Finite Group Databasebeta

← #29700758

Subgroups — #29700758

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#21455041C211yesmaximal, characteristic
2C2×#16839883C211yesmaximal, characteristic, complemented
3#21454544C211yesmaximal, characteristic, complemented
4C2×#16839778C211yesmaximal, characteristic, complemented
5#21454269C211yesmaximal, characteristic, complemented
6#21446705C211yesmaximal, characteristic, complemented
7#21446528C211yesmaximal, characteristic, complemented
8#21446466C211yesmaximal, characteristic, complemented
9#21446265C211yesmaximal, characteristic, complemented
10#21446147C211yesmaximal, characteristic, complemented
11#21446147C211yesmaximal, characteristic, complemented
12#21446091C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519799C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519785C2211yescharacteristic
21C2×#14519785C2211yescharacteristic, complemented
22#16840273C2211yescharacteristic
23C2×#14519736C2211yescharacteristic
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#16839883—24no—
33#16839838—21no—
34#16839833—21no—
35#16839831—21no—
36C8×C22⋊D61—21no—
37#16839790C2211yescharacteristic, complemented
38#16839778—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×#14519687C2211yescharacteristic, 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—
83C22×C4×D61—21no—
84#14519799—22no—
85#14519799—22no—
86#14519799—41no—
87#14519799—41no—
88C2×Dic244C2×C411yescharacteristic
89C2×Dic244C2×C411yescharacteristic
90C2×#11758190C2×C411yescharacteristic
91C2×#11758190C2×C411yescharacteristic
92C2×#11758190C2×C411yescharacteristic
93C2×#11758190C2×C411yescharacteristic
94C2×D488C2×C411yescharacteristic
95C2×D488C2×C411yescharacteristic
96#14519785—22no—
97#14519785—22no—
98#14519785—22no—
99#14519785—41no—
100#14519785—41no—
101#14519785—41no—
102C2×#11758189—21no—
103C2×#11758189—21no—
104C2×#11758189—21no—
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107C2×C8×D61—21no—
108C2×C8×D61—21no—
109C2×C8×D61—21no—
110#14519760—21no—
111#14519756C2×C411yescharacteristic
112#14519756C2×C411yescharacteristic
113#14519751C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115#14519746—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118#14519736—22no—
119#14519736—41no—
120#14519736C2311yescharacteristic
121C2×C4⋊Dic61—21no—
122C2×C22⋊Dic61—21no—
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
134#14519702C2×C411yescharacteristic
135#14519702C2×C411yescharacteristic
136#14519702C2×C411yescharacteristic
137#14519699C2×C411yescharacteristic
138#14519699C2×C411yescharacteristic
139#14519699C2×C411yescharacteristic
140#14519699C2×C411yescharacteristic
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—22no—
152#14519687—21no—
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—21no—
197C22×Dic61—21no—
198#11758222—21no—
199#11758222—21no—
200#11758222—21no—
201#11758222—21no—
202#11758222—21no—
203#11758222—21no—
204#11758222—21no—
205#11758222—21no—
206#11758222—21no—
207#11758222—21no—
208#11758222—22no—
209#11758222—22no—
210#11758222—41no—
211#11758222—41no—
212#11758222—42no—
213#11758222—42no—
214#11758222—42no—
215#11758222—42no—
216#11758222C2×D412yes—
217#11758222#4112yes—
218C2×D244—22no—
219C2×D244—21no—
220C2×D244—41no—
221C2×D244C22×C411yescharacteristic
222C2×D244C22×C411yescharacteristic
223C2×D244C22×C411yescharacteristic
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×Dic122—22no—
232C2×Dic122—21no—
233C2×Dic122—41no—
234C2×Dic122C22×C411yescharacteristic
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—42no—
245M16×C61C2×D412yes—
246C2×C8×C61—21no—
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—21no—
254C2×C8×C61—42no—
255C2×C8×C61C22×C411yescharacteristic
256C2×C8×C61C22×C411yescharacteristic
257C2×C8×C61C22×C411yescharacteristic
258C2×C8×C61C22×C411yescharacteristic
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—42no—
263#11758198—21no—
264#11758198—21no—
265C4⋊Dic61—42no—
266C4⋊Dic61C22×C411yescharacteristic
267C4⋊Dic61C22×C411yescharacteristic
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61C2×D412yes—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D411yescharacteristic
280C2×#92418C2×D411yescharacteristic
281C2×#92418C2×D411yescharacteristic
282C2×#92418C2×D411yescharacteristic
283Dic244—22no—
284Dic244—41no—
285D488—22no—
286D488—41no—
287#11758190—22no—
288#11758190—22no—
289#11758190—41no—
290#11758190—41no—
291#11758189—42no—
292#11758189—42no—
293#11758189—42no—
294C8×D61—42no—
295C8×D61—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61C4×D411yescharacteristic
302C23×C61C4×D411yescharacteristic
303C23×C61C2×#4111yescharacteristic
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—81no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
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×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C22⋊D61—22no—
329C22⋊D61—22no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C22⋊D61—42no—
333C22⋊D61—41no—
334C22⋊D61—41no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—81no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—42no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350D244—21no—
351D244—21no—
352D244—21no—
353D244—21no—
354D244—21no—
355D244—42no—
356D244C4×D412yes—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365Dic122—21no—
366Dic122—21no—
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—42no—
371Dic122C4×D412yes—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—21no—
376C8×C61—22no—
377C8×C61—41no—
378C8×C61—41no—
379C8×C61—41no—
380#92418—21no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#22887—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—81no—
394C22×C61—81no—
395C22×C61C2×C4×D411yescharacteristic
396C22×C61#54611yescharacteristic
397C22×C61#55111yescharacteristic
398C2×D61—22no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
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×C61C2×C4×D411yescharacteristic
411C4×C61#51811yescharacteristic
412C4×C61D4211yescharacteristic
413C4×C61#54611yescharacteristic
414Dic61—22no—
415Dic61—42no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#444—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1974—611no—
427#1938—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855D6111yescharacteristic, complemented
434#1764—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61#235811yescharacteristic
441C2×C61#295511yescharacteristic
442C2×C61#295711yescharacteristic
443D61—42no—
444D61—81no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16C2×D6111yescharacteristic
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#444—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108C2×D6111yescharacteristic, complemented
469C2×#108C2×D6111yescharacteristic, complemented
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
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—1221no—
489C2×C22⋊C8C2×D6111yescharacteristic
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341C2×D6111yescharacteristic, complemented
494#341C2×D6111yescharacteristic, complemented
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288711yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—1221no—
508C2×#41—1221no—
509C2×#41—2441no—
510C2×#41—2441no—
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—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16C22×D6111yescharacteristic
541C2×M16C22×D6111yescharacteristic
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1221no—
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×C42—611no—
567#108—22no—
568#108—41no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—614no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
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—1221no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8C4×D6111yescharacteristic
598C22⋊C8C4×D6111yescharacteristic
599C22⋊C8C4×D6111yescharacteristic
600C22⋊C8C4×D6111yescharacteristic
601#97—1222no—
602#97—1221no—
603C4×C8—1221no—
604C4×C8—2441no—
605C24—1221no—
606C24#1175822611yescharacteristic
607#41—612no—
608#41—612no—
609#41—1222no—
610#41—1222no—
611#41—1221no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
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—611no—
630C2×Q8—1222no—
631C2×Q8—1221no—
632C2×Q8—2441no—
633C2×D4—611no—
634C2×D4—611no—
635C2×D4—611no—
636C2×D4—1222no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—2441no—
646C2×D4—2442no—
647C2×D4—2442no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
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#1175822611yescharacteristic
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—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16D4×D6112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—2442no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C4×D6111yescharacteristic
709C2×C8C2×C4×D6111yescharacteristic
710C2×C8C2×C4×D6111yescharacteristic
711C2×C8C2×C4×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—612no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2442no—
737C23—2442no—
738C23#1451973911yescharacteristic
739C23#1451973911yescharacteristic
740C23C2×#1175822611yescharacteristic
741Q8—612no—
742Q8—1221no—
743Q8—1221no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—2442no—
748D4—612no—
749D4—1222no—
750D4—1222no—
751D4—1221no—
752D4—1221no—
753D4—1221no—
754D4—1221no—
755D4—1221no—
756D4—4881no—
757D4—2442no—
758D4—2442no—
759D4—2442no—
760D4—2442no—
761D4—2441no—
762D4—2441no—
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—1221no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1222no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4#1451973911yescharacteristic
796C2×C4#1451973911yescharacteristic
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4#41×D6111yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—1221no—
812C8—1221no—
813C8—1221no—
814C8—1221no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—81no—
824C22—81no—
825C22—1222no—
826C22—4884no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×#1451973911yescharacteristic
836C22#1684040311yescharacteristic
837C22#1684043911yescharacteristic
838C4—21no—
839C4—21no—
840C4—1222no—
841C4—4881no—
842C4—2442no—
843C4—2441no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4C4×D4×D6111yescharacteristic
848C4#1684023411yescharacteristic
849C4#1684039411yescharacteristic
850C4#1684040411yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—4881no—
856C2—4881no—
857C2—2442no—
858C2#2144879511yescharacteristic
859C2#2145472111yescharacteristic
860C2#2145473511yescharacteristic
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#22887
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×#16839883C2semidirect
3. #21454544C2semidirect
4. C2×#16839778C2semidirect
5. #21454269C2semidirect
6. #21446705C2semidirect
7. #21446528C2semidirect
8. #21446466C2semidirect
9. #21446265C2semidirect
10. #21446147C2semidirect
11. #21446147C2semidirect
12. #21446091C2semidirect
13. #21445655C2semidirect
14. #21445587C2semidirect
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×#14519687C22semidirect
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
132. #14519703D4semidirect
433. #1855D61semidirect
468. C2×#108C2×D61semidirect
469. C2×#108C2×D61semidirect
493. #341C2×D61semidirect
494. #341C2×D61semidirect
499. C61#22887semidirect

Maximal subgroups

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

subgroupindex
#214550412
C2×#168398832
#214545442
C2×#168397782
#214542692
#214467052
#214465282
#214464662
#214462652
#214461472
#214460912
#214456552
#214455872
C61×#18552
#2288761