Finite Group Databasebeta

← #29685785

Subgroups — #29685785

Order 15616.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840240C211yesmaximal, characteristic, complemented
2C2×#16839901C211yesmaximal, characteristic
3C2×#16839865C211yesmaximal, characteristic, complemented
4C2×#16839847C211yesmaximal, characteristic, complemented
5#21448508C211yesmaximal, characteristic
6#21446172C211yesmaximal, characteristic, complemented
7#21446172C211yesmaximal, characteristic, complemented
8#21446139C211yesmaximal, characteristic
9#21446085C211yesmaximal, characteristic, complemented
10#21446071C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19#16840240—24no—
20#16840240—24no—
21C2×Q8×Dic61—21no—
22C2×Q8×Dic61—21no—
23C2×Q8×Dic61C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×#14519736—21no—
29C2×#14519736—21no—
30C2×#14519736C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32#16839901C418yescomplemented
33#16839865—24no—
34#16839847—24no—
35C2×#14519710C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839663C2211yescharacteristic
45#16839662—21no—
46#16839658C2211yescharacteristic
47#16839654—21no—
48#16839638—21no—
49#16839636—21no—
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758201—22no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201C2×C414yes—
72C2×#11758201C2×C414yes—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519751—22no—
76#14519751C2×C414yes—
77Q8×Dic61—28no—
78Q8×Dic61—28no—
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81Q8×Dic61—22no—
82Q8×Dic61—22no—
83Q8×Dic61—22no—
84Q8×Dic61—22no—
85Q8×Dic61D414yescomplemented
86Q8×Dic61D414yescomplemented
87#14519739—22no—
88#14519739—22no—
89#14519736—28no—
90#14519736—28no—
91#14519736—22no—
92#14519736—22no—
93#14519736—22no—
94#14519736—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61D411yescharacteristic
100C2×C4⋊Dic61D411yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×C22⋊Dic61D411yescharacteristic
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120#14519710—22no—
121#14519708—22no—
122#14519701C2×C414yescomplemented
123#14519701C2×C414yescomplemented
124#14519699—22no—
125#14519699—22no—
126C22⋊#92418C2×C414yescomplemented
127#14519687—22no—
128C8×Dic61—22no—
129#14519684—21no—
130#14519684—21no—
131C22×Q8×C61—22no—
132C22×Q8×C61—22no—
133C22×Q8×C61—22no—
134C22×Q8×C61—22no—
135C22×Q8×C61—21no—
136C22×Q8×C61—22no—
137C22×Q8×C61C2×C414yescomplemented
138C22×Q8×C61C2311yescharacteristic
139C22×Q8×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—22no—
148#103×C61—22no—
149#103×C61—22no—
150#103×C61—22no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C2×Q8×C61—28no—
156C2×Q8×C61—28no—
157C2×Q8×C61—24no—
158C2×Q8×C61—24no—
159C2×Q8×C61—28no—
160C2×Q8×C61—28no—
161C2×Q8×C61—24no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61C22×C412yes—
169C2×Q8×C61C22×C412yes—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C2×Q8×C61#4112yes—
174C22×C4×C61—24no—
175C22×C4×C61—24no—
176C22×C4×C61—24no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61#4112yes—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—81no—
191C2×C22⋊D61—81no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C22×C412yes—
205C2×C4×D61—42no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C22⋊C4×C61—81no—
219C22⋊Dic61—24no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222#11758201—28no—
223#11758201—28no—
224#11758198—24no—
225#11758198—42no—
226#11758198—81no—
227#11758198—81no—
228C4⋊Dic61—24no—
229C4⋊Dic61—24no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—24no—
234C4⋊Dic61—24no—
235C4⋊Dic61—22no—
236C4⋊Dic61—22no—
237C4⋊Dic61C22×C412yes—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240#11758196—81no—
241C4×Dic61—24no—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—81no—
249C4×Dic61C2×D412yes—
250C4×Dic61C2×D412yes—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C22×C412yes—
256C2×#92418C22×C412yes—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61C4×D412yes—
264C23×C61C22×D411yescharacteristic
265C22×D61—22no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272Q8×C61—216no—
273Q8×C61—22no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61C4×D414yes—
280Q8×C61C4×D414yes—
281C2×C4×C61—216no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61C4×D412yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C22⋊D61—84no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61#12012yes—
328C2×Dic61#12012yes—
329D244—22no—
330D244—22no—
331D244—41no—
332D244—41no—
333C4×D61—84no—
334C8×C61—41no—
335C8×C61—41no—
336#92418—22no—
337#92418—22no—
338#21462—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61C2×#12011yescharacteristic
348C22×C61#52511yescharacteristic
349C22×C61#57711yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—24no—
361C4×C61—24no—
362C4×C61—22no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×C4×D411yescharacteristic
366C4×C61C2×C4×D411yescharacteristic
367C4×C61#52511yescharacteristic
368C4×C61#52511yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—42no—
372Dic61—41no—
373Dic61—42no—
374Dic61—41no—
375Dic61—42no—
376C2×#519—611no—
377C2×#448—611no—
378C2×#440—611no—
379C2×C4×SD16—611no—
380#2324—611no—
381#1880—611no—
382#1880—611no—
383#1875—611no—
384#1865—611no—
385#1863—611no—
386#1854—611no—
387#1787D6111yescharacteristic, complemented
388#1763—611no—
389C4×#103—611no—
390#1750—611no—
391C2×C61—42no—
392C2×C61C4×#12011yescharacteristic
393C2×C61#294711yescharacteristic
394C2×C61#294911yescharacteristic
395C2×C61#301011yescharacteristic
396C2×C61#301311yescharacteristic
397C2×C61#312111yescharacteristic
398C2×C61#312611yescharacteristic
399D61—82no—
400C23×Q8C2×D6111yescharacteristic
401C22×SD16—611no—
402C22×SD16—611no—
403C2×#121—611no—
404#519—1224no—
405#519—1224no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—1221no—
411C2×C4×Q8—1221no—
412C2×C4×D4—611no—
413C2×#117—611no—
414C2×#117—611no—
415C2×#117—1221no—
416C2×#117—1221no—
417#448—618no—
418#440—1224no—
419C4×SD16—1224no—
420C2×#107—611no—
421C2×#106—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#103C2×D6111yescharacteristic
425C2×#103C2×D6111yescharacteristic
426C2×#103C2×D6111yescharacteristic
427C2×#103C2×D6111yescharacteristic
428C2×#102—611no—
429C2×#102—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8C2×D6111yescharacteristic
432C2×#97—611no—
433C2×C4×C8—611no—
434#390—611no—
435#390—1221no—
436#389—611no—
437#388—1221no—
438#386—1221no—
439#385—1221no—
440#380C2×D6111yescharacteristic
441C4×C4⋊C4—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#336—611no—
447#336—611no—
448C61#2146211yescharacteristic, complemented, Sylow
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—21no—
454C22×Q8—22no—
455C22×Q8C4×D6114yescomplemented
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×SD16—614no—
464C2×SD16—614no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473#121—614no—
474#121—1222no—
475C4×Q8—614no—
476C4×Q8—614no—
477C4×Q8—1222no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—1228no—
482C4×Q8—1228no—
483C4×Q8—1222no—
484C4×Q8—1222no—
485C4×D4—1222no—
486C4×D4—1222no—
487#117—1222no—
488#117—1222no—
489#117—1222no—
490#117—1222no—
491#117—1228no—
492#117—1228no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
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×C22⋊C4—21no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1221no—
521#107—1222no—
522#106—1222no—
523#103—22no—
524#103—22no—
525#103—22no—
526#103—22no—
527#103—614no—
528#103—614no—
529#102—1222no—
530#102—1222no—
531C22⋊C8—22no—
532C22⋊C8—614no—
533#97—1222no—
534C4×C8—1222no—
535#95—21no—
536#95—1221no—
537#95—1221no—
538C24—1221no—
539C24D4×D6111yescharacteristic
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8C2×C4×D6112yes—
554C2×Q8C2×C4×D6112yes—
555C2×Q8D4×D6112yes—
556C2×Q8D4×D6112yes—
557C2×Q8#1175822412yes—
558C2×Q8#1175822412yes—
559C2×D4—612no—
560C2×D4—1224no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—4881no—
567C2×D4—4881no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—4881no—
587C22×C4—4881no—
588C22×C4—2442no—
589C22×C4C2×C4×D6112yes—
590C22×C4D4×D6111yescharacteristic
591C22×C4#1175822412yes—
592C22×C4C23×D6111yescharacteristic
593SD16—1228no—
594SD16—1228no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—612no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—4881no—
624C22⋊C4—81no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—2442no—
632C42—612no—
633C42—612no—
634C42—1224no—
635C42—1224no—
636C42—1224no—
637C42—1224no—
638C42—1224no—
639C42—1221no—
640C42—1221no—
641C42—4881no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—1222no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23#1451973712yes—
656C23C2×D4×D6111yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8#1451973714yes—
665Q8#1451973714yes—
666D4—1222no—
667D4—1222no—
668D4—4884no—
669D4—2441no—
670D4—2441no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
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—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—4884no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4#1451973712yes—
713C2×C4C22×C4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4C2×#1175822411yescharacteristic
717C2×C4C2×#1175822411yescharacteristic
718C2×C4C2×#1175822411yescharacteristic
719C8—41no—
720C8—41no—
721C8—1222no—
722C8—1222no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22C2×#1451973711yescharacteristic
738C22#120×D6111yescharacteristic
739C22#1684026811yescharacteristic
740C22#1684056811yescharacteristic
741C22#1684057111yescharacteristic
742C22#1684057111yescharacteristic
743C22#1684057511yescharacteristic
744C4—24no—
745C4—24no—
746C4—22no—
747C4—81no—
748C4—81no—
749C4—1222no—
750C4—1222no—
751C4—2441no—
752C4—2442no—
753C4—2442no—
754C4—2441no—
755C4—2442no—
756C4C2×#1451973711yescharacteristic
757C4C2×#1451973711yescharacteristic
758C4#1684026811yescharacteristic
759C4#1684026811yescharacteristic
760C2—42no—
761C2—4882no—
762C2#2144831811yescharacteristic
763C2#2145465611yescharacteristic
764C2#2145467411yescharacteristic
765C2#2145510011yescharacteristic
766C2#2145513511yescharacteristic
767C2#2145604911yescharacteristic
768C2#2145610411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1787C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1787D61
hypocenterC61#21462
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
1. C2×#16840240C2semidirect
3. C2×#16839865C2semidirect
4. C2×#16839847C2semidirect
6. #21446172C2semidirect
7. #21446172C2semidirect
9. #21446085C2semidirect
10. #21446071C2semidirect
11. #21446016C2semidirect
12. #21445651C2semidirect
13. #103×Dic61C2semidirect
14. #21445587C2semidirect
15. C61×#1787C2semidirect
32. #16839901C4semidirect
85. Q8×Dic61D4semidirect
86. Q8×Dic61D4semidirect
122. #14519701C2×C4semidirect
123. #14519701C2×C4semidirect
126. C22⋊#92418C2×C4semidirect
137. C22×Q8×C61C2×C4semidirect
387. #1787D61semidirect
448. C61#21462semidirect
455. C22×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402402
C2×#168399012
C2×#168398652
C2×#168398472
#214485082
#214461722
#214461392
#214460852
#214460712
#214460162
#214456512
#103×Dic612
#214455872
C61×#17872
#2146261