Finite Group Databasebeta

← #29700410

Subgroups — #29700410

Order 15616.

1190 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×#16839909C211yesmaximal, characteristic
2C2×#16839864C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic, complemented
5#21448659C211yesmaximal, characteristic, complemented
6#21446685C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446440C211yesmaximal, characteristic, complemented
9#21446257C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446076C211yesmaximal, characteristic, complemented
13#21446009C211yesmaximal, characteristic, complemented
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519737—21no—
24C22×C4⋊Dic61C2211yescharacteristic
25#16839909C418yescomplemented
26#16839864—24no—
27C2×#14519711C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839764—24no—
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839662—21no—
42#16839662—21no—
43#16839660C2211yescharacteristic
44#16839654—21no—
45#16839639—21no—
46#16839636—21no—
47#16839622C2211yescharacteristic
48#16839621—21no—
49C4×C4⋊Dic61C2211yescharacteristic
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×#11758190—22no—
77C2×#11758190—22no—
78C2×#11758190C2×C414yescomplemented
79C2×D488—41no—
80C2×D488—41no—
81C2×D488C2×C414yescomplemented
82#14519751—22no—
83#14519751C2×C414yes—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—41no—
87C4×Dic122—41no—
88C4×D244—22no—
89C4×D244—41no—
90#14519737—44no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114#14519711—22no—
115#14519711—41no—
116#14519702—22no—
117#14519702C2×C414yescomplemented
118#14519702D414yescomplemented
119#14519699—22no—
120#14519699—22no—
121#14519699—22no—
122#14519699—41no—
123#14519699C2×C414yescomplemented
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61C2×C414yescomplemented
140#97×C61—22no—
141C4×C8×C61—41no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—81no—
174#11758222—28no—
175#11758222—44no—
176#11758222—44no—
177#11758222—44no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244C22×C412yes—
189C2×D244C22×C412yes—
190C2×C4×D61—24no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—81no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122C22×C412yes—
200C2×Dic122C2×D412yes—
201C2×Dic122#4112yes—
202M16×C61—44no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61C22×C412yes—
213C2×C8×C61C22×C412yes—
214C2×C8×C61C2×D412yes—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—41no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—81no—
222#11758198—24no—
223#11758198—42no—
224#11758198—42no—
225#11758198—42no—
226#11758198—42no—
227#11758198—81no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—42no—
239C4⋊Dic61C22×C412yes—
240C4⋊Dic61C2×D412yes—
241#11758196—42no—
242#11758196—42no—
243#11758196—42no—
244C4×Dic61—42no—
245C4×Dic61—42no—
246C4×Dic61—42no—
247D488—44no—
248#11758190—28no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C4×D412yes—
256C23×C61C22×D411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61C4×D412yes—
289C2×C4×C61AGL(1,ℤ/8)12yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C22⋊D61—48no—
297C22⋊D61—48no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—84no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244—41no—
322D244—41no—
323D244—41no—
324D244—41no—
325C4×D61—48no—
326C4×D61—84no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122C4×D414yescomplemented
331C8×C61—22no—
332C8×C61—22no—
333C8×C61—22no—
334C8×C61—41no—
335#22863—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×C4×D411yescharacteristic
344C22×C61D4211yescharacteristic
345C22×C61#54611yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61#57511yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57811yescharacteristic
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61C2×C4×D411yescharacteristic
370C4×C61#51811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#55111yescharacteristic
373Dic61—24no—
374Dic61—42no—
375Dic61—42no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#449—611no—
380C2×#440—611no—
381C2×#417—611no—
382#2361—611no—
383#2341—611no—
384#1970—611no—
385#1936—611no—
386#1925—611no—
387#1895—611no—
388#1880—611no—
389#1879—611no—
390#1863—611no—
391#1852—611no—
392C4×#103—611no—
393#1753D6111yescharacteristic, complemented
394C2×C61—42no—
395C2×C61#235811yescharacteristic
396C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
397C2×C61#295111yescharacteristic
398C2×C61#327411yescharacteristic
399C2×C61#327711yescharacteristic
400C2×C61#330811yescharacteristic
401C2×C61#330911yescharacteristic
402D61—82no—
403D61—82no—
404C22×#41—611no—
405C22×SD16—611no—
406C22×D8—611no—
407C22×M16C2×D6111yescharacteristic
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C22×C4⋊C4—611no—
414#449—618no—
415#440—1224no—
416C2×#107—611no—
417C2×#107—611no—
418#417—1224no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8C2×D6111yescharacteristic
428C2×#97C2×D6111yescharacteristic
429C2×C4×C8C2×D6111yescharacteristic
430#390—611no—
431#390—611no—
432#390—611no—
433#390—1221no—
434#390—1221no—
435#389—611no—
436#388—1221no—
437#386—1221no—
438#385—1221no—
439#380—611no—
440#380—1221no—
441C4×C4⋊C4—611no—
442C4×C22⋊C4—1221no—
443C4×C22⋊C4C2×D6111yescharacteristic
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#336C2×D6111yescharacteristic
449#336C2×D6111yescharacteristic
450C61#2286311yescharacteristic, complemented, Sylow
451C2×#41—614no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—2441no—
456C2×#41—2441no—
457C22×Q8—611no—
458C22×D4—611no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4C22×D6111yescharacteristic
466C2×SD16—614no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×D8—614no—
470C2×D8—2441no—
471C2×D8—2441no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—41no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479#121—614no—
480#121—1222no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×Q8—2441no—
484C4×Q8—2441no—
485C4×D4—1222no—
486C4×D4—2441no—
487C4×D4—2444no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—2441no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4D24411yescharacteristic
509C2×C22⋊C4D24411yescharacteristic
510C2×C42—1221no—
511C2×C42—1221no—
512C2×C42—1221no—
513C2×C42C22×D6111yescharacteristic
514C2×C42C22×D6111yescharacteristic
515#107—1222no—
516#107—2441no—
517#103—614no—
518#103—614no—
519#103—1222no—
520#102—614no—
521#102—1222no—
522#102—1222no—
523#102—1222no—
524#102—2441no—
525C22⋊C8C4×D6114yescomplemented
526#97—22no—
527C4×C8—41no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95D24411yescharacteristic
532#95D24411yescharacteristic
533C24—1221no—
534C24—1221no—
535C24C2×D24411yescharacteristic
536#41—1228no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540C2×Q8—612no—
541C2×Q8—612no—
542C2×Q8—612no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×D4—612no—
547C2×D4—612no—
548C2×D4—1224no—
549C2×D4—1224no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4—2442no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1224no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—4881no—
576C22×C4—4881no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4C2×C4×D6112yes—
584C22×C4C2×D24411yescharacteristic
585C22×C4C2×D24411yescharacteristic
586C22×C4C2×D24411yescharacteristic
587C22×C4C2×D24411yescharacteristic
588C22×C4C2×D24411yescharacteristic
589C22×C4#1175822212yes—
590C22×C4C23×D6111yescharacteristic
591SD16—1228no—
592D8—2444no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8C2×C4×D6112yes—
604C2×C8C2×C4×D6112yes—
605C2×C8D4×D6112yes—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—1224no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C22⋊C4—4881no—
626C22⋊C4—4881no—
627C22⋊C4—2442no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—2442no—
636C42—2442no—
637C42—2442no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—1222no—
645C23—1222no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23C4×D24412yes—
659C23C22×D24411yescharacteristic
660Q8—614no—
661Q8—1222no—
662Q8—1222no—
663Q8—1222no—
664D4—1222no—
665D4—1222no—
666D4—1222no—
667D4—1222no—
668D4—2448no—
669D4—2448no—
670D4—2441no—
671D4—2441no—
672D4—2441no—
673D4—2441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—4884no—
697C2×C4—4884no—
698C2×C4—2448no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4C4×D24412yes—
713C2×C4#1451980512yes—
714C2×C4C22×C4×D6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4C2×#1175822211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C2×C4#1451982311yescharacteristic
720C8—22no—
721C8—22no—
722C8—22no—
723C8—41no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—4881no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22C2×C4×D24411yescharacteristic
746C22D4×D24411yescharacteristic
747C22#1684040711yescharacteristic
748C22C2×#1451980511yescharacteristic
749C22#1684056211yescharacteristic
750C22#1684056711yescharacteristic
751C22#1684057911yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—1224no—
758C4—4881no—
759C4—4881no—
760C4—4881no—
761C4—2442no—
762C4—2442no—
763C4C4×D4×D6111yescharacteristic
764C4#1684023411yescharacteristic
765C4#1684040211yescharacteristic
766C4#1684043611yescharacteristic
767C2—42no—
768C2—4882no—
769C2—4882no—
770C2#2144880111yescharacteristic
771C2C4×#1451980511yescharacteristic
772C2#2145469611yescharacteristic
773C2#2145744111yescharacteristic
774C2#2145747711yescharacteristic
775C2#2145781211yescharacteristic
776C2#2145782711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1753C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#16839864C2semidirect
3. C2×#16839764C2semidirect
4. #21448833C2semidirect
5. #21448659C2semidirect
6. #21446685C2semidirect
7. #21446516C2semidirect
8. #21446440C2semidirect
9. #21446257C2semidirect
10. #21446173C2semidirect
11. #21446166C2semidirect
12. #21446076C2semidirect
13. #21446009C2semidirect
14. C4×#14519702C2semidirect
15. C61×#1753C2semidirect
25. #16839909C4semidirect
67. C2×#11758222C2×C4semidirect
78. C2×#11758190C2×C4semidirect
81. C2×D488C2×C4semidirect
117. #14519702C2×C4semidirect
118. #14519702D4semidirect
123. #14519699C2×C4semidirect
139. C22⋊C8×C61C2×C4semidirect
330. Dic122C4×D4semidirect
393. #1753D61semidirect
450. C61#22863semidirect
525. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399092
C2×#168398642
C2×#168397642
#214488332
#214486592
#214466852
#214465162
#214464402
#214462572
#214461732
#214461662
#214460762
#214460092
C4×#145197022
C61×#17532
#2286361