Finite Group Databasebeta

← #29700361

Subgroups — #29700361

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×#16839756C211yesmaximal, characteristic, complemented
4#21448650C211yesmaximal, characteristic, complemented
5#21446699C211yesmaximal, characteristic, complemented
6#21446508C211yesmaximal, characteristic, complemented
7#21446453C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#2363C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22#16839905C418yescomplemented
23#16839872—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26#16839756—24no—
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839638—21no—
41#16839638—21no—
42#16839624—21no—
43#16839622C2211yescharacteristic
44#95×D61—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C61×#390—21no—
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#388—21no—
58C61×#386—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758200—41no—
75C2×#11758200—41no—
76C2×#11758200C2×C414yescomplemented
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199C2×C414yes—
80C22×#92418—22no—
81C22×#92418—22no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—41no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96#14519710—41no—
97#14519708—22no—
98#14519700—22no—
99#14519700—22no—
100#14519700C2×C414yescomplemented
101#14519698—22no—
102#14519698—41no—
103#14519697—22no—
104#14519697C2×C414yescomplemented
105#14519697D414yescomplemented
106C22⋊#92418C2×C414yescomplemented
107#14519688—22no—
108#14519688—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114C22×D4×C61—21no—
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118#121×C61—22no—
119#121×C61C2×C414yescomplemented
120C4×D4×C61—22no—
121C4×D4×C61—41no—
122#117×C61—22no—
123#117×C61—41no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139#95×C61—21no—
140#95×C61—21no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C2×D4×C61—24no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—81no—
153C2×D4×C61—81no—
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—81no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—24no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179#11758222—28no—
180#11758222—44no—
181#11758222—44no—
182#11758222—44no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244C22×C412yes—
187C2×D244C2×D412yes—
188C2×D244#4112yes—
189C2×C4×D61—24no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122C22×C412yes—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—81no—
209C4⋊C4×C61C22×C412yes—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—41no—
213C22⋊C4×C61—41no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—42no—
223C42×C61—81no—
224C22⋊Dic61—81no—
225#11758200—44no—
226#11758199—28no—
227#11758198—42no—
228#11758198—42no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—44no—
243C2×#92418C22×C412yes—
244C2×#92418C22×C412yes—
245C2×#92418C2×D412yes—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C4×D412yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
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—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
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×C61—84no—
301C2×C4×C61C4×D412yes—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—22no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244C4×D414yes—
322C4×D61—48no—
323C4×D61—84no—
324C4×D61—84no—
325Dic122—22no—
326Dic122—22no—
327Dic122—41no—
328Dic122—41no—
329#92418—22no—
330#92418—22no—
331#92418—22no—
332#92418—41no—
333#22860—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61D4211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61#57511yescharacteristic
352C22×C61#57511yescharacteristic
353C22×C61#57611yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—24no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—42no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—81no—
370C4×C61C2×C4×D411yescharacteristic
371C4×C61#51811yescharacteristic
372C4×C61#54611yescharacteristic
373C4×C61#55111yescharacteristic
374Dic61—42no—
375Dic61—81no—
376Dic61—81no—
377C2×#449—611no—
378C2×#442—611no—
379C2×#416—611no—
380#2363D6111yescharacteristic, complemented
381#2339—611no—
382#1973—611no—
383#1935—611no—
384#1927—611no—
385#1893—611no—
386#1879—611no—
387#1877—611no—
388#1862—611no—
389#1854—611no—
390#1762—611no—
391#1752—611no—
392C2×C61—42no—
393C2×C61—82no—
394C2×C61#235811yescharacteristic
395C2×C61#294311yescharacteristic
396C2×C61#294611yescharacteristic
397C2×C61#326711yescharacteristic
398C2×C61#326811yescharacteristic
399C2×C61#330711yescharacteristic
400C2×C61#331911yescharacteristic
401D61—44no—
402C22×#41—611no—
403C22×SD16—611no—
404C22×D8—611no—
405C23×C8—611no—
406C2×#121C2×D6111yescharacteristic
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4C2×D6111yescharacteristic
410C2×#117C2×D6111yescharacteristic
411#449—618no—
412#442—1224no—
413C2×#107—611no—
414C2×#106—611no—
415#416—1224no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×C22⋊C8—611no—
425C2×#97—611no—
426C2×#97—611no—
427#391—611no—
428#391—611no—
429#390—21no—
430#390C2×D6111yescharacteristic
431#389C2×D6111yescharacteristic
432#388—21no—
433#386—21no—
434#386—1221no—
435#386—1221no—
436#381—1221no—
437#380—611no—
438C4×C4⋊C4C2×D6111yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2×D6111yescharacteristic
441C2×#95—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#336—611no—
447#336—611no—
448C61#2286011yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—1222no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—2441no—
454C2×#41—2441no—
455C22×Q8—611no—
456C22×D4—21no—
457C22×D4—611no—
458C22×D4—1221no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×SD16—614no—
466C2×SD16—2441no—
467C2×SD16—2441no—
468C2×D8—614no—
469C2×D8—1222no—
470C2×D8—1222no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—1222no—
476C22×C8—1222no—
477C22×C8—2441no—
478#121—22no—
479#121C4×D6114yescomplemented
480C4×D4—22no—
481C4×D4—41no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—2441no—
485C4×D4—2441no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C22×D6111yescharacteristic
507C2×C42C22×D6111yescharacteristic
508#107—2441no—
509#106—1222no—
510#103—614no—
511#103—1222no—
512#103—1222no—
513#102—614no—
514#102—614no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—614no—
519#97—1222no—
520#97—2441no—
521#95—21no—
522#95—21no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95C22⋊D6111yescharacteristic
529#95C22⋊D6111yescharacteristic
530C24—21no—
531C24—1221no—
532C24C2×C22⋊D6111yescharacteristic
533#41—1228no—
534#41—2444no—
535#41—2444no—
536#41—2444no—
537C2×Q8—612no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—612no—
552C2×D4—612no—
553C2×D4—612no—
554C2×D4—1224no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4C2×C4×D6112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4—1221no—
572C22×C4—1224no—
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×C4#1175822212yes—
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C23×D6111yescharacteristic
591SD16—2444no—
592D8—1228no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—612no—
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—2444no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—81no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4C2×C4×D6112yes—
616C4⋊C4D4×D6112yes—
617C22⋊C4—24no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—4881no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C42—81no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23C4×C22⋊D6112yes—
654C23C22×C22⋊D6111yescharacteristic
655Q8—1222no—
656Q8—1222no—
657Q8—2441no—
658Q8—2441no—
659D4—22no—
660D4—22no—
661D4—41no—
662D4—41no—
663D4—84no—
664D4—614no—
665D4—1222no—
666D4—1222no—
667D4—1222no—
668D4—2448no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—1222no—
698C2×C4—4884no—
699C2×C4—4884no—
700C2×C4—2448no—
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×C4C4×C22⋊D6112yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4C2×#1175822211yescharacteristic
714C2×C4#1451982211yescharacteristic
715C2×C4#1451982311yescharacteristic
716C8—1222no—
717C8—1222no—
718C8—1222no—
719C8—2441no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—1224no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C2×C4×C22⋊D6111yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684040011yescharacteristic
744C22#1684056011yescharacteristic
745C22#1684056011yescharacteristic
746C22#1684056511yescharacteristic
747C22#1684057311yescharacteristic
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—41no—
755C4—81no—
756C4—4881no—
757C4—4881no—
758C4—2442no—
759C4C4×D4×D6111yescharacteristic
760C4#1684023411yescharacteristic
761C4#1684040811yescharacteristic
762C4#1684044111yescharacteristic
763C2—42no—
764C2—82no—
765C2—2444no—
766C2#2144879611yescharacteristic
767C2#2145461711yescharacteristic
768C2#2145465111yescharacteristic
769C2#2145734011yescharacteristic
770C2#2145736011yescharacteristic
771C2#2145778911yescharacteristic
772C2#2145796911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2363C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
cosocleC22×C4×C61C24
hypercenter#2363D61
hypocenterC61#22860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×#16839756C2semidirect
4. #21448650C2semidirect
5. #21446699C2semidirect
6. #21446508C2semidirect
7. #21446453C2semidirect
8. #21446248C2semidirect
9. #21446170C2semidirect
10. #21446153C2semidirect
11. #21446065C2semidirect
12. #21446018C2semidirect
13. #21445647C2semidirect
14. #21445597C2semidirect
15. C61×#2363C2semidirect
22. #16839905C4semidirect
67. C2×#11758222C2×C4semidirect
76. C2×#11758200C2×C4semidirect
100. #14519700C2×C4semidirect
104. #14519697C2×C4semidirect
105. #14519697D4semidirect
106. C22⋊#92418C2×C4semidirect
119. #121×C61C2×C4semidirect
380. #2363D61semidirect
448. C61#22860semidirect
479. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168398722
C2×#168397562
#214486502
#214466992
#214465082
#214464532
#214462482
#214461702
#214461532
#214460652
#214460182
#214456472
#214455972
C61×#23632
#2286061