Finite Group Databasebeta

← #29689844

Subgroups — #29689844

Order 15616.

1324 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21446806C212yesmaximal, complemented
5#21446657C212yesmaximal, complemented
6#21446281C212yesmaximal, complemented
7#21446279C212yesmaximal, complemented
8#21445811C211yesmaximal, characteristic, complemented
9#21445808C211yesmaximal, characteristic, complemented
10#21445808C211yesmaximal, characteristic, complemented
11C61×#1800C211yesmaximal, characteristic, complemented
12C22×#11758222C412yes—
13C2×M16×D61C2212yes—
14#16840309—21no—
15#16840309—21no—
16#16840309—21no—
17#16840309—21no—
18#16840309—21no—
19#16840309—21no—
20#16840309—21no—
21#16840309—21no—
22C2×#14519776C2211yescharacteristic
23C2×#14519773C2211yescharacteristic
24C2×#14519763C412yes—
25C2×#14519752C2211yescharacteristic
26C2×#14519750C412yes—
27C2×#14519748C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×C4×C22⋊D61C412yes—
30C2×C42×D61C2211yescharacteristic
31#16839818—21no—
32#16839818—21no—
33#16839814—21no—
34#16839814—21no—
35#16839786C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839785C2212yes—
38#16839784—21no—
39#16839784—21no—
40C4⋊C8×D61—21no—
41C4⋊C8×D61—21no—
42C2×#14519694C2212yes—
43C2×#14519693C2212yes—
44C2×#14519693C2212yes—
45#16839725C2212yes—
46M16×Dic61C2212yes—
47#16839531C2212yes—
48#16839530C2212yes—
49#16839530C2212yes—
50C2×C4×D4×C61C2211yescharacteristic
51C61×#423C2211yescharacteristic
52C61×#423C2211yescharacteristic
53C2×#100×C61C2212yes—
54C61×#343C2212yes—
55C2×#11758222—22no—
56C2×#11758222—22no—
57C2×#11758222—22no—
58C2×#11758222—22no—
59C2×#11758222—48no—
60C22×Dic122C2×C412yes—
61C22×D244C2×C412yes—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61C2×C412yes—
64C22×C22⋊D61C2×C412yes—
65C22×C22⋊D61C2×C412yes—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C412yes—
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758194C2312yes—
71C2×#11758194C2312yes—
72C2×#11758189—22no—
73M16×D61—42no—
74M16×D61—42no—
75C2×C8×D61—22no—
76#14519776—21no—
77#14519776—21no—
78#14519776—21no—
79#14519776—21no—
80#14519773—21no—
81#14519773—21no—
82#14519773—21no—
83#14519773—21no—
84#14519763—22no—
85#14519763—22no—
86#14519763—22no—
87#14519763—22no—
88#14519752—21no—
89#14519752—21no—
90#14519752—21no—
91#14519752—21no—
92#14519750—22no—
93#14519750—22no—
94#14519750—22no—
95#14519750—22no—
96#14519748—21no—
97#14519748—21no—
98#14519748—21no—
99#14519748—21no—
100C4×D244—21no—
101C4×D244—21no—
102C4×D244—21no—
103C4×D244—21no—
104C4×C22⋊D61—22no—
105C4×C22⋊D61—22no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196C2×C412yes—
110C2×C22⋊Dic61C2×C412yes—
111C2×#11758198C2×C412yes—
112C2×#11758198C2×C412yes—
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61D411yescharacteristic
122C42×D61D411yescharacteristic
123C42×D61D411yescharacteristic
124C4⋊#92418—21no—
125C4⋊#92418—21no—
126C4⋊#92418—21no—
127C4⋊#92418—21no—
128#14519706—22no—
129#14519706—22no—
130#14519694—42no—
131#14519693—42no—
132#14519693—42no—
133#14519689—22no—
134#14519689—22no—
135#14519687—22no—
136C8×Dic61—22no—
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61C2×C412yes—
139C2×M16×C61C2312yes—
140C2×M16×C61C2312yes—
141C4×D4×C61—21no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61C2×C412yes—
147C2×C42×C61C2311yescharacteristic
148C4⋊C8×C61—21no—
149C4⋊C8×C61—21no—
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152#100×C61—42no—
153C24×C61C22×C412yes—
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C412yes—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—44no—
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C412yes—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—44no—
176C2×C22⋊D61—44no—
177C2×C22⋊D61—44no—
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C412yes—
182#11758222—48no—
183#11758222—48no—
184#11758222—48no—
185#11758222—48no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—44no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—24no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—42no—
203C2×C4×D61—44no—
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—44no—
219M16×C61—22no—
220M16×C61—22no—
221M16×C61—22no—
222M16×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C42×C61C2×D411yescharacteristic
230C42×C61C2×D411yescharacteristic
231C42×C61C2×D411yescharacteristic
232C42×C61C2×D411yescharacteristic
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61C22⋊C411yescharacteristic
244C4×Dic61C22⋊C411yescharacteristic
245C4×Dic61C22⋊C411yescharacteristic
246C4×Dic61C22⋊C411yescharacteristic
247C4×Dic61C22⋊C411yescharacteristic
248C4×Dic61C22⋊C411yescharacteristic
249C4×Dic61C22⋊C411yescharacteristic
250C4×Dic61C22⋊C411yescharacteristic
251C4×Dic61C2×D411yescharacteristic
252C4×Dic61C2×D411yescharacteristic
253C4×Dic61C2×D411yescharacteristic
254C4×Dic61C2×D411yescharacteristic
255#11758194—22no—
256#11758194—22no—
257#11758194—22no—
258#11758194—22no—
259C2×#92418—22no—
260C2×#92418—22no—
261#11758189—44no—
262C8×D61—44no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C23×C411yescharacteristic
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—41no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61C2×C22⋊C411yescharacteristic
279C22×D61C2×C22⋊C411yescharacteristic
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—41no—
287C2×C4×C61—44no—
288C2×C4×C61—44no—
289C2×C4×C61—42no—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C612−1+411yescharacteristic
299C2×C4×C612−1+411yescharacteristic
300C22⋊D61—44no—
301C22⋊D61—44no—
302C22⋊D61—44no—
303C22⋊D61—44no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C2×C22⋊C411yescharacteristic
318D244—44no—
319D244—44no—
320D244—41no—
321D244—41no—
322D244—41no—
323D244—41no—
324C4×D61—22no—
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—44no—
340C4×D61—44no—
341C4×D61#10014yescomplemented
342Dic122—44no—
343Dic122—44no—
344C8×C61—42no—
345C8×C61—42no—
346#92418—42no—
347#92418—42no—
348#21878—611nomaximal, Sylow
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—82no—
355C22×C61—82no—
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61#52011yescharacteristic
358C22×C61#52011yescharacteristic
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—82no—
370C2×D61—82no—
371C2×D61C2×#10012yes—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—42no—
376C4×C61C2×#10012yes—
377C4×C61#53511yescharacteristic
378C4×C61#53611yescharacteristic
379C4×C61#53711yescharacteristic
380C4×C61#53711yescharacteristic
381Dic61—21no—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—42no—
386Dic61C2×#10012yes—
387Dic61#41312yes—
388C2×#532—611no—
389#2920—611no—
390C2×#423—611no—
391#1997—612no—
392#1965—612no—
393#1900—612no—
394#1900—612no—
395#1800—611no—
396#1800—611no—
397#1800—611no—
398#1800D6111yescharacteristic, complemented
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—82no—
402C2×C61#231111yescharacteristic
403C2×C61C22×#10011yescharacteristic
404C2×C61C2×#41311yescharacteristic
405D61—22no—
406D61—41no—
407D61—82no—
408C22×#41—612no—
409C22×M16—612no—
410#532—1221no—
411#532—1221no—
412#532—1221no—
413#532—1221no—
414#532—1221no—
415#532—1221no—
416#532—1221no—
417#532—1221no—
418C2×C4⋊Q8—611no—
419C2×#127—611no—
420C2×#124—612no—
421C2×#121—611no—
422C2×#121—611no—
423C2×#121—612no—
424C2×C4×D4—612no—
425C2×C4×D4—611no—
426C2×C4×D4C2×D6111yescharacteristic
427C22×C42—611no—
428#432—1221no—
429#432—1221no—
430#431—1221no—
431#431—1221no—
432#423—612no—
433#423—611no—
434#423—611no—
435#423—1221no—
436#423—1221no—
437#423C2×D6111yescharacteristic
438#423C2×D6111yescharacteristic
439C2×C4⋊C8—1221no—
440C2×C4⋊C8—1221no—
441C2×#100—612no—
442C2×#100—612no—
443C2×#100—612no—
444C2×#100C2×D6112yes—
445#407—612no—
446C4×M16—612no—
447#343—612no—
448#343—612no—
449#343—612no—
450#343C2×D6112yes—
451C61#2187811yescharacteristic, complemented, Sylow
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—2448no—
457C22×Q8—612no—
458C22×D4—612no—
459C22×D4—612no—
460C22×D4—612no—
461C22×D4—612no—
462C22×D4—611no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—612no—
468C23×C4C4×D6112yes—
469C2×M16—612no—
470C2×M16—612no—
471C2×M16—1222no—
472C2×M16—2442no—
473C2×M16—2442no—
474C2×M16C22×D6112yes—
475C2×M16C22×D6112yes—
476C22×C8—1222no—
477C4⋊Q8—1221no—
478C4⋊Q8—1221no—
479C4⋊Q8—1221no—
480C4⋊Q8—1221no—
481#127—1221no—
482#127—1221no—
483#127—1221no—
484#127—1221no—
485#124—1222no—
486#124—1222no—
487#124—1222no—
488#124—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492#121—1222no—
493#121—1221no—
494#121—1221no—
495#121—1221no—
496#121—1221no—
497#121—1221no—
498#121—1221no—
499#121—1221no—
500#121—1221no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1221no—
513C2×C4⋊C4—612no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4C22×D6111yescharacteristic
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4C4×D6112yes—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42C22×D6111yescharacteristic
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536C4⋊C8—1222no—
537C4⋊C8—1222no—
538C4⋊C8—1221no—
539C4⋊C8—1221no—
540C4⋊C8—1221no—
541C4⋊C8—1221no—
542#100—42no—
543#100—2442no—
544#100—2442no—
545#100—2442no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548#97—1222no—
549C4×C8—1222no—
550C24—611no—
551C24—612no—
552C24C2×C4×D6112yes—
553#41—2448no—
554#41—2448no—
555#41—2448no—
556#41—2448no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—2444no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—2444no—
581C2×D4—2444no—
582C2×D4—2444no—
583C2×D4—2444no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—44no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—612no—
603C22×C4—1224no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—2444no—
611C22×C4—2442no—
612C22×C4C2×C4×D6111yescharacteristic
613C22×C4C2×C4×D6112yes—
614C22×C4C2×C4×D6111yescharacteristic
615C22×C4C23×D6111yescharacteristic
616M16—22no—
617M16—22no—
618M16—22no—
619M16—22no—
620M16—1222no—
621M16—1222no—
622M16—1222no—
623M16—1222no—
624M16—2444no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—1222no—
628C2×C8—1222no—
629C2×C8—2444no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C42—611no—
645C42—611no—
646C42—611no—
647C42—611no—
648C42—611no—
649C42—611no—
650C42—611no—
651C42—611no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42D4×D6111yescharacteristic
657C42D4×D6111yescharacteristic
658C42D4×D6111yescharacteristic
659C42D4×D6111yescharacteristic
660C23—22no—
661C23—22no—
662C23—22no—
663C23—42no—
664C23—42no—
665C23—611no—
666C23—611no—
667C23—1222no—
668C23—1221no—
669C23—1221no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—2441no—
674C23—2442no—
675C23—2442no—
676C23C22×C4×D6111yescharacteristic
677Q8—2444no—
678Q8—2444no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—2444no—
684D4—2444no—
685D4—2444no—
686D4—2444no—
687D4—2444no—
688D4—2444no—
689D4—2444no—
690D4—2444no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—614no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2442no—
731C2×C4C22⋊C4×D6111yescharacteristic
732C2×C4C22⋊C4×D6111yescharacteristic
733C2×C4C22⋊C4×D6111yescharacteristic
734C2×C4C22⋊C4×D6111yescharacteristic
735C2×C4C2×D4×D6111yescharacteristic
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4#1451982211yescharacteristic
738C2×C4#1451982311yescharacteristic
739C2×C4#1451982411yescharacteristic
740C2×C4#1451982511yescharacteristic
741C8—42no—
742C8—42no—
743C8—2442no—
744C8—2442no—
745C22—21no—
746C22—21no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—82no—
751C22—82no—
752C22—612no—
753C22—1221no—
754C22—1221no—
755C22—1221no—
756C22—1221no—
757C22—1221no—
758C22—4882no—
759C22—4882no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22C2×C22⋊C4×D6111yescharacteristic
766C22#1684024211yescharacteristic
767C22#1684024311yescharacteristic
768C4—21no—
769C4—21no—
770C4—21no—
771C4—42no—
772C4—612no—
773C4—612no—
774C4—1221no—
775C4—1221no—
776C4—1221no—
777C4—1221no—
778C4—2442no—
779C4#100×D6112yes—
780C4#1684032811yescharacteristic
781C4#1684033511yescharacteristic
782C4#1684034111yescharacteristic
783C4#1684034211yescharacteristic
784C2—21no—
785C2—21no—
786C2—82no—
787C2—1222no—
788C2—4882no—
789C2—2441no—
790C2#2144840811yescharacteristic
791C2C2×#100×D6111yescharacteristic
792C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1800C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC22×C4×C61C24
hypercenter#1800D61
hypocenterC61#21878
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. #423×D61C2semidirect
4. #21446806C2semidirect
5. #21446657C2semidirect
6. #21446281C2semidirect
7. #21446279C2semidirect
8. #21445811C2semidirect
9. #21445808C2semidirect
10. #21445808C2semidirect
11. C61×#1800C2semidirect
341. C4×D61#100semidirect
398. #1800D61semidirect
451. C61#21878semidirect

Maximal subgroups

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

subgroupindex
C2×#168403092
#214544512
#423×D612
#214468062
#214466572
#214462812
#214462792
#214458112
#214458082
C61×#18002
#2187861