Finite Group Databasebeta

← #30620799

Subgroups — #30620799

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462329C211yesmaximal, characteristic
2#21462328C211yesmaximal, characteristic
3#21461924C211yesmaximal, characteristic, complemented
4#21461923C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461882C211yesmaximal, characteristic, complemented
7#21461881C211yesmaximal, characteristic, complemented
8#21461880C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic
10#21461722C211yesmaximal, characteristic
11#21461697C211yesmaximal, characteristic
12#21461635C211yesmaximal, characteristic, complemented
13#106×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic
15#428×D61C211yesmaximal, characteristic
16C2×#14519846C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18D61⋊(C22⋊C8)C2211yescharacteristic
19C2×#14519831C2211yescharacteristic
20C2×C8×#6923C2211yescharacteristic
21#16840713C2211yescharacteristic
22#16840713C2211yescharacteristic
23#16840713C2211yescharacteristic
24#16840713C2211yescharacteristic
25#16840712—21no—
26#16840712—21no—
27#16840711—21no—
28#16840711—21no—
29#16840706—21no—
30#16840704—21no—
31#16840704C2211yescharacteristic
32#16840704C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4×C22⋊#6923—21no—
38C4×C22⋊#6923C2211yescharacteristic
39#16840698—21no—
40#16840636C2211yescharacteristic
41#16840636C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×M16×D61C2211yescharacteristic
53#117×D61C2211yescharacteristic
54C2×C4⋊C4×D61C2211yescharacteristic
55#16839805C411yescharacteristic, complemented
56#16839804C411yescharacteristic, complemented
57#16839803C411yescharacteristic, complemented
58#16839803C411yescharacteristic, complemented
59#16839802C411yescharacteristic, complemented
60#16839801C411yescharacteristic, complemented
61#16839801C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#107×D61C2211yescharacteristic
64#106×D61C2211yescharacteristic
65#106×D61C2211yescharacteristic
66C61×#428C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923C2311yescharacteristic
74C2×C4⋊#6923C2311yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C22⋊#6923—21no—
78C2×C22⋊#6923—21no—
79C2×C22⋊#6923D411yescharacteristic
80C2×C22⋊#6923D411yescharacteristic
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923C2311yescharacteristic
86C2×C4×#6923C2311yescharacteristic
87#14519846—22no—
88#14519845—22no—
89#14519834—21no—
90C22⋊#92420—21no—
91#14519831—22no—
92C8×#6923—22no—
93(C2×#6923)⋊C4—21no—
94(C2×#6923)⋊C4—21no—
95(C2×#6923)⋊C4—21no—
96(C2×#6923)⋊C4—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4D411yescharacteristic
104(C2×#6923)⋊C4D411yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C2×#11758194C2×C411yescharacteristic
108C2×#11758189C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110M16×D61—22no—
111M16×D61—22no—
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519736C2×C411yescharacteristic
115#14519735C2×C411yescharacteristic
116#14519735C2×C411yescharacteristic
117#14519734—21no—
118#14519733—21no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×#11758196—21no—
121C4⋊C4×D61—21no—
122C4⋊C4×D61—21no—
123C4⋊C4×D61C2×C411yescharacteristic
124C4⋊C4×D61C2×C411yescharacteristic
125C4⋊C4×D61C2311yescharacteristic
126C4⋊C4×D61C2311yescharacteristic
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C22⋊C4×D61—21no—
130C42×D61—21no—
131#14519711C2×C411yescharacteristic
132#14519711C2×C411yescharacteristic
133#14519710C2×C411yescharacteristic
134#14519710C2×C411yescharacteristic
135#14519710C2×C411yescharacteristic
136#14519710C2×C411yescharacteristic
137#14519709C2×C411yescharacteristic
138#14519709C2×C411yescharacteristic
139#14519708C2×C411yescharacteristic
140#14519708C2×C411yescharacteristic
141#14519708C2×C411yescharacteristic
142#14519708C2×C411yescharacteristic
143C2×M16×C61C2×C411yescharacteristic
144#117×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146#107×C61C2×C411yescharacteristic
147#107×C61C2×C411yescharacteristic
148#106×C61C2×C411yescharacteristic
149#106×C61C2×C411yescharacteristic
150C23×D61C2×D411yescharacteristic
151C22×#6923—21no—
152C22×#6923—21no—
153C22×#6923—21no—
154C22×#6923—21no—
155C22×#6923C2×D411yescharacteristic
156C22×#6923C2×D411yescharacteristic
157C22×#6923C2×D411yescharacteristic
158C22×#6923C2×D411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61C22×C411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61#4111yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—81no—
174C2×C4×D61—81no—
175C2×C4×D61C22×C411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61#4111yescharacteristic
178C2×C4×D61C2411yescharacteristic
179C22⋊#6923—22no—
180C22⋊#6923—41no—
181C22⋊#6923—42no—
182C22⋊#6923—81no—
183C2×#92420—21no—
184C2×#92420—21no—
185C4⋊#6923—21no—
186C4⋊#6923—21no—
187C4⋊#6923—21no—
188C4⋊#6923—21no—
189C4⋊#6923—21no—
190C4⋊#6923—21no—
191C4⋊#6923—21no—
192C4⋊#6923—21no—
193C4⋊#6923—81no—
194C4⋊#6923—81no—
195C4⋊#6923—81no—
196C4⋊#6923—81no—
197C4×#6923—21no—
198C4×#6923—21no—
199C4×#6923—21no—
200C4×#6923—21no—
201C4×#6923—42no—
202C4×#6923—42no—
203C4×#6923—81no—
204C4×#6923—81no—
205D61⋊C8—21no—
206D61⋊C8—21no—
207D61⋊C8—21no—
208D61⋊C8—21no—
209M16×C61—22no—
210C2×C8×C61C22×C411yescharacteristic
211C2×C8×C61C22×C411yescharacteristic
212C4⋊C4×C61—21no—
213C4⋊C4×C61C22×C411yescharacteristic
214C4⋊C4×C61C22×C411yescharacteristic
215C4⋊C4×C61C22×C411yescharacteristic
216C4⋊C4×C61C22×C411yescharacteristic
217C22⋊C4×C61—21no—
218C42×C61—21no—
219C22⋊Dic61—21no—
220#11758198—21no—
221#11758198—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61C22×C411yescharacteristic
224C4⋊Dic61C22×C411yescharacteristic
225C4⋊Dic61C22×C411yescharacteristic
226C4⋊Dic61C22×C411yescharacteristic
227#11758196—21no—
228#11758196—21no—
229#11758196—21no—
230#11758196—21no—
231#11758196—21no—
232#11758196—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236#11758194—22no—
237C2×#92418C22×C411yescharacteristic
238C2×#92418C22×C411yescharacteristic
239#11758189—22no—
240#11758189—22no—
241C8×D61—21no—
242C8×D61—21no—
243C8×D61#4112yes—
244C8×D61#4112yes—
245C23×C61C4×D411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61C4×D411yescharacteristic
253C22×D61C22×D411yescharacteristic
254C2×#6923—21no—
255C2×#6923—21no—
256C2×#6923—21no—
257C2×#6923—21no—
258C2×#6923—21no—
259C2×#6923—21no—
260C2×#6923—21no—
261C2×#6923—21no—
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—41no—
266C2×#6923—41no—
267C2×#6923—41no—
268C2×#6923—41no—
269C2×#6923—41no—
270C2×#6923—41no—
271C2×#6923—41no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923#13712yes—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—81no—
285C2×C4×C61C4×D411yescharacteristic
286C2×C4×C61C23×C411yescharacteristic
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—81no—
294C2×Dic61C4×D411yescharacteristic
295C2×Dic61C2×#4111yescharacteristic
296C4×D61—21no—
297C4×D61—21no—
298C4×D61—21no—
299C4×D61—21no—
300C4×D61—21no—
301C4×D61—21no—
302C4×D61—41no—
303C4×D61—41no—
304C4×D61—41no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—81no—
311C4×D61—81no—
312C4×D61C2×#4111yescharacteristic
313C4×D61C2×#4111yescharacteristic
314C4×D612−1+411yescharacteristic
315C4×D612−1+411yescharacteristic
316#92420—41no—
317#92420—41no—
318C8×C61—21no—
319C8×C61#11712yes—
320#92418—21no—
321#92418#11712yes—
322#22621—611nomaximal, Sylow
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61C2×C4×D411yescharacteristic
327C2×D61—21no—
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61#54711yescharacteristic
335C2×D61#54711yescharacteristic
336C2×D61C2×#13711yescharacteristic
337C2×D61#57511yescharacteristic
338C2×D61#57611yescharacteristic
339C2×D61#57711yescharacteristic
340#6923—22no—
341#6923—41no—
342#6923—41no—
343#6923—41no—
344#6923—81no—
345#6923—81no—
346#6923—81no—
347#6923—81no—
348C4×C61—21no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61C2×#11711yescharacteristic
354C4×C61#51911yescharacteristic
355Dic61—21no—
356Dic61—41no—
357Dic61—41no—
358Dic61—41no—
359Dic61—41no—
360Dic61#55211yescharacteristic
361Dic61#55211yescharacteristic
362C2×#428—611no—
363#2346—611no—
364#2345—611no—
365#1943—611no—
366#1942—611no—
367#1921—611no—
368#1920—611no—
369#1919—611no—
370#1918—611no—
371#1825—611no—
372#1823—611no—
373#1809—611no—
374#1776—611no—
375C4×#106—611no—
376#1753—611no—
377C2×C61—41no—
378C2×C61#234411yescharacteristic
379C2×C61C4×#13711yescharacteristic
380C2×C61#294611yescharacteristic
381D61—41no—
382D61#334411yescharacteristic
383D61#334711yescharacteristic
384D61#335111yescharacteristic
385D61#335711yescharacteristic
386C22×M16—611no—
387C2×#117—611no—
388C22×C4⋊C4—611no—
389#428—611no—
390#428—611no—
391#428—611no—
392#428—611no—
393#428—611no—
394#428—611no—
395#428—611no—
396#428#692311yescharacteristic, complemented
397C2×#107—611no—
398C2×#107—611no—
399C2×#107—611no—
400C2×#106—611no—
401C2×#106—611no—
402C2×#106—611no—
403C2×C22⋊C8—611no—
404C2×#97—611no—
405C2×C4×C8—611no—
406#389—611no—
407#389—611no—
408#389—611no—
409#389—611no—
410#388—1221no—
411#388—1221no—
412#387—1221no—
413#387—1221no—
414#382—1221no—
415#380—611no—
416#380—611no—
417#380—1221no—
418C4×C4⋊C4—611no—
419C4×C4⋊C4—611no—
420C4×C4⋊C4—611no—
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424#376—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#336—611no—
436#336—611no—
437C61#2262111yescharacteristic, complemented, Sylow
438C23×C4—611no—
439C23×C4—1221no—
440C2×M16—611no—
441C2×M16—611no—
442C2×M16—611no—
443C2×M16—1222no—
444C2×M16—1222no—
445C2×M16C2×#692311yescharacteristic
446C22×C8—611no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450#117—611no—
451#117—611no—
452#117—611no—
453#117—1221no—
454#117—1221no—
455#117C2×#692311yescharacteristic
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4C2×#692311yescharacteristic
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—1221no—
483C2×C42—1221no—
484C2×C42—1221no—
485C2×C42—1221no—
486C2×C42—1221no—
487#107—611no—
488#107—611no—
489#107—611no—
490#107—611no—
491#107—611no—
492#107—611no—
493#107—1222no—
494#107C2×#692311yescharacteristic
495#107C2×#692311yescharacteristic
496#106—611no—
497#106—611no—
498#106—611no—
499#106—611no—
500#106—611no—
501#106—611no—
502#106—1222no—
503#106C2×#692311yescharacteristic
504#106C2×#692311yescharacteristic
505C22⋊C8—1221no—
506C22⋊C8—1221no—
507#97—1222no—
508C4×C8—1222no—
509#95—611no—
510#95—611no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521C24—611no—
522C22×C4—21no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—4881no—
548C22×C4—4881no—
549C22×C4C22×#692311yescharacteristic
550M16—22no—
551M16—1222no—
552M16—1222no—
553M16—1222no—
554C2×C8—611no—
555C2×C8—612no—
556C2×C8—612no—
557C2×C8—611no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8C22×#692311yescharacteristic
567C2×C8C22×#692311yescharacteristic
568C4⋊C4—21no—
569C4⋊C4—611no—
570C4⋊C4—611no—
571C4⋊C4—611no—
572C4⋊C4—611no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—4881no—
589C4⋊C4—4881no—
590C4⋊C4—4881no—
591C4⋊C4—4881no—
592C4⋊C4C22×#692311yescharacteristic
593C4⋊C4C22×#692311yescharacteristic
594C4⋊C4C22×#692311yescharacteristic
595C4⋊C4C22×#692311yescharacteristic
596C22⋊C4—21no—
597C22⋊C4—1221no—
598C22⋊C4—1221no—
599C22⋊C4—1222no—
600C22⋊C4—1221no—
601C22⋊C4—4881no—
602C22⋊C4—2441no—
603C22⋊C4—2442no—
604C42—21no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—4881no—
613C42—4881no—
614C42—2442no—
615C42—2442no—
616C23—611no—
617C23—611no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23D4×#692311yescharacteristic
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—81no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—611no—
637C2×C4—612no—
638C2×C4—611no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—4881no—
663C2×C4—4881no—
664C2×C4—4881no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4D4×#692311yescharacteristic
686C2×C4C23×#692311yescharacteristic
687C8—21no—
688C8—612no—
689C8—1221no—
690C8—2441no—
691C8—2441no—
692C8#1451985612yes—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—611no—
697C22—611no—
698C22—611no—
699C22—611no—
700C22—611no—
701C22—611no—
702C22—1221no—
703C22—1221no—
704C22—1221no—
705C22—2441no—
706C22—2441no—
707C22—2441no—
708C22—2441no—
709C22C2×D4×#692311yescharacteristic
710C4—21no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—611no—
716C4—611no—
717C4—1222no—
718C4—1221no—
719C4—4881no—
720C4—4881no—
721C4—4881no—
722C4—4881no—
723C4—2441no—
724C4—2441no—
725C4—2441no—
726C4—2441no—
727C4—2441no—
728C4—2441no—
729C4—2441no—
730C4C2×#1451985611yescharacteristic
731C4#1684083011yescharacteristic
732C2—41no—
733C2—611no—
734C2—611no—
735C2—611no—
736C2—611no—
737C2—2441no—
738C2#2146232711yescharacteristic
739C2#137×#692311yescharacteristic
740C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#428C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#428#6923
hypocenterC61#22621
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #21461924C2semidirect
4. #21461923C2semidirect
5. #21461883C2semidirect
6. #21461882C2semidirect
7. #21461881C2semidirect
8. #21461880C2semidirect
12. #21461635C2semidirect
13. #106×#6923C2semidirect
55. #16839805C4semidirect
56. #16839804C4semidirect
57. #16839803C4semidirect
58. #16839803C4semidirect
59. #16839802C4semidirect
60. #16839801C4semidirect
61. #16839801C4semidirect
66. C61×#428C4semidirect
396. #428#6923semidirect
437. C61#22621semidirect

Maximal subgroups

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

subgroupindex
#214623292
#214623282
#214619242
#214619232
#214618832
#214618822
#214618812
#214618802
#214617242
#214617222
#214616972
#214616352
#106×#69232
#214615592
#428×D612
#2262161