Finite Group Databasebeta

← #29656431

Subgroups — #29656431

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456538C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic, complemented
3#21455283C211yesmaximal, characteristic, complemented
4#21445075C211yesmaximal, characteristic, complemented
5#21445054C211yesmaximal, characteristic, complemented
6#21445047C211yesmaximal, characteristic, complemented
7#21445026C211yesmaximal, characteristic, complemented
8#21444929C211yesmaximal, characteristic, complemented
9#21444908C211yesmaximal, characteristic, complemented
10#21444902C211yesmaximal, characteristic, complemented
11#21444891C211yesmaximal, characteristic, complemented
12#21444549C211yesmaximal, characteristic, complemented
13#21444262C211yesmaximal, characteristic, complemented
14#21444258C211yesmaximal, characteristic, complemented
15C61×#3475C211yesmaximal, characteristic, complemented
16C2×#14519803—21no—
17#16840312C2211yescharacteristic
18#16840165C2211yescharacteristic, complemented
19#16840136C2211yescharacteristic, complemented
20#16840112C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic, complemented
22#16840086—21no—
23#16840047C2211yescharacteristic, complemented
24#16840042C2211yescharacteristic, complemented
25#16840010—22no—
26#16839977—21no—
27#16839977—21no—
28#16839967C2211yescharacteristic
29#16839967C2211yescharacteristic
30#16839962C2211yescharacteristic, complemented
31#16839957C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic, complemented
34#16839907—21no—
35#16839872—21no—
36#16839860—21no—
37#16839860—22no—
38#16839819C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839761—21no—
41C4×#11758194C2211yescharacteristic
42#16839511C2211yescharacteristic, complemented
43#16839511C2211yescharacteristic, complemented
44#16839508C2211yescharacteristic, complemented
45#16839508C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#556C2211yescharacteristic
55C61×#555C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#553—21no—
58C61×#552—21no—
59C61×#552—21no—
60C61×#551—22no—
61C61×#547C2211yescharacteristic
62C61×#546—21no—
63C61×#533C2211yescharacteristic
64C61×#529—22no—
65C61×#529—21no—
66C61×#525—21no—
67C4×#41×C61—21no—
68C4×#41×C61C2211yescharacteristic
69C2×C4×D4×C61C2211yescharacteristic
70C2×#117×C61—21no—
71C2×#11758222—21no—
72#14519803—44no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758201—21no—
76C2×#11758201—22no—
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244—21no—
89#14519710—22no—
90#14519710—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—22no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—22no—
107C22⋊#92418—21no—
108#14519688—21no—
109#14519688—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61—21no—
113C2×#41×C61D411yescharacteristic
114C22×D4×C61D411yescharacteristic
115C23×C4×C61—21no—
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#126×C61—22no—
119#126×C61—22no—
120#126×C61—22no—
121#125×C61—22no—
122#125×C61—21no—
123#125×C61—21no—
124#124×C61—22no—
125#124×C61—21no—
126#123×C61—22no—
127#123×C61—22no—
128#123×C61—22no—
129#123×C61—22no—
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61D412yes—
136#121×C61—22no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#120×C61—22no—
141C4×Q8×C61—21no—
142C4×Q8×C61—21no—
143C4×Q8×C61D412yes—
144C4×Q8×C61D411yescharacteristic
145C4×Q8×C61C2311yescharacteristic
146C4×D4×C61—22no—
147C4×D4×C61—22no—
148C4×D4×C61—22no—
149C4×D4×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C4×D4×C61D411yescharacteristic
155C4×D4×C61D411yescharacteristic
156C4×D4×C61D411yescharacteristic
157C4×D4×C61C2311yescharacteristic
158C4×D4×C61C2311yescharacteristic
159C4×D4×C61C2311yescharacteristic
160#117×C61—22no—
161#117×C61—22no—
162#117×C61—22no—
163#117×C61—21no—
164#117×C61—21no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D411yescharacteristic
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—22no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C24×C61—21no—
178#41×C61—41no—
179#41×C61—41no—
180#41×C61—42no—
181#41×C61—42no—
182C2×Q8×C61—21no—
183C2×Q8×C61C2×D411yescharacteristic
184C2×Q8×C61C2×D412yes—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—41no—
191C2×D4×C61C2×D411yescharacteristic
192C2×D4×C61C2×D411yescharacteristic
193C2×D4×C61C2×D411yescharacteristic
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C2×C22⋊D61—41no—
210#11758222—42no—
211#11758222—42no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×C4×D61—41no—
216C2×Dic122—21no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D411yescharacteristic
230C4⋊C4×C61C2×D411yescharacteristic
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C4⋊C4×C61C2×D412yes—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C42×C61—22no—
249C42×C61—22no—
250C42×C61—21no—
251C42×C61—22no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61C2×D411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2411yescharacteristic
258#11758201—44no—
259#11758201—42no—
260#11758200—42no—
261#11758200—42no—
262#11758199—42no—
263#11758199—42no—
264#11758199—42no—
265#11758198—41no—
266#11758198—41no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269#11758194—42no—
270#11758194—42no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—81no—
283C23×C61#12011yescharacteristic
284C22×D61—41no—
285Q8×C61—21no—
286Q8×C61—21no—
287Q8×C61—42no—
288Q8×C61—41no—
289Q8×C61—41no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—21no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—44no—
298D4×C61—82no—
299D4×C61AGL(1,ℤ/8)12yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—44no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—81no—
324C2×C4×C61—82no—
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
327C2×C4×C61#12011yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C22⋊D61—82no—
332C2×Dic61—41no—
333D244—42no—
334D244—41no—
335D244—41no—
336D244—41no—
337D244—41no—
338C4×D61—82no—
339Dic122—41no—
340Dic122—41no—
341#92418—22no—
342#92418—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#18560—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—22no—
351C22×C61—21no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—84no—
361C22×C61C2×#12011yescharacteristic
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
377C4×C61#57511yescharacteristic
378C4×C61#57511yescharacteristic
379C4×C61#57511yescharacteristic
380Dic61—81no—
381#3475D6111yescharacteristic, complemented
382#3182—611no—
383#3115—611no—
384#3036—611no—
385#1650—611no—
386#1647—611no—
387#1646—611no—
388#1643—611no—
389#1628—611no—
390#1625—611no—
391#1624—611no—
392#1622—611no—
393#1559—611no—
394#1490—611no—
395#1489—611no—
396C2×C61—41no—
397C2×C61—42no—
398C2×C61—81no—
399C2×C61—81no—
400C2×C61#300511yescharacteristic
401C2×C61#300611yescharacteristic
402C2×C61#301811yescharacteristic
403D61—161no—
404C2×AGL(1,ℤ/8)—1221no—
405#556C2×D6111yescharacteristic
406#555C2×D6111yescharacteristic
407#554C2×D6111yescharacteristic
408#553—21no—
409#552—21no—
410#552—21no—
411#551—22no—
412#547C2×D6111yescharacteristic
413#546—21no—
414#533C2×D6111yescharacteristic
415#532—611no—
416#529—22no—
417#529—21no—
418#525—21no—
419C4×#41—21no—
420C4×#41C2×D6111yescharacteristic
421C2×C4×D4C2×D6111yescharacteristic
422C2×#117—21no—
423#500—611no—
424#492—611no—
425#487—611no—
426#486—611no—
427#482—1221no—
428#475—611no—
429#474—611no—
430#468—1222no—
431#463—1221no—
432#463—1221no—
433#461—611no—
434#461—611no—
435#460—611no—
436#459—611no—
437#459—611no—
438#459—611no—
439#449—1221no—
440#442—1221no—
441#440—1221no—
442#440—1222no—
443#432—611no—
444#423—611no—
445#417—1221no—
446C4×M16—611no—
447#333—611no—
448#333—611no—
449#332—611no—
450#332—611no—
451Q8⋊C8—611no—
452Q8⋊C8—611no—
453D4⋊C8—611no—
454D4⋊C8—611no—
455D4⋊C8—611no—
456D4⋊C8—611no—
457D4⋊C8—611no—
458D4⋊C8—611no—
459C61#1856011yescharacteristic, complemented, Sylow
460C2×#41—21no—
461C2×#41—1221no—
462C2×#41C22⋊D6111yescharacteristic
463C22×D4C22⋊D6111yescharacteristic
464C23×C4—21no—
465AGL(1,ℤ/8)—2444no—
466C2×SD16—1221no—
467C2×SD16—1222no—
468C2×SD16—1221no—
469C2×SD16—1221no—
470C2×D8—1221no—
471C2×D8—1221no—
472C2×D8—1221no—
473C2×M16—1221no—
474C2×M16—1221no—
475C4⋊Q8—611no—
476C4⋊Q8C22×D6111yescharacteristic
477C4⋊Q8C22×D6111yescharacteristic
478#127—611no—
479#126—22no—
480#126—22no—
481#126—22no—
482#125—22no—
483#125—21no—
484#125—21no—
485#124—22no—
486#124—21no—
487#124—1221no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8C22⋊D6112yes—
498#121—22no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—1221no—
503#121—1221no—
504#120—22no—
505C4×Q8—21no—
506C4×Q8—21no—
507C4×Q8C22⋊D6111yescharacteristic
508C4×Q8C22⋊D6112yes—
509C4×Q8C22×D6111yescharacteristic
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4C22⋊D6111yescharacteristic
521C4×D4C22⋊D6111yescharacteristic
522C4×D4C22⋊D6111yescharacteristic
523C4×D4C22×D6111yescharacteristic
524C4×D4C22×D6111yescharacteristic
525C4×D4C22×D6111yescharacteristic
526#117—22no—
527#117—22no—
528#117—22no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117C22⋊D6111yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4C22⋊D6111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—21no—
540C2×C42—22no—
541C2×C42—21no—
542C2×C42C22×D6111yescharacteristic
543#107—1222no—
544#107—1221no—
545#106—1221no—
546C4⋊C8—611no—
547C4⋊C8—611no—
548C4⋊C8—611no—
549C4⋊C8—611no—
550C4⋊C8—1221no—
551#103—1221no—
552#103—1222no—
553#103—1221no—
554#103—1221no—
555#102—1221no—
556#102—1221no—
557#102—1221no—
558#102—1221no—
559#102—1222no—
560#102—1221no—
561C22⋊C8—1221no—
562#97—1221no—
563#97—1221no—
564C4×C8—611no—
565C4×C8—611no—
566C24—21no—
567#41—41no—
568#41—41no—
569#41—42no—
570#41—42no—
571#41—2442no—
572#41—2442no—
573C2×Q8—21no—
574C2×Q8—1221no—
575C2×Q8C2×C22⋊D6111yescharacteristic
576C2×Q8C2×C22⋊D6112yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—2441no—
587C2×D4C2×C22⋊D6111yescharacteristic
588C2×D4C2×C22⋊D6111yescharacteristic
589C2×D4C2×C22⋊D6111yescharacteristic
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—2441no—
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606SD16—2444no—
607SD16—2442no—
608SD16—2442no—
609SD16—2442no—
610D8—2442no—
611D8—2442no—
612D8—2442no—
613M16—2442no—
614M16—2442no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4C2×C22⋊D6111yescharacteristic
636C4⋊C4C2×C22⋊D6111yescharacteristic
637C4⋊C4C2×C22⋊D6111yescharacteristic
638C4⋊C4C2×C22⋊D6111yescharacteristic
639C4⋊C4C2×C22⋊D6112yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—2441no—
655C22⋊C4—2441no—
656C42—22no—
657C42—22no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—21no—
662C42C2×C22⋊D6111yescharacteristic
663C42C2×C22⋊D6111yescharacteristic
664C42C2×C22⋊D6111yescharacteristic
665C42C23×D6111yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—2441no—
673C23#1451974611yescharacteristic
674Q8—21no—
675Q8—21no—
676Q8—42no—
677Q8—41no—
678Q8—41no—
679Q8—2441no—
680Q8—2441no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—42no—
687D4—42no—
688D4—44no—
689D4—82no—
690D4—4882no—
691D4—2442no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695D4—2441no—
696D4#1451980212yes—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—81no—
721C2×C4—82no—
722C2×C4—4882no—
723C2×C4—2441no—
724C2×C4#1451974611yescharacteristic
725C2×C4#1451974611yescharacteristic
726C2×C4#1451974611yescharacteristic
727C2×C4C22×C22⋊D6111yescharacteristic
728C2×C4C22×C22⋊D6111yescharacteristic
729C2×C4C22×C22⋊D6111yescharacteristic
730C8—1222no—
731C8—2441no—
732C8—2441no—
733C8—2441no—
734C8—2441no—
735C8—2441no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—84no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22C2×#1451974611yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—41no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—4881no—
765C4C2×#1451980211yescharacteristic
766C4#1684056011yescharacteristic
767C4#1684056011yescharacteristic
768C4#1684056011yescharacteristic
769C2—41no—
770C2—42no—
771C2—81no—
772C2—81no—
773C2—9761no—
774C2#2145506111yescharacteristic
775C2#2145507111yescharacteristic
776C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3475C2
socleC22×C61C2×#120
hypercenter#3475D61
hypocenterC61#18560
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #21456538C2semidirect
2. #21455970C2semidirect
3. #21455283C2semidirect
4. #21445075C2semidirect
5. #21445054C2semidirect
6. #21445047C2semidirect
7. #21445026C2semidirect
8. #21444929C2semidirect
9. #21444908C2semidirect
10. #21444902C2semidirect
11. #21444891C2semidirect
12. #21444549C2semidirect
13. #21444262C2semidirect
14. #21444258C2semidirect
15. C61×#3475C2semidirect
18. #16840165C22semidirect
19. #16840136C22semidirect
20. #16840112C22semidirect
21. #16840110C22semidirect
23. #16840047C22semidirect
24. #16840042C22semidirect
30. #16839962C22semidirect
33. #16839957C22semidirect
42. #16839511C22semidirect
43. #16839511C22semidirect
44. #16839508C22semidirect
45. #16839508C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
381. #3475D61semidirect
459. C61#18560semidirect

Maximal subgroups

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

subgroupindex
#214565382
#214559702
#214552832
#214450752
#214450542
#214450472
#214450262
#214449292
#214449082
#214449022
#214448912
#214445492
#214442622
#214442582
C61×#34752
#1856061