Finite Group Databasebeta

← D61×#3497 #30588182

Subgroups — D61×#3497 #30588182

Order 15616.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D61C212yesmaximal, complemented
2#21459590C211yesmaximal, characteristic, complemented
3#21459589C214yesmaximal, complemented
4#21459588C216yesmaximal, complemented
5#21459587C218yesmaximal, complemented
6#21459586C212yesmaximal, complemented
7#21459585C216yesmaximal, complemented
8#21459584C214yesmaximal, complemented
9#550×D61C214yesmaximal, complemented
10D4×Q8×D61C214yesmaximal, complemented
11#548×D61C218yesmaximal, complemented
12#537×D61C216yesmaximal, complemented
13#532×D61C216yesmaximal, complemented
14C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
15C61×#3497C211yesmaximal, characteristic, complemented
16C2×#14519825C2212yescomplemented
17C2×#14519825C2218yescomplemented
18C2×#14519824C2218yescomplemented
19C2×#14519824C22112yescomplemented
202−1+4×D61—232no—
21C2×#41×D61C2218yes—
22C2×#41×D61C22112yes—
23C22×Q8×D61C2218yes—
24C22×Q8×D61C2211yescharacteristic
25#16840434C2214yescomplemented
26#16840433C22112yescomplemented
27#16840432C22112yescomplemented
28#16840431C2218yescomplemented
29#16840430C22124yescomplemented
30Q8×D244C2214yescomplemented
31D4×Dic122C22112yescomplemented
32#16840427C22112yescomplemented
33Q8×C22⋊D61C2218yescomplemented
34#16840425C22124yescomplemented
35#16840424C2218yescomplemented
36#16840423C2218yescomplemented
37#16840422C22124yescomplemented
38#16840421C22124yescomplemented
39#16840420C22124yescomplemented
40#16840419C2218yescomplemented
41#16840418C22124yescomplemented
42#16840343C2216yescomplemented
43#16840342C22124yescomplemented
44#16840341C22124yescomplemented
45#16840340C22112yescomplemented
46#16840339C22124yescomplemented
47#16840313C2216yescomplemented
48#16840312C2216yescomplemented
49#16840311C22112yescomplemented
50#16840310C2216yescomplemented
51#16840309C22112yescomplemented
52#16840309C22112yescomplemented
53#16840308C22112yescomplemented
54#16840307C22112yescomplemented
55#16840307C22112yescomplemented
56C4⋊Q8×D61C2216yes—
57#127×D61C2216yes—
58#124×D61C22112yes—
59C22⋊Q8×D61C22124yes—
60#121×D61C22124yes—
61#121×D61C2214yes—
62#121×D61C22112yes—
63C2×Q8×Dic61C2211yescharacteristic, complemented
64C2×C4×Dic122C2213yescomplemented
65C2×#14519742C2213yescomplemented
66C4×Q8×D61C2214yes—
67C4×Q8×D61C2214yes—
68C4×Q8×D61C2214yescomplemented
69C4×Q8×D61C2214yescomplemented
70C4×D4×D61C22112yes—
71C4×D4×D61C22112yes—
72C2×C4⋊C4×D61C2213yes—
73C2×C42×D61C2213yes—
74C2×2−1+4×C61C2212yescomplemented
75C61×#550C2214yescomplemented
76D4×Q8×C61C2214yescomplemented
77C61×#548C2218yescomplemented
78C61×#537C2216yescomplemented
79C61×#532C2216yescomplemented
80C2×C4×Q8×C61C2211yescharacteristic, complemented
81#14519825—216no—
82#14519825—264no—
83#14519824—264no—
84#14519824—296no—
85C2×#11758226C23112yes—
86C2×#11758226C2318yes—
87C2×#11758222C23112yes—
88C2×#11758222C23124yes—
89C2×#11758222C23124yes—
90C2×#11758224C23124yes—
91C2×#11758224C23112yes—
92C2×#11758224C23124yes—
93#41×D61—264no—
94#41×D61—296no—
95C22×Dic122C23124yes—
96C22×Dic122C2313yes—
97C2×Q8×D61—264no—
98C2×Q8×D61D4116yescomplemented
99C2×Q8×D61C23112yes—
100C2×Q8×D61C2318yes—
101C2×Q8×D61C23124yes—
102C2×Q8×D61C2314yes—
103C2×Q8×D61C2314yes—
104C2×D4×D61C2314yes—
105C2×D4×D61C2318yes—
106C2×D4×D61C23112yes—
107C2×D4×D61C23112yes—
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C23124yes—
110C22×C4×D61C2313yes—
111C22×C4×D61C2313yes—
112#14519777C2316yes—
113#14519776C23112yes—
114#14519776C23112yes—
115#14519775C23112yes—
116#14519774C2316yes—
117#14519773C23112yes—
118#14519773C23112yes—
119#14519773C23112yes—
120#14519766C23112yes—
121#14519765C23112yes—
122#14519764C23112yes—
123#14519763C23124yes—
124#14519763C23124yes—
125#14519757C23124yes—
126#14519756C23124yes—
127#14519755C23148yes—
128#14519754C23148yes—
129#14519753C23124yes—
130#14519752C2314yes—
131#14519752C23112yes—
132#14519752C23124yes—
133#14519751C2314yes—
134#14519751C23112yes—
135#14519751C23124yes—
136#14519750C2318yes—
137#14519750C23124yes—
138#14519750C23148yes—
139#14519749C2318yes—
140#14519749C23124yes—
141#14519749C23148yes—
142#14519748C2314yes—
143#14519748C23112yes—
144#14519748C23124yes—
145Q8×Dic61C2314yes—
146Q8×Dic61C2314yes—
147C4×Dic122C23112yes—
148C4×Dic122C23112yes—
149#14519742C23112yes—
150#14519742C23112yes—
151C4×D244C23112yes—
152C4×D244C23112yes—
153D4×Dic61C23112yes—
154D4×Dic61C23112yes—
155#14519739C23112yes—
156#14519739C23112yes—
157C4×C22⋊D61C23124yes—
158C4×C22⋊D61C23124yes—
159#14519737C23124yes—
160#14519737C23124yes—
161C2×C4⋊Dic61C2313yes—
162C2×#11758196C2316yes—
163C4⋊C4×D61C23112yes—
164C4⋊C4×D61C23112yes—
165C4⋊C4×D61C2314yes—
166C4⋊C4×D61C23112yes—
167C22⋊C4×D61C2318yes—
168C22⋊C4×D61C23124yes—
169C2×C4×Dic61C2313yes—
170C2×C4×Dic61C2313yes—
171C2×C4×Dic61C2313yes—
172C42×D61C2316yes—
173C42×D61C2316yes—
174C42×D61C2316yes—
175C42×D61C2316yes—
1762−1+4×C61—216no—
177C2×#41×C61C23112yes—
178C2×#41×C61C2318yes—
179C22×Q8×C61C2318yes—
180C22×Q8×C61C2311yescharacteristic
181C4⋊Q8×C61C2316yes—
182#127×C61C2316yes—
183#124×C61C23112yes—
184C22⋊Q8×C61C23124yes—
185#121×C61C2314yes—
186#121×C61C23112yes—
187#121×C61C23124yes—
188C4×Q8×C61C2314yes—
189C4×Q8×C61C2314yes—
190C4×D4×C61C23112yes—
191C4×D4×C61C23112yes—
192C2×C4⋊C4×C61C2313yes—
193C2×C42×C61C2313yes—
194C23×D61C2418yes—
195C23×D61C2411yescharacteristic
196#41×C61—232no—
197#41×C61—248no—
198C2×Q8×C61—232no—
199C2×Q8×C61C2×D418yescomplemented
200C2×Q8×C61C24112yes—
201C2×Q8×C61C2414yes—
202C2×D4×C61C2418yes—
203C2×D4×C61C24112yes—
204C2×D4×C61C2414yes—
205C2×D4×C61C24112yes—
206C22×C4×C61C24124yes—
207C22×C4×C61C2411yescharacteristic
208C22×C4×C61C2413yes—
209C22×C4×C61C2413yes—
210C2×C22⋊D61C2418yes—
211C2×C22⋊D61C2418yes—
212C2×C22⋊D61C24124yes—
213C2×C22⋊D61C2418yes—
214C2×C22⋊D61C24124yes—
215C22×Dic61C24124yes—
216C22×Dic61C2411yescharacteristic
217C22×Dic61C2413yes—
218C22×Dic61C2413yes—
219#11758226—232no—
220#11758226—248no—
221Q8×D61—232no—
222Q8×D61—248no—
223Q8×D61—296no—
224Q8×D61C2×D4132yes—
225Q8×D61C2×D4132yescomplemented
226#11758224—296no—
227#11758224—248no—
228#11758224—296no—
229D4×D61—232no—
230D4×D61—248no—
231D4×D61—216no—
232D4×D61—424no—
233#11758222—248no—
234#11758222—296no—
235#11758222—296no—
236C2×D244C2418yes—
237C2×D244C24112yes—
238C2×D244C2414yes—
239C2×D244C24112yes—
240C2×C4×D61—296no—
241C2×C4×D61—24no—
242C2×C4×D61—46no—
243C2×C4×D61C2×D4124yes—
244C2×C4×D61C2418yes—
245C2×C4×D61C2416yes—
246C2×C4×D61C24124yes—
247C2×C4×D61C24124yes—
248C2×C4×D61C2411yescharacteristic
249C2×C4×D61C2411yescharacteristic
250C2×C4×D61C2411yescharacteristic
251C2×C4×D61C2416yes—
252C2×C4×D61C2416yes—
253C2×C4×D61C2416yes—
254C2×C4×D61C2411yescharacteristic
255C2×Dic122—296no—
256C2×Dic122C2×D4124yescomplemented
257C2×Dic122C24124yes—
258C2×Dic122C24112yes—
259C2×Dic122C24112yes—
260C4⋊C4×C61C24112yes—
261C4⋊C4×C61C2414yes—
262C4⋊C4×C61C24112yes—
263C22⋊C4×C61C2418yes—
264C22⋊C4×C61C24124yes—
265C42×C61C2416yes—
266C42×C61C2416yes—
267C22⋊Dic61C2418yes—
268C22⋊Dic61C24124yes—
269#11758198C2418yes—
270#11758198C24124yes—
271#11758198C2418yes—
272#11758198C24124yes—
273C4⋊Dic61C24112yes—
274C4⋊Dic61C2414yes—
275C4⋊Dic61C24112yes—
276#11758196C24124yes—
277#11758196C2418yes—
278#11758196C24124yes—
279C4×Dic61C2416yes—
280C4×Dic61C2416yes—
281C4×Dic61C2416yes—
282C4×Dic61C2416yes—
283C4×Dic61C2416yes—
284C4×Dic61C2416yes—
285C23×C61C2518yes—
286C23×C61C2511yescharacteristic
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—216no—
290C22×D61—216no—
291C22×D61—216no—
292C22×D61C22×D414yes—
293C22×D61C2518yes—
294C22×D61C2511yescharacteristic
295C22×D61C2511yescharacteristic
296Q8×C61—224no—
297Q8×C61C22×D4116yes—
298D4×C61—216no—
299D4×C61—224no—
300D4×C61—28no—
301D4×C61—412no—
302C2×C4×C61—248no—
303C2×C4×C61—22no—
304C2×C4×C61—43no—
305C2×C4×C61C22×D4112yes—
306C2×C4×C61C2511yescharacteristic
307C2×C4×C61C2516yes—
308C2×C4×C61C2518yes—
309C2×C4×C61C2516yes—
310C2×C4×C61C2511yescharacteristic
311C22⋊D61—216no—
312C22⋊D61—216no—
313C22⋊D61—248no—
314C22⋊D61—216no—
315C22⋊D61—424no—
316C2×Dic61—248no—
317C2×Dic61—22no—
318C2×Dic61—43no—
319C2×Dic61C22×D4112yes—
320C2×Dic61C2511yescharacteristic
321C2×Dic61C2516yes—
322C2×Dic61C2518yes—
323C2×Dic61C2516yes—
324C2×Dic61C2511yescharacteristic
325D244—216no—
326D244—224no—
327D244—28no—
328D244—412no—
329C4×D61—216no—
330C4×D61—22no—
331C4×D61—212no—
332C4×D61—248no—
333C4×D61—22no—
334C4×D61—248no—
335C4×D61—22no—
336C4×D61—46no—
337C4×D61C22×D4124yes—
338C4×D61C22×D4124yes—
339C4×D612−1+414yescomplemented
340Dic122—224no—
341Dic122—248no—
342Dic122C22×D4148yes—
343C2×#3497—611nomaximal, Sylow
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—28no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61C23×D412yes—
350C22×C61C2611yescharacteristic
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—28no—
354C2×D61—28no—
355C2×D61—28no—
356C2×D61—28no—
357C2×D61—432no—
358C2×D61C23×D412yes—
359C2×D61C23×D412yes—
360C2×D61C2×2−1+412yes—
361C2×D61#58512yes—
362C4×C61—28no—
363C4×C61—21no—
364C4×C61—26no—
365C4×C61C23×D4112yes—
366C4×C61C2×2−1+412yescomplemented
367Dic61—28no—
368Dic61—21no—
369Dic61—26no—
370Dic61C23×D4112yes—
371Dic61C2×2−1+412yescomplemented
372C22×2−1+4—612no—
373#3497—612no—
374#3497—614no—
375#3497—614no—
376#3497—618no—
377#3497—616no—
378#3497—616no—
379#3497—611no—
380#3497D6111yescharacteristic, direct product factor
381C2×#550—614no—
382C2×D4×Q8—614no—
383C2×#548—618no—
384C2×#537—616no—
385C2×#532—616no—
386C22×C4×Q8—611no—
387C2×C61—22no—
388C2×C61—48no—
389C2×C61C24×D411yescharacteristic
390C2×C61C22×2−1+411yescharacteristic
391C2×C61C2×#58511yescharacteristic
392D61—22no—
393D61—48no—
394D61#349714yesdirect product factor
395C2×2−1+4—618no—
396C2×2−1+4—6112no—
397C2×2−1+4—618no—
398C2×2−1+4—612no—
399C2×2−1+4—12232no—
400C2×2−1+4C2×D6112yescomplemented
401C22×#41—6112no—
402C22×#41—618no—
403C23×Q8—611no—
404C23×Q8—618no—
405#550—618no—
406#550—6112no—
407#550—6124no—
408#550—614no—
409#550—6112no—
410#550C2×D6114yescomplemented
411D4×Q8—618no—
412D4×Q8—6112no—
413D4×Q8—6124no—
414D4×Q8—614no—
415D4×Q8—6112no—
416D4×Q8C2×D6114yescomplemented
417#548—618no—
418#548—618no—
419#548—6124no—
420#548—6124no—
421#548—6124no—
422#548—618no—
423#548—6124no—
424#548C2×D6118yescomplemented
425#537—6112no—
426#537—6124no—
427#537—6124no—
428#537—6124no—
429#537—616no—
430#537C2×D6116yescomplemented
431#532—6112no—
432#532—616no—
433#532—616no—
434#532—6112no—
435#532—6112no—
436#532—6112no—
437#532—6112no—
438#532—6112no—
439#532—616no—
440#532C2×D6116yescomplemented
441C2×C4⋊Q8—616no—
442C2×#127—616no—
443C2×#124—6112no—
444C2×C22⋊Q8—6124no—
445C2×#121—614no—
446C2×#121—6112no—
447C2×#121—6124no—
448C2×C4×Q8—611no—
449C2×C4×Q8—614no—
450C2×C4×Q8—614no—
451C2×C4×Q8—614no—
452C2×C4×Q8—614no—
453C2×C4×Q8—613no—
454C2×C4×Q8—613no—
455C2×C4×Q8C2×D6111yescharacteristic, complemented
456C2×C4×D4—6112no—
457C2×C4×D4—6112no—
458C22×C4⋊C4—613no—
459C22×C42—613no—
460C61C2×#349711yescharacteristic, complemented, Sylow
4612−1+4—216no—
4622−1+4—12264no—
4632−1+4—12264no—
4642−1+4—12296no—
4652−1+4—12216no—
466C2×#41—6112no—
467C2×#41—618no—
468C2×#41—6124no—
469C2×#41—6112no—
470C2×#41—6124no—
471C2×#41—6124no—
472C2×#41—6112no—
473C2×#41—6124no—
474C2×#41—12296no—
475C2×#41—12264no—
476C2×#41C22×D61112yes—
477C2×#41C22×D6118yes—
478C22×Q8—6116no—
479C22×Q8—614no—
480C22×Q8—614no—
481C22×Q8—6112no—
482C22×Q8—6124no—
483C22×Q8—618no—
484C22×Q8—613no—
485C22×Q8—6124no—
486C22×Q8—12264no—
487C22×Q8C22×D6118yes—
488C22×Q8C22×D6111yescharacteristic
489C22×D4—614no—
490C22×D4—618no—
491C22×D4—6112no—
492C22×D4—6112no—
493C23×C4—613no—
494C23×C4—6124no—
495C23×C4—611no—
496C23×C4—613no—
497C4⋊Q8—6112no—
498C4⋊Q8—6112no—
499C4⋊Q8—6112no—
500C4⋊Q8—616no—
501C4⋊Q8C22×D6116yes—
502#127—6112no—
503#127—6112no—
504#127—6112no—
505#127—616no—
506#127C22×D6116yes—
507#124—6112no—
508#124—6112no—
509#124—6124no—
510#124—6124no—
511#124—6112no—
512#124C22×D61112yes—
513C22⋊Q8—6124no—
514C22⋊Q8—6124no—
515C22⋊Q8—6148no—
516C22⋊Q8—6124no—
517C22⋊Q8—6148no—
518C22⋊Q8C22×D61124yes—
519#121—614no—
520#121—618no—
521#121—6112no—
522#121—6124no—
523#121—6124no—
524#121—6148no—
525#121—614no—
526#121—6112no—
527#121—6124no—
528#121—614no—
529#121—6112no—
530#121—6124no—
531#121—618no—
532#121—6124no—
533#121—6148no—
534#121C22×D6114yes—
535#121C22×D61112yes—
536#121C22×D61124yes—
537C4×Q8—614no—
538C4×Q8—614no—
539C4×Q8—6112no—
540C4×Q8—6112no—
541C4×Q8—6112no—
542C4×Q8—6112no—
543C4×Q8C22×D6114yes—
544C4×Q8C22×D6114yes—
545C4×D4—6112no—
546C4×D4—6112no—
547C4×D4—6124no—
548C4×D4—6124no—
549C4×D4—6112no—
550C4×D4—6112no—
551C4×D4—6124no—
552C4×D4—6124no—
553C4×D4—6112no—
554C4×D4—6112no—
555C4×D4C22×D61112yes—
556C4×D4C22×D61112yes—
557C2×C4⋊C4—616no—
558C2×C4⋊C4—613no—
559C2×C4⋊C4—6112no—
560C2×C4⋊C4—6112no—
561C2×C4⋊C4—614no—
562C2×C4⋊C4—6112no—
563C2×C4⋊C4C22×D6113yes—
564C2×C22⋊C4—618no—
565C2×C22⋊C4—6124no—
566C2×C42—613no—
567C2×C42—613no—
568C2×C42—613no—
569C2×C42—616no—
570C2×C42—616no—
571C2×C42—616no—
572C2×C42—616no—
573C2×C42C22×D6113yes—
574C24—611no—
575C24—618no—
576#41—232no—
577#41—248no—
578#41—12296no—
579#41—12296no—
580#41—12296no—
581#41—12248no—
582#41—12248no—
583#41—12296no—
584#41—12232no—
585#41—12248no—
586C2×Q8—232no—
587C2×Q8—6132no—
588C2×Q8—6132no—
589C2×Q8—6124no—
590C2×Q8—6112no—
591C2×Q8—6124no—
592C2×Q8—6112no—
593C2×Q8—12296no—
594C2×Q8—12248no—
595C2×Q8—12296no—
596C2×Q8—12232no—
597C2×Q8D4×D6118yescomplemented
598C2×Q8C23×D61112yes—
599C2×Q8C23×D6114yes—
600C2×D4—618no—
601C2×D4—618no—
602C2×D4—618no—
603C2×D4—6124no—
604C2×D4—6124no—
605C2×D4—614no—
606C2×D4—618no—
607C2×D4—6112no—
608C2×D4—6112no—
609C2×D4—12248no—
610C2×D4—12216no—
611C2×D4—12232no—
612C2×D4—24424no—
613C2×D4C23×D6114yes—
614C2×D4C23×D6118yes—
615C2×D4C23×D61112yes—
616C2×D4C23×D61112yes—
617C22×C4—613no—
618C22×C4—6124no—
619C22×C4—611no—
620C22×C4—616no—
621C22×C4—616no—
622C22×C4—611no—
623C22×C4—6124no—
624C22×C4—613no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—616no—
629C22×C4—618no—
630C22×C4—6124no—
631C22×C4—6124no—
632C22×C4—616no—
633C22×C4—12296no—
634C22×C4—1224no—
635C22×C4—2446no—
636C22×C4C23×D6111yescharacteristic
637C22×C4C23×D61124yes—
638C22×C4C23×D6113yes—
639C22×C4C23×D6113yes—
640C4⋊C4—6124no—
641C4⋊C4—6112no—
642C4⋊C4—618no—
643C4⋊C4—6124no—
644C4⋊C4—614no—
645C4⋊C4—6112no—
646C4⋊C4C23×D61112yes—
647C4⋊C4C23×D6114yes—
648C4⋊C4C23×D61112yes—
649C22⋊C4—618no—
650C22⋊C4—6124no—
651C22⋊C4—618no—
652C22⋊C4—618no—
653C22⋊C4—6124no—
654C22⋊C4—6124no—
655C22⋊C4C23×D6118yes—
656C22⋊C4C23×D61124yes—
657C42—616no—
658C42—616no—
659C42—616no—
660C42—616no—
661C42—616no—
662C42—616no—
663C42C23×D6116yes—
664C42C23×D6116yes—
665C23—611no—
666C23—614no—
667C23—611no—
668C23—618no—
669C23—1222no—
670C23—1222no—
671C23—12216no—
672C23—12216no—
673C23—12216no—
674C23C24×D6118yes—
675C23C24×D6111yescharacteristic
676Q8—224no—
677Q8—6148no—
678Q8—12248no—
679Q8—12224no—
680Q8C2×D4×D61116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—12216no—
686D4—12216no—
687D4—12248no—
688D4—12216no—
689D4—12216no—
690D4—12224no—
691D4—1228no—
692D4—24412no—
693D4—24424no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—6112no—
698C2×C4—611no—
699C2×C4—616no—
700C2×C4—6124no—
701C2×C4—6124no—
702C2×C4—614no—
703C2×C4—611no—
704C2×C4—616no—
705C2×C4—618no—
706C2×C4—1222no—
707C2×C4—12248no—
708C2×C4—1222no—
709C2×C4—12216no—
710C2×C4—12212no—
711C2×C4—1222no—
712C2×C4—12248no—
713C2×C4—12248no—
714C2×C4—1222no—
715C2×C4—2446no—
716C2×C4—2443no—
717C2×C4C2×D4×D61112yes—
718C2×C4C24×D6111yescharacteristic
719C2×C4C24×D6116yes—
720C2×C4C24×D6118yes—
721C2×C4C24×D6116yes—
722C2×C4C24×D6111yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—612no—
729C22—612no—
730C22—612no—
731C22—612no—
732C22—1228no—
733C22—1221no—
734C22—1221no—
735C22—1228no—
736C22—1228no—
737C22—1228no—
738C22—24432no—
739C22C22×D4×D6112yes—
740C22C25×D6111yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—6112no—
745C4—612no—
746C4—1228no—
747C4—1221no—
748C4—1226no—
749C4C22×D4×D61112yes—
750C42−1+4×D6112yescomplemented
751C2—22no—
752C2—48no—
753C2—614no—
754C2—1222no—
755C2—2448no—
756C2C23×D4×D6111yescharacteristic
757C2C2×2−1+4×D6111yescharacteristic
758C2#585×D6111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3497C2
hypercenter#3497D61
hypocenterC61C2×#3497
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D61C2semidirect
2. #21459590C2semidirect
3. #21459589C2semidirect
4. #21459588C2semidirect
5. #21459587C2semidirect
6. #21459586C2semidirect
7. #21459585C2semidirect
8. #21459584C2semidirect
9. #550×D61C2semidirect
10. D4×Q8×D61C2semidirect
11. #548×D61C2semidirect
12. #537×D61C2semidirect
13. #532×D61C2semidirect
14. C2×C4×Q8×D61C2semidirect
15. C61×#3497C2semidirect
16. C2×#14519825C22semidirect
17. C2×#14519825C22semidirect
18. C2×#14519824C22semidirect
19. C2×#14519824C22semidirect
25. #16840434C22semidirect
26. #16840433C22semidirect
27. #16840432C22semidirect
28. #16840431C22semidirect
29. #16840430C22semidirect
30. Q8×D244C22semidirect
31. D4×Dic122C22semidirect
32. #16840427C22semidirect
33. Q8×C22⋊D61C22semidirect
34. #16840425C22semidirect
35. #16840424C22semidirect
36. #16840423C22semidirect
37. #16840422C22semidirect
38. #16840421C22semidirect
39. #16840420C22semidirect
40. #16840419C22semidirect
41. #16840418C22semidirect
42. #16840343C22semidirect
43. #16840342C22semidirect
44. #16840341C22semidirect
45. #16840340C22semidirect
46. #16840339C22semidirect
47. #16840313C22semidirect
48. #16840312C22semidirect
49. #16840311C22semidirect
50. #16840310C22semidirect
51. #16840309C22semidirect
52. #16840309C22semidirect
53. #16840308C22semidirect
54. #16840307C22semidirect
55. #16840307C22semidirect
63. C2×Q8×Dic61C22semidirect
64. C2×C4×Dic122C22semidirect
65. C2×#14519742C22semidirect
68. C4×Q8×D61C22semidirect
69. C4×Q8×D61C22semidirect
74. C2×2−1+4×C61C22semidirect
75. C61×#550C22semidirect
76. D4×Q8×C61C22semidirect
77. C61×#548C22semidirect
78. C61×#537C22semidirect
79. C61×#532C22semidirect
80. C2×C4×Q8×C61C22semidirect
98. C2×Q8×D61D4semidirect
199. C2×Q8×C61C2×D4semidirect
225. Q8×D61C2×D4semidirect
256. C2×Dic122C2×D4semidirect
339. C4×D612−1+4semidirect
366. C4×C61C2×2−1+4semidirect
371. Dic61C2×2−1+4semidirect
380. #3497D61direct (N × H)
394. D61#3497direct (N × H)
400. C2×2−1+4C2×D61semidirect
410. #550C2×D61semidirect
416. D4×Q8C2×D61semidirect
424. #548C2×D61semidirect
430. #537C2×D61semidirect
440. #532C2×D61semidirect
455. C2×C4×Q8C2×D61semidirect
460. C61C2×#3497semidirect
597. C2×Q8D4×D61semidirect
750. C42−1+4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D612
#214595902
#214595892
#214595882
#214595872
#214595862
#214595852
#214595842
#550×D612
D4×Q8×D612
#548×D612
#537×D612
#532×D612
C2×C4×Q8×D612
C61×#34972
C2×#349761