Finite Group Databasebeta

← #29700773

Subgroups — #29700773

Order 15616.

1070 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#21455041C211yesmaximal, characteristic
2C2×#16839878C211yesmaximal, characteristic, complemented
3#21454544C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5#21454269C211yesmaximal, characteristic, complemented
6#21446705C211yesmaximal, characteristic, complemented
7#21446521C211yesmaximal, characteristic, complemented
8#21446466C211yesmaximal, characteristic, complemented
9#21446260C211yesmaximal, characteristic, complemented
10#21446147C211yesmaximal, characteristic, complemented
11#21446147C211yesmaximal, characteristic, complemented
12#21446091C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519799C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519785C2211yescharacteristic
21C2×#14519785C2211yescharacteristic, complemented
22#16840273C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24#16839926C411yescharacteristic, complemented
25#16839926C411yescharacteristic, complemented
26#16839920C411yescharacteristic, complemented
27#16839915C411yescharacteristic, complemented
28#16839909C411yescharacteristic, complemented
29#16839909C411yescharacteristic, complemented
30#16839903C411yescharacteristic, complemented
31#16839898C411yescharacteristic, complemented
32#16839878—24no—
33#16839838—21no—
34#16839833—21no—
35#16839831—21no—
36C8×C22⋊D61—21no—
37#16839790C2211yescharacteristic, complemented
38C2×#14519703—24no—
39C2×#14519703C2211yescharacteristic
40C2×#14519703C2211yescharacteristic
41C2×#14519703C2211yescharacteristic
42C2×#14519703C2211yescharacteristic
43C2×#14519703C2211yescharacteristic, complemented
44C2×#14519703C2211yescharacteristic, complemented
45#16839759C2211yescharacteristic
46#16839759C2211yescharacteristic
47#16839730C2211yescharacteristic
48#16839730C2211yescharacteristic
49#16839730C2211yescharacteristic, complemented
50#16839727—21no—
51#16839727—21no—
52#16839724—21no—
53C2×C22⋊#92418C2211yescharacteristic
54C22⋊C8×D61—21no—
55#16839720C2211yescharacteristic, complemented
56C2×C8×Dic61C2211yescharacteristic, complemented
57C2×C8×Dic61C2211yescharacteristic, complemented
58#16839523C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C22×M16×C61C2211yescharacteristic
63C2×#108×C61C2211yescharacteristic, complemented
64C2×#108×C61C2211yescharacteristic, complemented
65C61×#407C2211yescharacteristic
66C2×C22⋊C8×C61C2211yescharacteristic
67C61×#341C2211yescharacteristic, complemented
68C61×#341C2211yescharacteristic, 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
79C2×#11758222C2311yescharacteristic
80C22×Dic122C2×C411yescharacteristic
81C22×D244C2×C411yescharacteristic
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85#14519799—22no—
86#14519799—22no—
87#14519799—41no—
88#14519799—41no—
89C2×Dic244C2×C411yescharacteristic, complemented
90C2×Dic244C2×C411yescharacteristic, complemented
91C2×#11758190C2×C411yescharacteristic, complemented
92C2×#11758190C2×C411yescharacteristic, complemented
93C2×#11758190C2×C411yescharacteristic, complemented
94C2×#11758190C2×C411yescharacteristic, complemented
95C2×D488C2×C411yescharacteristic, complemented
96C2×D488C2×C411yescharacteristic, complemented
97#14519785—22no—
98#14519785—22no—
99#14519785—22no—
100#14519785—41no—
101#14519785—41no—
102#14519785—41no—
103C2×#11758189—21no—
104C2×#11758189—21no—
105C2×#11758189—21no—
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108C2×C8×D61—21no—
109C2×C8×D61—21no—
110C2×C8×D61—21no—
111#14519760—21no—
112#14519756C2×C411yescharacteristic
113#14519756C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115#14519751C2×C411yescharacteristic
116#14519746—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519736C2311yescharacteristic
120C2×C4×Dic61—22no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—41no—
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125#14519706—21no—
126#14519706—21no—
127#14519703—22no—
128#14519703—22no—
129#14519703—22no—
130#14519703—22no—
131#14519703—41no—
132#14519703D414yescomplemented
133#14519702C2×C411yescharacteristic, complemented
134#14519702C2×C411yescharacteristic, complemented
135#14519702C2×C411yescharacteristic, complemented
136#14519702C2×C411yescharacteristic, complemented
137#14519699C2×C411yescharacteristic, complemented
138#14519699C2×C411yescharacteristic, complemented
139#14519699C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic, complemented
141C22⋊#92418D411yescharacteristic
142C22⋊#92418D411yescharacteristic
143C22⋊#92418D411yescharacteristic
144C22⋊#92418D411yescharacteristic
145#14519689—21no—
146#14519689—21no—
147#14519689—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519687—21no—
152C8×Dic61—22no—
153C8×Dic61—21no—
154C8×Dic61—41no—
155C23×C4×C61C2311yescharacteristic
156C2×M16×C61—21no—
157C2×M16×C61—22no—
158C2×M16×C61—41no—
159C2×M16×C61C2311yescharacteristic
160C2×M16×C61C2311yescharacteristic
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C22×C8×C61—21no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#108×C61—22no—
167#108×C61—41no—
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61C2×C411yescharacteristic
171C22⋊C8×C61C2×C411yescharacteristic
172C22⋊C8×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic
174C24×C61#4111yescharacteristic
175C23×D61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C22×Dic61—21no—
196C22×Dic61—24no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—42no—
200C22×Dic61—42no—
201#11758222—21no—
202#11758222—21no—
203#11758222—21no—
204#11758222—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×D244C22×C411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×Dic122—22no—
235C2×Dic122—21no—
236C2×Dic122—41no—
237C2×Dic122C22×C411yescharacteristic
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—21no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—42no—
248M16×C61C2×D412yes—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—42no—
258C2×C8×C61C22×C411yescharacteristic
259C2×C8×C61C22×C411yescharacteristic
260C2×C8×C61C22×C411yescharacteristic
261C2×C8×C61C22×C411yescharacteristic
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758198—21no—
266#11758198—21no—
267C4⋊Dic61C22×C411yescharacteristic
268C4⋊Dic61C22×C411yescharacteristic
269#11758196—21no—
270#11758196—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—42no—
276C4×Dic61C2×D412yes—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418C2×D411yescharacteristic
282C2×#92418C2×D411yescharacteristic
283C2×#92418C2×D411yescharacteristic
284C2×#92418C2×D411yescharacteristic
285Dic244—22no—
286Dic244—41no—
287D488—22no—
288D488—41no—
289#11758190—22no—
290#11758190—22no—
291#11758190—41no—
292#11758190—41no—
293#11758189—42no—
294#11758189—42no—
295#11758189—42no—
296C8×D61—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—41no—
303C23×C61C4×D411yescharacteristic
304C23×C61C4×D411yescharacteristic
305C23×C61C2×#4111yescharacteristic
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—81no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C22⋊D61—22no—
331C22⋊D61—22no—
332C22⋊D61—42no—
333C22⋊D61—42no—
334C22⋊D61—41no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C22⋊D61—42no—
339C22⋊D61—81no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61—48no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353D244—21no—
354D244—21no—
355D244—21no—
356D244—21no—
357D244—21no—
358D244—42no—
359D244C4×D412yes—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—42no—
363C4×D61—42no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368Dic122—21no—
369Dic122—21no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—21no—
378C8×C61—21no—
379C8×C61—22no—
380C8×C61—41no—
381C8×C61—41no—
382C8×C61—41no—
383#92418—21no—
384#92418—21no—
385#92418—21no—
386#92418—21no—
387#22888—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#44312yescomplemented
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—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—84no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61C2×C4×D411yescharacteristic
414C4×C61#51811yescharacteristic
415C4×C61D4211yescharacteristic
416C4×C61#54611yescharacteristic
417Dic61—24no—
418Dic61—22no—
419Dic61—42no—
420Dic61—41no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1974—611no—
430#1937—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855D6111yescharacteristic, complemented
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61#235811yescharacteristic
444C2×C61C2×#44311yescharacteristic
445C2×C61#295611yescharacteristic
446D61—42no—
447D61—81no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16C2×D6111yescharacteristic
456#525—611no—
457C22×C42—611no—
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#443—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108C2×D6111yescharacteristic, complemented
472C2×#108C2×D6111yescharacteristic, complemented
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—611no—
480C2×#104—1224no—
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—1221no—
492C2×C22⋊C8C2×D6111yescharacteristic
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8—611no—
496#341C2×D6111yescharacteristic, complemented
497#341C2×D6111yescharacteristic, complemented
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—611no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1221no—
511C2×#41—1221no—
512C2×#41—2441no—
513C2×#41—2441no—
514C22×Q8—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C23×C4—1221no—
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—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16C22×D6111yescharacteristic
545C2×M16C22×D6111yescharacteristic
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—1221no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8C22×D6111yescharacteristic
555C22×C8C22×D6111yescharacteristic
556#123—1221no—
557C22⋊Q8—611no—
558C22⋊Q8—611no—
559#121—611no—
560#121—611no—
561#120—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569C2×C42—2441no—
570#108—22no—
571#108—41no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—614no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
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—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8C4×D6111yescharacteristic
601C22⋊C8C4×D6111yescharacteristic
602C22⋊C8C4×D6111yescharacteristic
603C22⋊C8C4×D6111yescharacteristic
604#97—1221no—
605C4×C8—1222no—
606C4×C8—1221no—
607C4×C8—2441no—
608C24—1221no—
609C24#1175822611yescharacteristic
610#41—612no—
611#41—612no—
612#41—1222no—
613#41—1222no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
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—611no—
633C2×Q8—1222no—
634C2×Q8—1221no—
635C2×Q8—2441no—
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—1222no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—2441no—
649C2×D4—2442no—
650C2×D4—2442no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—2442no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4D4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4#1175822611yescharacteristic
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—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16D4×D6112yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—611no—
706C2×C8—611no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C4×D6111yescharacteristic
715C2×C8C2×C4×D6111yescharacteristic
716C2×C8C2×C4×D6111yescharacteristic
717C2×C8C2×C4×D6111yescharacteristic
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C42—612no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—4881no—
741C23—2442no—
742C23—2442no—
743C23#1451973911yescharacteristic
744C23#1451973911yescharacteristic
745C23C2×#1175822611yescharacteristic
746Q8—612no—
747Q8—1221no—
748Q8—1221no—
749Q8—1221no—
750Q8—1221no—
751Q8—1221no—
752Q8—2442no—
753D4—612no—
754D4—1222no—
755D4—1222no—
756D4—1221no—
757D4—1221no—
758D4—1221no—
759D4—1221no—
760D4—1221no—
761D4—4881no—
762D4—2442no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766D4—2441no—
767D4—2441no—
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—1222no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2448no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4#1451973911yescharacteristic
802C2×C4#1451973911yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4#41×D6111yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—1221no—
818C8—1221no—
819C8—1221no—
820C8—1221no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—1222no—
831C22—4884no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22#1683987812yescomplemented
841C22C2×#1451973911yescharacteristic
842C22#1684040311yescharacteristic
843C22#1684043911yescharacteristic
844C4—21no—
845C4—21no—
846C4—1224no—
847C4—1222no—
848C4—2442no—
849C4—2441no—
850C4—2441no—
851C4—2441no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023411yescharacteristic
855C4#1684039411yescharacteristic
856C4#1684040411yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—4881no—
862C2—4881no—
863C2—2442no—
864C2#2144879511yescharacteristic
865C2C2×#1683987811yescharacteristic
866C2#2145472811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1855C2
socleC22×C61C2×C4×D4
prime radical#21455041C2
cosocleC22×C4×C61C24
hypercenter#1855D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
2. C2×#16839878C2semidirect
3. #21454544C2semidirect
4. C22×#14519703C2semidirect
5. #21454269C2semidirect
6. #21446705C2semidirect
7. #21446521C2semidirect
8. #21446466C2semidirect
9. #21446260C2semidirect
10. #21446147C2semidirect
11. #21446147C2semidirect
12. #21446091C2semidirect
13. #21445655C2semidirect
14. C22⋊C8×Dic61C2semidirect
15. C61×#1855C2semidirect
21. C2×#14519785C22semidirect
24. #16839926C4semidirect
25. #16839926C4semidirect
26. #16839920C4semidirect
27. #16839915C4semidirect
28. #16839909C4semidirect
29. #16839909C4semidirect
30. #16839903C4semidirect
31. #16839898C4semidirect
37. #16839790C22semidirect
43. C2×#14519703C22semidirect
44. C2×#14519703C22semidirect
49. #16839730C22semidirect
55. #16839720C22semidirect
56. C2×C8×Dic61C22semidirect
57. C2×C8×Dic61C22semidirect
58. #16839523C22semidirect
59. #16839523C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
63. C2×#108×C61C22semidirect
64. C2×#108×C61C22semidirect
67. C61×#341C22semidirect
68. C61×#341C22semidirect
89. C2×Dic244C2×C4semidirect
90. C2×Dic244C2×C4semidirect
91. C2×#11758190C2×C4semidirect
92. C2×#11758190C2×C4semidirect
93. C2×#11758190C2×C4semidirect
94. C2×#11758190C2×C4semidirect
95. C2×D488C2×C4semidirect
96. C2×D488C2×C4semidirect
132. #14519703D4semidirect
133. #14519702C2×C4semidirect
134. #14519702C2×C4semidirect
135. #14519702C2×C4semidirect
136. #14519702C2×C4semidirect
137. #14519699C2×C4semidirect
138. #14519699C2×C4semidirect
139. #14519699C2×C4semidirect
140. #14519699C2×C4semidirect
397. C22×C61#443semidirect
436. #1855D61semidirect
471. C2×#108C2×D61semidirect
472. C2×#108C2×D61semidirect
496. #341C2×D61semidirect
497. #341C2×D61semidirect
502. C61#22888semidirect
840. C22#16839878semidirect

Maximal subgroups

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

subgroupindex
#214550412
C2×#168398782
#214545442
C22×#145197032
#214542692
#214467052
#214465212
#214464662
#214462602
#214461472
#214460912
#214456552
C22⋊C8×Dic612
C61×#18552
#2288861