Finite Group Databasebeta

← #29696397

Subgroups — #29696397

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×#16840470C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic
3#21448750C211yesmaximal, characteristic
4#21446790C211yesmaximal, characteristic, complemented
5#21446769C211yesmaximal, characteristic, complemented
6#21446249C211yesmaximal, characteristic, complemented
7#21446128C211yesmaximal, characteristic, complemented
8#21446127C211yesmaximal, characteristic, complemented
9#21445907C211yesmaximal, characteristic, complemented
10#21445904C211yesmaximal, characteristic, complemented
11#21445832C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14C2×#16839525C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17#16840470—24no—
18#16840470C418yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757—21no—
22C2×#14519754—21no—
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519737—21no—
27C2×#14519735C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839833—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839654—21no—
39#16839649—21no—
40#16839639—21no—
41#16839627C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×C22⋊D61D411yescharacteristic
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519776—22no—
74#14519776C2×C414yescomplemented
75#14519767—28no—
76#14519757—28no—
77#14519754—28no—
78#14519753—22no—
79#14519753C2×C414yescomplemented
80Q8×Dic61—22no—
81Q8×Dic61C2×C414yescomplemented
82C4×C22⋊D61C2×C414yes—
83C4×C22⋊D61D414yes—
84#14519737—28no—
85#14519735—22no—
86#14519735—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61C2×C414yes—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C4⋊C4×D61—22no—
103C4⋊C4×D61C2×C414yescomplemented
104C2×C22⋊Dic61D411yescharacteristic
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198D411yescharacteristic
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519701—22no—
115#14519701—41no—
116C22⋊#92418—22no—
117#14519689—22no—
118#14519687—22no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×Q8×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C22×C8×C61—22no—
126C22×C8×C61—22no—
127C22×C8×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61C2×C414yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138#103×C61—22no—
139#103×C61—41no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
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×C61C22×C412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61C22⋊C414yes—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—24no—
168C22×Dic61—21no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61—81no—
172C22×Dic61—81no—
173C22×Dic61—81no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—24no—
182C2×C4×D61—81no—
183C2×C4×D61—81no—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×D412yes—
186C2×Dic122—24no—
187C2×Dic122—81no—
188C2×Dic122—81no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—44no—
195C2×C8×C61#4112yes—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—42no—
205C22⋊Dic61C22⋊C414yes—
206#11758198—24no—
207#11758198—42no—
208#11758198—81no—
209#11758198C22⋊C414yes—
210C4⋊Dic61—24no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—24no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—42no—
218C4⋊Dic61C22×C412yes—
219C4⋊Dic61C22×C412yes—
220C4⋊Dic61#4112yes—
221#11758196—24no—
222#11758196—24no—
223#11758196—24no—
224#11758196C22⋊C414yes—
225C4×Dic61—24no—
226C4×Dic61—42no—
227C4×Dic61—81no—
228C4×Dic61C22×C412yes—
229C4×Dic61C2×D412yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236#11758189—44no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61C2×C22⋊C412yes—
242C23×C61#13712yes—
243C23×C61#13712yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61C2×C22⋊C412yes—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—41no—
255Q8×C61—41no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
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—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C2×C22⋊C412yes—
275C2×C4×C61C23×C411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C22⋊D61—28no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
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—84no—
301C2×Dic61—84no—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61C2×C22⋊C412yes—
304C2×Dic61C2×C22⋊C412yes—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—84no—
310Dic122—84no—
311C8×C61—22no—
312C8×C61—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#41914yes—
323C22×C61C22×C22⋊C411yescharacteristic
324C22×C61#54611yescharacteristic
325C22×C61#54711yescharacteristic
326C22×C61C2×#13711yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57611yescharacteristic
329C22×C61#57711yescharacteristic
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C4×C61—22no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61C4×#4111yescharacteristic
343C4×C61#52011yescharacteristic
344C4×C61#54611yescharacteristic
345C4×C61#54711yescharacteristic
346Dic61—22no—
347Dic61—22no—
348Dic61—22no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—81no—
353C2×#554—611no—
354C2×#435—611no—
355#2352—611no—
356#1993—611no—
357#1988—611no—
358#1894—611no—
359#1892D6111yescharacteristic, complemented
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#233911yescharacteristic
370C2×C61C2×#41911yescharacteristic
371C2×C61#289711yescharacteristic
372C2×C61#331411yescharacteristic
373C2×C61#331611yescharacteristic
374C2×C61#334411yescharacteristic
375C2×C61#334611yescharacteristic
376D61—42no—
377C22×M16—611no—
378C23×C8C2×D6111yescharacteristic
379#554—618no—
380#554—1224no—
381C2×C4⋊Q8—611no—
382C2×#125—1221no—
383C2×C22⋊Q8—611no—
384C2×C22⋊Q8—1221no—
385C2×C22⋊Q8—1221no—
386C2×C22⋊Q8C2×D6111yescharacteristic
387C2×C4×Q8—611no—
388C2×C4×D4—611no—
389C2×C4×D4—1221no—
390C2×#117—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394#435—1224no—
395C2×C4⋊C8—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103C2×D6111yescharacteristic
399C2×#103C2×D6111yescharacteristic
400C2×C22⋊C8—611no—
401C2×C22⋊C8—611no—
402C2×#97—611no—
403#388—1221no—
404#387—1221no—
405#386—1221no—
406#382—611no—
407#380—611no—
408#380C2×D6111yescharacteristic
409C4×C4⋊C4—611no—
410C4×C22⋊C4—1221no—
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#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2249711yescharacteristic, complemented, Sylow
424C22×Q8—1221no—
425C22×Q8C22×D6111yescharacteristic
426C22×D4—611no—
427C23×C4—611no—
428C23×C4—1221no—
429C23×C4—1221no—
430C23×C4—1221no—
431C23×C4C22×D6111yescharacteristic
432C2×M16—1222no—
433C2×M16—1222no—
434C2×M16—2441no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—611no—
439C22×C8—611no—
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C4⋊Q8—614no—
443C4⋊Q8—1222no—
444#125—1228no—
445C22⋊Q8—22no—
446C22⋊Q8—614no—
447C22⋊Q8—1228no—
448C22⋊Q8—1228no—
449C22⋊Q8—1222no—
450C22⋊Q8C4×D6114yes—
451C4×Q8—614no—
452C4×Q8—1222no—
453C4×D4—614no—
454C4×D4—614no—
455C4×D4—1228no—
456#117—1222no—
457#117—2441no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—614no—
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—1222no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—2441no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—611no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C4⋊C8—1222no—
491#103—22no—
492#103—41no—
493#103—1222no—
494#103—2441no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497#97—1222no—
498#95—21no—
499#95—1221no—
500#95—1221no—
501#95—1221no—
502#95—1221no—
503C24—611no—
504C24D4×D6111yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—1224no—
511C2×Q8—4881no—
512C2×Q8—4881no—
513C2×Q8C2×C4×D6112yes—
514C2×D4—614no—
515C2×D4—1222no—
516C2×D4—1222no—
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—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—1224no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1224no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—4881no—
543C22×C4—4881no—
544C22×C4—4881no—
545C22×C4—2442no—
546C22×C4—2442no—
547C22×C4C2×C4×D6112yes—
548C22×C4D4×D6112yes—
549C22×C4D4×D6111yescharacteristic
550C22×C4C23×D6111yescharacteristic
551M16—2444no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—44no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8#1175822412yes—
565C4⋊C4—21no—
566C4⋊C4—24no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—614no—
572C4⋊C4—612no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—1224no—
576C4⋊C4—1224no—
577C4⋊C4—1224no—
578C4⋊C4—1224no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1224no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—2442no—
586C4⋊C4C2×C4×D6112yes—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—614no—
590C22⋊C4—614no—
591C22⋊C4—1224no—
592C22⋊C4—4881no—
593C22⋊C4—2442no—
594C42—612no—
595C42—612no—
596C42—1224no—
597C42—4881no—
598C42—2442no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—612no—
604C23—1221no—
605C23—1221no—
606C23—1221no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23C22⋊C4×D6112yes—
611C23#1451980612yes—
612C23#1451980912yes—
613C23C2×D4×D6111yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—4884no—
619D4—1228no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—4884no—
655C2×C4—4884no—
656C2×C4—4884no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4C22⋊C4×D6112yes—
667C2×C4C22×C4×D6111yescharacteristic
668C2×C4C2×D4×D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—22no—
674C8—41no—
675C8—2441no—
676C8—2441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—2441no—
687C22—2441no—
688C22—2441no—
689C22—2441no—
690C22#1683976914yes—
691C22C2×C22⋊C4×D6111yescharacteristic
692C22#1684040111yescharacteristic
693C22#1684041211yescharacteristic
694C22C2×#1451980611yescharacteristic
695C22C2×#1451980911yescharacteristic
696C22#1684056411yescharacteristic
697C22#1684056911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—1222no—
704C4—1222no—
705C4—1222no—
706C4—4881no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4C4×#1175822411yescharacteristic
711C4#1684024111yescharacteristic
712C4#1684039911yescharacteristic
713C4#1684041011yescharacteristic
714C2—24no—
715C2—2442no—
716C2#2144864511yescharacteristic
717C2C2×#1683976911yescharacteristic
718C2#2145434111yescharacteristic
719C2#2145790611yescharacteristic
720C2#2145793611yescharacteristic
721C2#2145828011yescharacteristic
722C2#2145831011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#22497
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #21446790C2semidirect
5. #21446769C2semidirect
6. #21446249C2semidirect
7. #21446128C2semidirect
8. #21446127C2semidirect
9. #21445907C2semidirect
10. #21445904C2semidirect
11. #21445832C2semidirect
12. #21445651C2semidirect
13. #21445537C2semidirect
14. C2×#16839525C2semidirect
15. C61×#1892C2semidirect
18. #16840470C4semidirect
74. #14519776C2×C4semidirect
79. #14519753C2×C4semidirect
81. Q8×Dic61C2×C4semidirect
103. C4⋊C4×D61C2×C4semidirect
359. #1892D61semidirect
423. C61#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168398332
#214487502
#214467902
#214467692
#214462492
#214461282
#214461272
#214459072
#214459042
#214458322
#214456512
#214455372
C2×#168395252
C61×#18922
#2249761