Finite Group Databasebeta

← #29714522

Subgroups — #29714522

Order 15616.

1142 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic, complemented
2C2×#16839974C211yesmaximal, characteristic, complemented
3#21448512C211yesmaximal, characteristic, complemented
4#21447012C211yesmaximal, characteristic, complemented
5#21447005C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic
8#21446772C211yesmaximal, characteristic, complemented
9#21446752C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446087C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445803C211yesmaximal, characteristic, complemented
15C2×C61×#542C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840049—24no—
21#16839974—24no—
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839662—21no—
38#16839660C2211yescharacteristic
39#16839652—21no—
40#16839638—21no—
41#16839633—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#542—24no—
51C61×#542—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#126×C61—21no—
54C2×#124×C61—21no—
55C2×#124×C61C2211yescharacteristic
56C2×#123×C61—21no—
57C2×C22⋊Q8×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C2×#117×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C4×D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—41no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519751—22no—
77#14519751—22no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—21no—
90#14519708—22no—
91#14519708—22no—
92C4⋊#92418—22no—
93C4⋊#92418—22no—
94#14519701—22no—
95#14519701—22no—
96#14519701—41no—
97#14519698—22no—
98#14519698—22no—
99#14519698—41no—
100#14519697—22no—
101#14519697—22no—
102C22⋊#92418—41no—
103C22⋊#92418—41no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61D414yescomplemented
115#126×C61—28no—
116#124×C61—28no—
117#124×C61—22no—
118#124×C61D414yescomplemented
119#123×C61—28no—
120C22⋊Q8×C61—28no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129#117×C61—22no—
130#117×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×Q8×C61—24no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—81no—
158C2×Q8×C61—81no—
159C2×Q8×C61C2×D412yes—
160C2×D4×C61—24no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C2×D4×C61C2×D412yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—24no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—81no—
180C22×C4×C61—81no—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—81no—
189C2×C22⋊D61—81no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244#4112yes—
199C2×C4×D61—42no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C2×D412yes—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—24no—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C42×C61—24no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61C2×D412yes—
222C42×C61C2×D412yes—
223C22⋊Dic61—81no—
224#11758201—44no—
225#11758199—44no—
226#11758198—24no—
227#11758198—42no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61#4112yes—
236#11758196—81no—
237C4×Dic61—81no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
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—22no—
273Q8×C61—22no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—84no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—84no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—84no—
309C2×C4×C61#12012yes—
310C2×C4×C61#12012yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C612−1+411yescharacteristic
317C22⋊D61—84no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327D244—22no—
328D244—22no—
329D244—41no—
330D244—41no—
331C4×D61—84no—
332#92418—41no—
333#92418—41no—
334#92418—41no—
335#92418—41no—
336#24166—611nomaximal, Sylow
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—42no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61C2×#12011yescharacteristic
352C22×C61#52511yescharacteristic
353C22×C61#53711yescharacteristic
354C22×C61#57611yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—41no—
368C4×C61—42no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61#54611yescharacteristic
374C4×C61#54711yescharacteristic
375C4×C61#54811yescharacteristic
376C4×C61#55011yescharacteristic
377Dic61—42no—
378Dic61—81no—
379Dic61—81no—
380C2×#542D6111yescharacteristic, complemented
381C2×#476—611no—
382C2×#463—611no—
383#2324—611no—
384#2035—611no—
385#2034—611no—
386#2000—611no—
387#1999—611no—
388#1988—611no—
389#1983—611no—
390#1880—611no—
391#1879—611no—
392#1865—611no—
393#1864—611no—
394#1798—611no—
395C2×C61—81no—
396C2×C61—82no—
397C2×C61#240711yescharacteristic
398C2×C61#301011yescharacteristic
399C2×C61#301211yescharacteristic
400C2×C61#311811yescharacteristic
401C2×C61#312511yescharacteristic
402C2×C61#325711yescharacteristic
403C2×C61#326311yescharacteristic
404D61—82no—
405C22×SD16—611no—
406C22×D8—611no—
407#542—24no—
408#542—24no—
409C2×C4⋊Q8C2×D6111yescharacteristic
410C2×#126—21no—
411C2×#124—21no—
412C2×#124C2×D6111yescharacteristic
413C2×#123—21no—
414C2×C22⋊Q8—21no—
415C2×C22⋊Q8C2×D6111yescharacteristic
416C2×#121—611no—
417C2×#121C2×D6111yescharacteristic
418C2×C4×Q8C2×D6111yescharacteristic
419C2×C4×D4—611no—
420C2×C4×D4C2×D6111yescharacteristic
421C2×#117C2×D6111yescharacteristic
422#476—1224no—
423#463—1224no—
424C2×#106—611no—
425C2×#106—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8—611no—
438#390—611no—
439#390—1221no—
440#389—611no—
441#388—1221no—
442#386—1221no—
443#385—1221no—
444#380—611no—
445C4×C4⋊C4—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#336—611no—
451#336—611no—
452C61#2416611yescharacteristic, complemented, Sylow
453C22×Q8—21no—
454C22×Q8C22×D6111yescharacteristic
455C22×D4—21no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C2×SD16—1222no—
463C2×SD16—1222no—
464C2×SD16—2441no—
465C2×D8—1222no—
466C2×D8—1222no—
467C2×D8—2441no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—611no—
472C4⋊Q8—22no—
473C4⋊Q8C22⋊D6114yescomplemented
474#126—28no—
475#124—28no—
476#124—22no—
477#124C22⋊D6114yescomplemented
478#123—28no—
479C22⋊Q8—28no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482#121—22no—
483#121—22no—
484#121—1222no—
485#121—1222no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—1222no—
491C4×D4—1222no—
492#117—22no—
493#117—22no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4C22⋊D6111yescharacteristic
502C2×C4⋊C4C22⋊D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4C22⋊D6111yescharacteristic
516C2×C22⋊C4C22⋊D6111yescharacteristic
517C2×C42—21no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520C2×C42C22×D6111yescharacteristic
521#106—1222no—
522#106—1222no—
523C4⋊C8—1222no—
524C4⋊C8—1222no—
525#103—1222no—
526#103—1222no—
527#103—2441no—
528#102—1222no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532#102—2441no—
533C22⋊C8—2441no—
534C22⋊C8—2441no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538C24—21no—
539C24—1221no—
540C24C2×C22⋊D6111yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—81no—
548C2×Q8—81no—
549C2×Q8C2×C22⋊D6112yes—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—612no—
559C2×D4—1224no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—4881no—
566C2×D4—4881no—
567C2×D4C2×C22⋊D6112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—4881no—
584C22×C4—4881no—
585C22×C4—2442no—
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592SD16—2444no—
593D8—2444no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—612no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—4881no—
620C4⋊C4C2×C22⋊D6112yes—
621C4⋊C4C2×C22⋊D6112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—1224no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—2442no—
634C42—24no—
635C42—21no—
636C42—21no—
637C42—4881no—
638C42C2×C22⋊D6112yes—
639C42C2×C22⋊D6112yes—
640C23—21no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—1222no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23C22×C22⋊D6111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666Q8—84no—
667D4—22no—
668D4—22no—
669D4—41no—
670D4—41no—
671D4—84no—
672D4—1222no—
673D4—1222no—
674D4—4884no—
675D4—2441no—
676D4—2441no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—1222no—
705C2×C4—4884no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4#1451974612yes—
715C2×C4#1451974612yes—
716C2×C4C22×C22⋊D6111yescharacteristic
717C2×C4C22×C22⋊D6111yescharacteristic
718C2×C4#41×D6111yescharacteristic
719C2×C4#41×D6111yescharacteristic
720C2×C4#1451982311yescharacteristic
721C2×C4#1451982411yescharacteristic
722C8—2441no—
723C8—2441no—
724C8—2441no—
725C8—2441no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—4881no—
741C22—4881no—
742C22—4881no—
743C22—4881no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22C2×#1451974611yescharacteristic
748C22#1684026911yescharacteristic
749C22#1684034011yescharacteristic
750C22#1684056511yescharacteristic
751C22#1684057011yescharacteristic
752C22#1684057011yescharacteristic
753C22#1684057311yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—42no—
760C4—41no—
761C4—42no—
762C4—4881no—
763C4—4881no—
764C4—2442no—
765C4#1684040011yescharacteristic
766C4#1684041111yescharacteristic
767C4#1684041911yescharacteristic
768C4#1684043111yescharacteristic
769C2—81no—
770C2—82no—
771C2—4882no—
772C2#2144915811yescharacteristic
773C2#2145510511yescharacteristic
774C2#2145512311yescharacteristic
775C2#2145599711yescharacteristic
776C2#2145609011yescharacteristic
777C2#2145723011yescharacteristic
778C2#2145728411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenterC2×#542D61
hypocenterC61#24166
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840049C2semidirect
2. C2×#16839974C2semidirect
3. #21448512C2semidirect
4. #21447012C2semidirect
5. #21447005C2semidirect
6. #21446820C2semidirect
8. #21446772C2semidirect
9. #21446752C2semidirect
10. #21446174C2semidirect
11. #21446167C2semidirect
12. #21446087C2semidirect
13. #21446080C2semidirect
14. #21445803C2semidirect
15. C2×C61×#542C2semidirect
114. C4⋊Q8×C61D4semidirect
118. #124×C61D4semidirect
380. C2×#542D61semidirect
452. C61#24166semidirect
473. C4⋊Q8C22⋊D61semidirect
477. #124C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
C2×#168399742
#214485122
#214470122
#214470052
#214468202
#214468152
#214467722
#214467522
#214461742
#214461672
#214460872
#214460802
#214458032
C2×C61×#5422
#2416661