Finite Group Databasebeta

← #29696348

Subgroups — #29696348

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840482C211yesmaximal, characteristic
2#21448748C211yesmaximal, characteristic
3#21446792C211yesmaximal, characteristic, complemented
4#21446766C211yesmaximal, characteristic, complemented
5#21446252C211yesmaximal, characteristic, complemented
6#21446242C211yesmaximal, characteristic, complemented
7#21446129C211yesmaximal, characteristic, complemented
8#21446124C211yesmaximal, characteristic, complemented
9#21445915C211yesmaximal, characteristic, complemented
10#21445915C211yesmaximal, characteristic, complemented
11#21445835C211yesmaximal, characteristic, complemented
12#21445650C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14#21445536C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16#16840482—24no—
17#16840482C418yescomplemented
18C2×#14519777C2211yescharacteristic
19C2×#14519770—21no—
20C2×#14519770—21no—
21C2×#14519764—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742—21no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34#16839655—21no—
35#16839648—21no—
36#16839642—21no—
37#16839628C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C22⋊C4×Dic61—21no—
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#435—24no—
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65#14519777—22no—
66#14519777C2×C414yescomplemented
67#14519770—28no—
68#14519770—28no—
69#14519764—28no—
70#14519756—22no—
71#14519756—22no—
72#14519756C2×C414yes—
73#14519756C2×C414yescomplemented
74C4×Dic122—22no—
75C4×Dic122C2×C414yescomplemented
76#14519742—28no—
77#14519736—22no—
78#14519736—22no—
79#14519736—22no—
80#14519736—41no—
81#14519736C2×C414yes—
82#14519736C2×C414yescomplemented
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109#14519702—22no—
110#14519702—22no—
111#14519702—41no—
112#14519702—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×D4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61—41no—
124C22×C8×C61—22no—
125C22×C8×C61—22no—
126C22×C8×C61—41no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4×D4×C61C2×C414yes—
132C4×D4×C61D414yes—
133C2×C4⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—22no—
138C22⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140#97×C61—22no—
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C2×D4×C61C22⋊C414yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—81no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—24no—
179C2×Dic122—21no—
180C2×Dic122—42no—
181C2×Dic122—42no—
182C2×Dic122C22×C412yes—
183M16×C61—44no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—44no—
196C2×C8×C61#4112yes—
197C4⋊C4×C61C22⋊C414yes—
198C22⋊C4×C61C22⋊C414yes—
199C22⋊C4×C61C22⋊C414yes—
200C42×C61C22×C412yes—
201C42×C61C2×D412yes—
202C22⋊Dic61—24no—
203C22⋊Dic61—24no—
204C22⋊Dic61—24no—
205C22⋊Dic61—24no—
206C22⋊Dic61—42no—
207C22⋊Dic61—42no—
208C22⋊Dic61—81no—
209C4⋊Dic61—24no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—42no—
221C4⋊Dic61C22×C412yes—
222C4⋊Dic61C22×C412yes—
223C4⋊Dic61C22×C412yes—
224C4⋊Dic61#4112yes—
225#11758196—24no—
226#11758196—24no—
227#11758196—24no—
228C4×Dic61—24no—
229C4×Dic61—24no—
230C4×Dic61—24no—
231C4×Dic61—42no—
232C4×Dic61—81no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C2×C22⋊C412yes—
246C23×C61C2×C22⋊C412yes—
247C23×C61C22×D411yescharacteristic
248D4×C61—44no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C2×C22⋊C412yes—
269C2×C4×C61C23×C411yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×C4×C612−1+411yescharacteristic
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
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—84no—
300Dic122—22no—
301Dic122—22no—
302Dic122—48no—
303Dic122—41no—
304Dic122—41no—
305C8×C61—22no—
306C8×C61—41no—
307C8×C61—41no—
308C8×C61—41no—
309#22494—611nomaximal, Sylow
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61#54611yescharacteristic
326C22×C61#54711yescharacteristic
327C22×C61#57511yescharacteristic
328C22×C61#57511yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57811yescharacteristic
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61C4×#4111yescharacteristic
336C4×C61#52011yescharacteristic
337C4×C61#54611yescharacteristic
338C4×C61#54711yescharacteristic
339Dic61—42no—
340Dic61—42no—
341Dic61—42no—
342Dic61—42no—
343Dic61—42no—
344Dic61—81no—
345Dic61—81no—
346Dic61—81no—
347C2×#556—611no—
348C2×#435D6111yescharacteristic
349#2352—611no—
350#1993—611no—
351#1987—611no—
352#1894—611no—
353#1892—611no—
354#1873—611no—
355#1872—611no—
356#1825—611no—
357#1825—611no—
358#1805—611no—
359#1763—611no—
360#1736—611no—
361#1735—611no—
362C2×C61—42no—
363C2×C61—42no—
364C2×C61#233911yescharacteristic
365C2×C61#289611yescharacteristic
366C2×C61#289811yescharacteristic
367C2×C61#331111yescharacteristic
368C2×C61#331311yescharacteristic
369C2×C61#334911yescharacteristic
370C2×C61#335011yescharacteristic
371C22×M16C2×D6111yescharacteristic
372C23×C8C2×D6111yescharacteristic
373#556—618no—
374#556—1224no—
375C2×C4⋊Q8—611no—
376C2×#126—1221no—
377C2×#126—1221no—
378C2×#124—1221no—
379C2×C22⋊Q8—611no—
380C2×C22⋊Q8—611no—
381C2×C4×Q8—611no—
382C2×C4×Q8—1221no—
383C2×C4×D4C2×D6111yescharacteristic
384C2×#117—611no—
385C2×#117—611no—
386C2×#117—611no—
387C22×C4⋊C4—611no—
388#435—24no—
389C2×C4⋊C8C2×D6111yescharacteristic
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×C22⋊C8C2×D6111yescharacteristic
395C2×C22⋊C8C2×D6111yescharacteristic
396C2×#97C2×D6111yescharacteristic
397#388—1221no—
398#387—1221no—
399#386—1221no—
400#382—611no—
401#380—611no—
402#380—611no—
403C4×C4⋊C4—611no—
404C4×C22⋊C4—1221no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417C61#2249411yescharacteristic, complemented, Sylow
418C22×Q8—611no—
419C22×Q8—1221no—
420C22×D4D24411yescharacteristic
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C23×C4C22×D6111yescharacteristic
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—41no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—41no—
430C22×C8C22×D6111yescharacteristic
431C22×C8C22×D6111yescharacteristic
432C22×C8C22×D6111yescharacteristic
433C22×C8C22×D6111yescharacteristic
434C4⋊Q8—614no—
435C4⋊Q8—1222no—
436#126—1228no—
437#126—1228no—
438#124—1228no—
439C22⋊Q8—614no—
440C22⋊Q8—614no—
441C22⋊Q8—1222no—
442C22⋊Q8—1222no—
443C4×Q8—614no—
444C4×Q8—1228no—
445C4×Q8—1222no—
446C4×D4C4×D6114yes—
447C4×D4C22⋊D6114yes—
448#117—614no—
449#117—614no—
450#117—1222no—
451#117—1222no—
452#117—1222no—
453#117—2441no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—1222no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—2441no—
468C2×C4⋊C4D24411yescharacteristic
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4D24411yescharacteristic
477C2×C22⋊C4D24411yescharacteristic
478C2×C42—1221no—
479C2×C42—1221no—
480C2×C42—1221no—
481C2×C42—1221no—
482C2×C42—1221no—
483C2×C42C22×D6111yescharacteristic
484C4⋊C8—22no—
485#103—1222no—
486#103—1222no—
487#103—2441no—
488#103—2441no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491#97—22no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497C24C2×D24411yescharacteristic
498C24C2×D24411yescharacteristic
499C2×Q8—612no—
500C2×Q8—1221no—
501C2×Q8—1224no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—2442no—
507C2×Q8—2442no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4#1175819814yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—4881no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4C2×C4×D6112yes—
531C22×C4C2×C4×D6112yes—
532C22×C4C2×D24411yescharacteristic
533C22×C4C2×D24411yescharacteristic
534C22×C4C2×D24411yescharacteristic
535C22×C4C2×D24411yescharacteristic
536C22×C4C2×C22⋊D6112yes—
537C22×C4C2×C22⋊D6112yes—
538C22×C4C23×D6111yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8#1175822412yes—
553C4⋊C4—612no—
554C4⋊C4—612no—
555C4⋊C4—612no—
556C4⋊C4—612no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1224no—
562C4⋊C4—1224no—
563C4⋊C4—1224no—
564C4⋊C4—1224no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—2442no—
572C4⋊C4#1175819814yes—
573C22⋊C4—1224no—
574C22⋊C4—1224no—
575C22⋊C4—1224no—
576C22⋊C4—1224no—
577C22⋊C4—4881no—
578C22⋊C4—2442no—
579C22⋊C4—2442no—
580C22⋊C4#1175819814yes—
581C22⋊C4#1175819814yes—
582C42—1224no—
583C42—1224no—
584C42—1224no—
585C42—4881no—
586C42—2442no—
587C42C2×C4×D6112yes—
588C42C2×C22⋊D6112yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×#1175819812yes—
602C23C2×#1175819812yes—
603C23C22×D24411yescharacteristic
604Q8—1222no—
605Q8—1222no—
606Q8—2448no—
607Q8—2441no—
608Q8—2441no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—4884no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4C2×#1175819812yes—
652C2×C4C2×#1175819812yes—
653C2×C4C2×#1175819812yes—
654C2×C4C2×#1175819812yes—
655C2×C4C22×C4×D6111yescharacteristic
656C2×C4C22×C22⋊D6111yescharacteristic
657C2×C4#41×D6111yescharacteristic
658C2×C4C2×#1175822411yescharacteristic
659C2×C4#1451982211yescharacteristic
660C2×C4#1451982411yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×#1175819811yescharacteristic
680C22#1684040711yescharacteristic
681C22#1684041611yescharacteristic
682C22#1684056211yescharacteristic
683C22#1684056211yescharacteristic
684C22#1684057411yescharacteristic
685C22#1684057911yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—4881no—
691C4—4881no—
692C4—4881no—
693C4—2442no—
694C4—2442no—
695C4—2442no—
696C4—2442no—
697C4—2442no—
698C4C4×#1175822411yescharacteristic
699C4#1684024111yescharacteristic
700C4#1684040611yescharacteristic
701C4#1684041111yescharacteristic
702C2—42no—
703C2—42no—
704C2#2144864411yescharacteristic
705C2#2145433911yescharacteristic
706C2#2145435311yescharacteristic
707C2#2145785711yescharacteristic
708C2#2145788711yescharacteristic
709C2#2145835111yescharacteristic
710C2#2145836611yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #21446792C2semidirect
4. #21446766C2semidirect
5. #21446252C2semidirect
6. #21446242C2semidirect
7. #21446129C2semidirect
8. #21446124C2semidirect
9. #21445915C2semidirect
10. #21445915C2semidirect
11. #21445835C2semidirect
12. #21445650C2semidirect
13. #21445539C2semidirect
14. #21445536C2semidirect
17. #16840482C4semidirect
66. #14519777C2×C4semidirect
73. #14519756C2×C4semidirect
75. C4×Dic122C2×C4semidirect
82. #14519736C2×C4semidirect
417. C61#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#168404822
#214487482
#214467922
#214467662
#214462522
#214462422
#214461292
#214461242
#214459152
#214458352
#214456502
#214455392
#214455362
C2×C61×#4352
#2249461