Finite Group Databasebeta

← #29713965

Subgroups — #29713965

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic
2C2×#16840055C211yesmaximal, characteristic, complemented
3C2×Q16×Dic61C211yesmaximal, characteristic, complemented
4#21450738C211yesmaximal, characteristic
5#21447021C211yesmaximal, characteristic, complemented
6#21447019C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446778C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic
10#21446127C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21446009C211yesmaximal, characteristic, complemented
13#21446008C211yesmaximal, characteristic, complemented
14#21445822C211yesmaximal, characteristic, complemented
15C61×#2001C211yesmaximal, characteristic, complemented
16#16840470—24no—
17#16840470—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519767—21no—
20C2×#14519757—21no—
21C2×#14519754—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×#14519737—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840055—24no—
31Q16×Dic61—24no—
32C2×#14519711C2211yescharacteristic
33C2×#14519711C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839685—21no—
45#16839684—21no—
46#16839662—21no—
47#16839657—21no—
48#16839631C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×C22⋊D61D411yescharacteristic
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519776—22no—
71#14519776D414yes—
72#14519767—28no—
73#14519757—28no—
74#14519754—28no—
75#14519753—22no—
76#14519753—22no—
77#14519753—22no—
78#14519753—41no—
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81Q8×Dic61—22no—
82Q8×Dic61D414yes—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85#14519737—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C4⋊C4×D61—22no—
103C4⋊C4×D61—22no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61D411yescharacteristic
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519711—22no—
114#14519711—22no—
115#14519710—22no—
116#14519706—22no—
117#14519701—22no—
118#14519701—22no—
119#14519701—22no—
120#14519701—41no—
121C22⋊#92418—41no—
122#14519689—22no—
123#14519689—41no—
124C8×Dic61—22no—
125#14519684—21no—
126#14519684—21no—
127C22×Q8×C61C2311yescharacteristic
128C22×Q8×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×Q16×C61—22no—
131C2×Q16×C61—22no—
132C2×Q16×C61—22no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145#103×C61—22no—
146#103×C61—41no—
147C22⋊C8×C61—22no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61Q1614yescomplemented
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—24no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—81no—
183C22×Dic61—81no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—24no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C2×Dic122—24no—
197C2×Dic122—81no—
198C2×Dic122—81no—
199Q16×C61—28no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61#4112yes—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—42no—
214C22⋊Dic61—22no—
215C22⋊Dic61—81no—
216#11758198—24no—
217#11758198—22no—
218#11758198—42no—
219#11758198—81no—
220C4⋊Dic61—24no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—24no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61C2×D412yes—
230C4⋊Dic61C2×D412yes—
231#11758196—24no—
232#11758196—24no—
233#11758196—24no—
234#11758196—22no—
235#11758196—42no—
236#11758196—42no—
237#11758196—81no—
238C4×Dic61—24no—
239C4×Dic61—42no—
240C4×Dic61C2×D412yes—
241C4×Dic61C2×D412yes—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61C2×Q1612yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C2×Q1612yes—
263Q8×C61—22no—
264Q8×C61—22no—
265Q8×C61—22no—
266Q8×C61—22no—
267Q8×C61—41no—
268Q8×C61—41no—
269Q8×C61—41no—
270Q8×C61—41no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C612−1+411yescharacteristic
296C22⋊D61—28no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—84no—
315C2×Dic61#12012yes—
316C2×Dic61#12012yes—
317C2×Dic61C2×Q1612yes—
318C2×Dic61#13712yes—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—84no—
324Dic122—84no—
325C8×C61—22no—
326C8×C61—41no—
327#92418—41no—
328#92418—41no—
329#24122—611nomaximal, Sylow
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C2×#12011yescharacteristic
338C22×C61#54611yescharacteristic
339C22×C61#54711yescharacteristic
340C22×C61C22×Q1611yescharacteristic
341C22×C61C2×#13711yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57711yescharacteristic
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C4×C61—41no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—81no—
356C4×C61#52511yescharacteristic
357C4×C61#53711yescharacteristic
358C4×C61#54811yescharacteristic
359C4×C61#55011yescharacteristic
360Dic61—22no—
361Dic61—41no—
362Dic61—42no—
363Dic61—42no—
364Dic61—81no—
365Dic61—81no—
366Dic61#45114yes—
367C2×#554—611no—
368C2×#477—611no—
369C2×C4×Q16—611no—
370#2538—611no—
371#2036—611no—
372#2036—611no—
373#2001—611no—
374#2001D6111yescharacteristic, complemented
375#1990—611no—
376#1954—611no—
377#1872—611no—
378#1872—611no—
379#1852—611no—
380#1852—611no—
381#1803—611no—
382C2×C61—42no—
383C2×C61#240711yescharacteristic
384C2×C61C2×#45111yescharacteristic
385C2×C61#301211yescharacteristic
386C2×C61#329911yescharacteristic
387C2×C61#333311yescharacteristic
388C2×C61#333811yescharacteristic
389C2×C61#335611yescharacteristic
390D61—42no—
391C22×Q16C2×D6111yescharacteristic
392#554—1224no—
393#554—1224no—
394C2×C4⋊Q8—611no—
395C2×#125—1221no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—611no—
398C2×C22⋊Q8—1221no—
399C2×C22⋊Q8—1221no—
400C2×C22⋊Q8C2×D6111yescharacteristic
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×C4×Q8—611no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—1221no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408#477—1224no—
409C4×Q16—1224no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#107—611no—
413C2×C4⋊C8—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103C2×D6111yescharacteristic
419C2×#103C2×D6111yescharacteristic
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8C2×D6111yescharacteristic
424C2×C4×C8—611no—
425#396—1221no—
426#396—1221no—
427#390—1221no—
428#389—1221no—
429#384—611no—
430#380—611no—
431#380—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340C2×D6111yescharacteristic
438C61#2412211yescharacteristic, complemented, Sylow
439C22×Q8—1221no—
440C22×Q8C22×D6111yescharacteristic
441C22×Q8C22×D6111yescharacteristic
442C22×D4—611no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4C22×D6111yescharacteristic
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—22no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454C4⋊Q8—614no—
455C4⋊Q8—1222no—
456#125—1228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—41no—
461C22⋊Q8—1228no—
462C22⋊Q8—1228no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—2441no—
467C4×Q8—614no—
468C4×Q8—1222no—
469C4×Q8—1222no—
470C4×Q8—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1228no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—1221no—
506C2×C42—1221no—
507#107—1222no—
508#107—1222no—
509#107—1222no—
510C4⋊C8—1222no—
511#103—22no—
512#103—41no—
513#103—1222no—
514#103—1222no—
515#103—1222no—
516#103—2441no—
517C22⋊C8—22no—
518C22⋊C8—1222no—
519C22⋊C8—2441no—
520C22⋊C8—2441no—
521C4×C8—1222no—
522#95—1221no—
523#95—1221no—
524C24—611no—
525C24D4×D6111yescharacteristic
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—1224no—
537C2×Q8—4881no—
538C2×Q8—4881no—
539C2×Q8D4×D6112yes—
540C2×Q8#1175822412yes—
541C2×D4—614no—
542C2×D4—1222no—
543C2×D4—1222no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1224no—
558C22×C4—1224no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—4881no—
573C22×C4D4×D6111yescharacteristic
574C22×C4C23×D6111yescharacteristic
575Q16—28no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8#1175822412yes—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—612no—
594C4⋊C4—612no—
595C4⋊C4—1222no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C4⋊C4—1224no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—4881no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4D4×D6112yes—
612C22⋊C4—24no—
613C22⋊C4—42no—
614C22⋊C4—1222no—
615C22⋊C4—1224no—
616C22⋊C4—1222no—
617C22⋊C4—4881no—
618C22⋊C4—4881no—
619C22⋊C4—2442no—
620C42—612no—
621C42—612no—
622C42—1224no—
623C42—2442no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—612no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23Q16×D6112yes—
638C23C2×D4×D6111yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—4884no—
648D4—1228no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—4884no—
680C2×C4—4884no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4C2×D4×D6111yescharacteristic
696C2×C4C2×D4×D6111yescharacteristic
697C2×C4C2×#1175822411yescharacteristic
698C2×C4C2×#1175822411yescharacteristic
699C2×C4#1451982211yescharacteristic
700C2×C4#1451982411yescharacteristic
701C8—22no—
702C8—41no—
703C8—2441no—
704C8—2441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22#120×D6111yescharacteristic
720C22#1684039911yescharacteristic
721C22#1684041211yescharacteristic
722C22C2×Q16×D6111yescharacteristic
723C22#137×D6111yescharacteristic
724C22#1684056411yescharacteristic
725C22#1684057111yescharacteristic
726C4—42no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—614no—
732C4—1222no—
733C4—4881no—
734C4—4881no—
735C4—2442no—
736C4—2442no—
737C4—2441no—
738C4#1684026811yescharacteristic
739C4#1684033911yescharacteristic
740C4#1684041811yescharacteristic
741C4#1684043211yescharacteristic
742C2—42no—
743C2—2442no—
744C2#2144915711yescharacteristic
745C2#451×D6111yescharacteristic
746C2#2145512711yescharacteristic
747C2#2145768811yescharacteristic
748C2#2145815011yescharacteristic
749C2#2145820811yescharacteristic
750C2#2145842911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2001D61
hypocenterC61#24122
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#16840055C2semidirect
3. C2×Q16×Dic61C2semidirect
5. #21447021C2semidirect
6. #21447019C2semidirect
7. #21446826C2semidirect
8. #21446778C2semidirect
10. #21446127C2semidirect
11. #21446123C2semidirect
12. #21446009C2semidirect
13. #21446008C2semidirect
14. #21445822C2semidirect
15. C61×#2001C2semidirect
176. C2×C22⋊D61Q16semidirect
374. #2001D61semidirect
438. C61#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168400552
C2×Q16×Dic612
#214507382
#214470212
#214470192
#214468262
#214467782
#214466112
#214461272
#214461232
#214460092
#214460082
#214458222
C61×#20012
#2412261