Finite Group Databasebeta

← #29685646

Subgroups — #29685646

Order 15616.

1480 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×#16839921C211yesmaximal, characteristic
3C2×#16839854C211yesmaximal, characteristic, complemented
4C2×SD16×Dic61C211yesmaximal, characteristic, complemented
5#21448357C211yesmaximal, characteristic, complemented
6#21446163C211yesmaximal, characteristic, complemented
7#21446128C211yesmaximal, characteristic, complemented
8#21446090C211yesmaximal, characteristic, complemented
9#21446066C211yesmaximal, characteristic, complemented
10#21446019C211yesmaximal, characteristic, complemented
11#21445756C211yesmaximal, characteristic
12#21445638C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1877C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C4×#11758224—24no—
20C4×#11758224—24no—
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×#14519737—21no—
27C2×#14519735C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4×Dic61—21no—
30C2×C42×D61C2211yescharacteristic
31#16839921C418yescomplemented
32#16839854—24no—
33SD16×Dic61—24no—
34C2×#14519710C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×C8×Dic61C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839649—21no—
48#16839636—21no—
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51#16839613—21no—
52#16839609—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#391C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C23×Dic61—21no—
73C23×Dic61—21no—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519753—22no—
83#14519753C2×C414yescomplemented
84Q8×Dic61—22no—
85Q8×Dic61—22no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88#14519742—22no—
89#14519742D414yes—
90D4×Dic61—22no—
91D4×Dic61D414yes—
92C4×C22⋊D61—28no—
93#14519737—28no—
94#14519735—22no—
95#14519735—22no—
96#14519733—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61—28no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—22no—
119C42×D61—22no—
120#14519710—22no—
121#14519709—22no—
122#14519702—22no—
123#14519702C2×C414yescomplemented
124#14519701—22no—
125#14519700—22no—
126#14519698—22no—
127#14519698C2×C414yescomplemented
128#14519689—22no—
129#14519689C2×C414yescomplemented
130C8×Dic61—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C2×SD16×C61—22no—
139C2×SD16×C61—22no—
140C2×SD16×C61C2×C414yescomplemented
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#103×C61—22no—
150#102×C61—22no—
151#95×C61—21no—
152#95×C61—21no—
153C24×C61—21no—
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C22×C412yes—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C2×D412yes—
166C2×D4×C61#4112yes—
167C22×C4×C61—24no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C22×Dic61—24no—
180C22×Dic61—24no—
181C22×Dic61—21no—
182C22×Dic61—24no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—24no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758224—28no—
193#11758224—28no—
194#11758224—28no—
195#11758224—28no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—41no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61#4112yes—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122C22×C412yes—
212C2×Dic122C2×D412yes—
213C2×Dic122#4112yes—
214SD16×C61—28no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61C22×C412yes—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61C2×D412yes—
225C22⋊C4×C61—24no—
226C42×C61—21no—
227C42×C61—21no—
228C22⋊Dic61—24no—
229#11758202—28no—
230#11758198—24no—
231#11758198—24no—
232#11758198—42no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—42no—
238C4⋊Dic61C22×C412yes—
239C4⋊Dic61C2×D412yes—
240#11758196—24no—
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—42no—
250C4×Dic61—42no—
251C4×Dic61C2×D412yes—
252C4×Dic61C2×D412yes—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418C22×C412yes—
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—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—41no—
277Q8×C61—41no—
278D4×C61—22no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61C4×D414yes—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—48no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61#13512yes—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C22⋊D61—216no—
305C2×Dic61—216no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—48no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61C4×D412yes—
324C2×Dic61#12012yes—
325C2×Dic61#12012yes—
326C2×Dic61#13512yes—
327C2×Dic61#13712yes—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—44no—
333C4×D61—44no—
334Dic122—22no—
335Dic122—22no—
336Dic122—22no—
337Dic122C4×D414yes—
338C8×C61—22no—
339C8×C61—41no—
340#92418—22no—
341#92418—41no—
342C4×#452—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×#13511yescharacteristic
354C22×C61C2×#13511yescharacteristic
355C22×C61C2×#13711yescharacteristic
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—41no—
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—42no—
377Dic61—42no—
378Dic61—81no—
379Dic61#45214yescomplemented
380C2×C4×#41—611no—
381C2×#452—611no—
382C2×C4×Q16—611no—
383C2×C4×SD16—611no—
384C4×C22⋊Q8—611no—
385#1878—611no—
386#1877D6111yescharacteristic, complemented
387#1873—611no—
388#1865—611no—
389#1862—611no—
390#1854—611no—
391#1788—611no—
392C4×#103—611no—
393C4×#102—611no—
394C4×C22⋊C8—611no—
395C2×C61—44no—
396C2×C61C4×#12011yescharacteristic
397C2×C61C4×#13511yescharacteristic
398C2×C61C4×#13711yescharacteristic
399C2×C61C2×#45211yescharacteristic
400C2×C61#300211yescharacteristic
401C2×C61#310211yescharacteristic
402C2×C61#310711yescharacteristic
403D61—42no—
404C22×#41—611no—
405C22×Q16—611no—
406C22×SD16C2×D6111yescharacteristic
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—
422C4×Q16—1224no—
423C4×SD16—1224no—
424C2×#107—611no—
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103C2×D6111yescharacteristic
431C2×#102—611no—
432C2×#102—611no—
433C2×#102C2×D6111yescharacteristic
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C4×C8—611no—
437C2×C4×C8—611no—
438#391C2×D6111yescharacteristic
439#389—611no—
440#387—1221no—
441#385—1221no—
442#380—611no—
443C4×C4⋊C4—611no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340C2×D6111yescharacteristic
450#336—611no—
451#336C2×D6111yescharacteristic
452C61C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1222no—
458C2×#41—1222no—
459C22×Q8—611no—
460C22×Q8C22×D6111yescharacteristic
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—22no—
473C2×SD16—22no—
474C2×SD16C4×D6114yescomplemented
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—22no—
489C4×D4—614no—
490C4×D4—1222no—
491C4×D4—1228no—
492C4×D4—1228no—
493#117—1228no—
494#117—1222no—
495#117—1222no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
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—611no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—1222no—
515C2×C42—1222no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1228no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42C22×D6111yescharacteristic
523#107—1222no—
524#106—1222no—
525#103—22no—
526#103—614no—
527#103—1222no—
528#103—1222no—
529#103—1222no—
530#102—22no—
531#102—614no—
532#102—1222no—
533C22⋊C8—614no—
534C22⋊C8—1222no—
535C4×C8—1222no—
536C4×C8—1222no—
537#95—21no—
538#95—21no—
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—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—612no—
554C2×Q8—612no—
555C2×Q8—612no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8C2×C4×D6112yes—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4C2×C4×D6112yes—
567C2×D4D4×D6112yes—
568C2×D4#1175822412yes—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1224no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1221no—
597C22×C4—2441no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—1228no—
604SD16—28no—
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—612no—
621C4⋊C4—612no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—2442no—
630C4⋊C4—2442no—
631C4⋊C4D4×D6112yes—
632C22⋊C4—24no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—2442no—
637C42—21no—
638C42—21no—
639C42—612no—
640C42—612no—
641C42—1222no—
642C42—1222no—
643C42—1224no—
644C42—1224no—
645C42—1224no—
646C42—2442no—
647C42—2442no—
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—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—614no—
668Q8—1222no—
669Q8—1222no—
670Q8—1222no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—12216no—
675D4#1451973714yes—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—12216no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1222no—
700C2×C4—1221no—
701C2×C4—1222no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—2448no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4#1451979812yes—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×D4×D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#41×D6111yescharacteristic
726C2×C4C2×#1175822411yescharacteristic
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
746C22#120×D6111yescharacteristic
747C22#1684027211yescharacteristic
748C22#135×D6111yescharacteristic
749C22C2×#1451979811yescharacteristic
750C22#137×D6111yescharacteristic
751C22#1684055811yescharacteristic
752C4—22no—
753C4—42no—
754C4—41no—
755C4—42no—
756C4—81no—
757C4—614no—
758C4—1222no—
759C4—1224no—
760C4—1222no—
761C4—4881no—
762C4—2442no—
763C4—2442no—
764C4C4×D4×D6111yescharacteristic
765C4C2×#1451973711yescharacteristic
766C4#1684027011yescharacteristic
767C4#1684027211yescharacteristic
768C2—44no—
769C2—2442no—
770C2#2144832411yescharacteristic
771C2C4×#1451979811yescharacteristic
772C2#2145464111yescharacteristic
773C2#452×D6111yescharacteristic
774C2#2145503811yescharacteristic
775C2#2145583411yescharacteristic
776C2#2145588711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1877C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1877D61
hypocenterC61C4×#452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. C2×#16839854C2semidirect
4. C2×SD16×Dic61C2semidirect
5. #21448357C2semidirect
6. #21446163C2semidirect
7. #21446128C2semidirect
8. #21446090C2semidirect
9. #21446066C2semidirect
10. #21446019C2semidirect
12. #21445638C2semidirect
13. #102×Dic61C2semidirect
14. #21445576C2semidirect
15. C61×#1877C2semidirect
31. #16839921C4semidirect
79. C2×#11758202C2×C4semidirect
83. #14519753C2×C4semidirect
123. #14519702C2×C4semidirect
127. #14519698C2×C4semidirect
129. #14519689C2×C4semidirect
140. C2×SD16×C61C2×C4semidirect
379. Dic61#452semidirect
386. #1877D61semidirect
452. C61C4×#452semidirect
474. C2×SD16C4×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×#168399212
C2×#168398542
C2×SD16×Dic612
#214483572
#214461632
#214461282
#214460902
#214460662
#214460192
#214457562
#214456382
#102×Dic612
#214455762
C61×#18772
C4×#45261