Finite Group Databasebeta

← #29716629

Subgroups — #29716629

Order 15616.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C2×#16839872C211yesmaximal, characteristic
3#21450737C211yesmaximal, characteristic, complemented
4#21447154C211yesmaximal, characteristic, complemented
5#21447149C211yesmaximal, characteristic, complemented
6#21446962C211yesmaximal, characteristic, complemented
7#21446952C211yesmaximal, characteristic, complemented
8#21446789C211yesmaximal, characteristic, complemented
9#21446760C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic
11#21446167C211yesmaximal, characteristic
12#21446080C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445819C211yesmaximal, characteristic, complemented
15C2×C61×#554C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519753—21no—
18C2×C4×D244C2211yescharacteristic
19#16840059—24no—
20#16839872—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32#16839684—21no—
33#16839684—21no—
34#16839664C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839632C2211yescharacteristic
39#16839619—21no—
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#554—24no—
51C61×#554—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#125×C61C2211yescharacteristic
54C2×#125×C61C2211yescharacteristic
55C2×C22⋊Q8×C61—21no—
56C2×C22⋊Q8×C61—21no—
57C2×C22⋊Q8×C61—21no—
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C22×C4⋊C4×C61—21no—
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199Q814yescomplemented
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519753—44no—
73C4×D244—22no—
74C4×D244—22no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87#14519710—22no—
88#14519708—22no—
89#14519708—22no—
90C4⋊#92418—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519697—22no—
95#14519697—22no—
96#14519697—22no—
97#14519688—22no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61D411yescharacteristic
102C22×D4×C61C2311yescharacteristic
103C23×C4×C61—21no—
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C4⋊Q8×C61—22no—
107C4⋊Q8×C61—22no—
108#125×C61—22no—
109#125×C61—22no—
110#125×C61—22no—
111#125×C61D414yes—
112C22⋊Q8×C61—28no—
113C22⋊Q8×C61—28no—
114C22⋊Q8×C61—28no—
115C4×Q8×C61—22no—
116C4×Q8×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61D414yes—
123C2×C4⋊C4×C61—28no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C24×C61—21no—
142C23×D61—21no—
143C2×Q8×C61—24no—
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61—41no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C2×D412yes—
153C2×D4×C61C2×Q812yes—
154C2×D4×C61#4112yes—
155C22×C4×C61—24no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—24no—
160C22×C4×C61—24no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61—81no—
166C22×C4×C61—81no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244C2×Q812yes—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—24no—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C2×D412yes—
198C4⋊C4×C61C2×D412yes—
199C4⋊C4×C61C2×D412yes—
200C22⋊C4×C61—24no—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—24no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61C2×D412yes—
208C42×C61C2×D412yes—
209#11758199—28no—
210#11758198—42no—
211#11758198—42no—
212#11758198—42no—
213#11758198—81no—
214#11758198—81no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61—81no—
223#11758196—42no—
224#11758196—42no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×Q812yes—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C22×D411yescharacteristic
245C22×D61—22no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252Q8×C61—44no—
253Q8×C61—84no—
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61C22⋊Q814yescomplemented
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—48no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—84no—
284C2×C4×C61—84no—
285C2×C4×C61#12012yes—
286C2×C4×C61#12012yes—
287C2×C4×C61AGL(1,ℤ/8)12yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×Q811yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C612−1+411yescharacteristic
293C2×C4×C612−1+411yescharacteristic
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303D244—22no—
304D244—22no—
305D244—41no—
306D244—41no—
307C4×D61—84no—
308#92418—22no—
309#92418—41no—
310#92418—41no—
311#92418—41no—
312#24347—611nomaximal, Sylow
313C22×C61—24no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61C2×#12011yescharacteristic
321C22×C61#54811yescharacteristic
322C22×C61D4×Q811yescharacteristic
323C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C61#57511yescharacteristic
325C22×C61#57611yescharacteristic
326C22×C61#57711yescharacteristic
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61C2×C22⋊Q811yescharacteristic
344C4×C61#53611yescharacteristic
345C4×C61#54811yescharacteristic
346C4×C61D4×Q811yescharacteristic
347Dic61—81no—
348Dic61—81no—
349Dic61—81no—
350C2×#554D6111yescharacteristic, complemented
351C2×#478—611no—
352C2×#442—611no—
353#2538—611no—
354#2059—611no—
355#2058—611no—
356#2025—611no—
357#2023—611no—
358#1992—611no—
359#1985—611no—
360#1879—611no—
361#1879—611no—
362#1864—611no—
363#1862—611no—
364#1802—611no—
365C2×C61—44no—
366C2×C61#240911yescharacteristic
367C2×C61#300611yescharacteristic
368C2×C61#301211yescharacteristic
369C2×C61#336611yescharacteristic
370C2×C61#337611yescharacteristic
371C2×C61#338411yescharacteristic
372C2×C61#338911yescharacteristic
373D61—82no—
374C22×D8—611no—
375#554—24no—
376#554—24no—
377C2×C4⋊Q8C2×D6111yescharacteristic
378C2×#125C2×D6111yescharacteristic
379C2×#125C2×D6111yescharacteristic
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—1221no—
384C2×C4×Q8C2×D6111yescharacteristic
385C2×C4×D4—611no—
386C2×C4×D4C2×D6111yescharacteristic
387C2×C4×D4C2×D6111yescharacteristic
388C2×C4×D4C2×D6111yescharacteristic
389C22×C4⋊C4—21no—
390#478—1224no—
391#442—1224no—
392C2×#107—611no—
393C2×#106—611no—
394C2×#106—611no—
395C2×C4⋊C8—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#97—611no—
403#396—1221no—
404#396—1221no—
405#390—611no—
406#390—611no—
407#389—611no—
408#389—611no—
409#384—611no—
410#380—1221no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#336—611no—
418#336—611no—
419#336—611no—
420#336—611no—
421C61#2434711yescharacteristic, complemented, Sylow
422C22×Q8—21no—
423C22×Q8C22⋊D6111yescharacteristic
424C22×D4—611no—
425C22×D4C22×D6111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—1221no—
430C2×D8—614no—
431C2×D8—1222no—
432C2×D8—1222no—
433C22×C8—611no—
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—611no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439#125—22no—
440#125—22no—
441#125—22no—
442#125C22⋊D6114yes—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—2444no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4C22⋊D6114yes—
457C2×C4⋊C4—28no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4C22⋊D6111yescharacteristic
471C2×C4⋊C4C22⋊D6111yescharacteristic
472C2×C4⋊C4C22⋊D6111yescharacteristic
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C42C22×D6111yescharacteristic
485C2×C42C22×D6111yescharacteristic
486C2×C42C22×D6111yescharacteristic
487#107—1222no—
488#106—1222no—
489#106—1222no—
490C4⋊C8—1222no—
491#102—1222no—
492#102—1222no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—1222no—
497#97—1222no—
498#95—1221no—
499#95—1221no—
500C24—21no—
501C24—1221no—
502C2×Q8—24no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—41no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—612no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4Q8×D6112yes—
518C2×D4#1175822612yes—
519C2×D4C2×C22⋊D6112yes—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—2442no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4C2×C22⋊D6111yescharacteristic
539C22×C4C2×C22⋊D6111yescharacteristic
540C22×C4C2×C22⋊D6111yescharacteristic
541C22×C4C2×C22⋊D6111yescharacteristic
542C22×C4C2×C22⋊D6111yescharacteristic
543C22×C4C2×C22⋊D6111yescharacteristic
544C22×C4C23×D6111yescharacteristic
545D8—1228no—
546C2×C8—612no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—4881no—
576C4⋊C4—2442no—
577C4⋊C4—2442no—
578C4⋊C4—2442no—
579C4⋊C4C2×C22⋊D6112yes—
580C4⋊C4C2×C22⋊D6112yes—
581C4⋊C4C2×C22⋊D6112yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—4881no—
586C22⋊C4—4881no—
587C22⋊C4—2442no—
588C22⋊C4—2442no—
589C22⋊C4—2442no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42C2×C22⋊D6112yes—
595C42C2×C22⋊D6112yes—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—1222no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23—2441no—
610C23C22×C22⋊D6111yescharacteristic
611Q8—44no—
612Q8—84no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—1222no—
617D4—1222no—
618D4—2441no—
619D4—2441no—
620D4#1451975314yescomplemented
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4—4884no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4#1451974612yes—
659C2×C4#1451974612yes—
660C2×C4#1451980212yes—
661C2×C4C22×C22⋊D6111yescharacteristic
662C2×C4C22×C22⋊D6111yescharacteristic
663C2×C4C2×Q8×D6111yescharacteristic
664C2×C4C2×#1175822611yescharacteristic
665C2×C4#1451982511yescharacteristic
666C2×C4#1451982511yescharacteristic
667C8—1222no—
668C8—2441no—
669C8—2441no—
670C8—2441no—
671C22—24no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—4881no—
679C22—4881no—
680C22—4881no—
681C22—4881no—
682C22—2442no—
683C22—2442no—
684C22—2442no—
685C22C2×#1451974611yescharacteristic
686C22#1684042311yescharacteristic
687C22Q8×C22⋊D6111yescharacteristic
688C22C2×#1451980211yescharacteristic
689C22#1684056011yescharacteristic
690C22#1684056511yescharacteristic
691C22#1684057311yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—4881no—
702C4—4881no—
703C4—4881no—
704C4C2×#1451975311yescharacteristic
705C4#1684033611yescharacteristic
706C4#1684042311yescharacteristic
707C4Q8×C22⋊D6111yescharacteristic
708C2—44no—
709C2—4882no—
710C2#2144917811yescharacteristic
711C2#2145507111yescharacteristic
712C2#2145512311yescharacteristic
713C2#2145852611yescharacteristic
714C2#2145864611yescharacteristic
715C2#2145871811yescharacteristic
716C2#2145877311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#554D61
hypocenterC61#24347
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
3. #21450737C2semidirect
4. #21447154C2semidirect
5. #21447149C2semidirect
6. #21446962C2semidirect
7. #21446952C2semidirect
8. #21446789C2semidirect
9. #21446760C2semidirect
12. #21446080C2semidirect
13. #21446066C2semidirect
14. #21445819C2semidirect
15. C2×C61×#554C2semidirect
67. C2×#11758199Q8semidirect
257. D4×C61C22⋊Q8semidirect
350. C2×#554D61semidirect
421. C61#24347semidirect
620. D4#14519753semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×#168398722
#214507372
#214471542
#214471492
#214469622
#214469522
#214467892
#214467602
#214461672
#214460802
#214460662
#214458192
C2×C61×#5542
#2434761