Finite Group Databasebeta

← #29841065

Subgroups — #29841065

Order 15616.

5106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic, complemented
3C2×C4×#11758226C211yesmaximal, characteristic, complemented
4Q8×C22⋊Dic61C211yesmaximal, characteristic, complemented
5Q8×#11758198C211yesmaximal, characteristic, complemented
6Q8×#11758198C211yesmaximal, characteristic, complemented
7#21448650C213yesmaximal, complemented
8#21448648C213yesmaximal, complemented
9#21448648C213yesmaximal, complemented
10#21448647C213yesmaximal, complemented
11#21448408C213yesmaximal, complemented
12#21448402C213yesmaximal, complemented
13#21448305C213yesmaximal, complemented
14#391×D61C213yesmaximal, complemented
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C2×#14519825—28no—
17C2×#14519825—28no—
18C2×#14519825C4116yescomplemented
19C22×#11758226C2213yes—
20C22×#11758226C2211yescharacteristic
21C22×#11758222C2213yes—
22C22×#11758222C2213yes—
23C22×Q8×D61C2213yes—
24C22×Q8×D61C2211yescharacteristic
25#16840244—28no—
26C4×#11758226—28no—
27C2×Q8×Dic61C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×D244C2213yes—
30C2×C4×D244C2213yes—
31C2×#14519739C2213yes—
32C2×#14519739C2213yes—
33C2×#14519735C2213yes—
34C2×#14519734C2213yes—
35C2×C4⋊C4×D61C2213yes—
36C2×C42×D61C2213yes—
37#16839669C2213yes—
38#16839669C2213yes—
39#16839668C2213yes—
40#16839668C2213yes—
41#16839667C2213yes—
42#16839667C2213yes—
43#16839666C2213yes—
44#16839666C2216yes—
45#16839666C2213yes—
46#16839662C2211yescharacteristic
47#16839662C2213yes—
48#16839640C2213yes—
49#16839640C2213yes—
50#16839640C2216yes—
51#16839638C2213yes—
52#16839638C2213yes—
53#16839638C2216yes—
54#16839624C2216yes—
55#16839624C2216yes—
56#16839622C2213yes—
57#16839619C2213yes—
58#16839619C2213yes—
59C4×#11758198C2213yes—
60C4×#11758198C2213yes—
61C4×C22⋊Dic61C2213yes—
62#95×D61C2216yes—
63#95×D61C2216yes—
64C23×Q8×C61C2211yescharacteristic
65C2×C4×Q8×C61C2211yescharacteristic
66C2×C4×Q8×C61C2211yescharacteristic
67C61×#391C2213yes—
68C61×#391C2213yes—
69C61×#380C2213yes—
70C4×C22⋊C4×C61C2213yes—
71#14519825—2128no—
72C2×#11758226—212no—
73C2×#11758226—212no—
74C2×#11758226C2×C418yes—
75C2×#11758226C2×C4124yescomplemented
76C2×#11758226D418yes—
77C2×#11758226D418yes—
78C2×#11758222—212no—
79C2×#11758222—212no—
80C2×#11758222—212no—
81C2×#11758222—212no—
82C2×#11758222C2×C4124yescomplemented
83C2×#11758222C2×C4124yescomplemented
84C22×Dic122C2313yes—
85C22×Dic122C2313yes—
86C2×Q8×D61—24no—
87C2×Q8×D61—24no—
88C2×Q8×D61—212no—
89C2×Q8×D61—212no—
90C2×Q8×D61C2×C418yescomplemented
91C2×Q8×D61C2×C4124yescomplemented
92C22×D244C2313yes—
93C22×D244C2313yes—
94C22×C22⋊D61C2313yes—
95C22×C22⋊D61C2311yescharacteristic
96C22×C4×D61C2313yes—
97C22×C4×D61C2313yes—
98C22×C4×D61C2316yes—
99C22×C4×D61C2313yes—
100C22×C4×D61C2316yes—
101C22×C4×D61C2313yes—
102Q8×Dic61—24no—
103Q8×Dic61—24no—
104C4×D244—212no—
105C4×D244—212no—
106#14519739—212no—
107#14519739—212no—
108#14519735—212no—
109#14519734—212no—
110C2×C4⋊Dic61C2313yes—
111C2×C4⋊Dic61C2313yes—
112C2×#11758196C2313yes—
113C2×#11758196C2311yescharacteristic
114C4⋊C4×D61—212no—
115C2×C22⋊Dic61C2311yescharacteristic
116C2×C22⋊Dic61C2313yes—
117C2×#11758198C2313yes—
118C2×#11758198C2313yes—
119C2×#11758198C2316yes—
120C2×#11758198C2311yescharacteristic
121C2×#11758198C2311yescharacteristic
122C2×#11758198C2313yes—
123C2×#11758198C2313yes—
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2313yes—
126C2×C4×Dic61C2313yes—
127C2×C4×Dic61C2313yes—
128C42×D61—212no—
129#14519684C2313yes—
130#14519684C2313yes—
131#14519684C2313yes—
132#14519684C2316yes—
133#14519684C2316yes—
134#14519684C2316yes—
135#14519684C2313yes—
136#14519684C2313yes—
137#14519684C2313yes—
138C22×Q8×C61—24no—
139C22×Q8×C61—24no—
140C22×Q8×C61C2×C418yescomplemented
141C22×Q8×C61C2313yes—
142C22×Q8×C61C2311yescharacteristic
143C23×C4×C61C2313yes—
144C4×Q8×C61—24no—
145C4×Q8×C61—24no—
146C2×C4⋊C4×C61C2313yes—
147C2×C4⋊C4×C61C2313yes—
148C2×C22⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61C2313yes—
150C2×C42×C61C2313yes—
151C2×C42×C61C2313yes—
152#95×C61C2313yes—
153#95×C61C2313yes—
154#95×C61C2316yes—
155C24×C61C2411yescharacteristic
156C23×D61C2411yescharacteristic
157C23×D61C2413yes—
158C2×Q8×C61—232no—
159C2×Q8×C61—26no—
160C2×Q8×C61—26no—
161C2×Q8×C61C22×C4112yes—
162C2×Q8×C61C22×C414yes—
163C2×Q8×C61C2×D414yes—
164C2×Q8×C61C2×D414yes—
165C22×C4×C61—26no—
166C22×C4×C61—26no—
167C22×C4×C61C22×C4112yes—
168C22×C4×C61C2413yes—
169C22×C4×C61C2413yes—
170C22×C4×C61C2411yescharacteristic
171C22×C4×C61C2413yes—
172C22×C4×C61C2411yescharacteristic
173C22×C4×C61C2413yes—
174C2×C22⋊D61—26no—
175C2×C22⋊D61—26no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61C22×C4112yes—
179C2×C22⋊D61C22×C414yes—
180C22×Dic61C2413yes—
181C22×Dic61C2413yes—
182C22×Dic61C2411yescharacteristic
183C22×Dic61C2413yes—
184C22×Dic61C2411yescharacteristic
185C22×Dic61C2411yescharacteristic
186#11758226—296no—
187#11758226C22⋊C4164yescomplemented
188Q8×D61—232no—
189Q8×D61—296no—
190#11758222—296no—
191#11758222—296no—
192C2×D244—26no—
193C2×D244—26no—
194C2×D244C22×C4112yes—
195C2×D244C22×C4112yes—
196C2×D244C2×D4112yes—
197C2×D244C2×D4112yes—
198C2×C4×D61—212no—
199C2×C4×D61—212no—
200C2×C4×D61—26no—
201C2×C4×D61—26no—
202C2×C4×D61—26no—
203C2×C4×D61—26no—
204C2×C4×D61—26no—
205C2×C4×D61—26no—
206C2×C4×D61—212no—
207C2×C4×D61—43no—
208C2×C4×D61—43no—
209C2×C4×D61—46no—
210C2×C4×D61—46no—
211C2×C4×D61C22×C4124yes—
212C2×C4×D61C22×C4112yes—
213C2×C4×D61C22×C4112yes—
214C2×C4×D61C2×D4112yes—
215C2×C4×D61C2×D4112yes—
216C2×Dic122—26no—
217C2×Dic122—26no—
218C2×Dic122—26no—
219C2×Dic122—26no—
220C2×Dic122C22×C4112yes—
221C2×Dic122C22×C4112yes—
222C4⋊C4×C61—26no—
223C4⋊C4×C61—26no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—43no—
226C42×C61—26no—
227C42×C61—26no—
228C22⋊Dic61—22no—
229C22⋊Dic61—43no—
230#11758198—26no—
231#11758198—26no—
232#11758198—212no—
233#11758198—22no—
234#11758198—22no—
235#11758198—43no—
236#11758198—43no—
237C4⋊Dic61—26no—
238C4⋊Dic61—26no—
239#11758196—26no—
240#11758196—22no—
241C4×Dic61—26no—
242C4×Dic61—26no—
243C4×Dic61—22no—
244C4×Dic61—26no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61C23×C412yes—
252C23×C61C2511yescharacteristic
253C22×D61—23no—
254C22×D61—23no—
255C22×D61—23no—
256C22×D61—23no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61C23×C412yes—
264C22×D61C23×C416yes—
265C22×D61C22×D416yes—
266C22×D61C22×D416yes—
267Q8×C61—224no—
268Q8×C61C2×C22⋊C4116yes—
269C2×C4×C61—21no—
270C2×C4×C61—23no—
271C2×C4×C61—23no—
272C2×C4×C61—21no—
273C2×C4×C61—224no—
274C2×C4×C61—23no—
275C2×C4×C61—21no—
276C2×C4×C61—23no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—23no—
280C2×C4×C61—23no—
281C2×C4×C61—23no—
282C2×C4×C61—23no—
283C2×C4×C61C23×C416yes—
284C2×C4×C61C23×C416yes—
285C2×C4×C61C22×D416yes—
286C2×C4×C61C22×D416yes—
287C2×C4×C612−1+412yescomplemented
288C22⋊D61—224no—
289C22⋊D61—28no—
290C2×Dic61—21no—
291C2×Dic61—23no—
292C2×Dic61—23no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—23no—
296C2×Dic61—23no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—23no—
300C2×Dic61—23no—
301C2×Dic61—23no—
302C2×Dic61—23no—
303C2×Dic61C23×C416yes—
304C2×Dic61C23×C412yes—
305C2×Dic61C22×D412yes—
306C2×Dic61C22×D412yes—
307C2×Dic612−1+412yescomplemented
308D244—224no—
309D244C2×C22⋊C4148yes—
310C4×D61—248no—
311C4×D61—224no—
312C4×D61—412no—
313C4×D61—412no—
314C4×D61—812no—
315C4×D61C2×C22⋊C4148yes—
316Dic122—224no—
317Dic122—224no—
318#34259—611nomaximal, Sylow
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61C24×C411yescharacteristic
327C22×C61C23×D411yescharacteristic
328C22×C61C23×D411yescharacteristic
329C22×C61C2×2−1+411yescharacteristic
330C22×C61C2×2−1+411yescharacteristic
331C22×C61#58511yescharacteristic
332C22×C61#58511yescharacteristic
333C2×D61—26no—
334C2×D61—26no—
335C2×D61—26no—
336C2×D61—26no—
337C2×D61—26no—
338C2×D61—26no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61C22×C22⋊C4112yes—
347C4×C61—26no—
348C4×C61—22no—
349C4×C61—43no—
350C4×C61—41no—
351C4×C61—43no—
352C4×C61C22×C22⋊C4112yes—
353Dic61—26no—
354Dic61—22no—
355Dic61—43no—
356Dic61—41no—
357Dic61—43no—
358Dic61C22×C22⋊C414yes—
359C22×2−1+4—611no—
360C2×#520—611no—
361C2×C4×#41—611no—
362Q8×C22⋊C4—611no—
363Q8×C22⋊C4—611no—
364Q8×C22⋊C4—611no—
365Q8×C22⋊C4D6111yescharacteristic, complemented
366#2339—613no—
367#2339—613no—
368#2339—613no—
369#2339—613no—
370#2311—613no—
371#2310—613no—
372#2297—613no—
373C2×#391—613no—
374C2×C61—42no—
375C2×C61C23×C22⋊C411yescharacteristic
376C2×C61C4×2−1+411yescharacteristic
377C2×C61C4×2−1+411yescharacteristic
378C2×C61#348911yescharacteristic
379C2×C61#348911yescharacteristic
380C2×C61#349911yescharacteristic
381C2×C61#350011yescharacteristic
382D61—212no—
383D61—42no—
384C2×2−1+4—6116no—
385C2×2−1+4—1228no—
386C2×2−1+4—1228no—
387C22×#41—611no—
388C22×#41—613no—
389C22×#41—613no—
390C22×#41—613no—
391C23×Q8—613no—
392C23×Q8—611no—
393C23×Q8C2×D6111yescharacteristic
394#520—1228no—
395C4×#41—1228no—
396C2×C4×Q8—611no—
397C2×C4×Q8—611no—
398C2×C4×Q8C2×D6111yescharacteristic
399C2×C4×Q8C2×D6111yescharacteristic
400C2×C4×D4—613no—
401C2×C4×D4—613no—
402C2×C4×D4—613no—
403C2×C4×D4—613no—
404C2×#117—613no—
405C2×#117—613no—
406C22×C4⋊C4—613no—
407C22×C42—613no—
408#391—613no—
409#391—613no—
410#391—613no—
411#391—613no—
412#391—613no—
413#391—613no—
414#391—613no—
415#391—616no—
416#391—613no—
417#391C2×D6113yes—
418#391C2×D6113yes—
419#390—613no—
420#390—611no—
421#386—616no—
422#386—613no—
423#386—613no—
424#386—616no—
425#386—613no—
426#386—613no—
427#381—616no—
428#381—616no—
429#380—613no—
430#380—613no—
431#380—613no—
432#380C2×D6113yes—
433C4×C22⋊C4—613no—
434C4×C22⋊C4—613no—
435C4×C22⋊C4—613no—
436C4×C22⋊C4C2×D6113yes—
437C2×#95—616no—
438C2×#95—616no—
439C61#3425911yescharacteristic, complemented, Sylow
4402−1+4—122128no—
441C2×#41—618no—
442C2×#41—6124no—
443C2×#41—618no—
444C2×#41—618no—
445C2×#41—6124no—
446C2×#41—6124no—
447C2×#41—12212no—
448C2×#41—12212no—
449C2×#41—12212no—
450C2×#41—12212no—
451C2×#41—12212no—
452C2×#41—12212no—
453C22×Q8—24no—
454C22×Q8—24no—
455C22×Q8—6124no—
456C22×Q8—618no—
457C22×Q8—613no—
458C22×Q8—613no—
459C22×Q8—12212no—
460C22×Q8—12212no—
461C22×Q8—1224no—
462C22×Q8—1224no—
463C22×Q8C4×D6118yescomplemented
464C22×Q8C22×D6113yes—
465C22×Q8C22×D6111yescharacteristic
466C22×D4—613no—
467C22×D4—611no—
468C22×D4—613no—
469C22×D4—613no—
470C23×C4—613no—
471C23×C4—616no—
472C23×C4—613no—
473C23×C4—613no—
474C23×C4—613no—
475C23×C4—616no—
476C23×C4C22×D6113yes—
477C4×Q8—24no—
478C4×Q8—24no—
479C4×Q8—1224no—
480C4×Q8—1224no—
481C4×D4—12212no—
482C4×D4—12212no—
483C4×D4—12212no—
484C4×D4—12212no—
485#117—12212no—
486#117—12212no—
487C2×C4⋊C4—613no—
488C2×C4⋊C4—613no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—613no—
491C2×C4⋊C4—12212no—
492C2×C4⋊C4C22×D6113yes—
493C2×C4⋊C4C22×D6113yes—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—613no—
496C2×C22⋊C4—616no—
497C2×C22⋊C4—613no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—613no—
501C2×C22⋊C4—613no—
502C2×C22⋊C4—613no—
503C2×C22⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4C22×D6113yes—
505C2×C42—613no—
506C2×C42—613no—
507C2×C42—613no—
508C2×C42—611no—
509C2×C42—12212no—
510C2×C42C22×D6113yes—
511C2×C42C22×D6113yes—
512#95—613no—
513#95—613no—
514#95—613no—
515#95—616no—
516#95—616no—
517#95—616no—
518#95—613no—
519#95—613no—
520#95—613no—
521#95C22×D6113yes—
522#95C22×D6116yes—
523#95C22×D6113yes—
524C24—613no—
525C24—611no—
526C24C23×D6111yescharacteristic
527#41—6164no—
528#41—12296no—
529#41—12296no—
530#41—12296no—
531C2×Q8—232no—
532C2×Q8—26no—
533C2×Q8—26no—
534C2×Q8—6112no—
535C2×Q8—6112no—
536C2×Q8—1226no—
537C2×Q8—1226no—
538C2×Q8—12296no—
539C2×Q8—12232no—
540C2×Q8—1226no—
541C2×Q8—1226no—
542C2×Q8C2×C4×D61112yes—
543C2×Q8C2×C4×D6114yes—
544C2×Q8D4×D6114yes—
545C2×Q8D4×D6114yes—
546C2×D4—614no—
547C2×D4—6112no—
548C2×D4—6112no—
549C2×D4—6112no—
550C2×D4—6112no—
551C2×D4—6112no—
552C2×D4—1226no—
553C2×D4—1226no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1226no—
557C2×D4—1226no—
558C22×C4—26no—
559C22×C4—26no—
560C22×C4—611no—
561C22×C4—6112no—
562C22×C4—6112no—
563C22×C4—6112no—
564C22×C4—613no—
565C22×C4—611no—
566C22×C4—6124no—
567C22×C4—6112no—
568C22×C4—611no—
569C22×C4—613no—
570C22×C4—613no—
571C22×C4—1226no—
572C22×C4—12212no—
573C22×C4—12212no—
574C22×C4—12212no—
575C22×C4—1226no—
576C22×C4—1226no—
577C22×C4—1226no—
578C22×C4—1226no—
579C22×C4—1226no—
580C22×C4—2446no—
581C22×C4—2446no—
582C22×C4—2443no—
583C22×C4—2443no—
584C22×C4C2×C4×D61112yes—
585C22×C4C23×D6113yes—
586C22×C4C23×D6111yescharacteristic
587C22×C4C23×D6113yes—
588C22×C4C23×D6113yes—
589C22×C4C23×D6111yescharacteristic
590C22×C4C23×D6113yes—
591C4⋊C4—26no—
592C4⋊C4—26no—
593C4⋊C4—1226no—
594C4⋊C4—1222no—
595C4⋊C4—1226no—
596C4⋊C4—1226no—
597C22⋊C4—22no—
598C22⋊C4—43no—
599C22⋊C4—1222no—
600C22⋊C4—1226no—
601C22⋊C4—12212no—
602C22⋊C4—1226no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—2443no—
606C22⋊C4—2443no—
607C22⋊C4—2443no—
608C42—26no—
609C42—26no—
610C42—1222no—
611C42—1226no—
612C42—1226no—
613C42—1226no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—616no—
621C23—616no—
622C23—616no—
623C23—612no—
624C23—1223no—
625C23—1223no—
626C23—1223no—
627C23—1223no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23C22×C4×D6112yes—
635C23C24×D6111yescharacteristic
636Q8—224no—
637Q8—12224no—
638Q8—12224no—
639Q8C22⋊C4×D61116yes—
640D4—6148no—
641D4—12224no—
642D4—1228no—
643D4—12224no—
644C2×C4—21no—
645C2×C4—23no—
646C2×C4—23no—
647C2×C4—21no—
648C2×C4—224no—
649C2×C4—21no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—21no—
655C2×C4—23no—
656C2×C4—23no—
657C2×C4—23no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—6148no—
662C2×C4—616no—
663C2×C4—612no—
664C2×C4—12248no—
665C2×C4—1221no—
666C2×C4—1223no—
667C2×C4—1223no—
668C2×C4—1221no—
669C2×C4—12224no—
670C2×C4—1221no—
671C2×C4—1223no—
672C2×C4—1223no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1223no—
676C2×C4—1223no—
677C2×C4—1223no—
678C2×C4—1223no—
679C2×C4—48812no—
680C2×C4—24412no—
681C2×C4—24412no—
682C2×C4C22×C4×D6116yes—
683C2×C4C22×C4×D6116yes—
684C2×C4C2×D4×D6116yes—
685C2×C4C2×D4×D6116yes—
686C2×C4#1451982512yescomplemented
687C22—22no—
688C22—22no—
689C22—22no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—6112no—
695C22—1226no—
696C22—1226no—
697C22—1226no—
698C22—1226no—
699C22—1226no—
700C22—1226no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22—2441no—
708C22C23×C4×D6111yescharacteristic
709C22C22×D4×D6111yescharacteristic
710C22C22×D4×D6111yescharacteristic
711C222−1+4×D6111yescharacteristic
712C22C2×#1451982511yescharacteristic
713C22#1684059811yescharacteristic
714C22#1684059911yescharacteristic
715C4—26no—
716C4—22no—
717C4—43no—
718C4—41no—
719C4—43no—
720C4—614no—
721C4—1226no—
722C4—1222no—
723C4—2443no—
724C4—2441no—
725C4—2443no—
726C4C2×C22⋊C4×D61112yes—
727C2—42no—
728C2—12212no—
729C2—2442no—
730C2C22×C22⋊C4×D6111yescharacteristic
731C2#2145902811yescharacteristic
732C2C4×#1451982511yescharacteristic
733C2#2145949611yescharacteristic
734C2#2145949811yescharacteristic
735C2#2145960311yescharacteristic
736C2#2145961011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingQ8×C22⋊C4×C61C2
socle, cosocleC23×C61C25
prime radicalC22×#14519825C2
hypercenterQ8×C22⋊C4D61
hypocenterC61#34259
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16840244C2semidirect
3. C2×C4×#11758226C2semidirect
4. Q8×C22⋊Dic61C2semidirect
5. Q8×#11758198C2semidirect
6. Q8×#11758198C2semidirect
7. #21448650C2semidirect
8. #21448648C2semidirect
9. #21448648C2semidirect
10. #21448647C2semidirect
11. #21448408C2semidirect
12. #21448402C2semidirect
13. #21448305C2semidirect
14. #391×D61C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
18. C2×#14519825C4semidirect
75. C2×#11758226C2×C4semidirect
82. C2×#11758222C2×C4semidirect
83. C2×#11758222C2×C4semidirect
90. C2×Q8×D61C2×C4semidirect
91. C2×Q8×D61C2×C4semidirect
140. C22×Q8×C61C2×C4semidirect
187. #11758226C22⋊C4semidirect
287. C2×C4×C612−1+4semidirect
307. C2×Dic612−1+4semidirect
365. Q8×C22⋊C4D61semidirect
439. C61#34259semidirect
463. C22×Q8C4×D61semidirect
686. C2×C4#14519825semidirect

Maximal subgroups

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

subgroupindex
C22×#145198252
C2×#168402442
C2×C4×#117582262
Q8×C22⋊Dic612
Q8×#117581982
#214486502
#214486482
#214486472
#214484082
#214484022
#214483052
#391×D612
Q8×C22⋊C4×C612
#3425961