Finite Group Databasebeta

← #29696385

Subgroups — #29696385

Order 15616.

1174 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×#16840469C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic
3#21446791C211yesmaximal, characteristic, complemented
4#21446771C211yesmaximal, characteristic, complemented
5#21446250C211yesmaximal, characteristic, complemented
6#21446240C211yesmaximal, characteristic, complemented
7#21446131C211yesmaximal, characteristic, complemented
8#21446126C211yesmaximal, characteristic, complemented
9#21445907C211yesmaximal, characteristic, complemented
10#21445903C211yesmaximal, characteristic, complemented
11#21445831C211yesmaximal, characteristic, complemented
12#21445652C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16840469—24no—
19#16840469C418yescomplemented
20C2×#14519777C2211yescharacteristic
21C2×#14519768—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519754—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×D4×Dic61—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C61×#388—21no—
55C61×#387—21no—
56C61×#386—21no—
57C61×#382C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—41no—
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519777—22no—
77#14519777C2×C414yescomplemented
78#14519768—28no—
79#14519756—22no—
80#14519756—22no—
81#14519756C2×C414yes—
82#14519756C2×C414yescomplemented
83#14519754—28no—
84#14519754—28no—
85C4×Dic122—22no—
86C4×Dic122C2×C414yescomplemented
87D4×Dic61—28no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C414yes—
94C2×C4⋊Dic61C2×C414yescomplemented
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×C4×Dic61—21no—
104C4⋊#92418—22no—
105#14519700—22no—
106#14519700—22no—
107#14519700—41no—
108#14519700—41no—
109C22⋊#92418—22no—
110C22⋊#92418—22no—
111#14519688—22no—
112C22×D4×C61D411yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C4×D4×C61C2×C414yes—
117C4×D4×C61D414yes—
118#117×C61—22no—
119#117×C61—41no—
120C2×C4⋊C4×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
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×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—81no—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—24no—
175C22×Dic61—24no—
176C22×Dic61—81no—
177C22×Dic61—81no—
178C22×Dic61—81no—
179C22×Dic61—81no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—24no—
186C2×Dic122—81no—
187C2×Dic122—81no—
188C2×Dic122C22×C412yes—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61C22⋊C414yes—
198C4⋊C4×C61#4112yes—
199C22⋊C4×C61—42no—
200C22⋊C4×C61—42no—
201C22⋊C4×C61—81no—
202C22⋊C4×C61C22⋊C414yes—
203C22⋊C4×C61C22⋊C414yes—
204C42×C61—42no—
205C42×C61—81no—
206C42×C61C22×C412yes—
207C42×C61C2×D412yes—
208C22⋊Dic61—24no—
209C22⋊Dic61—24no—
210C4⋊Dic61—24no—
211C4⋊Dic61—24no—
212C4⋊Dic61—24no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61C22×C412yes—
217C4⋊Dic61C22×C412yes—
218C4⋊Dic61C22×C412yes—
219#11758196—24no—
220#11758196—24no—
221#11758196—24no—
222C4×Dic61—24no—
223#11758194—44no—
224C2×#92418—21no—
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—44no—
236C2×#92418#4112yes—
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×C61—21no—
246C23×C61—21no—
247C23×C61C2×C22⋊C412yes—
248C23×C61C2×C22⋊C412yes—
249C23×C61#13712yes—
250C23×C61#13712yes—
251C23×C61C22×D411yescharacteristic
252D4×C61—28no—
253C2×C4×C61—21no—
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—22no—
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×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—84no—
282C2×C4×C61C2×C22⋊C412yes—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
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—
305C2×Dic61—84no—
306Dic122—22no—
307Dic122—22no—
308Dic122—41no—
309Dic122—41no—
310Dic122—84no—
311#92418—22no—
312#92418—41no—
313#92418—41no—
314#92418—41no—
315#22497—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#41914yes—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61C2×#13711yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57711yescharacteristic
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—42no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61C4×#4111yescharacteristic
346C4×C61#52011yescharacteristic
347C4×C61#54611yescharacteristic
348C4×C61#54711yescharacteristic
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353C2×#554—611no—
354C2×#435—611no—
355#2352D6111yescharacteristic
356#1993—611no—
357#1988—611no—
358#1894—611no—
359#1892—611no—
360#1873—611no—
361#1872—611no—
362#1824—611no—
363#1823—611no—
364#1805—611no—
365#1763—611no—
366#1736—611no—
367C2×#340—611no—
368C2×C61—24no—
369C2×C61—42no—
370C2×C61#233911yescharacteristic
371C2×C61C2×#41911yescharacteristic
372C2×C61#289711yescharacteristic
373C2×C61#331411yescharacteristic
374C2×C61#331611yescharacteristic
375C2×C61#334411yescharacteristic
376C2×C61#334611yescharacteristic
377C22×M16—611no—
378C23×C8—611no—
379#554—618no—
380#554—1224no—
381C2×C4⋊Q8—611no—
382C2×#125—1221no—
383C2×C22⋊Q8—611no—
384C2×C22⋊Q8—611no—
385C2×C22⋊Q8—1221no—
386C2×C22⋊Q8—1221no—
387C2×C4×Q8—611no—
388C2×C4×D4—1221no—
389C2×C4×D4C2×D6111yescharacteristic
390C2×#117C2×D6111yescharacteristic
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4C2×D6111yescharacteristic
394#435—1224no—
395C2×C4⋊C8—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×C22⋊C8—611no—
401C2×C22⋊C8—611no—
402C2×#97—611no—
403#388—21no—
404#387—21no—
405#386—21no—
406#382C2×D6111yescharacteristic
407#380C2×D6111yescharacteristic
408#380C2×D6111yescharacteristic
409C4×C4⋊C4C2×D6111yescharacteristic
410C4×C22⋊C4—21no—
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#2249711yescharacteristic, complemented, Sylow
424C22×Q8—611no—
425C22×Q8—1221no—
426C22×D4C22⋊D6111yescharacteristic
427C23×C4—21no—
428C23×C4—1221no—
429C23×C4—1221no—
430C23×C4C22×D6111yescharacteristic
431C23×C4C22×D6111yescharacteristic
432C2×M16—1222no—
433C2×M16—1222no—
434C2×M16—2441no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8—611no—
439C22×C8—1222no—
440C22×C8—1222no—
441C22×C8—2441no—
442C4⋊Q8—614no—
443C4⋊Q8—1222no—
444#125—1228no—
445C22⋊Q8—614no—
446C22⋊Q8—614no—
447C22⋊Q8—1222no—
448C22⋊Q8—1222no—
449C22⋊Q8—1228no—
450C22⋊Q8—1228no—
451C4×Q8—614no—
452C4×Q8—1222no—
453C4×D4—1228no—
454C4×D4C4×D6114yes—
455C4×D4D24414yes—
456#117—22no—
457#117—41no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—614no—
462C2×C4⋊C4—614no—
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⋊C4C22⋊D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4C22⋊D6111yescharacteristic
485C2×C22⋊C4C22⋊D6111yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—1221no—
489C2×C42C22×D6111yescharacteristic
490C4⋊C8—1222no—
491#103—1222no—
492#103—1222no—
493#103—2441no—
494#103—2441no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497#97—1222no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503C24C2×C22⋊D6111yescharacteristic
504C24C2×C22⋊D6111yescharacteristic
505C2×Q8—612no—
506C2×Q8—1221no—
507C2×Q8—1224no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×Q8—4881no—
513C2×Q8—4881no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4#1175819814yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—1224no—
533C22×C4—1224no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—4881no—
539C22×C4—4881no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4C2×C4×D6112yes—
543C22×C4C2×C4×D6112yes—
544C22×C4C2×D24412yes—
545C22×C4C2×D24412yes—
546C22×C4C2×C22⋊D6111yescharacteristic
547C22×C4C2×C22⋊D6111yescharacteristic
548C22×C4C2×C22⋊D6111yescharacteristic
549C22×C4C2×C22⋊D6111yescharacteristic
550C22×C4C23×D6111yescharacteristic
551M16—2444no—
552C2×C8—612no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—2444no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—612no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1224no—
580C4⋊C4—1224no—
581C4⋊C4—1224no—
582C4⋊C4—1224no—
583C4⋊C4—1224no—
584C4⋊C4—1224no—
585C4⋊C4#1175819814yes—
586C4⋊C4#1175822412yes—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—1224no—
591C22⋊C4—1224no—
592C22⋊C4#1175819814yes—
593C22⋊C4#1175819814yes—
594C42—42no—
595C42—81no—
596C42—1224no—
597C42C2×C4×D6112yes—
598C42C2×D24412yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×#1175819812yes—
610C23C2×#1175819812yes—
611C23#1451980712yes—
612C23#1451980712yes—
613C23C22×C22⋊D6111yescharacteristic
614Q8—1222no—
615Q8—1222no—
616Q8—4884no—
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—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—4884no—
654C2×C4—4884no—
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×D24411yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—1222no—
674C8—2441no—
675C8—2441no—
676C8—2441no—
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#1683977014yes—
691C22C22×#1175819811yescharacteristic
692C22#1684040611yescharacteristic
693C22#1684041111yescharacteristic
694C22C2×#1451980711yescharacteristic
695C22C2×#1451980711yescharacteristic
696C22#1684056511yescharacteristic
697C22#1684057011yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4C4×#1175822411yescharacteristic
711C4#1684024111yescharacteristic
712C4#1684040711yescharacteristic
713C4#1684041611yescharacteristic
714C2—24no—
715C2—42no—
716C2#2144864411yescharacteristic
717C2C2×#1683977011yescharacteristic
718C2#2145434211yescharacteristic
719C2#2145790011yescharacteristic
720C2#2145793011yescharacteristic
721C2#2145827411yescharacteristic
722C2#2145830411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenter#2352D61
hypocenterC61#22497
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #21446791C2semidirect
4. #21446771C2semidirect
5. #21446250C2semidirect
6. #21446240C2semidirect
7. #21446131C2semidirect
8. #21446126C2semidirect
9. #21445907C2semidirect
10. #21445903C2semidirect
11. #21445831C2semidirect
12. #21445652C2semidirect
13. #21445540C2semidirect
14. C2×#16839524C2semidirect
19. #16840469C4semidirect
77. #14519777C2×C4semidirect
82. #14519756C2×C4semidirect
86. C4×Dic122C2×C4semidirect
94. C2×C4⋊Dic61C2×C4semidirect
423. C61#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168398342
#214467912
#214467712
#214462502
#214462402
#214461312
#214461262
#214459072
#214459032
#214458312
#214456522
#214455402
C2×#168395242
C61×#23522
#2249761