Finite Group Databasebeta

← #29700792

Subgroups — #29700792

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#21455035C211yesmaximal, characteristic
2C2×#16839876C211yesmaximal, characteristic, complemented
3#21454546C211yesmaximal, characteristic, complemented
4C2×#16839780C211yesmaximal, characteristic, complemented
5#21454269C211yesmaximal, characteristic, complemented
6#21446709C211yesmaximal, characteristic, complemented
7#21446524C211yesmaximal, 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#21445585C211yesmaximal, characteristic, complemented
15C61×#1897C211yesmaximal, 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#16839876—24no—
32#16839840—21no—
33#16839834—21no—
34#16839834—21no—
35D4×#92418—21no—
36C2×#14519712C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38#16839789C2211yescharacteristic, complemented
39#16839780—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×C4×#92418C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839526C2211yescharacteristic, complemented
60#16839517C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C61×#525C2211yescharacteristic
63C2×#117×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
88C2×#11758202C2×C411yescharacteristic
89C2×#11758200C2×C411yescharacteristic
90C2×#11758200C2×C411yescharacteristic
91C2×#11758201C2×C411yescharacteristic
92C2×#11758201C2×C411yescharacteristic
93C2×#11758199C2×C411yescharacteristic
94C2×#11758199C2×C411yescharacteristic
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
126#14519700C2×C411yescharacteristic
127#14519700C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519697C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
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—21no—
148#14519688—41no—
149C4×#92418—22no—
150C4×#92418—21no—
151C2×#41×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C2×M16×C61C2311yescharacteristic
154C2×M16×C61C2311yescharacteristic
155#123×C61—21no—
156C22⋊Q8×C61C2×C411yescharacteristic
157C22⋊Q8×C61C2×C411yescharacteristic
158#121×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160#120×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163#117×C61—22no—
164#117×C61—41no—
165#117×C61C2311yescharacteristic
166C2×C4⋊C4×C61—21no—
167C2×C22⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61#4111yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C22×Dic61—21no—
205#11758222—21no—
206#11758222—21no—
207#11758222—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—22no—
212#11758222—22no—
213#11758222—41no—
214#11758222—41no—
215#11758222—42no—
216#11758222—42no—
217#11758222—42no—
218#11758222—42no—
219#11758222C2×D412yes—
220#11758222#4112yes—
221C2×D244—22no—
222C2×D244—21no—
223C2×D244—41no—
224C2×D244C22×C411yescharacteristic
225C2×D244C22×C411yescharacteristic
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122—41no—
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—42no—
246C4⋊C4×C61C22×C411yescharacteristic
247C4⋊C4×C61C22×C411yescharacteristic
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—42no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61C2×D412yes—
259#11758202—22no—
260#11758202—41no—
261#11758201—22no—
262#11758201—41no—
263#11758200—22no—
264#11758200—41no—
265#11758199—22no—
266#11758199—41no—
267#11758194—21no—
268#11758194—21no—
269#11758194—21no—
270#11758194—42no—
271#11758194—42no—
272#11758194C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
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—42no—
284C2×#92418—42no—
285C2×#92418C22×C411yescharacteristic
286C2×#92418C22×C411yescharacteristic
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293#11758189—42no—
294#11758189—42no—
295C8×D61—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61C4×D411yescharacteristic
303C23×C61C4×D411yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—81no—
310Q8×C61—21no—
311Q8×C61—21no—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—42no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—81no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
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—21no—
331C2×C4×C61—22no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61C4×D411yescharacteristic
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C22⋊D61—22no—
348C22⋊D61—22no—
349C22⋊D61—42no—
350C22⋊D61—42no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—42no—
356D244—21no—
357D244—21no—
358D244—21no—
359D244—42no—
360D244C4×D412yes—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—41no—
366C4×D61—41no—
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—42no—
371Dic122C4×D412yes—
372C8×C61—41no—
373C8×C61—41no—
374#92418—21no—
375#92418—21no—
376#92418—21no—
377#92418—21no—
378#92418—21no—
379#92418—21no—
380#92418—22no—
381#92418—21no—
382#92418—21no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C2×C4×D411yescharacteristic
399C22×C61#54611yescharacteristic
400C22×C61#55111yescharacteristic
401C2×D61—22no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—84no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—42no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—81no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—22no—
420Dic61—41no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897D6111yescharacteristic, complemented
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—41no—
439C2×C61—41no—
440C2×C61—81no—
441C2×C61#235811yescharacteristic
442C2×C61#295511yescharacteristic
443C2×C61#295711yescharacteristic
444D61—42no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16—611no—
453#525C2×D6111yescharacteristic
454C2×#117C2×D6111yescharacteristic
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—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108—611no—
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104C2×D6111yescharacteristic, complemented
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—1221no—
486#407C2×D6111yescharacteristic
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339C2×D6111yescharacteristic, complemented
496#339C2×D6111yescharacteristic, complemented
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1222no—
505C2×#41—1222no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41—2441no—
509C2×#41—2441no—
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—1221no—
515C23×C4C22×D6111yescharacteristic
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×D8—611no—
527C2×D8—611no—
528#131—1222no—
529#131—1222no—
530#131—1222no—
531#131—2441no—
532#131—2441no—
533#131—2441no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—1221no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8—1221no—
551C22×C8—1221no—
552#123—21no—
553C22⋊Q8C4×D6111yescharacteristic
554C22⋊Q8C4×D6111yescharacteristic
555#121C4×D6111yescharacteristic
556#121C4×D6111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C22×D6111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D6111yescharacteristic
566C2×C42C22×D6111yescharacteristic
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—22no—
572#104—41no—
573#104—614no—
574#104—1222no—
575#104—1222no—
576#104—1222no—
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—21no—
586C22⋊C8—21no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
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—1221no—
604C4×C8—1222no—
605C24—1221no—
606C24#1175822411yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—612no—
612#41—612no—
613#41—1222no—
614#41—1222no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—2442no—
622#41—2442no—
623#41—2441no—
624#41—2441no—
625#41—2442no—
626#41—2442no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—1222no—
630C2×Q8—1221no—
631C2×Q8—2441no—
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2441no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4#1175822411yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—1222no—
669Q16—2441no—
670SD16—1222no—
671SD16—1222no—
672SD16—2441no—
673SD16—2441no—
674D8—1222no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—612no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16—2442no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—611no—
691C2×C8—611no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2442no—
709C2×C8—2442no—
710C2×C8—2442no—
711C2×C8—2442no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C2×C4×D6111yescharacteristic
716C4⋊C4C2×C4×D6111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42D4×D6112yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2442no—
737C23—2442no—
738C23#1451973711yescharacteristic
739C23#1451973711yescharacteristic
740C23C2×#1175822411yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—612no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—2442no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—612no—
755D4—1222no—
756D4—1222no—
757D4—1221no—
758D4—1221no—
759D4—1221no—
760D4—2442no—
761D4—2442no—
762D4—2442no—
763D4—2441no—
764D4—2441no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
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—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4#1451973711yescharacteristic
796C2×C4#1451973711yescharacteristic
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4#41×D6111yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—41no—
804C8—41no—
805C8—1221no—
806C8—1221no—
807C8—1221no—
808C8—1221no—
809C8—1221no—
810C8—1221no—
811C8—1222no—
812C8—1221no—
813C8—1221no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—1222no—
829C22—4884no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×#1451973711yescharacteristic
836C22#1684039911yescharacteristic
837C22#1684043511yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C4—1222no—
846C4—2441no—
847C4C4×D4×D6111yescharacteristic
848C4#1684023411yescharacteristic
849C4#1684039611yescharacteristic
850C4#1684040111yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—4881no—
857C2—2442no—
858C2#2144879911yescharacteristic
859C2#2145471811yescharacteristic
860C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1897C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#1897D61
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. C2×#16839876C2semidirect
3. #21454546C2semidirect
4. C2×#16839780C2semidirect
5. #21454269C2semidirect
6. #21446709C2semidirect
7. #21446524C2semidirect
8. #21446465C2semidirect
9. #21446144C2semidirect
10. #21446143C2semidirect
11. #21446095C2semidirect
12. #21446023C2semidirect
13. #21445660C2semidirect
14. #21445585C2semidirect
15. C61×#1897C2semidirect
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×C4×#92418C22semidirect
58. #16839526C22semidirect
59. #16839526C22semidirect
60. #16839517C22semidirect
61. #16839517C22semidirect
64. C2×#104×C61C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#339C22semidirect
68. C61×#339C22semidirect
124. #14519705D4semidirect
429. #1897D61semidirect
476. C2×#104C2×D61semidirect
477. C2×#104C2×D61semidirect
495. #339C2×D61semidirect
496. #339C2×D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550352
C2×#168398762
#214545462
C2×#168397802
#214542692
#214467092
#214465242
#214464652
#214461442
#214461432
#214460952
#214460232
#214456602
#214455852
C61×#18972
#2288961