Finite Group Databasebeta

← #29700747

Subgroups — #29700747

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455035C211yesmaximal, characteristic
2C2×#16839881C211yesmaximal, characteristic, complemented
3#21454546C211yesmaximal, characteristic, complemented
4C22×#14519705C211yesmaximal, characteristic, complemented
5#21454269C211yesmaximal, characteristic, complemented
6#21446709C211yesmaximal, characteristic, complemented
7#21446531C211yesmaximal, characteristic, complemented
8#21446465C211yesmaximal, characteristic, complemented
9#21446144C211yesmaximal, characteristic, complemented
10#21446143C211yesmaximal, characteristic, complemented
11#21446095C211yesmaximal, characteristic, complemented
12#21446023C211yesmaximal, characteristic, complemented
13#21445660C211yesmaximal, characteristic, complemented
14#21445581C211yesmaximal, characteristic, complemented
15C61×#1896C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519785C2211yescharacteristic
21C2×#14519784C2211yescharacteristic, complemented
22C22×#11758194C2211yescharacteristic
23#16839922C411yescharacteristic, complemented
24#16839922C411yescharacteristic, complemented
25#16839917C411yescharacteristic, complemented
26#16839912C411yescharacteristic, complemented
27#16839905C411yescharacteristic, complemented
28#16839905C411yescharacteristic, complemented
29#16839900C411yescharacteristic, complemented
30#16839895C411yescharacteristic, complemented
31#16839881—24no—
32#16839840—21no—
33#16839834—21no—
34#16839834—21no—
35D4×#92418—21no—
36C2×#14519712C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38#16839789C2211yescharacteristic, complemented
39C2×#14519705—24no—
40C2×#14519705C2211yescharacteristic
41C2×#14519705C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519705C2211yescharacteristic
44#16839756C2211yescharacteristic
45#16839756C2211yescharacteristic
46#16839730C2211yescharacteristic
47#16839730C2211yescharacteristic
48#16839729C2211yescharacteristic, complemented
49#16839727—21no—
50#16839727—21no—
51#16839724—21no—
52C2×C22⋊#92418C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54C22⋊C8×D61—21no—
55#16839718C2211yescharacteristic, complemented
56C2×#14519688C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839526C2211yescharacteristic, complemented
60#16839517C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C61×#525C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C2×#104×C61C2211yescharacteristic, complemented
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#407C2211yescharacteristic
67C61×#339C2211yescharacteristic, complemented
68C61×#339C2211yescharacteristic, complemented
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—22no—
72C2×#11758222—22no—
73C2×#11758222—41no—
74C2×#11758222—41no—
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222C2311yescharacteristic
78C2×#11758222C2311yescharacteristic
79C22×Dic122C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C22×C22⋊D61—21no—
82C22×C4×D61—21no—
83#14519797—22no—
84#14519797—22no—
85#14519797—41no—
86#14519797—41no—
87C2×#11758202C2×C411yescharacteristic, complemented
88C2×#11758202C2×C411yescharacteristic, complemented
89C2×#11758200C2×C411yescharacteristic, complemented
90C2×#11758200C2×C411yescharacteristic, complemented
91C2×#11758201C2×C411yescharacteristic, complemented
92C2×#11758201C2×C411yescharacteristic, complemented
93C2×#11758199C2×C411yescharacteristic, complemented
94C2×#11758199C2×C411yescharacteristic, complemented
95#14519785—22no—
96#14519785—22no—
97#14519785—41no—
98#14519785—41no—
99#14519784—22no—
100#14519784—41no—
101C2×#11758194—21no—
102C2×#11758194—21no—
103C2×#11758194—22no—
104C2×#11758194—41no—
105C2×#11758194C2311yescharacteristic
106C2×#11758194C2311yescharacteristic
107C2×#11758189—21no—
108C2×#11758189—21no—
109C22×#92418—21no—
110C22×#92418—21no—
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114C22×#92418C2311yescharacteristic
115C2×C8×D61—21no—
116C2×C8×D61—21no—
117#14519712—22no—
118#14519712—41no—
119C4⋊#92418—21no—
120C4⋊#92418—21no—
121#14519705—22no—
122#14519705—22no—
123#14519705—22no—
124#14519705D414yescomplemented
125#14519700C2×C411yescharacteristic, complemented
126#14519700C2×C411yescharacteristic, complemented
127#14519700C2×C411yescharacteristic, complemented
128#14519700C2×C411yescharacteristic, complemented
129#14519697C2×C411yescharacteristic, complemented
130#14519697C2×C411yescharacteristic, complemented
131#14519697C2×C411yescharacteristic, complemented
132#14519697C2×C411yescharacteristic, complemented
133C22⋊#92418—21no—
134C22⋊#92418—21no—
135C22⋊#92418C2×C411yescharacteristic
136C22⋊#92418C2×C411yescharacteristic
137C22⋊#92418C2×C411yescharacteristic
138C22⋊#92418C2×C411yescharacteristic
139C22⋊#92418D411yescharacteristic
140C22⋊#92418D411yescharacteristic
141C22⋊#92418D411yescharacteristic
142C22⋊#92418D411yescharacteristic
143#14519689—21no—
144#14519689—21no—
145#14519689—21no—
146#14519689—21no—
147#14519688—22no—
148#14519688—21no—
149#14519688—41no—
150C4×#92418—21no—
151C2×#41×C61C2311yescharacteristic
152C23×C4×C61—21no—
153C23×C4×C61C2311yescharacteristic
154C2×M16×C61C2311yescharacteristic
155C2×M16×C61C2311yescharacteristic
156#123×C61—21no—
157C22⋊Q8×C61C2×C411yescharacteristic
158C22⋊Q8×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160#121×C61C2×C411yescharacteristic
161#120×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—21no—
164#117×C61C2311yescharacteristic
165C2×C42×C61—22no—
166C2×C42×C61—21no—
167C2×C42×C61—41no—
168C2×C42×C61C2311yescharacteristic
169C2×C42×C61C2311yescharacteristic
170#104×C61—22no—
171#104×C61—41no—
172C22⋊C8×C61—21no—
173C22⋊C8×C61—21no—
174C24×C61#4111yescharacteristic
175C23×D61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61—42no—
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61#4111yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C22×Dic61—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—21no—
212#11758222—21no—
213#11758222—21no—
214#11758222—22no—
215#11758222—22no—
216#11758222—41no—
217#11758222—41no—
218#11758222—42no—
219#11758222—42no—
220#11758222—42no—
221#11758222—42no—
222#11758222C2×D412yes—
223#11758222#4112yes—
224C2×D244—22no—
225C2×D244—21no—
226C2×D244—41no—
227C2×D244C22×C411yescharacteristic
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—41no—
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61—42no—
260C42×C61C2×D412yes—
261#11758202—22no—
262#11758202—41no—
263#11758201—22no—
264#11758201—41no—
265#11758200—22no—
266#11758200—41no—
267#11758199—22no—
268#11758199—41no—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—42no—
273#11758194—42no—
274#11758194C2×D412yes—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—42no—
286C2×#92418—42no—
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295#11758189—42no—
296#11758189—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—41no—
304C23×C61C4×D411yescharacteristic
305C23×C61C4×D411yescharacteristic
306C23×C61C2×#4111yescharacteristic
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—81no—
312Q8×C61—21no—
313Q8×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—42no—
319D4×C61—81no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—48no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61C4×D411yescharacteristic
343C2×C4×C61C4×D411yescharacteristic
344C2×C4×C61C23×C411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—42no—
353C22⋊D61—42no—
354C22⋊D61—41no—
355C22⋊D61—41no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—42no—
359D244—21no—
360D244—21no—
361D244—21no—
362D244—42no—
363D244C4×D412yes—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
375C8×C61—41no—
376C8×C61—41no—
377#92418—21no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—21no—
382#92418—21no—
383#92418—22no—
384#92418—21no—
385#92418—21no—
386#92418—41no—
387#22886—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61#44412yescomplemented
401C22×C61C2×C4×D411yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61#55111yescharacteristic
404C2×D61—22no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—84no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61C2×C4×D411yescharacteristic
419C4×C61#51811yescharacteristic
420C4×C61D4211yescharacteristic
421C4×C61#54611yescharacteristic
422Dic61—22no—
423Dic61—41no—
424#3002—611no—
425C2×#444—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1975—611no—
430#1938—611no—
431#1929—611no—
432#1896D6111yescharacteristic, complemented
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1765—611no—
438#1749—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61—81no—
444C2×C61#235811yescharacteristic
445C2×C61C2×#44411yescharacteristic
446C2×C61#295611yescharacteristic
447D61—42no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16—611no—
456#525C2×D6111yescharacteristic
457C22×C42C2×D6111yescharacteristic
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447—611no—
466#444—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—1224no—
479C2×#104C2×D6111yescharacteristic, complemented
480C2×#104C2×D6111yescharacteristic, complemented
481#416—611no—
482#416—611no—
483#408—611no—
484#408—611no—
485#408—611no—
486#408—1221no—
487#408—1221no—
488#407—1221no—
489#407C2×D6111yescharacteristic
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1221no—
493#405—611no—
494C2×#97—611no—
495C2×#97—611no—
496#341—611no—
497#341—611no—
498#339C2×D6111yescharacteristic, complemented
499#339C2×D6111yescharacteristic, complemented
500#336—611no—
501#336—611no—
502C61#2288611yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1221no—
510C2×#41—1221no—
511C2×#41—2441no—
512C2×#41—2441no—
513C2×#41C22×D6111yescharacteristic
514C22×Q8—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C23×C4—21no—
518C23×C4—1221no—
519C23×C4C22×D6111yescharacteristic
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8—611no—
531C2×D8—611no—
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8—1221no—
555C22×C8—1221no—
556#123—21no—
557C22⋊Q8C4×D6111yescharacteristic
558C22⋊Q8C4×D6111yescharacteristic
559#121C4×D6111yescharacteristic
560#121C4×D6111yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D6111yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D6111yescharacteristic
569C2×C42C22×D6111yescharacteristic
570#108—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—22no—
575#104—41no—
576#104—614no—
577#104—1222no—
578#104—1222no—
579#104—1222no—
580#103—611no—
581#103—611no—
582#103—611no—
583#103—611no—
584#102—611no—
585#102—611no—
586#102—611no—
587#102—611no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605#97—1222no—
606#97—2441no—
607C4×C8—1221no—
608C24—1221no—
609C24#1175822411yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—612no—
615#41—612no—
616#41—1222no—
617#41—1222no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627#41—2441no—
628#41—2442no—
629#41—2442no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—1222no—
633C2×Q8—1221no—
634C2×Q8—2441no—
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—611no—
640C2×D4—611no—
641C2×D4—1222no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4D4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4#1175822411yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—612no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—2442no—
715C2×C8—2442no—
716C2×C8—2442no—
717C2×C8—2442no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D6111yescharacteristic
721C4⋊C4C2×C4×D6111yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D6112yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—1221no—
739C23—1221no—
740C23—4881no—
741C23—2442no—
742C23—2442no—
743C23#1451973711yescharacteristic
744C23#1451973711yescharacteristic
745C23C2×#1175822411yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—612no—
749Q8—1221no—
750Q8—1221no—
751Q8—1221no—
752Q8—2442no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—612no—
760D4—1222no—
761D4—1222no—
762D4—1221no—
763D4—1221no—
764D4—1221no—
765D4—2442no—
766D4—2442no—
767D4—2442no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4#1451973711yescharacteristic
802C2×C4#1451973711yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4#41×D6111yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—41no—
810C8—41no—
811C8—1221no—
812C8—1221no—
813C8—1221no—
814C8—1221no—
815C8—1221no—
816C8—1221no—
817C8—1222no—
818C8—1221no—
819C8—1221no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—1222no—
834C22—4884no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22#1683988112yescomplemented
841C22C2×#1451973711yescharacteristic
842C22#1684039911yescharacteristic
843C22#1684043511yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—1222no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023411yescharacteristic
855C4#1684039611yescharacteristic
856C4#1684040111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4881no—
863C2—2442no—
864C2#2144879911yescharacteristic
865C2C2×#1683988111yescharacteristic
866C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#22886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#16839881C2semidirect
3. #21454546C2semidirect
4. C22×#14519705C2semidirect
5. #21454269C2semidirect
6. #21446709C2semidirect
7. #21446531C2semidirect
8. #21446465C2semidirect
9. #21446144C2semidirect
10. #21446143C2semidirect
11. #21446095C2semidirect
12. #21446023C2semidirect
13. #21445660C2semidirect
14. #21445581C2semidirect
15. C61×#1896C2semidirect
21. C2×#14519784C22semidirect
23. #16839922C4semidirect
24. #16839922C4semidirect
25. #16839917C4semidirect
26. #16839912C4semidirect
27. #16839905C4semidirect
28. #16839905C4semidirect
29. #16839900C4semidirect
30. #16839895C4semidirect
36. C2×#14519712C22semidirect
37. C2×#14519712C22semidirect
38. #16839789C22semidirect
48. #16839729C22semidirect
55. #16839718C22semidirect
56. C2×#14519688C22semidirect
57. C2×#14519688C22semidirect
58. #16839526C22semidirect
59. #16839526C22semidirect
60. #16839517C22semidirect
61. #16839517C22semidirect
64. C2×#104×C61C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#339C22semidirect
68. C61×#339C22semidirect
87. C2×#11758202C2×C4semidirect
88. C2×#11758202C2×C4semidirect
89. C2×#11758200C2×C4semidirect
90. C2×#11758200C2×C4semidirect
91. C2×#11758201C2×C4semidirect
92. C2×#11758201C2×C4semidirect
93. C2×#11758199C2×C4semidirect
94. C2×#11758199C2×C4semidirect
124. #14519705D4semidirect
125. #14519700C2×C4semidirect
126. #14519700C2×C4semidirect
127. #14519700C2×C4semidirect
128. #14519700C2×C4semidirect
129. #14519697C2×C4semidirect
130. #14519697C2×C4semidirect
131. #14519697C2×C4semidirect
132. #14519697C2×C4semidirect
400. C22×C61#444semidirect
432. #1896D61semidirect
479. C2×#104C2×D61semidirect
480. C2×#104C2×D61semidirect
498. #339C2×D61semidirect
499. #339C2×D61semidirect
502. C61#22886semidirect
840. C22#16839881semidirect

Maximal subgroups

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

subgroupindex
#214550352
C2×#168398812
#214545462
C22×#145197052
#214542692
#214467092
#214465312
#214464652
#214461442
#214461432
#214460952
#214460232
#214456602
#214455812
C61×#18962
#2288661