Finite Group Databasebeta

← #29700789

Subgroups — #29700789

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455033C211yesmaximal, characteristic
2#21454541C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4#21454266C211yesmaximal, characteristic, complemented
5#21446709C211yesmaximal, characteristic, complemented
6#21446523C211yesmaximal, characteristic, complemented
7#21446466C211yesmaximal, characteristic, complemented
8#21446264C211yesmaximal, characteristic, complemented
9#21446148C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446094C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445664C211yesmaximal, characteristic, complemented
14#21445586C211yesmaximal, characteristic, complemented
15C2×C61×#443C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20#16840269C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22#16839923C411yescharacteristic, complemented
23#16839921C411yescharacteristic, complemented
24#16839916C411yescharacteristic, complemented
25#16839911C411yescharacteristic, complemented
26#16839906C411yescharacteristic, complemented
27#16839904C411yescharacteristic, complemented
28#16839899C411yescharacteristic, complemented
29#16839894C411yescharacteristic, complemented
30#16839838—21no—
31#16839833—21no—
32#16839831—21no—
33C8×C22⋊D61—21no—
34C2×#14519712C2211yescharacteristic, complemented
35#16839788C2211yescharacteristic, complemented
36#16839777—24no—
37C2×#14519705C2211yescharacteristic
38C2×#14519704C2211yescharacteristic
39C2×#14519704C2211yescharacteristic, complemented
40C2×#14519703C2211yescharacteristic
41#16839759C2211yescharacteristic
42#16839758C2211yescharacteristic
43#16839730—21no—
44#16839730C2211yescharacteristic
45#16839729C2211yescharacteristic, complemented
46#16839728—21no—
47#16839728C2211yescharacteristic
48#16839725—21no—
49#16839725C2211yescharacteristic
50C2×#14519689—21no—
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53#16839720C2211yescharacteristic, complemented
54C2×#14519688C2211yescharacteristic, complemented
55#16839527C2211yescharacteristic, complemented
56#16839526C2211yescharacteristic, complemented
57#16839523C2211yescharacteristic, complemented
58#16839522C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61C2×#135×C61C2211yescharacteristic
62C2×#131×C61C2211yescharacteristic
63C2×#131×C61C2211yescharacteristic, complemented
64C61×#443—24no—
65C2×#108×C61C2211yescharacteristic, complemented
66C2×#104×C61C2211yescharacteristic
67C2×#104×C61C2211yescharacteristic, complemented
68C2×C4×C8×C61C2211yescharacteristic, complemented
69C2×#11758226C2×C411yescharacteristic
70C2×#11758222—21no—
71C2×#11758222C2311yescharacteristic
72C2×#11758224—21no—
73C2×#11758224C2×C411yescharacteristic
74#41×D61—22no—
75#41×D61—22no—
76#41×D61—41no—
77#41×D61—41no—
78C2×Q8×D61C2×C411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83#14519797—41no—
84#14519797—41no—
85C2×#11758202C2×C411yescharacteristic
86C2×#11758200C2×C411yescharacteristic
87C2×#11758201C2×C411yescharacteristic
88C2×#11758199C2×C411yescharacteristic
89#14519784—22no—
90#14519784—41no—
91C2×#11758194—21no—
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758189—21no—
95M16×D61—22no—
96M16×D61—41no—
97C22×#92418—21no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—21no—
101#14519758—21no—
102#14519753C2×C411yescharacteristic
103#14519753C2×C411yescharacteristic
104#14519748C2×C411yescharacteristic
105#14519748C2×C411yescharacteristic
106#14519745—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109#14519736C2311yescharacteristic
110#14519734—22no—
111#14519734—41no—
112C2×#11758196—21no—
113C2×#11758198—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519712—41no—
116#14519706—21no—
117#14519706—21no—
118#14519705—22no—
119#14519704—22no—
120#14519704—41no—
121#14519703—22no—
122#14519702C2×C411yescharacteristic
123#14519702C2×C411yescharacteristic
124#14519701C2×C411yescharacteristic
125#14519701C2×C411yescharacteristic
126#14519699C2×C411yescharacteristic
127#14519699C2×C411yescharacteristic
128#14519698C2×C411yescharacteristic
129#14519698C2×C411yescharacteristic
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519689—21no—
133#14519689—21no—
134#14519689—21no—
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689C2×C411yescharacteristic
139#14519689C2×C411yescharacteristic
140#14519689C2×C411yescharacteristic
141#14519689C2×C411yescharacteristic
142#14519689D411yescharacteristic
143#14519689D411yescharacteristic
144#14519689D411yescharacteristic
145#14519689D411yescharacteristic
146#14519688—41no—
147#14519687—21no—
148C8×Dic61—21no—
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151#135×C61—22no—
152#135×C61—22no—
153C2×Q16×C61C2×C411yescharacteristic
154C2×SD16×C61C2×C411yescharacteristic
155C2×SD16×C61C2×C411yescharacteristic
156C2×D8×C61C2×C411yescharacteristic
157#131×C61—22no—
158#131×C61—22no—
159#131×C61—41no—
160#131×C61—41no—
161C2×M16×C61—21no—
162C2×M16×C61—21no—
163C2×M16×C61C2311yescharacteristic
164C2×M16×C61C2311yescharacteristic
165C22×C8×C61—21no—
166C22×C8×C61—21no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C2×C42×C61C2311yescharacteristic
170#108×C61—22no—
171#104×C61—22no—
172#104×C61D414yescomplemented
173C4×C8×C61—22no—
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61C2×D412yes—
183#41×C61#4112yes—
184C2×Q8×C61C22×C411yescharacteristic
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61#4111yescharacteristic
202#11758226—22no—
203#11758226—41no—
204Q8×D61—22no—
205Q8×D61—41no—
206#11758224—22no—
207#11758224—41no—
208#11758224—42no—
209#11758224—42no—
210D4×D61—22no—
211D4×D61—41no—
212D4×D61—42no—
213D4×D61—42no—
214#11758222—21no—
215#11758222—21no—
216#11758222—21no—
217#11758222—21no—
218#11758222—42no—
219#11758222—42no—
220C2×D244—21no—
221C2×D244C22×C411yescharacteristic
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C22×C411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237Q16×C61—22no—
238SD16×C61—22no—
239SD16×C61—22no—
240D8×C61—22no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—42no—
245M16×C61—42no—
246M16×C61C2×D412yes—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—42no—
254C2×C8×C61—42no—
255C2×C8×C61C22×C411yescharacteristic
256C2×C8×C61C22×C411yescharacteristic
257C2×C8×C61C2×D411yescharacteristic
258C2×C8×C61C2×D411yescharacteristic
259C42×C61—21no—
260C42×C61C2×D412yes—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758202—41no—
265#11758201—41no—
266#11758200—41no—
267#11758199—41no—
268#11758198—21no—
269#11758198—21no—
270#11758198—42no—
271C4⋊Dic61C22×C411yescharacteristic
272C4⋊Dic61C22×C411yescharacteristic
273#11758196—21no—
274#11758196—21no—
275#11758196—42no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283#11758194—42no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—42no—
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295#11758189—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61C2×#4111yescharacteristic
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—81no—
308C22×D61C4×D411yescharacteristic
309C22×D61C4×D411yescharacteristic
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61C4×D412yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—21no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61C4×D412yes—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—81no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—42no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61C4×D411yescharacteristic
353C2×Dic61C4×D411yescharacteristic
354D244—21no—
355D244—21no—
356D244—42no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—41no—
368C4×D61—41no—
369Dic122—21no—
370Dic122—21no—
371Dic122—42no—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—22no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—41no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—21no—
382#92418—41no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#55111yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—84no—
408C4×C61—22no—
409C4×C61—42no—
410C4×C61—41no—
411C4×C61C2×C4×D411yescharacteristic
412C4×C61#51811yescharacteristic
413C4×C61D4211yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—21no—
416Dic61—21no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#443D6111yescharacteristic, complemented
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61—81no—
440C2×C61#235811yescharacteristic
441C2×C61#295511yescharacteristic
442C2×C61#295711yescharacteristic
443D61—41no—
444D61—41no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135C2×D6111yescharacteristic
449C2×#131—611no—
450C2×#131C2×D6111yescharacteristic
451C2×#131C2×D6111yescharacteristic, complemented
452C22×M16—611no—
453#525—611no—
454C2×#117—611no—
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449—611no—
461#448—611no—
462#447—611no—
463#443—24no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108C2×D6111yescharacteristic, complemented
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104C2×D6111yescharacteristic
477C2×#104C2×D6111yescharacteristic, complemented
478#416—611no—
479#416—611no—
480#408—611no—
481#408—611no—
482#408—611no—
483#408—1221no—
484#408—1221no—
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8C2×D6111yescharacteristic, complemented
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—1221no—
516#135—22no—
517#135—22no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16C4×D6111yescharacteristic
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16C4×D6111yescharacteristic
525C2×SD16C4×D6111yescharacteristic
526C2×D8—611no—
527C2×D8C4×D6111yescharacteristic
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—1222no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555#121—611no—
556#121—611no—
557#120—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560#117—611no—
561#117—1222no—
562#117—2441no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42C22×D6111yescharacteristic
567#108—22no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—22no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—2441no—
576#104C22⋊D6114yescomplemented
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#102—611no—
582#102—611no—
583#102—611no—
584#102—611no—
585C22⋊C8—611no—
586C22⋊C8—611no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—1221no—
602#97—2441no—
603C4×C8—22no—
604C4×C8—1221no—
605C24—611no—
606C24—1221no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—1222no—
614#41—1222no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—2442no—
620#41—2442no—
621#41—2441no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625#41#1175822212yes—
626#41C2×C22⋊D6112yes—
627C2×Q8—611no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—2441no—
631C2×Q8C2×C4×D6111yescharacteristic
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—2441no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C2×C4×D6111yescharacteristic
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4C23×D6111yescharacteristic
668Q16—22no—
669Q16—2441no—
670SD16—22no—
671SD16—22no—
672SD16—2441no—
673SD16—2441no—
674D8—22no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—42no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—2442no—
686M16—2442no—
687M16C2×C22⋊D6112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C4×D6111yescharacteristic
709C2×C8C2×C4×D6111yescharacteristic
710C2×C8D4×D6111yescharacteristic
711C2×C8D4×D6111yescharacteristic
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—2442no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—2442no—
723C42—21no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42C2×C22⋊D6112yes—
728C23—21no—
729C23—21no—
730C23—611no—
731C23—611no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23#41×D6111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—1221no—
745Q8—1221no—
746Q8—2442no—
747Q8C4×C22⋊D6112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—41no—
754D4—41no—
755D4—1221no—
756D4—1221no—
757D4—4881no—
758D4—2442no—
759D4—2442no—
760D4—2442no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4C4×C22⋊D6112yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C22×C22⋊D6111yescharacteristic
800C2×C4C2×#1175822211yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—22no—
808C8—41no—
809C8—1221no—
810C8—1221no—
811C8—1221no—
812C8—1221no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—4881no—
830C22—4881no—
831C22—4884no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22#1684040011yescharacteristic
837C22#1684044111yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—1221no—
842C4—1221no—
843C4—4881no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4C2×C4×C22⋊D6111yescharacteristic
848C4#1684023411yescharacteristic
849C4D4×C22⋊D6111yescharacteristic
850C4#1684040811yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—81no—
855C2—4881no—
856C2—2441no—
857C2—2441no—
858C2#2144879611yescharacteristic
859C2#2145471711yescharacteristic
860C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#443C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenterC2×#443D61
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. #21454541C2semidirect
3. C2×#16839777C2semidirect
4. #21454266C2semidirect
5. #21446709C2semidirect
6. #21446523C2semidirect
7. #21446466C2semidirect
8. #21446264C2semidirect
9. #21446148C2semidirect
10. #21446146C2semidirect
11. #21446094C2semidirect
12. #21446022C2semidirect
13. #21445664C2semidirect
14. #21445586C2semidirect
15. C2×C61×#443C2semidirect
22. #16839923C4semidirect
23. #16839921C4semidirect
24. #16839916C4semidirect
25. #16839911C4semidirect
26. #16839906C4semidirect
27. #16839904C4semidirect
28. #16839899C4semidirect
29. #16839894C4semidirect
34. C2×#14519712C22semidirect
35. #16839788C22semidirect
39. C2×#14519704C22semidirect
45. #16839729C22semidirect
53. #16839720C22semidirect
54. C2×#14519688C22semidirect
55. #16839527C22semidirect
56. #16839526C22semidirect
57. #16839523C22semidirect
58. #16839522C22semidirect
59. #16839516C22semidirect
60. #16839516C22semidirect
63. C2×#131×C61C22semidirect
65. C2×#108×C61C22semidirect
67. C2×#104×C61C22semidirect
68. C2×C4×C8×C61C22semidirect
172. #104×C61D4semidirect
422. C2×#443D61semidirect
451. C2×#131C2×D61semidirect
469. C2×#108C2×D61semidirect
477. C2×#104C2×D61semidirect
492. C2×C4×C8C2×D61semidirect
499. C61#22889semidirect
576. #104C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214550332
#214545412
C2×#168397772
#214542662
#214467092
#214465232
#214464662
#214462642
#214461482
#214461462
#214460942
#214460222
#214456642
#214455862
C2×C61×#4432
#2288961