Finite Group Databasebeta

← D61×#3499 #30588421

Subgroups — D61×#3499 #30588421

Order 15616.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D61C212yesmaximal, complemented
2#21459604C211yesmaximal, characteristic, complemented
3#21459603C214yesmaximal, complemented
4#21459602C213yesmaximal, complemented
5#21459601C216yesmaximal, complemented
6#21459600C212yesmaximal, complemented
7#21459599C213yesmaximal, complemented
8#21459598C2112yesmaximal, complemented
9D4×Q8×D61C214yesmaximal, complemented
10#547×D61C2112yesmaximal, complemented
11#536×D61C216yesmaximal, complemented
12#532×D61C213yesmaximal, complemented
13C2×C4⋊Q8×D61C213yesmaximal, complemented
14C4×#41×D61C211yesmaximal, characteristic, complemented
15C61×#3499C211yesmaximal, characteristic, complemented
16C2×#14519825C2216yescomplemented
17C2×#14519825C2214yescomplemented
18C2×#14519824C22112yescomplemented
19C2×#14519824C2216yescomplemented
20C2×#14519824C2212yescomplemented
212−1+4×D61—232no—
22C2×#41×D61C22112yes—
23C2×#41×D61C2216yes—
24C2×#41×D61C2211yescharacteristic
25C22×Q8×D61C2214yes—
26C22×Q8×D61C2216yes—
27Q8×D244C2214yescomplemented
28D4×Dic122C22112yescomplemented
29#16840427C22112yescomplemented
30Q8×C22⋊D61C2218yescomplemented
31#16840425C22124yescomplemented
32#16840417C22112yescomplemented
33#16840416C22112yescomplemented
34#16840415C22112yescomplemented
35#16840414C22124yescomplemented
36#16840413C22124yescomplemented
37#16840412C22124yescomplemented
38#16840411C22124yescomplemented
39#16840410C22148yescomplemented
40#16840338C2216yescomplemented
41#16840337C22112yescomplemented
42#16840336C2216yescomplemented
43#16840335C22124yescomplemented
44#16840334C22124yescomplemented
45#16840333C2216yescomplemented
46#16840332C22112yescomplemented
47#16840313C2213yescomplemented
48#16840312C2213yescomplemented
49#16840311C2216yescomplemented
50#16840310C2213yescomplemented
51#16840309C22112yescomplemented
52#16840308C2216yescomplemented
53#16840307C22112yescomplemented
54C2×#14519777C2213yescomplemented
55C2×#14519776C22112yescomplemented
56C2×#14519775C2216yescomplemented
57C4⋊Q8×D61C22112yes—
58C4⋊Q8×D61C2213yes—
59C4⋊Q8×D61C2216yes—
60C4⋊Q8×D61C22112yescomplemented
61C4⋊Q8×D61C2216yescomplemented
62C4⋊Q8×D61C2216yescomplemented
63#127×D61C2211yescharacteristic
64#124×D61C2216yes—
65#123×D61C22124yes—
66C22⋊Q8×D61C22124yes—
67#121×D61C22112yes—
68#41×Dic61C2211yescharacteristic, complemented
69C4×#11758226C2212yescomplemented
70C4×#11758222C2213yescomplemented
71#16840230C2213yescomplemented
72C4×#11758224C2216yescomplemented
73C4×Q8×D61C2212yes—
74C4×D4×D61C2216yes—
75C4×D4×D61C22112yes—
76#117×D61C2213yes—
77C2×C4⋊C4×D61C22112yes—
78C2×C42×D61C2213yes—
79C2×2−1+4×C61C2212yescomplemented
80D4×Q8×C61C2214yescomplemented
81C61×#547C22112yescomplemented
82C61×#536C2216yescomplemented
83C61×#532C2213yescomplemented
84C2×C4⋊Q8×C61C2213yescomplemented
85C4×#41×C61C2211yescharacteristic, complemented
86#14519825—232no—
87#14519825—248no—
88#14519824—216no—
89#14519824—296no—
90#14519824—248no—
91C2×#11758226C2316yes—
92C2×#11758226C23112yes—
93C2×#11758226C2311yescharacteristic
94C2×#11758222C2316yes—
95C2×#11758222C23112yes—
96C2×#11758222C23124yes—
97C2×#11758222C23112yes—
98C2×#11758222C2313yes—
99C2×#11758224C23112yes—
100C2×#11758224C2316yes—
101C2×#11758224C23124yes—
102C2×#11758224C23112yes—
103C2×#11758224C2313yes—
104#41×D61—296no—
105#41×D61—248no—
106#41×D61D4116yescomplemented
107C22×Dic122C2316yes—
108C22×Dic122C23112yes—
109C22×Dic122C23112yes—
110C2×Q8×D61—232no—
111C2×Q8×D61—248no—
112C2×Q8×D61C23112yes—
113C2×Q8×D61C2316yes—
114C2×Q8×D61C23112yes—
115C2×Q8×D61C23112yes—
116C2×Q8×D61C23112yes—
117C2×Q8×D61C2314yes—
118C2×Q8×D61C2311yescharacteristic
119C2×D4×D61C2314yes—
120C2×D4×D61C23112yes—
121C2×D4×D61C2312yes—
122C2×D4×D61C2313yes—
123C22×C4×D61C2316yes—
124C22×C4×D61C23112yes—
125C22×C4×D61C23112yes—
126C22×C4×D61C2313yes—
127#14519777C2313yes—
128#14519777C2316yes—
129#14519777C23112yes—
130#14519776C23112yes—
131#14519776C23124yes—
132#14519776C23124yes—
133#14519776C23124yes—
134#14519775C2316yes—
135#14519775C23112yes—
136#14519775C23124yes—
137#14519774C2311yescharacteristic
138#14519773C2314yes—
139#14519773C2312yes—
140#14519766C2316yes—
141#14519765C2316yes—
142#14519764C2316yes—
143#14519763C23124yes—
144#14519762C23148yes—
145#14519761C23124yes—
146#14519760C23124yes—
147#14519759C23148yes—
148#14519758C23124yes—
149#14519757C23124yes—
150#14519756C23124yes—
151#14519755C23148yes—
152#14519754C23148yes—
153#14519753C23124yes—
154#14519752C23112yes—
155#14519751C23112yes—
156#14519750C23124yes—
157#14519749C23124yes—
158#14519748C23112yes—
159Q8×Dic61C2312yes—
160C4×Dic122C2316yes—
161#14519742C2316yes—
162C4×D244C2316yes—
163C4×D244C23112yes—
164D4×Dic61C2316yes—
165D4×Dic61C23112yes—
166#14519739C2316yes—
167#14519739C23112yes—
168C4×C22⋊D61C23112yes—
169C4×C22⋊D61C23124yes—
170#14519737C23112yes—
171#14519737C23124yes—
172#14519736C2313yes—
173#14519735C2316yes—
174#14519734C2316yes—
175#14519733C2316yes—
176C2×C4⋊Dic61C23112yes—
177C2×#11758196C23124yes—
178C4⋊C4×D61C23112yes—
179C4⋊C4×D61C23124yes—
180C4⋊C4×D61C23124yes—
181C4⋊C4×D61C23124yes—
182C4⋊C4×D61C2316yes—
183C22⋊C4×D61C2316yes—
184C22⋊C4×D61C23124yes—
185C2×C4×Dic61C2316yes—
186C2×C4×Dic61C2313yes—
187C42×D61C2311yescharacteristic
188C42×D61C2313yes—
189C42×D61C2316yes—
190C42×D61C2316yes—
191C42×D61C2313yes—
192C42×D61C2313yes—
1932−1+4×C61—216no—
194C2×#41×C61C2316yes—
195C2×#41×C61C23112yes—
196C2×#41×C61C2311yescharacteristic
197C22×Q8×C61C2316yes—
198C22×Q8×C61C2314yes—
199C4⋊Q8×C61C2313yes—
200C4⋊Q8×C61C2316yes—
201C4⋊Q8×C61C23112yes—
202#127×C61C2311yescharacteristic
203#124×C61C2316yes—
204#123×C61C23124yes—
205C22⋊Q8×C61C23124yes—
206#121×C61C23112yes—
207C4×Q8×C61C2312yes—
208C4×D4×C61C23112yes—
209C4×D4×C61C2316yes—
210#117×C61C2313yes—
211C2×C4⋊C4×C61C23112yes—
212C2×C42×C61C2313yes—
213C23×D61C2414yes—
214C23×D61C2413yes—
215#41×C61—248no—
216#41×C61—224no—
217#41×C61C2×D418yescomplemented
218C2×Q8×C61—216no—
219C2×Q8×C61—224no—
220C2×Q8×C61C24112yes—
221C2×Q8×C61C2416yes—
222C2×Q8×C61C2411yescharacteristic
223C2×D4×C61C24112yes—
224C2×D4×C61C2412yes—
225C2×D4×C61C2414yes—
226C2×D4×C61C2413yes—
227C22×C4×C61C24112yes—
228C22×C4×C61C24112yes—
229C22×C4×C61C2416yes—
230C22×C4×C61C2413yes—
231C2×C22⋊D61C24112yes—
232C2×C22⋊D61C24112yes—
233C2×C22⋊D61C2414yes—
234C2×C22⋊D61C2418yes—
235C2×C22⋊D61C2416yes—
236C22×Dic61C24112yes—
237C22×Dic61C24112yes—
238C22×Dic61C2416yes—
239C22×Dic61C2413yes—
240#11758226—248no—
241#11758226—224no—
242#11758226C2×D418yescomplemented
243Q8×D61—216no—
244Q8×D61—248no—
245Q8×D61—224no—
246Q8×D61—248no—
247Q8×D61—248no—
248Q8×D61—248no—
249Q8×D61C2×D418yes—
250#11758224—248no—
251#11758224—296no—
252#11758224—248no—
253#11758224—224no—
254#11758224C2×D4124yescomplemented
255D4×D61—248no—
256D4×D61—28no—
257D4×D61—216no—
258D4×D61C2×D4124yes—
259#11758222—224no—
260#11758222—296no—
261#11758222—248no—
262#11758222—248no—
263#11758222C2×D4124yescomplemented
264C2×D244C24112yes—
265C2×D244C2412yes—
266C2×D244C2414yes—
267C2×D244C2413yes—
268C2×C4×D61—248no—
269C2×C4×D61—248no—
270C2×C4×D61—224no—
271C2×C4×D61C2×D4124yes—
272C2×C4×D61C24112yes—
273C2×C4×D61C24124yes—
274C2×C4×D61C24112yes—
275C2×C4×D61C24112yes—
276C2×C4×D61C2416yes—
277C2×C4×D61C2416yes—
278C2×C4×D61C2416yes—
279C2×C4×D61C2413yes—
280C2×C4×D61C2411yescharacteristic
281C2×C4×D61C2413yes—
282C2×C4×D61C2413yes—
283C2×C4×D61C2412yes—
284C2×Dic122—224no—
285C2×Dic122—248no—
286C2×Dic122—248no—
287C2×Dic122C24124yes—
288C2×Dic122C24112yes—
289C2×Dic122C24112yes—
290C2×Dic122C2416yes—
291C2×Dic122C2413yes—
292C4⋊C4×C61C24112yes—
293C4⋊C4×C61C24124yes—
294C4⋊C4×C61C2416yes—
295C22⋊C4×C61C2416yes—
296C22⋊C4×C61C24124yes—
297C42×C61C2411yescharacteristic
298C42×C61C2413yes—
299C42×C61C2416yes—
300C22⋊Dic61C2416yes—
301C22⋊Dic61C24124yes—
302#11758198C24112yes—
303#11758198C24124yes—
304#11758198C24124yes—
305C4⋊Dic61C24112yes—
306C4⋊Dic61C24124yes—
307C4⋊Dic61C2416yes—
308#11758196C24124yes—
309#11758196C24148yes—
310#11758196C24112yes—
311C4×Dic61C2411yescharacteristic
312C4×Dic61C2412yes—
313C4×Dic61C2416yes—
314C4×Dic61C2413yes—
315C4×Dic61C2416yes—
316C4×Dic61C2416yes—
317C4×Dic61C2416yes—
318C23×C61C2514yes—
319C23×C61C2513yes—
320C22×D61—212no—
321C22×D61—28no—
322C22×D61—216no—
323C22×D61C22×D4112yes—
324C22×D61C2514yes—
325C22×D61C2513yes—
326C22×D61C2511yescharacteristic
327Q8×C61—212no—
328Q8×C61—224no—
329Q8×C61C22×D414yes—
330D4×C61—224no—
331D4×C61—24no—
332D4×C61—28no—
333D4×C61C22×D4112yes—
334C2×C4×C61—224no—
335C2×C4×C61—224no—
336C2×C4×C61—212no—
337C2×C4×C61C22×D4112yes—
338C2×C4×C61C2516yes—
339C2×C4×C61C25112yes—
340C2×C4×C61C2511yescharacteristic
341C2×C4×C61C2513yes—
342C2×C4×C61C2512yes—
343C22⋊D61—224no—
344C22⋊D61—224no—
345C22⋊D61—28no—
346C22⋊D61—216no—
347C22⋊D61C22×D4124yes—
348C2×Dic61—224no—
349C2×Dic61—224no—
350C2×Dic61—212no—
351C2×Dic61C22×D4112yes—
352C2×Dic61C2516yes—
353C2×Dic61C25112yes—
354C2×Dic61C2511yescharacteristic
355C2×Dic61C2513yes—
356C2×Dic61C2512yes—
357D244—224no—
358D244—24no—
359D244—28no—
360D244C22×D4112yes—
361C4×D61—224no—
362C4×D61—248no—
363C4×D61—212no—
364C4×D61—224no—
365C4×D61—212no—
366C4×D61—224no—
367C4×D61—212no—
368C4×D61C22×D4112yes—
369C4×D61C22×D414yes—
370C4×D61C22×D4112yes—
371C4×D61C22×D4112yes—
372C4×D612−1+418yescomplemented
373Dic122—212no—
374Dic122—224no—
375Dic122—224no—
376Dic122—248no—
377Dic122C22×D4112yes—
378C2×#3499—611nomaximal, Sylow
379C22×C61—26no—
380C22×C61—24no—
381C22×C61—28no—
382C22×C61C23×D416yes—
383C22×C61C2611yescharacteristic
384C2×D61—26no—
385C2×D61—224no—
386C2×D61—24no—
387C2×D61—28no—
388C2×D61—416no—
389C2×D61C23×D416yes—
390C2×D61C23×D412yes—
391C2×D61C2×2−1+414yes—
392C4×C61—212no—
393C4×C61—26no—
394C4×C61C23×D412yes—
395C4×C61C23×D416yes—
396C4×C61C2×2−1+414yescomplemented
397Dic61—212no—
398Dic61—26no—
399Dic61C23×D412yes—
400Dic61C23×D416yes—
401Dic61C2×2−1+414yescomplemented
402C22×2−1+4—612no—
403#3499—612no—
404#3499—614no—
405#3499—6112no—
406#3499—616no—
407#3499—613no—
408#3499—613no—
409#3499—611no—
410#3499D6111yescharacteristic, direct product factor
411C2×D4×Q8—614no—
412C2×#547—6112no—
413C2×#536—616no—
414C2×#532—613no—
415C22×C4⋊Q8—613no—
416C2×C4×#41—611no—
417C2×C61—26no—
418C2×C61—44no—
419C2×C61C24×D411yescharacteristic
420C2×C61C22×2−1+412yes—
421D61—26no—
422D61—44no—
423D61#349914yesdirect product factor
424C2×2−1+4—616no—
425C2×2−1+4—6112no—
426C2×2−1+4—612no—
427C2×2−1+4—614no—
428C2×2−1+4—616no—
429C2×2−1+4—12232no—
430C2×2−1+4C2×D6112yescomplemented
431C22×#41—611no—
432C22×#41—616no—
433C22×#41—6112no—
434C23×Q8—616no—
435C23×Q8—614no—
436D4×Q8—618no—
437D4×Q8—6112no—
438D4×Q8—6124no—
439D4×Q8—614no—
440D4×Q8—6112no—
441D4×Q8C2×D6114yescomplemented
442#547—6124no—
443#547—6112no—
444#547—6148no—
445#547—6124no—
446#547—6124no—
447#547—6112no—
448#547—6112no—
449#547—6124no—
450#547C2×D61112yescomplemented
451#536—616no—
452#536—616no—
453#536—6112no—
454#536—6112no—
455#536—6124no—
456#536—6124no—
457#536—616no—
458#536C2×D6116yescomplemented
459#532—616no—
460#532—613no—
461#532—613no—
462#532—616no—
463#532—6112no—
464#532—6112no—
465#532—613no—
466#532C2×D6113yescomplemented
467C2×C4⋊Q8—616no—
468C2×C4⋊Q8—613no—
469C2×C4⋊Q8—616no—
470C2×C4⋊Q8—6112no—
471C2×C4⋊Q8—616no—
472C2×C4⋊Q8—616no—
473C2×C4⋊Q8—6112no—
474C2×C4⋊Q8—6112no—
475C2×C4⋊Q8—613no—
476C2×C4⋊Q8C2×D6113yescomplemented
477C2×#127—611no—
478C2×#124—616no—
479C2×#123—6124no—
480C2×C22⋊Q8—6124no—
481C2×#121—6112no—
482C4×#41—611no—
483C4×#41—612no—
484C4×#41—616no—
485C4×#41—613no—
486C4×#41—613no—
487C4×#41C2×D6111yescharacteristic, complemented
488C2×C4×Q8—612no—
489C2×C4×D4—616no—
490C2×C4×D4—6112no—
491C2×#117—613no—
492C22×C4⋊C4—6112no—
493C22×C42—613no—
494C61C2×#349911yescharacteristic, complemented, Sylow
4952−1+4—216no—
4962−1+4—12232no—
4972−1+4—12248no—
4982−1+4—12296no—
4992−1+4—12248no—
5002−1+4—12216no—
501C2×#41—6116no—
502C2×#41—611no—
503C2×#41—616no—
504C2×#41—6112no—
505C2×#41—613no—
506C2×#41—6112no—
507C2×#41—616no—
508C2×#41—6112no—
509C2×#41—6124no—
510C2×#41—613no—
511C2×#41—6112no—
512C2×#41—616no—
513C2×#41—6112no—
514C2×#41—6124no—
515C2×#41—12248no—
516C2×#41—12296no—
517C2×#41C22×D6116yes—
518C2×#41C22×D61112yes—
519C2×#41C22×D6111yescharacteristic
520C22×Q8—611no—
521C22×Q8—6112no—
522C22×Q8—616no—
523C22×Q8—6112no—
524C22×Q8—6112no—
525C22×Q8—6112no—
526C22×Q8—614no—
527C22×Q8—6112no—
528C22×Q8—616no—
529C22×Q8—6112no—
530C22×Q8—12248no—
531C22×Q8—12232no—
532C22×Q8C22×D6116yes—
533C22×Q8C22×D6114yes—
534C22×D4—613no—
535C22×D4—614no—
536C22×D4—6112no—
537C22×D4—612no—
538C23×C4—613no—
539C23×C4—616no—
540C23×C4—6112no—
541C23×C4—6112no—
542C4⋊Q8—616no—
543C4⋊Q8—6112no—
544C4⋊Q8—6124no—
545C4⋊Q8—6112no—
546C4⋊Q8—6124no—
547C4⋊Q8—6124no—
548C4⋊Q8—6124no—
549C4⋊Q8—613no—
550C4⋊Q8—616no—
551C4⋊Q8—6112no—
552C4⋊Q8C22×D6113yes—
553C4⋊Q8C22×D6116yes—
554C4⋊Q8C22×D61112yes—
555#127—612no—
556#127—614no—
557#127—611no—
558#127C22×D6111yescharacteristic
559#124—616no—
560#124—616no—
561#124—6124no—
562#124—616no—
563#124C22×D6116yes—
564#123—6124no—
565#123—6124no—
566#123—6148no—
567#123—6148no—
568#123—6124no—
569#123C22×D61124yes—
570C22⋊Q8—6124no—
571C22⋊Q8—6124no—
572C22⋊Q8—6148no—
573C22⋊Q8—6124no—
574C22⋊Q8—6148no—
575C22⋊Q8C22×D61124yes—
576#121—6112no—
577#121—6124no—
578#121—6112no—
579#121—6112no—
580#121—6124no—
581#121C22×D61112yes—
582C4×Q8—612no—
583C4×Q8—616no—
584C4×Q8—616no—
585C4×Q8C22×D6112yes—
586C4×D4—616no—
587C4×D4—6112no—
588C4×D4—6112no—
589C4×D4—6124no—
590C4×D4—616no—
591C4×D4—6112no—
592C4×D4—6112no—
593C4×D4—6124no—
594C4×D4—616no—
595C4×D4—6112no—
596C4×D4C22×D6116yes—
597C4×D4C22×D61112yes—
598#117—613no—
599#117—616no—
600#117—616no—
601#117—616no—
602#117C22×D6113yes—
603C2×C4⋊C4—6124no—
604C2×C4⋊C4—6112no—
605C2×C4⋊C4—6112no—
606C2×C4⋊C4—6124no—
607C2×C4⋊C4—6124no—
608C2×C4⋊C4—6124no—
609C2×C4⋊C4—616no—
610C2×C4⋊C4C22×D61112yes—
611C2×C22⋊C4—616no—
612C2×C22⋊C4—6124no—
613C2×C42—616no—
614C2×C42—613no—
615C2×C42—613no—
616C2×C42—616no—
617C2×C42—616no—
618C2×C42—613no—
619C2×C42—613no—
620C2×C42—611no—
621C2×C42C22×D6113yes—
622C24—613no—
623C24—614no—
624#41—248no—
625#41—224no—
626#41—618no—
627#41—6124no—
628#41—6124no—
629#41—12248no—
630#41—12296no—
631#41—12248no—
632#41—12248no—
633#41—12224no—
634#41—12224no—
635#41—12296no—
636#41—12248no—
637#41—12248no—
638#41—12224no—
639#41D4×D6118yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—618no—
643C2×Q8—613no—
644C2×Q8—6124no—
645C2×Q8—6112no—
646C2×Q8—6112no—
647C2×Q8—616no—
648C2×Q8—12248no—
649C2×Q8—12248no—
650C2×Q8—12224no—
651C2×Q8—12248no—
652C2×Q8—12248no—
653C2×Q8—12248no—
654C2×Q8—12248no—
655C2×Q8—12216no—
656C2×Q8—12224no—
657C2×Q8C23×D61112yes—
658C2×Q8C23×D6116yes—
659C2×Q8C23×D6111yescharacteristic
660C2×D4—616no—
661C2×D4—6124no—
662C2×D4—618no—
663C2×D4—6112no—
664C2×D4—6112no—
665C2×D4—614no—
666C2×D4—613no—
667C2×D4—614no—
668C2×D4—6112no—
669C2×D4—612no—
670C2×D4—1228no—
671C2×D4—12216no—
672C2×D4—12248no—
673C2×D4C23×D6114yes—
674C2×D4C23×D61112yes—
675C2×D4C23×D6112yes—
676C2×D4C23×D6113yes—
677C22×C4—613no—
678C22×C4—6124no—
679C22×C4—612no—
680C22×C4—611no—
681C22×C4—613no—
682C22×C4—613no—
683C22×C4—613no—
684C22×C4—616no—
685C22×C4—6112no—
686C22×C4—6112no—
687C22×C4—616no—
688C22×C4—616no—
689C22×C4—616no—
690C22×C4—6112no—
691C22×C4—6124no—
692C22×C4—6112no—
693C22×C4—6112no—
694C22×C4—12248no—
695C22×C4—12224no—
696C22×C4—12248no—
697C22×C4C23×D6116yes—
698C22×C4C23×D61112yes—
699C22×C4C23×D61112yes—
700C22×C4C23×D6113yes—
701C4⋊C4—6124no—
702C4⋊C4—6112no—
703C4⋊C4—6148no—
704C4⋊C4—6124no—
705C4⋊C4—6112no—
706C4⋊C4—616no—
707C4⋊C4C23×D61112yes—
708C4⋊C4C23×D61124yes—
709C4⋊C4C23×D6116yes—
710C22⋊C4—616no—
711C22⋊C4—6124no—
712C22⋊C4—6112no—
713C22⋊C4—6124no—
714C22⋊C4—6124no—
715C22⋊C4C23×D6116yes—
716C22⋊C4C23×D61124yes—
717C42—611no—
718C42—612no—
719C42—616no—
720C42—613no—
721C42—616no—
722C42—616no—
723C42—616no—
724C42C23×D6111yescharacteristic
725C42C23×D6113yes—
726C42C23×D6116yes—
727C23—611no—
728C23—6112no—
729C23—613no—
730C23—614no—
731C23—12212no—
732C23—1228no—
733C23—12216no—
734C23C24×D6114yes—
735C23C24×D6113yes—
736Q8—224no—
737Q8—212no—
738Q8—6112no—
739Q8—12224no—
740Q8—12248no—
741Q8—12224no—
742Q8—12212no—
743Q8C2×D4×D6114yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—6124no—
748D4—6112no—
749D4—12224no—
750D4—12216no—
751D4—1228no—
752D4—12224no—
753D4—12224no—
754D4—1224no—
755D4—1228no—
756D4C2×D4×D61112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—6112no—
761C2×C4—612no—
762C2×C4—611no—
763C2×C4—613no—
764C2×C4—614no—
765C2×C4—6112no—
766C2×C4—6112no—
767C2×C4—6112no—
768C2×C4—618no—
769C2×C4—616no—
770C2×C4—6112no—
771C2×C4—12212no—
772C2×C4—12224no—
773C2×C4—12212no—
774C2×C4—12224no—
775C2×C4—12248no—
776C2×C4—12212no—
777C2×C4—12224no—
778C2×C4—12224no—
779C2×C4—12224no—
780C2×C4—12212no—
781C2×C4C2×D4×D61112yes—
782C2×C4C24×D6116yes—
783C2×C4C24×D61112yes—
784C2×C4C24×D6111yescharacteristic
785C2×C4C24×D6113yes—
786C2×C4C24×D6112yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—612no—
791C22—614no—
792C22—616no—
793C22—12224no—
794C22—1226no—
795C22—1224no—
796C22—1228no—
797C22—24416no—
798C22C22×D4×D6116yes—
799C22C25×D6111yescharacteristic
800C4—212no—
801C4—26no—
802C4—612no—
803C4—616no—
804C4—614no—
805C4—12212no—
806C4—1226no—
807C4C22×D4×D6116yes—
808C4C22×D4×D6112yes—
809C42−1+4×D6114yescomplemented
810C2—26no—
811C2—44no—
812C2—614no—
813C2—1226no—
814C2—2444no—
815C2C23×D4×D6111yescharacteristic
816C2C2×2−1+4×D6112yes—
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3499C2
hypercenter#3499D61
hypocenterC61C2×#3499
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D61C2semidirect
2. #21459604C2semidirect
3. #21459603C2semidirect
4. #21459602C2semidirect
5. #21459601C2semidirect
6. #21459600C2semidirect
7. #21459599C2semidirect
8. #21459598C2semidirect
9. D4×Q8×D61C2semidirect
10. #547×D61C2semidirect
11. #536×D61C2semidirect
12. #532×D61C2semidirect
13. C2×C4⋊Q8×D61C2semidirect
14. C4×#41×D61C2semidirect
15. C61×#3499C2semidirect
16. C2×#14519825C22semidirect
17. C2×#14519825C22semidirect
18. C2×#14519824C22semidirect
19. C2×#14519824C22semidirect
20. C2×#14519824C22semidirect
27. Q8×D244C22semidirect
28. D4×Dic122C22semidirect
29. #16840427C22semidirect
30. Q8×C22⋊D61C22semidirect
31. #16840425C22semidirect
32. #16840417C22semidirect
33. #16840416C22semidirect
34. #16840415C22semidirect
35. #16840414C22semidirect
36. #16840413C22semidirect
37. #16840412C22semidirect
38. #16840411C22semidirect
39. #16840410C22semidirect
40. #16840338C22semidirect
41. #16840337C22semidirect
42. #16840336C22semidirect
43. #16840335C22semidirect
44. #16840334C22semidirect
45. #16840333C22semidirect
46. #16840332C22semidirect
47. #16840313C22semidirect
48. #16840312C22semidirect
49. #16840311C22semidirect
50. #16840310C22semidirect
51. #16840309C22semidirect
52. #16840308C22semidirect
53. #16840307C22semidirect
54. C2×#14519777C22semidirect
55. C2×#14519776C22semidirect
56. C2×#14519775C22semidirect
60. C4⋊Q8×D61C22semidirect
61. C4⋊Q8×D61C22semidirect
62. C4⋊Q8×D61C22semidirect
68. #41×Dic61C22semidirect
69. C4×#11758226C22semidirect
70. C4×#11758222C22semidirect
71. #16840230C22semidirect
72. C4×#11758224C22semidirect
79. C2×2−1+4×C61C22semidirect
80. D4×Q8×C61C22semidirect
81. C61×#547C22semidirect
82. C61×#536C22semidirect
83. C61×#532C22semidirect
84. C2×C4⋊Q8×C61C22semidirect
85. C4×#41×C61C22semidirect
106. #41×D61D4semidirect
217. #41×C61C2×D4semidirect
242. #11758226C2×D4semidirect
254. #11758224C2×D4semidirect
263. #11758222C2×D4semidirect
372. C4×D612−1+4semidirect
396. C4×C61C2×2−1+4semidirect
401. Dic61C2×2−1+4semidirect
410. #3499D61direct (N × H)
423. D61#3499direct (N × H)
430. C2×2−1+4C2×D61semidirect
441. D4×Q8C2×D61semidirect
450. #547C2×D61semidirect
458. #536C2×D61semidirect
466. #532C2×D61semidirect
476. C2×C4⋊Q8C2×D61semidirect
487. C4×#41C2×D61semidirect
494. C61C2×#3499semidirect
639. #41D4×D61semidirect
809. 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
#214596042
#214596032
#214596022
#214596012
#214596002
#214595992
#214595982
D4×Q8×D612
#547×D612
#536×D612
#532×D612
C2×C4⋊Q8×D612
C4×#41×D612
C61×#34992
C2×#349961