Finite Group Databasebeta

← #29685719

Subgroups — #29685719

Order 15616.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2C2×#16839925C211yesmaximal, characteristic
3C2×#16839870C211yesmaximal, characteristic, complemented
4C2×#16839862C211yesmaximal, characteristic, complemented
5C4×#14519757C211yesmaximal, characteristic, complemented
6#21446161C211yesmaximal, characteristic, complemented
7#21446151C211yesmaximal, characteristic, complemented
8#21446130C211yesmaximal, characteristic, complemented
9#21446082C211yesmaximal, characteristic, complemented
10#21446074C211yesmaximal, characteristic, complemented
11#21446019C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic
13#21445652C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C4×#11758224—24no—
21C4×#11758224—24no—
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×#14519742C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×#14519737—21no—
28C2×#14519735C2211yescharacteristic
29C2×#14519733—21no—
30C22×C4×Dic61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839925C418yescomplemented
33#16839870—24no—
34#16839862—24no—
35C2×#14519710C2211yescharacteristic
36C2×#14519709C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519688C2211yescharacteristic
46#16839667C2211yescharacteristic
47#16839661C2211yescharacteristic
48#16839647—21no—
49#16839636—21no—
50#16839619C2211yescharacteristic
51C4×C4⋊Dic61—21no—
52C4×#11758198—21no—
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×Dic122C2311yescharacteristic
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×Dic244—22no—
79C2×Dic244—22no—
80C2×Dic244C2×C414yescomplemented
81C2×#11758200—22no—
82C2×#11758200—22no—
83C2×#11758200C2×C414yescomplemented
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519757—22no—
87#14519757C2×C414yescomplemented
88C4×Dic122—22no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122D414yes—
92#14519742—22no—
93#14519742—22no—
94D4×Dic61—22no—
95D4×Dic61—22no—
96C4×C22⋊D61—28no—
97#14519737—28no—
98#14519735—22no—
99#14519735—22no—
100#14519733—28no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×C4×Dic61—28no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C42×D61—22no—
121C42×D61—22no—
122#14519710—22no—
123#14519709—22no—
124#14519702—22no—
125#14519702—22no—
126#14519700—22no—
127#14519700—22no—
128#14519700C2×C414yescomplemented
129#14519698—22no—
130#14519689—22no—
131#14519689C2×C414yescomplemented
132#14519688—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×D4×C61—22no—
142C4×D4×C61D414yes—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#102×C61—22no—
150#102×C61C2×C414yescomplemented
151#97×C61—22no—
152#95×C61—21no—
153C24×C61—21no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61C22×C412yes—
159C2×D4×C61C2×D412yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—24no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C22×Dic61—24no—
174C22×Dic61—24no—
175C22×Dic61—21no—
176C22×Dic61—24no—
177C22×Dic61—24no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186#11758224—28no—
187#11758224—28no—
188#11758224—28no—
189#11758224—28no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61—41no—
200C2×C4×D61C22×C412yes—
201C2×C4×D61#4112yes—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122C22×C412yes—
211C2×Dic122C22×C412yes—
212C2×Dic122C2×D412yes—
213C2×Dic122#4112yes—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61C22×C412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61C22×C412yes—
225C4⋊C4×C61C2×D412yes—
226C22⋊C4×C61—24no—
227C42×C61—42no—
228C42×C61C2×D412yes—
229C42×C61C2×D412yes—
230C22⋊Dic61—24no—
231#11758200—28no—
232#11758198—24no—
233#11758198—24no—
234#11758198—42no—
235C4⋊Dic61—21no—
236C4⋊Dic61—24no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—42no—
240C4⋊Dic61C2×D412yes—
241#11758196—24no—
242#11758196—24no—
243#11758196—42no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—24no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—42no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418C22×C412yes—
258Dic244—28no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61C22×D411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61C4×D412yes—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61C4×D414yes—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—48no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61#12012yes—
293C2×C4×C61#12012yes—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C22⋊D61—216no—
301C2×Dic61—216no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—48no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61C4×D412yes—
323C2×Dic61#13712yes—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—44no—
329C4×D61—44no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122—22no—
334Dic122—22no—
335Dic122—41no—
336Dic122—41no—
337Dic122C4×D414yes—
338C8×C61—22no—
339C8×C61—41no—
340#92418—22no—
341#92418—41no—
342#21457—611nomaximal, Sylow
343C22×C61—24no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61C2×C4×D411yescharacteristic
351C22×C61C2×#12011yescharacteristic
352C22×C61#52511yescharacteristic
353C22×C61C2×#13711yescharacteristic
354C22×C61#57511yescharacteristic
355C22×C61#57511yescharacteristic
356C22×C61#57511yescharacteristic
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—81no—
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×C4×D411yescharacteristic
371C4×C61#52511yescharacteristic
372C4×C61#52511yescharacteristic
373Dic61—22no—
374Dic61—24no—
375Dic61—22no—
376Dic61—41no—
377Dic61—42no—
378Dic61—42no—
379Dic61—81no—
380C2×C4×#41—611no—
381C2×#452—611no—
382C2×#441—611no—
383C2×#440—611no—
384C4×C22⋊Q8—611no—
385#1878—611no—
386#1877—611no—
387#1873—611no—
388#1864—611no—
389#1863—611no—
390#1854—611no—
391#1788—611no—
392#1763—611no—
393#1762D6111yescharacteristic, complemented
394#1749—611no—
395C2×C61—44no—
396C2×C61C4×#12011yescharacteristic
397C2×C61#294311yescharacteristic
398C2×C61C4×#13711yescharacteristic
399C2×C61#300511yescharacteristic
400C2×C61#300711yescharacteristic
401C2×C61#311111yescharacteristic
402C2×C61#311611yescharacteristic
403D61—42no—
404C22×#41—611no—
405C22×Q16—611no—
406C22×SD16—611no—
407C2×C22⋊Q8—611no—
408C4×#41—1224no—
409C4×#41—1224no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413C2×C4×D4—611no—
414C2×C4×D4—1221no—
415C2×C4×D4—1221no—
416C2×C4×D4C2×D6111yescharacteristic
417C2×#117—611no—
418C2×#117—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#452—618no—
422#441—1224no—
423#440—1224no—
424C2×#107—611no—
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#102—611no—
432C2×#102C2×D6111yescharacteristic
433C2×#102C2×D6111yescharacteristic
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×#97—611no—
437C2×#97C2×D6111yescharacteristic
438#391—611no—
439#389—611no—
440#387—1221no—
441#385—1221no—
442#380—611no—
443C4×C4⋊C4—1221no—
444C4×C4⋊C4C2×D6111yescharacteristic
445C4×C22⋊C4—1221no—
446#340—611no—
447#340—611no—
448#340C2×D6111yescharacteristic
449#340C2×D6111yescharacteristic
450#336—611no—
451#336—611no—
452C61#2145711yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1222no—
458C2×#41—1222no—
459C22×Q8—611no—
460C22×Q8—611no—
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C2×Q16—614no—
470C2×Q16—1222no—
471C2×Q16—1222no—
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C4×Q8—614no—
482C4×Q8—1222no—
483C4×Q8—1222no—
484C4×Q8—1222no—
485C4×Q8—1222no—
486C4×Q8—1222no—
487C4×D4—22no—
488C4×D4—1228no—
489C4×D4—1222no—
490C4×D4—1228no—
491C4×D4—1222no—
492C4×D4D24414yes—
493#117—1228no—
494#117—1222no—
495#117—1222no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C42—21no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1228no—
518C2×C42—1221no—
519C2×C42—1222no—
520C2×C42—1222no—
521C2×C42—1221no—
522C2×C42C22×D6111yescharacteristic
523#107—1222no—
524#106—1222no—
525#103—614no—
526#103—1222no—
527#103—1222no—
528#103—1222no—
529#103—1222no—
530#102—22no—
531#102—1222no—
532#102C4×D6114yescomplemented
533C22⋊C8—614no—
534C22⋊C8—1222no—
535#97—22no—
536#97—1222no—
537#95—21no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24—611no—
544#41—1228no—
545#41—1228no—
546#41—1228no—
547#41—1228no—
548C2×Q8—612no—
549C2×Q8—612no—
550C2×Q8—612no—
551C2×Q8—612no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4C2×C4×D6112yes—
567C2×D4C2×D24412yes—
568C2×D4#1175822212yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—611no—
580C22×C4—1222no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1224no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4—2441no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—1228no—
604SD16—1228no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—612no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8C2×C4×D6112yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—612no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1221no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—2442no—
629C4⋊C4—2442no—
630C4⋊C4C2×C4×D6112yes—
631C4⋊C4C2×D24412yes—
632C22⋊C4—24no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—2442no—
637C42—42no—
638C42—1224no—
639C42—1224no—
640C42—1221no—
641C42—1221no—
642C42—1222no—
643C42—1222no—
644C42—1224no—
645C42—2442no—
646C42C2×D24412yes—
647C42D4×D6112yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—612no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23C2×D4×D6111yescharacteristic
663Q8—614no—
664Q8—1222no—
665Q8—1222no—
666Q8—1222no—
667Q8—1222no—
668Q8—1222no—
669Q8—2441no—
670Q8—2441no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—12216no—
675D4C4×D24414yes—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—12216no—
693C2×C4—1222no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1221no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4—2448no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4#1451974712yes—
720C2×C4#1451974712yes—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C22×D24411yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#41×D6111yescharacteristic
726C2×C4C2×#1175822211yescharacteristic
727C8—22no—
728C8—41no—
729C8—1222no—
730C8—2441no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—2441no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22C4×D4×D6111yescharacteristic
746C22C2×#1451974711yescharacteristic
747C22#1684027111yescharacteristic
748C22#137×D6111yescharacteristic
749C22#1684055811yescharacteristic
750C22#1684055811yescharacteristic
751C22#1684055811yescharacteristic
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—81no—
757C4—1222no—
758C4—1224no—
759C4—1222no—
760C4—4881no—
761C4—2442no—
762C4—2441no—
763C4—2442no—
764C4C4×D4×D6111yescharacteristic
765C4C2×C4×D24411yescharacteristic
766C4#1684027111yescharacteristic
767C4#1684027411yescharacteristic
768C2—44no—
769C2—2442no—
770C2C4×#1451974711yescharacteristic
771C2#2145461611yescharacteristic
772C2#2145464111yescharacteristic
773C2#2145506311yescharacteristic
774C2#2145508011yescharacteristic
775C2#2145592411yescharacteristic
776C2#2145597711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21457
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C2×#16839870C2semidirect
4. C2×#16839862C2semidirect
5. C4×#14519757C2semidirect
6. #21446161C2semidirect
7. #21446151C2semidirect
8. #21446130C2semidirect
9. #21446082C2semidirect
10. #21446074C2semidirect
11. #21446019C2semidirect
13. #21445652C2semidirect
14. #21445582C2semidirect
15. C61×#1762C2semidirect
32. #16839925C4semidirect
80. C2×Dic244C2×C4semidirect
83. C2×#11758200C2×C4semidirect
87. #14519757C2×C4semidirect
128. #14519700C2×C4semidirect
131. #14519689C2×C4semidirect
150. #102×C61C2×C4semidirect
393. #1762D61semidirect
452. C61#21457semidirect
532. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
C2×#168399252
C2×#168398702
C2×#168398622
C4×#145197572
#214461612
#214461512
#214461302
#214460822
#214460742
#214460192
#214457562
#214456522
#214455822
C61×#17622
#2145761