Finite Group Databasebeta

← #29700315

Subgroups — #29700315

Order 15616.

1146 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×#16839907C211yesmaximal, characteristic
2C2×#16839865C211yesmaximal, characteristic, complemented
3#21448857C211yesmaximal, characteristic, complemented
4#21448660C211yesmaximal, characteristic, complemented
5#21446692C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446442C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446172C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446085C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445595C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16839907C418yescomplemented
23#16839865—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33#16839665—21no—
34#16839665—21no—
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839658C2211yescharacteristic
40#16839653—21no—
41#16839638—21no—
42#16839622—21no—
43#16839622C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758198—21no—
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#416—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201C2×C414yes—
68C2×#11758199—41no—
69C2×#11758199—41no—
70C2×#11758199C2×C414yes—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519751—22no—
74#14519751C2×C414yes—
75Q8×Dic61—22no—
76Q8×Dic61—22no—
77Q8×Dic61—41no—
78Q8×Dic61—41no—
79#14519739—22no—
80#14519739—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×C22⋊Dic61D411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519710—22no—
104#14519708—41no—
105#14519701C2×C414yescomplemented
106#14519699—22no—
107#14519699—41no—
108#14519698C2×C414yescomplemented
109C22⋊#92418C2×C414yescomplemented
110#14519687—22no—
111#14519687—41no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61C2×C414yescomplemented
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133#117×C61—22no—
134#117×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#103×C61—22no—
140#103×C61D414yescomplemented
141#102×C61—22no—
142#102×C61—22no—
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146#41×C61—28no—
147#41×C61—44no—
148#41×C61—44no—
149#41×C61—44no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C22×C412yes—
154C2×Q8×C61C2×D412yes—
155C2×Q8×C61#4112yes—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61C22×C412yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—24no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—81no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244C22×C412yes—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—81no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—44no—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61C2×D412yes—
209C22⋊C4×C61—42no—
210C42×C61—42no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213C22⋊Dic61—42no—
214C22⋊Dic61—42no—
215C22⋊Dic61—81no—
216C22⋊Dic61—81no—
217C22⋊Dic61—81no—
218#11758201—28no—
219#11758199—44no—
220#11758198—24no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—42no—
230C4⋊Dic61—42no—
231C4⋊Dic61C22×C412yes—
232#11758196—81no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—42no—
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—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—22no—
271Q8×C61C4×D414yes—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—48no—
275D4×C61—41no—
276D4×C61—41no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—48no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61C4×D412yes—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C22⋊D61—84no—
301C2×Dic61—22no—
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—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322D244—22no—
323D244—22no—
324D244—41no—
325D244—41no—
326C4×D61—84no—
327C8×C61—22no—
328C8×C61—41no—
329#92418—22no—
330#92418—22no—
331#22857—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61#54611yescharacteristic
349C22×C61#57511yescharacteristic
350C22×C61#57511yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57711yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—22no—
361C4×C61—24no—
362C4×C61—42no—
363C4×C61—81no—
364C4×C61C2×C4×D411yescharacteristic
365C4×C61#51811yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#55111yescharacteristic
368Dic61—42no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61—81no—
374Dic61—81no—
375C2×#449—611no—
376C2×#440—611no—
377C2×#416D6111yescharacteristic, complemented
378#2363—611no—
379#2341—611no—
380#1972—611no—
381#1936—611no—
382#1925—611no—
383#1893—611no—
384#1880—611no—
385#1879—611no—
386#1865—611no—
387#1854—611no—
388#1763—611no—
389#1752—611no—
390C2×C61—42no—
391C2×C61—82no—
392C2×C61#235811yescharacteristic
393C2×C61#294311yescharacteristic
394C2×C61#294611yescharacteristic
395C2×C61#326811yescharacteristic
396C2×C61#327111yescharacteristic
397C2×C61#330911yescharacteristic
398C2×C61#332111yescharacteristic
399D61—82no—
400C22×#41C2×D6111yescharacteristic
401C22×SD16—611no—
402C22×D8—611no—
403C23×C8C2×D6111yescharacteristic
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×D4—611no—
408C2×#117C2×D6111yescharacteristic
409#449—618no—
410#440—1224no—
411C2×#107—611no—
412C2×#106—611no—
413#416—24no—
414C2×#103—611no—
415C2×#103C2×D6111yescharacteristic
416C2×#103C2×D6111yescharacteristic
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102C2×D6111yescharacteristic
421C2×#102C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×#97—611no—
424C2×#97—611no—
425#390—611no—
426#390—611no—
427#390—611no—
428#390—1221no—
429#390—1221no—
430#390—1221no—
431#389—611no—
432#388—1221no—
433#386—1221no—
434#380—611no—
435#380—1221no—
436C4×C4⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—1221no—
439C4×C22⋊C4—1221no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2285711yescharacteristic, complemented, Sylow
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41C4×D6114yescomplemented
453C22×Q8C22×D6111yescharacteristic
454C22×D4—21no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×SD16—614no—
462C2×SD16—1222no—
463C2×SD16—1222no—
464C2×D8—614no—
465C2×D8—2441no—
466C2×D8—2441no—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—41no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474#121—614no—
475#121—1222no—
476C4×Q8—1222no—
477C4×Q8—1222no—
478C4×Q8—2441no—
479C4×Q8—2441no—
480C4×D4—1222no—
481C4×D4—2441no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
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—21no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—1221no—
508C2×C42—1221no—
509C2×C42—1221no—
510#107—1222no—
511#106—2441no—
512#103—22no—
513#103—614no—
514#103C22⋊D6114yescomplemented
515#102—22no—
516#102—22no—
517#102—614no—
518#102—1222no—
519#102—2441no—
520C22⋊C8—614no—
521#97—1222no—
522#97—2441no—
523#95—611no—
524#95—611no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—21no—
529C24—1221no—
530C24D4×D6111yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D6112yes—
539C2×Q8#1175822212yes—
540C2×Q8C2×C22⋊D6112yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—612no—
550C2×D4—1224no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—4881no—
557C2×D4—4881no—
558C2×D4C2×C4×D6112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—4881no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4C2×C4×D6112yes—
580C22×C4D4×D6111yescharacteristic
581C22×C4#1175822412yes—
582C22×C4C23×D6111yescharacteristic
583SD16—1228no—
584D8—2444no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8—612no—
592C2×C8—612no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8C2×C22⋊D6112yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—612no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—4881no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4C2×C22⋊D6112yes—
611C22⋊C4—42no—
612C22⋊C4—1224no—
613C22⋊C4—4881no—
614C22⋊C4—4881no—
615C22⋊C4—4881no—
616C22⋊C4—4881no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2441no—
620C22⋊C4—2441no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—42no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—4881no—
629C42—2442no—
630C42—2442no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—1222no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23#1451973712yes—
652C23C2×D4×D6111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×C22⋊D6114yes—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—1222no—
663D4—1222no—
664D4—4884no—
665D4—2441no—
666D4—2441no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—1222no—
684C2×C4—1221no—
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—1221no—
696C2×C4—4884no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4#1451973712yes—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4C2×#1175822411yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982211yescharacteristic
712C8—22no—
713C8—41no—
714C8—1222no—
715C8—1222no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22C2×#1451973711yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22#1684040211yescharacteristic
740C22#1684055911yescharacteristic
741C22#1684055911yescharacteristic
742C22#1684056411yescharacteristic
743C22#1684056911yescharacteristic
744C4—22no—
745C4—24no—
746C4—42no—
747C4—81no—
748C4—4881no—
749C4—4881no—
750C4—2442no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4—2441no—
755C4C2×C4×C22⋊D6111yescharacteristic
756C4#1684023511yescharacteristic
757C4#1684040611yescharacteristic
758C4#1684043811yescharacteristic
759C2—42no—
760C2—82no—
761C2—4882no—
762C2#2144879811yescharacteristic
763C2#2145461511yescharacteristic
764C2#2145465411yescharacteristic
765C2#2145735911yescharacteristic
766C2#2145740411yescharacteristic
767C2#2145782111yescharacteristic
768C2#2145800111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
cosocleC22×C4×C61C24
hypercenterC2×#416D61
hypocenterC61#22857
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16839865C2semidirect
3. #21448857C2semidirect
4. #21448660C2semidirect
5. #21446692C2semidirect
6. #21446513C2semidirect
7. #21446442C2semidirect
8. #21446247C2semidirect
9. #21446172C2semidirect
10. #21446164C2semidirect
11. #21446085C2semidirect
12. #21446018C2semidirect
13. #21445651C2semidirect
14. #21445595C2semidirect
15. C2×C61×#416C2semidirect
22. #16839907C4semidirect
105. #14519701C2×C4semidirect
108. #14519698C2×C4semidirect
109. C22⋊#92418C2×C4semidirect
122. C2×#41×C61C2×C4semidirect
140. #103×C61D4semidirect
377. C2×#416D61semidirect
446. C61#22857semidirect
452. C2×#41C4×D61semidirect
514. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
C2×#168398652
#214488572
#214486602
#214466922
#214465132
#214464422
#214462472
#214461722
#214461642
#214460852
#214460182
#214456512
#214455952
C2×C61×#4162
#2285761