4×C61#54611yescharacteristic
530Dic61—42no—
531Dic61—81no—
532Dic61—81no—
533#3488D6111yescharacteristic, complemented
534#3055—611no—
535C2×#453—611no—
536#3006—611no—
537C2×#421—611no—
538#2619—611no—
539#2040—611no—
540#2037—611no—
541#2006—611no—
542#2002—611no—
543#1900—611no—
544#1897—611no—
545#1883—611no—
546#1860—611no—
547#1792—611no—
548C2×C61—21no—
549C2×C61—21no—
550C2×C61—41no—
551C2×C61—41no—
552C2×C61—42no—
553C2×C61—81no—
554C2×C61—82no—
555C2×C61—81no—
556C2×C61#241011yescharacteristic
557C2×C61#301911yescharacteristic
558C2×C61#302111yescharacteristic
559D61—161no—
560C2×H(5,𝔽2)C2×D6111yescharacteristic
561C22×#41C2×D6111yescharacteristic
562C2×AGL(1,ℤ/8)—611no—
563C2×AGL(1,ℤ/8)—611no—
564C2×AGL(1,ℤ/8)—611no—
565C22×M16—611no—
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C2×D6111yescharacteristic
574#535—21no—
575#535C2×D6111yescharacteristic
576C2×#127—611no—
577#525—21no—
578#525C2×D6111yescharacteristic
579C2×#121—21no—
580C2×#121—611no—
581C2×#121C2×D6111yescharacteristic
582#520C2×D6111yescharacteristic
583C2×#117—611no—
584#469—1221no—
585#468—1221no—
586#466—1221no—
587#465—1221no—
588#453—1224no—
589#449—1221no—
590#449—1221no—
591#448—1221no—
592#447—1221no—
593#428—611no—
594#421—1224no—
595C2×#104—611no—
596C2×#104—611no—
597C2×#104—611no—
598C2×#104—611no—
599C2×#104—611no—
600C2×#104—611no—
601#418—611no—
602#417—611no—
603#417—611no—
604#417—611no—
605C2×#100—611no—
606C2×#100—611no—
607#407—611no—
608#394—1222no—
609#392—1222no—
610#390—611no—
611#390—611no—
612#382—611no—
613#343—611no—
614#343—611no—
615#339—611no—
616#339—611no—
617C61#2446811yescharacteristic, complemented, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41C22⋊D6111yescharacteristic, complemented
631C2×#41C22⋊D6111yescharacteristic, complemented
632C2×#41C22×D6111yescharacteristic
633C2×#41C22×D6111yescharacteristic
634C2×#41C22×D6111yescharacteristic
635C22×Q8C22⋊D6111yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—611no—
642C22×D4—1221no—
643C22×D4—1222no—
644C22×D4C22⋊D6112yes—
645C22×D4C22⋊D6111yescharacteristic, complemented
646C22×D4C22×D6111yescharacteristic
647C23×C4—21no—
648C23×C4C22×D6111yescharacteristic
649AGL(1,ℤ/8)—1222no—
650AGL(1,ℤ/8)—1222no—
651AGL(1,ℤ/8)—1222no—
652AGL(1,ℤ/8)—2441no—
653AGL(1,ℤ/8)—2441no—
654AGL(1,ℤ/8)—2441no—
655C2×SD16—1221no—
656C2×SD16—1221no—
657C2×SD16—1221no—
658C2×D8—1221no—
659C2×D8—1221no—
660C2×D8—1221no—
661C2×M16—611no—
662C2×M16—611no—
663C2×M16—611no—
664C2×M16—611no—
665C2×M16—1221no—
666C2×M16—1222no—
667C2×M16—2441no—
668C22×C8—1221no—
669#127—22no—
670#127—21no—
671#127—1222no—
672#127—2441no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8C22⋊D6111yescharacteristic, complemented
681C22⋊Q8C22⋊D6111yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—1221no—
697#121—1221no—
698#121—1221no—
699#121—1221no—
700#121C22⋊D6111yescharacteristic, complemented
701#121C22⋊D6111yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—1222no—
716#117—2441no—
717#117C22×D6111yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—611no—
720C2×C4⋊C4—1221no—
721C2×C4⋊C4C22×D6111yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1221no—
726C2×C22⋊C4—1221no—
727C2×C22⋊C4C22⋊D6112yes—
728C2×C42—611no—
729C2×C42—611no—
730#107—1221no—
731#106—1221no—
732#104—614no—
733#104—1222no—
734#104—1222no—
735#104—1222no—
736#104—1222no—
737#104—2441no—
738#103—1221no—
739#103—1221no—
740#103—1221no—
741#102—1221no—
742#102—1221no—
743#102—1221no—
744#102—1221no—
745#102—1221no—
746#100—1222no—
747#100—2441no—
748C22⋊C8—1221no—
749C22⋊C8—1221no—
750#95—1222no—
751C24—22no—
752C24—21no—
753C24—1221no—
754C24C2×C22⋊D6112yes—
755C24C2×C22⋊D6111yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41D4×D6112yes—
779#41#1175822412yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×C22⋊D6111yescharacteristic
784C2×Q8C2×C22⋊D6111yescharacteristic
785C2×Q8C2×C22⋊D6111yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—41no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—82no—
818C2×D4—84no—
819C2×D4—1221no—
820C2×D4—1221no—
821C2×D4—1221no—
822C2×D4—1221no—
823C2×D4—1221no—
824C2×D4—1221no—
825C2×D4—4882no—
826C2×D4—4882no—
827C2×D4—4882no—
828C2×D4—2444no—
829C2×D4—2441no—
830C2×D4—2441no—
831C2×D4C2×C22⋊D6111yescharacteristic
832C2×D4C2×C22⋊D6111yescharacteristic
833C2×D4C2×C22⋊D6111yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4C2×C22⋊D6111yescharacteristic
852C22×C4C2×C22⋊D6111yescharacteristic
853C22×C4C2×C22⋊D6111yescharacteristic
854C22×C4C2×C22⋊D6111yescharacteristic
855C22×C4C2×C22⋊D6111yescharacteristic
856C22×C4C2×C22⋊D6112yes—
857C22×C4C23×D6111yescharacteristic
858SD16—2442no—
859SD16—2442no—
860SD16—2442no—
861D8—2442no—
862D8—2442no—
863D8—2442no—
864M16—612no—
865M16—1221no—
866M16—1221no—
867M16—1221no—
868M16—1221no—
869M16—1221no—
870M16—1221no—
871M16—1221no—
872M16—2442no—
873C2×C8—1221no—
874C2×C8—1221no—
875C2×C8—1221no—
876C2×C8—1221no—
877C2×C8—2442no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—2442no—
887C4⋊C4C2×C22⋊D6111yescharacteristic
888C4⋊C4C2×C22⋊D6111yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—4882no—
902C22⋊C4—4882no—
903C22⋊C4—2442no—
904C22⋊C4—2441no—
905C22⋊C4—2441no—
906C42—22no—
907C42—21no—
908C42—612no—
909C42—1221no—
910C42—1221no—
911C42—1221no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—81no—
928C23—82no—
929C23—82no—
930C23—2442no—
931C23—2442no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23#1451974611yescharacteristic
936C23#1451974611yescharacteristic
937C23C22×C22⋊D6111yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#1451974912yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—81no—
968D4—82no—
969D4—82no—
970D4—82no—
971D4—82no—
972D4—4882no—
973D4—4882no—
974D4—4888no—
975D4—2441no—
976D4—2441no—
977D4—2441no—
978D4—2441no—
979D4#1451974912yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—44no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—42no—
1007C2×C4—82no—
1008C2×C4—1222no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2442no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4#1451974611yescharacteristic
1017C2×C4#1451974611yescharacteristic
1018C2×C4C2×D4×D6111yescharacteristic
1019C2×C4C22×C22⋊D6111yescharacteristic
1020C2×C4C22×C22⋊D6111yescharacteristic
1021C2×C4C2×#1175822411yescharacteristic
1022C2×C4#1451982211yescharacteristic
1023C2×C4#1451982211yescharacteristic
1024C8—1222no—
1025C8—2441no—
1026C8—2441no—
1027C8—2441no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—22no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—84no—
1053C22—164no—
1054C22—4882no—
1055C22—4882no—
1056C22—4881no—
1057C22—4881no—
1058C22—4881no—
1059C22C2×#1451974611yescharacteristic
1060C22D4×C22⋊D6111yescharacteristic
1061C22#1684040611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—4881no—
1071C4—4881no—
1072C4—2442no—
1073C4C2×#1451974911yescharacteristic
1074C4#1684032111yescharacteristic
1075C4D4×C22⋊D6111yescharacteristic
1076C4#1684040611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—9761no—
1086C2#2144919311yescharacteristic
1087C2#2145517611yescharacteristic
1088C2#2145519111yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24468
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #21455440C2semidirect
2. C2×#16839930C2semidirect
3. #21455071C2semidirect
4. C2×#16839779C2semidirect
5. #21451573C2semidirect
6. #21447045C2semidirect
7. #21447026C2semidirect
8. #21446861C2semidirect
9. #21446832C2semidirect
10. #21446283C2semidirect
11. #21446268C2semidirect
12. #21446195C2semidirect
13. #21446052C2semidirect
14. #21445773C2semidirect
15. C61×#3488C2semidirect
17. C2×#14519802C22semidirect
18. C2×#14519802C22semidirect
19. C22×#11758194C22semidirect
20. C2×#14519773C22semidirect
21. C2×#14519751C22semidirect
22. C2×#14519736C22semidirect
32. #16839805C22semidirect
36. C2×#14519704C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. #16839766C22semidirect
42. #16839763C22semidirect
43. #16839763C22semidirect
44. C2×#14519694C22semidirect
45. C2×#14519694C22semidirect
46. #16839726C22semidirect
49. #16839665C22semidirect
50. #16839663C22semidirect
51. #16839627C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
119. #14519704D4semidirect
145. C2×#41×C61D4semidirect
146. C2×#41×C61D4semidirect
150. C22×Q8×C61D4semidirect
157. C22×D4×C61D4semidirect
170. C22⋊Q8×C61D4semidirect
171. C22⋊Q8×C61D4semidirect
186. #121×C61D4semidirect
187. #121×C61D4semidirect
352. C4×Dic61C2×D4semidirect
361. #11758194C2×D4semidirect
533. #3488D61semidirect
617. C61#24468semidirect
630. C2×#41C22⋊D61semidirect
631. C2×#41C22⋊D61semidirect
635. C22×Q8C22⋊D61semidirect
645. C22×D4C22⋊D61semidirect
680. C22⋊Q8C22⋊D61semidirect
681. C22⋊Q8C22⋊D61semidirect
700. #121C22⋊D61semidirect
701. #121C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214554402
C2×#168399302
#214550712
C2×#168397792
#214515732
#214470452
#214470262
#214468612
#214468322
#214462832
#214462682
#214461952
#214460522
#214457732
C61×#34882
#2446861