Finite Group Databasebeta

← #29730755

Subgroups — #29730755

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840003C211yesmaximal, characteristic, complemented
2C2×#16840002C211yesmaximal, characteristic, complemented
3C2×#16839971C211yesmaximal, characteristic, complemented
4C2×C8×C22⋊D61C211yesmaximal, characteristic
5#21450769C211yesmaximal, characteristic
6#21450743C211yesmaximal, characteristic
7#21447022C211yesmaximal, characteristic, complemented
8#21447021C211yesmaximal, characteristic, complemented
9#21446830C211yesmaximal, characteristic, complemented
10#21446827C211yesmaximal, characteristic, complemented
11#21446619C211yesmaximal, characteristic, complemented
12#21446576C211yesmaximal, characteristic, complemented
13#21446241C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519775C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×#14519757C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519753C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27#16840003—24no—
28#16840002—24no—
29#16839971—24no—
30C8×C22⋊D61—24no—
31C2×#14519711C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519706C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43#16839698—21no—
44#16839697—21no—
45#16839686—21no—
46#16839685—21no—
47#16839662—21no—
48#16839662—21no—
49#16839659—21no—
50#16839631—21no—
51#16839631C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×Dic244—22no—
68C2×Dic244—22no—
69C2×Dic244—41no—
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—41no—
78#14519775—22no—
79#14519775—22no—
80#14519757—22no—
81#14519757—22no—
82#14519757—41no—
83#14519757—41no—
84#14519756—22no—
85#14519756—22no—
86#14519756—41no—
87#14519756—41no—
88#14519753—22no—
89#14519753—41no—
90#14519742—22no—
91#14519742—22no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519711—22no—
119#14519710—22no—
120#14519706D414yes—
121#14519702—22no—
122#14519702D414yescomplemented
123#14519701—41no—
124#14519700—22no—
125#14519700—22no—
126#14519700—41no—
127C22⋊#92418—22no—
128#14519689—22no—
129C8×Dic61—22no—
130#14519684—21no—
131#14519684—21no—
132C22×Q8×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C22×C8×C61—22no—
135C22×C8×C61—22no—
136C22×C8×C61—41no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—41no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#103×C61—22no—
149#95×C61—21no—
150C24×C61C2×D411yescharacteristic
151C23×D61C2×D411yescharacteristic
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61Q1614yescomplemented
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122C2×D412yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—44no—
203C2×C8×C61C2×D412yes—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61#4112yes—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—81no—
214C22⋊Dic61—22no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217#11758202—44no—
218#11758198—22no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—81no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—42no—
228C4⋊Dic61C2×D412yes—
229#11758196—22no—
230#11758196—42no—
231#11758196—42no—
232#11758196—42no—
233#11758196—42no—
234#11758196—42no—
235#11758196—42no—
236#11758196—42no—
237#11758196—81no—
238C4×Dic61—42no—
239C4×Dic61—42no—
240C4×Dic61C2×D412yes—
241C4×Dic61#4112yes—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C2×D412yes—
248Dic244—44no—
249C8×D61—44no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61C2×Q1612yes—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61C2×Q1612yes—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61—41no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
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—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×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C22⋊D61—28no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—21no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—41no—
303C2×Dic61—41no—
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#12112yes—
313C2×Dic61#12112yes—
314C2×Dic61C2×Q1612yes—
315C2×Dic61#13512yes—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320Dic122—22no—
321Dic122—22no—
322Dic122—41no—
323Dic122—41no—
324Dic122—41no—
325Dic122—41no—
326Dic122—41no—
327Dic122—41no—
328C8×C61—22no—
329C8×C61—22no—
330#92418—22no—
331#92418—41no—
332#25386—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×#12111yescharacteristic
341C22×C61D4211yescharacteristic
342C22×C61#54611yescharacteristic
343C22×C61C22×Q1611yescharacteristic
344C22×C61C2×#13511yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—41no—
355C4×C61—42no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61#53211yescharacteristic
360C4×C61#54011yescharacteristic
361C4×C61D4211yescharacteristic
362C4×C61#55011yescharacteristic
363Dic61—22no—
364Dic61—42no—
365Dic61—41no—
366Dic61—42no—
367Dic61—81no—
368Dic61—81no—
369Dic61#46714yescomplemented
370C2×#467—611no—
371C2×#467—611no—
372C2×#462—611no—
373C2×C8×D4—611no—
374#2542—611no—
375#2538—611no—
376#2036—611no—
377#2036—611no—
378#2001—611no—
379#2001—611no—
380#1956—611no—
381#1947—611no—
382#1892—611no—
383#1892D6111yescharacteristic, complemented
384C4×#103—611no—
385C2×C61—42no—
386C2×C61#242811yescharacteristic
387C2×C61C2×#46711yescharacteristic
388C2×C61#306311yescharacteristic
389C2×C61#328411yescharacteristic
390C2×C61D4×Q1611yescharacteristic
391C2×C61#329911yescharacteristic
392C2×C61#330211yescharacteristic
393D61—42no—
394C22×Q16—611no—
395C22×Q16—611no—
396C23×C8—611no—
397C23×C8C2×D6111yescharacteristic
398C2×C4⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×C22⋊Q8—611no—
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8C2×D6111yescharacteristic
405C2×C4×Q8—611no—
406C2×C4×D4—611no—
407#467—1224no—
408#467—1224no—
409#462—1224no—
410C8×D4—1224no—
411C2×#107—611no—
412C2×#107—611no—
413C2×C4⋊C8—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103C2×D6111yescharacteristic
421C2×#103C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C4×C8—611no—
425#399—1221no—
426#399—1221no—
427#396—1221no—
428#396—1221no—
429#390—1221no—
430#390—1221no—
431#389—1221no—
432#384—611no—
433#384—1221no—
434#380—611no—
435#380C2×D6111yescharacteristic
436C4×C4⋊C4—611no—
437#340—611no—
438#340—611no—
439#340C2×D6111yescharacteristic
440#340C2×D6111yescharacteristic
441C61#2538611yescharacteristic, complemented, Sylow
442C22×Q8—611no—
443C22×Q8—611no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—611no—
446C23×C4—611no—
447C23×C4C22×D6111yescharacteristic
448C2×Q16—1222no—
449C2×Q16—1222no—
450C2×Q16—1222no—
451C2×Q16—1222no—
452C2×Q16—2441no—
453C2×Q16—2441no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—41no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—2441no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464C4⋊Q8—1222no—
465C4⋊Q8—1222no—
466C22⋊Q8—22no—
467C22⋊Q8—41no—
468C22⋊Q8—1222no—
469C22⋊Q8—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474C22⋊Q8—2441no—
475C22⋊Q8—2441no—
476C22⋊Q8—2441no—
477C22⋊Q8—2441no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—1221no—
511C2×C42—1221no—
512#107—1222no—
513#107—1222no—
514C4⋊C8—614no—
515#103—22no—
516#103—22no—
517#103—614no—
518#103—1222no—
519#103—1222no—
520#103—1222no—
521#103—2441no—
522#103—2441no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C4×C8—1222no—
526#95—21no—
527#95—1221no—
528#95—1221no—
529C24—611no—
530C24D4×D6111yescharacteristic
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—612no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×D4—614no—
550C2×D4—1222no—
551C2×D4—1222no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4D4×D6111yescharacteristic
576C22×C4C23×D6111yescharacteristic
577Q16—2444no—
578Q16—2444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8—612no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—2444no—
591C2×C8D4×D6112yes—
592C2×C8D4×D6112yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—612no—
600C4⋊C4—1222no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—4881no—
605C4⋊C4—2442no—
606C4⋊C4—2442no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4—2442no—
614C4⋊C4#1175822212yes—
615C22⋊C4—42no—
616C22⋊C4—81no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—4881no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C42—612no—
626C42—612no—
627C42—2442no—
628C42—2442no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—612no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23Q16×D6112yes—
643C23C2×D4×D6111yescharacteristic
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—1222no—
649Q8—1222no—
650Q8—2441no—
651Q8—2441no—
652Q8—2441no—
653Q8—2441no—
654Q8—2441no—
655Q8—2441no—
656D4—1228no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
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×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4C2×#1175822211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982311yescharacteristic
707C8—22no—
708C8—22no—
709C8—1222no—
710C8—2441no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—1222no—
719C22—1222no—
720C22—1222no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22#121×D6111yescharacteristic
726C22#1684039611yescharacteristic
727C22#1684040211yescharacteristic
728C22C2×Q16×D6111yescharacteristic
729C22#135×D6111yescharacteristic
730C22#1684056811yescharacteristic
731C22#1684057611yescharacteristic
732C4—42no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—614no—
738C4—1222no—
739C4—4881no—
740C4—4881no—
741C4—2442no—
742C4—2441no—
743C4—2442no—
744C4#1684030911yescharacteristic
745C4#1684036411yescharacteristic
746C4#1684039411yescharacteristic
747C4#1684043311yescharacteristic
748C2—42no—
749C2—2442no—
750C2#2144940611yescharacteristic
751C2#467×D6111yescharacteristic
752C2#2145550311yescharacteristic
753C2#2145754611yescharacteristic
754C2#2145756811yescharacteristic
755C2#2145769111yescharacteristic
756C2#2145773211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1892D61
hypocenterC61#25386
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#16840003C2semidirect
2. C2×#16840002C2semidirect
3. C2×#16839971C2semidirect
7. #21447022C2semidirect
8. #21447021C2semidirect
9. #21446830C2semidirect
10. #21446827C2semidirect
11. #21446619C2semidirect
12. #21446576C2semidirect
13. #21446241C2semidirect
14. #21445638C2semidirect
15. C61×#1892C2semidirect
122. #14519702D4semidirect
172. C2×C22⋊D61Q16semidirect
369. Dic61#467semidirect
383. #1892D61semidirect
441. C61#25386semidirect

Maximal subgroups

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

subgroupindex
C2×#168400032
C2×#168400022
C2×#168399712
C2×C8×C22⋊D612
#214507692
#214507432
#214470222
#214470212
#214468302
#214468272
#214466192
#214465762
#214462412
#214456382
C61×#18922
#2538661