Finite Group Databasebeta

← #29700395

Subgroups — #29700395

Order 15616.

1134 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
1C2×#16839926C211yesmaximal, characteristic
2C2×#16839864C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic
4#21448822C211yesmaximal, characteristic, complemented
5#21448650C211yesmaximal, characteristic
6#21446680C211yesmaximal, characteristic, complemented
7#21446509C211yesmaximal, characteristic, complemented
8#21446461C211yesmaximal, characteristic, complemented
9#21446252C211yesmaximal, characteristic, complemented
10#21446159C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446069C211yesmaximal, characteristic, complemented
13#21446009C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24#16839926C418yescomplemented
25#16839864—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519711C2211yescharacteristic
28#16839764—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839659—21no—
42#16839649—21no—
43#16839638—21no—
44#16839638—21no—
45#16839634—21no—
46#16839624—21no—
47#16839622C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49C22⋊C4×Dic61—21no—
50#95×D61—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yes—
68C22×Dic122C2311yescharacteristic
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×Dic244—41no—
77C2×Dic244—41no—
78C2×Dic244C2×C414yescomplemented
79C2×#11758190—22no—
80C2×#11758190—22no—
81C2×#11758190C2×C414yescomplemented
82#14519756—22no—
83#14519756C2×C414yescomplemented
84C4×Dic122—22no—
85C4×Dic122—41no—
86C4×D244—22no—
87C4×D244—22no—
88C4×D244—41no—
89C4×D244—41no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107#14519711—22no—
108#14519711—41no—
109#14519702—22no—
110#14519702—22no—
111#14519702—22no—
112#14519702—41no—
113#14519702C2×C414yescomplemented
114#14519699—22no—
115#14519699C2×C414yescomplemented
116#14519699D414yes—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C22⋊C8×C61C2×C414yescomplemented
139#97×C61—22no—
140C4×C8×C61—41no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4112yes—
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—24no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—81no—
170#11758222—28no—
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244C22×C412yes—
178C2×D244C2×D412yes—
179C2×D244#4112yes—
180C2×C4×D61—24no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—81no—
188C2×C4×D61—81no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122C22×C412yes—
200C2×Dic122C22×C412yes—
201M16×C61—44no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C22×C412yes—
212C2×C8×C61C22×C412yes—
213C2×C8×C61C2×D412yes—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—41no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—24no—
221C22⋊Dic61—81no—
222#11758198—42no—
223#11758198—42no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—42no—
233C4⋊Dic61C22×C412yes—
234C4⋊Dic61C2×D412yes—
235#11758196—24no—
236#11758196—42no—
237#11758196—81no—
238C4×Dic61—42no—
239C4×Dic61—81no—
240Dic244—44no—
241#11758190—28no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61C4×D412yes—
275C2×C4×C61#13712yes—
276C2×C4×C61C23×C411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C22⋊D61—48no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
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—
303C2×Dic61—41no—
304C2×Dic61—84no—
305D244—22no—
306D244—22no—
307D244—22no—
308D244C4×D414yes—
309C4×D61—48no—
310C4×D61—84no—
311C4×D61—84no—
312Dic122—22no—
313Dic122—22no—
314Dic122—22no—
315Dic122—22no—
316Dic122—41no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320C8×C61—22no—
321C8×C61—22no—
322C8×C61—22no—
323C8×C61—41no—
324#22862—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61C2×C4×D411yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61C2×#13711yescharacteristic
336C22×C61#57511yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57811yescharacteristic
339C2×D61—24no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—41no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61C2×C4×D411yescharacteristic
352C4×C61#51811yescharacteristic
353C4×C61#54611yescharacteristic
354C4×C61#55111yescharacteristic
355Dic61—42no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—81no—
360Dic61—81no—
361Dic61—81no—
362C2×#452—611no—
363C2×#440—611no—
364C2×#417—611no—
365#2360—611no—
366#2339—611no—
367#1969—611no—
368#1935—611no—
369#1928—611no—
370#1894—611no—
371#1878—611no—
372#1877—611no—
373#1862—611no—
374#1852—611no—
375C4×#102—611no—
376#1753D6111yescharacteristic, complemented
377C2×C61—42no—
378C2×C61#235811yescharacteristic
379C2×C61C4×#13711yescharacteristic
380C2×C61#295111yescharacteristic
381C2×C61#327311yescharacteristic
382C2×C61#327611yescharacteristic
383C2×C61#331411yescharacteristic
384C2×C61#331511yescharacteristic
385D61—44no—
386C22×#41—611no—
387C22×Q16—611no—
388C22×SD16—611no—
389C22×M16C2×D6111yescharacteristic
390C2×C22⋊Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C22×C4⋊C4—611no—
395#452—618no—
396#440—1224no—
397C2×#107—611no—
398C2×#107—611no—
399#417—1224no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×C22⋊C8C2×D6111yescharacteristic
409C2×#97C2×D6111yescharacteristic
410C2×C4×C8C2×D6111yescharacteristic
411#391—611no—
412#391—611no—
413#391—611no—
414#389—611no—
415#389—1221no—
416#387—1221no—
417#386—1221no—
418#386—1221no—
419#385—1221no—
420#381—1221no—
421#380—611no—
422C4×C4⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4C2×D6111yescharacteristic
425C2×#95—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#336C2×D6111yescharacteristic
431#336C2×D6111yescharacteristic
432C61#2286211yescharacteristic, complemented, Sylow
433C2×#41—614no—
434C2×#41—1222no—
435C2×#41—1222no—
436C2×#41—1222no—
437C2×#41—2441no—
438C2×#41—2441no—
439C22×Q8—611no—
440C22×Q8—611no—
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—1221no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C23×C4C22×D6111yescharacteristic
448C2×Q16—614no—
449C2×Q16—2441no—
450C2×Q16—2441no—
451C2×SD16—614no—
452C2×SD16—1222no—
453C2×SD16—1222no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22⋊Q8—614no—
462C22⋊Q8—1222no—
463C4×Q8—1222no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—2441no—
468C4×D4—2441no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—2441no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4D24411yescharacteristic
485C2×C22⋊C4D24411yescharacteristic
486C2×C42—1221no—
487C2×C42—1221no—
488C2×C42C22×D6111yescharacteristic
489C2×C42C22×D6111yescharacteristic
490#107—1222no—
491#107—2441no—
492#103—614no—
493#103—1222no—
494#103—1222no—
495#103—1222no—
496#103—2441no—
497#102—614no—
498#102—614no—
499#102—1222no—
500C22⋊C8C4×D6114yescomplemented
501#97—22no—
502C4×C8—41no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95D24411yescharacteristic
513#95D24411yescharacteristic
514C24—1221no—
515C24C2×D24411yescharacteristic
516#41—1228no—
517#41—2444no—
518#41—2444no—
519#41—2444no—
520C2×Q8—612no—
521C2×Q8—612no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×D4—612no—
533C2×D4—612no—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2442no—
540C2×D4—2442no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1224no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4C2×C4×D6112yes—
565C22×C4C2×D24411yescharacteristic
566C22×C4C2×D24411yescharacteristic
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4#1175822212yes—
571C22×C4C23×D6111yescharacteristic
572Q16—2444no—
573SD16—1228no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8C2×C4×D6112yes—
585C2×C8C2×C4×D6112yes—
586C2×C8D4×D6112yes—
587C4⋊C4—612no—
588C4⋊C4—612no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1224no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—4881no—
599C4⋊C4—2442no—
600C4⋊C4—2442no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—1224no—
604C22⋊C4—4881no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—4881no—
612C42—2442no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23C4×D24412yes—
627C23C22×D24411yescharacteristic
628Q8—1222no—
629Q8—1222no—
630Q8—1222no—
631Q8—1222no—
632Q8—2441no—
633Q8—2441no—
634Q8—2441no—
635Q8—2441no—
636D4—614no—
637D4—1222no—
638D4—1222no—
639D4—1222no—
640D4—2448no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—4884no—
663C2×C4—4884no—
664C2×C4—4884no—
665C2×C4—2448no—
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×C4C4×D24412yes—
684C2×C4#1451981012yes—
685C2×C4C22×C4×D6111yescharacteristic
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822211yescharacteristic
689C2×C4#1451982211yescharacteristic
690C2×C4#1451982311yescharacteristic
691C8—22no—
692C8—22no—
693C8—22no—
694C8—41no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—1224no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22C2×C4×D24411yescharacteristic
710C22D4×D24411yescharacteristic
711C22#1684040711yescharacteristic
712C22C2×#1451981011yescharacteristic
713C22#1684056211yescharacteristic
714C22#1684056711yescharacteristic
715C22#1684057911yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—4881no—
722C4—4881no—
723C4—4881no—
724C4—2442no—
725C4—2442no—
726C4—2442no—
727C4—2442no—
728C4C4×D4×D6111yescharacteristic
729C4#1684023411yescharacteristic
730C4#1684040211yescharacteristic
731C4#1684043611yescharacteristic
732C2—42no—
733C2—2444no—
734C2#2144880111yescharacteristic
735C2C4×#1451981011yescharacteristic
736C2#2145469611yescharacteristic
737C2#2145743111yescharacteristic
738C2#2145746711yescharacteristic
739C2#2145790211yescharacteristic
740C2#2145791711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1753C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22862
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#16839864C2semidirect
4. #21448822C2semidirect
6. #21446680C2semidirect
7. #21446509C2semidirect
8. #21446461C2semidirect
9. #21446252C2semidirect
10. #21446159C2semidirect
11. #21446152C2semidirect
12. #21446069C2semidirect
13. #21446009C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1753C2semidirect
24. #16839926C4semidirect
78. C2×Dic244C2×C4semidirect
81. C2×#11758190C2×C4semidirect
83. #14519756C2×C4semidirect
113. #14519702C2×C4semidirect
115. #14519699C2×C4semidirect
138. C22⋊C8×C61C2×C4semidirect
376. #1753D61semidirect
432. C61#22862semidirect
500. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399262
C2×#168398642
C2×#168397642
#214488222
#214486502
#214466802
#214465092
#214464612
#214462522
#214461592
#214461522
#214460692
#214460092
C4×#145196992
C61×#17532
#2286261