Finite Group Databasebeta

← #29696303

Subgroups — #29696303

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic
2D4×C4⋊Dic61C211yesmaximal, characteristic
3#21446788C211yesmaximal, characteristic, complemented
4#21446774C211yesmaximal, characteristic, complemented
5#21446252C211yesmaximal, characteristic, complemented
6#21446242C211yesmaximal, characteristic, complemented
7#21446124C211yesmaximal, characteristic, complemented
8#21446124C211yesmaximal, characteristic, complemented
9#21445915C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445825C211yesmaximal, characteristic, complemented
12#21445650C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14C2×#16839525C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16#16840452—24no—
17#16840452C418yescomplemented
18C2×#14519770—21no—
19C2×#14519769C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519758—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×C4×Dic122C2211yescharacteristic
25C2×D4×Dic61—21no—
26C2×#14519736C2211yescharacteristic
27C2×#14519733—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35#16839661—21no—
36#16839637—21no—
37#16839637—21no—
38#16839632C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
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×Dic122C2311yescharacteristic
63C23×Dic61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66#14519770—28no—
67#14519769—22no—
68#14519769C2×C414yescomplemented
69#14519767—28no—
70#14519758—28no—
71#14519756—22no—
72#14519756—22no—
73#14519756C2×C414yescomplemented
74#14519756C2×C414yescomplemented
75C4×Dic122—22no—
76C4×Dic122C2×C414yescomplemented
77D4×Dic61—44no—
78#14519736—22no—
79#14519736C2×C414yescomplemented
80#14519733—28no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61—41no—
91C2×C4⋊Dic61C2×C414yescomplemented
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519702—22no—
113#14519702—22no—
114#14519702—41no—
115#14519702—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61D411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—41no—
125C22×C8×C61—22no—
126C22×C8×C61—22no—
127C22×C8×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61C2×C414yes—
133C4×D4×C61D414yes—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141#97×C61—22no—
142C24×C61C2×D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61C22⋊C414yes—
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×C61—21no—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2411yescharacteristic
164C22×Dic61—24no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—81no—
180C22×Dic61—81no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122C22×C412yes—
187M16×C61—44no—
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—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—44no—
200C2×C8×C61#4112yes—
201C4⋊C4×C61C22⋊C414yes—
202C22⋊C4×C61C22⋊C414yes—
203C22⋊C4×C61C22⋊C414yes—
204C42×C61C22×C412yes—
205C42×C61C2×D412yes—
206C22⋊Dic61—24no—
207C22⋊Dic61—24no—
208C22⋊Dic61—24no—
209C22⋊Dic61—42no—
210C22⋊Dic61—42no—
211C4⋊Dic61—24no—
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—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
223C4⋊Dic61—42no—
224C4⋊Dic61—42no—
225C4⋊Dic61—81no—
226C4⋊Dic61C22×C412yes—
227C4⋊Dic61C22×C412yes—
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61#4112yes—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—24no—
234#11758196—24no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61—42no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C2×C22⋊C412yes—
249C23×C61C2×C22⋊C412yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61#13712yes—
252C23×C61C22×D411yescharacteristic
253D4×C61—28no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61C2×C22⋊C412yes—
271C2×C4×C61C2×C22⋊C412yes—
272C2×C4×C61C2×C22⋊C412yes—
273C2×C4×C61C2×C22⋊C412yes—
274C2×C4×C61C23×C411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C612−1+411yescharacteristic
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
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—48no—
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—41no—
305C2×Dic61—84no—
306C2×Dic61—84no—
307Dic122—22no—
308Dic122—22no—
309Dic122—41no—
310Dic122—41no—
311C8×C61—22no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#22491—611nomaximal, Sylow
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61#41714yes—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57711yescharacteristic
336C22×C61#57811yescharacteristic
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—22no—
340C4×C61—22no—
341C4×C61C4×#4111yescharacteristic
342C4×C61#52011yescharacteristic
343C4×C61#54611yescharacteristic
344C4×C61#54711yescharacteristic
345Dic61—42no—
346Dic61—42no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—81no—
351Dic61—81no—
352Dic61—81no—
353C2×#552—611no—
354C2×#435D6111yescharacteristic
355D4×C4⋊C4—611no—
356#1992—611no—
357#1989—611no—
358#1894—611no—
359#1892—611no—
360#1872—611no—
361#1872—611no—
362#1825—611no—
363#1823—611no—
364#1803—611no—
365#1763—611no—
366#1736—611no—
367C2×#340—611no—
368C2×C61—24no—
369C2×C61—42no—
370C2×C61#233911yescharacteristic
371C2×C61C2×#41711yescharacteristic
372C2×C61#289811yescharacteristic
373C2×C61#331011yescharacteristic
374C2×C61#331211yescharacteristic
375C2×C61#334311yescharacteristic
376C2×C61#334411yescharacteristic
377C22×M16C2×D6111yescharacteristic
378C23×C8C2×D6111yescharacteristic
379#552—618no—
380#552—1224no—
381C2×#126—1221no—
382C2×#125—611no—
383C2×#125—1221no—
384C2×#123—1221no—
385C2×C22⋊Q8—611no—
386C2×C22⋊Q8—611no—
387C2×C4×Q8—611no—
388C2×C4×D4—1221no—
389C2×C4×D4C2×D6111yescharacteristic
390C2×#117—611no—
391C2×#117—1221no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4—611no—
395#435—24no—
396C2×C4⋊C8C2×D6111yescharacteristic
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×C22⋊C8C2×D6111yescharacteristic
402C2×C22⋊C8C2×D6111yescharacteristic
403C2×#97C2×D6111yescharacteristic
404#389—1221no—
405#385—1221no—
406#385—1221no—
407#384—611no—
408#380—611no—
409#380—611no—
410C4×C4⋊C4—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340—611no—
422#340—611no—
423C61#2249111yescharacteristic, complemented, Sylow
424C22×Q8—611no—
425C22×D4D24411yescharacteristic
426C23×C4—1221no—
427C23×C4—1221no—
428C23×C4—1221no—
429C23×C4C22×D6111yescharacteristic
430C23×C4C22×D6111yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C22×D6111yescharacteristic
438C22×C8C22×D6111yescharacteristic
439C22×C8C22×D6111yescharacteristic
440C22×C8C22×D6111yescharacteristic
441#126—1228no—
442#125—614no—
443#125—1228no—
444#125—1222no—
445#123—1228no—
446C22⋊Q8—614no—
447C22⋊Q8—614no—
448C22⋊Q8—1222no—
449C22⋊Q8—1222no—
450C4×Q8—614no—
451C4×Q8—1222no—
452C4×D4—2444no—
453C4×D4C4×D6114yes—
454C4×D4C22⋊D6114yes—
455#117—614no—
456#117—1222no—
457#117—1228no—
458C2×C4⋊C4—614no—
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—1222no—
467C2×C4⋊C4—1222no—
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⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—2441no—
480C2×C4⋊C4—2441no—
481C2×C4⋊C4D24411yescharacteristic
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4D24411yescharacteristic
488C2×C22⋊C4D24411yescharacteristic
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42C22×D6111yescharacteristic
493C4⋊C8—22no—
494#103—1222no—
495#103—1222no—
496#103—2441no—
497#103—2441no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—22no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504C24C2×D24411yescharacteristic
505C24C2×D24411yescharacteristic
506C2×Q8—612no—
507C2×Q8—1221no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4#1175819814yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1224no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—4881no—
533C22×C4—4881no—
534C22×C4—2442no—
535C22×C4—2442no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4—2442no—
539C22×C4—2442no—
540C22×C4C2×C4×D6112yes—
541C22×C4C2×C4×D6112yes—
542C22×C4C2×D24411yescharacteristic
543C22×C4C2×D24411yescharacteristic
544C22×C4C2×D24411yescharacteristic
545C22×C4C2×D24411yescharacteristic
546C22×C4C2×C22⋊D6112yes—
547C22×C4C2×C22⋊D6112yes—
548C22×C4C23×D6111yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8#1175822412yes—
563C4⋊C4—612no—
564C4⋊C4—612no—
565C4⋊C4—612no—
566C4⋊C4—612no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1224no—
572C4⋊C4—1224no—
573C4⋊C4—1224no—
574C4⋊C4—1224no—
575C4⋊C4—1224no—
576C4⋊C4—1224no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—4881no—
584C4⋊C4—2442no—
585C4⋊C4—2442no—
586C4⋊C4—2442no—
587C4⋊C4#1175819814yes—
588C22⋊C4—1224no—
589C22⋊C4—1224no—
590C22⋊C4—1224no—
591C22⋊C4—2442no—
592C22⋊C4—2442no—
593C22⋊C4#1175819814yes—
594C22⋊C4#1175819814yes—
595C42—1224no—
596C42—1224no—
597C42—2442no—
598C42C2×C4×D6112yes—
599C42C2×C22⋊D6112yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×#1175819812yes—
611C23C2×#1175819812yes—
612C23#1451980512yes—
613C23#1451981012yes—
614C23C22×D24411yescharacteristic
615Q8—1222no—
616Q8—1222no—
617Q8—2441no—
618Q8—2441no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—4884no—
642C2×C4—4884no—
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×C4—2441no—
652C2×C4—2448no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4C2×#1175819812yes—
664C2×C4C2×#1175819812yes—
665C2×C4C2×#1175819812yes—
666C2×C4C2×#1175819812yes—
667C2×C4C22×C4×D6111yescharacteristic
668C2×C4C22×C22⋊D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1683976414yes—
691C22C22×#1175819811yescharacteristic
692C22#1684040711yescharacteristic
693C22#1684041611yescharacteristic
694C22C2×#1451980511yescharacteristic
695C22C2×#1451981011yescharacteristic
696C22#1684057411yescharacteristic
697C22#1684057911yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—4881no—
703C4—4881no—
704C4—4881no—
705C4—2442no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4C4×#1175822411yescharacteristic
711C4#1684024111yescharacteristic
712C4#1684040611yescharacteristic
713C4#1684041111yescharacteristic
714C2—24no—
715C2—42no—
716C2#2144864411yescharacteristic
717C2C2×#1683976411yescharacteristic
718C2#2145435311yescharacteristic
719C2#2145784211yescharacteristic
720C2#2145787211yescharacteristic
721C2#2145826111yescharacteristic
722C2#2145827611yescharacteristic
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#22491
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. #21446788C2semidirect
4. #21446774C2semidirect
5. #21446252C2semidirect
6. #21446242C2semidirect
7. #21446124C2semidirect
8. #21446124C2semidirect
9. #21445915C2semidirect
10. #21445906C2semidirect
11. #21445825C2semidirect
12. #21445650C2semidirect
13. #21445539C2semidirect
14. C2×#16839525C2semidirect
17. #16840452C4semidirect
68. #14519769C2×C4semidirect
73. #14519756C2×C4semidirect
74. #14519756C2×C4semidirect
76. C4×Dic122C2×C4semidirect
79. #14519736C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
423. C61#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
D4×C4⋊Dic612
#214467882
#214467742
#214462522
#214462422
#214461242
#214459152
#214459062
#214458252
#214456502
#214455392
C2×#168395252
C2×C61×#4352
#2249161