Finite Group Databasebeta

← #29700357

Subgroups — #29700357

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×#16839871C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4#21448861C211yesmaximal, characteristic, complemented
5#21448647C211yesmaximal, characteristic, complemented
6#21446701C211yesmaximal, characteristic, complemented
7#21446510C211yesmaximal, characteristic, complemented
8#21446451C211yesmaximal, characteristic, complemented
9#21446164C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445595C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16839905C418yescomplemented
24#16839871—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27#16839759—24no—
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37#16839667C2211yescharacteristic
38#16839667C2211yescharacteristic
39#16839665—21no—
40#16839665C2211yescharacteristic
41#16839661C2211yescharacteristic
42#16839655—21no—
43#16839642—21no—
44#16839638—21no—
45#16839638—21no—
46#16839624—21no—
47C4⋊C4×Dic61C2211yescharacteristic
48C22⋊C4×Dic61—21no—
49C4×C22⋊Dic61C2211yescharacteristic
50#95×D61—21no—
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
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—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758200—41no—
76C2×#11758200—41no—
77C2×#11758200C2×C414yescomplemented
78C2×#11758199—22no—
79C2×#11758199—22no—
80C2×#11758199C2×C414yes—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83D4×Dic61—22no—
84D4×Dic61—41no—
85#14519739—22no—
86#14519739—22no—
87#14519739—41no—
88#14519739—41no—
89#14519736—22no—
90#14519736—41no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61D411yescharacteristic
99C2×C22⋊Dic61D411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519710—41no—
107#14519708—22no—
108#14519702—22no—
109#14519702—22no—
110#14519700C2×C414yescomplemented
111#14519699—22no—
112#14519699D414yescomplemented
113#14519697C2×C414yescomplemented
114C22⋊#92418C2×C414yescomplemented
115#14519687—22no—
116#14519687—41no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684D411yescharacteristic
124#14519684D411yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133#121×C61—22no—
134#121×C61C2×C414yescomplemented
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140#102×C61—22no—
141#102×C61—41no—
142#95×C61—21no—
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×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61#4112yes—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—42no—
173C22×Dic61—42no—
174C22×Dic61—81no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
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—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—44no—
210C2×C8×C61C2×D412yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61C22×C412yes—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—81no—
219C22⋊Dic61—41no—
220C22⋊Dic61—41no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
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—81no—
233C4⋊Dic61C2×D412yes—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—42no—
239C4×Dic61—81no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C22×C412yes—
245C2×#92418C22×C412yes—
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—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61C4×D412yes—
289C2×C4×C61C23×C411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C22⋊D61—48no—
296C2×Dic61—22no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
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—
329C8×C61—22no—
330C8×C61—41no—
331#92418—22no—
332#92418—22no—
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—81no—
365C4×C61—81no—
366C4×C61C2×C4×D411yescharacteristic
367C4×C61#51811yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55111yescharacteristic
370Dic61—42no—
371Dic61—41no—
372Dic61—42no—
373Dic61—41no—
374Dic61—41no—
375Dic61—41no—
376Dic61—81no—
377C2×#449—611no—
378C2×#442—611no—
379C2×#416—611no—
380#2363—611no—
381#2339—611no—
382#1973—611no—
383#1935—611no—
384#1927—611no—
385#1893D6111yescharacteristic, complemented
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×C8C2×D6111yescharacteristic
406C2×#121C2×D6111yescharacteristic
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×#117—611no—
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×#102C2×D6111yescharacteristic
423C2×#102C2×D6111yescharacteristic
424C2×C22⋊C8—611no—
425C2×#97—611no—
426C2×#97—611no—
427#391—611no—
428#391—611no—
429#390—611no—
430#390—1221no—
431#389—611no—
432#388—1221no—
433#386—1221no—
434#386—1221no—
435#386—1221no—
436#381—1221no—
437#380C2×D6111yescharacteristic
438C4×C4⋊C4—611no—
439C4×C22⋊C4—611no—
440C4×C22⋊C4—1221no—
441C2×#95—1221no—
442#340—611no—
443#340—611no—
444#340C2×D6111yescharacteristic
445#340C2×D6111yescharacteristic
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—1221no—
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—22no—
472C22×C8—22no—
473C22×C8—41no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478#121—22no—
479#121C4×D6114yescomplemented
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—2441no—
484C4×D4—2441no—
485C4×D4—2441no—
486#117—1222no—
487#117—2441no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—1221no—
507C2×C42—1221no—
508#107—2441no—
509#106—1222no—
510#103—614no—
511#103—1222no—
512#103—1222no—
513#102—22no—
514#102—41no—
515#102—614no—
516#102—614no—
517#102—1222no—
518C22⋊C8—614no—
519#97—1222no—
520#97—2441no—
521#95—21no—
522#95—611no—
523#95—611no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24—1221no—
532C24D4×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—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1224no—
575C22×C4—1221no—
576C22×C4—4881no—
577C22×C4—4881no—
578C22×C4—4881no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4C2×C4×D6112yes—
588C22×C4D4×D6111yescharacteristic
589C22×C4#1175822412yes—
590C22×C4C23×D6111yescharacteristic
591SD16—2444no—
592D8—1228no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8—612no—
600C2×C8—612no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8D4×D6112yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—612no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—4881no—
616C4⋊C4C2×C4×D6112yes—
617C22⋊C4—24no—
618C22⋊C4—81no—
619C22⋊C4—4881no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2441no—
623C22⋊C4—2441no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—1221no—
628C42—1221no—
629C42—1221no—
630C42—1221no—
631C42—4881no—
632C42—2442no—
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—
653C23#1451973712yes—
654C23C2×D4×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—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—4884no—
699C2×C4—4884no—
700C2×C4—4884no—
701C2×C4—2448no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4#1451973712yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4C2×#1175822411yescharacteristic
714C2×C4#1451982211yescharacteristic
715C2×C4#1451982311yescharacteristic
716C8—22no—
717C8—41no—
718C8—1222no—
719C8—1222no—
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×#1451973711yescharacteristic
742C22#1684039611yescharacteristic
743C22#1684040111yescharacteristic
744C22#1684055911yescharacteristic
745C22#1684055911yescharacteristic
746C22#1684056311yescharacteristic
747C22#1684056811yescharacteristic
748C4—22no—
749C4—42no—
750C4—81no—
751C4—81no—
752C4—4881no—
753C4—2441no—
754C4—2442no—
755C4—2441no—
756C4—2441no—
757C4—2442no—
758C4—2441no—
759C4C4×D4×D6111yescharacteristic
760C4#1684023411yescharacteristic
761C4#1684039911yescharacteristic
762C4#1684043511yescharacteristic
763C2—42no—
764C2—82no—
765C2—2444no—
766C2#2144879911yescharacteristic
767C2#2145461511yescharacteristic
768C2#2145464511yescharacteristic
769C2#2145734111yescharacteristic
770C2#2145735611yescharacteristic
771C2#2145780111yescharacteristic
772C2#2145798111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#16839759C2semidirect
4. #21448861C2semidirect
5. #21448647C2semidirect
6. #21446701C2semidirect
7. #21446510C2semidirect
8. #21446451C2semidirect
9. #21446164C2semidirect
10. #21446151C2semidirect
11. #21446067C2semidirect
12. #21446016C2semidirect
13. #21445643C2semidirect
14. #21445595C2semidirect
15. C61×#1893C2semidirect
23. #16839905C4semidirect
67. C2×#11758222C2×C4semidirect
77. C2×#11758200C2×C4semidirect
110. #14519700C2×C4semidirect
112. #14519699D4semidirect
113. #14519697C2×C4semidirect
114. C22⋊#92418C2×C4semidirect
134. #121×C61C2×C4semidirect
385. #1893D61semidirect
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×#168398712
C2×#168397592
#214488612
#214486472
#214467012
#214465102
#214464512
#214461642
#214461512
#214460672
#214460162
#214456432
#214455952
C61×#18932
#2286061