Finite Group Databasebeta

← #29700785

Subgroups — #29700785

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×#16839880C211yesmaximal, characteristic, complemented
3#21454540C211yesmaximal, characteristic, complemented
4C22×#14519705C211yesmaximal, characteristic, complemented
5#21454265C211yesmaximal, characteristic, complemented
6#21446707C211yesmaximal, characteristic, complemented
7#21446523C211yesmaximal, characteristic, complemented
8#21446468C211yesmaximal, characteristic, complemented
9#21446262C211yesmaximal, characteristic, complemented
10#21446145C211yesmaximal, characteristic, complemented
11#21446145C211yesmaximal, characteristic, complemented
12#21446097C211yesmaximal, characteristic, complemented
13#21446026C211yesmaximal, characteristic, complemented
14#21445656C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519799C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×#14519783C2211yescharacteristic
21C2×#14519783C2211yescharacteristic, complemented
22C22×#11758194C2211yescharacteristic
23#16840273C2211yescharacteristic
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#16839880—24no—
33#16839837—21no—
34#16839836—21no—
35#16839830—21no—
36#16839825—21no—
37C2×#14519713C2211yescharacteristic, complemented
38C2×#14519713C2211yescharacteristic, complemented
39#16839788C2211yescharacteristic, complemented
40C2×#14519705—24no—
41C2×#14519705C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519705C2211yescharacteristic
44C2×#14519705C2211yescharacteristic
45C2×#14519705C2211yescharacteristic, complemented
46C2×#14519705C2211yescharacteristic, complemented
47#16839759C2211yescharacteristic
48#16839759C2211yescharacteristic
49#16839728C2211yescharacteristic
50#16839728C2211yescharacteristic
51#16839728C2211yescharacteristic, complemented
52#16839727—21no—
53#16839727—21no—
54#16839726C2211yescharacteristic
55#16839724—21no—
56C22⋊C8×D61—21no—
57#16839717C2211yescharacteristic, complemented
58#16839527C2211yescharacteristic, complemented
59#16839527C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61#16839522C2211yescharacteristic, complemented
62C22×C42×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C2×C22⋊C8×C61C2211yescharacteristic
65C2×C4×C8×C61C2211yescharacteristic, complemented
66C2×C4×C8×C61C2211yescharacteristic, complemented
67C61×#336C2211yescharacteristic, complemented
68C61×#336C2211yescharacteristic, 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, complemented
89C2×Dic244C2×C411yescharacteristic, complemented
90C2×#11758190C2×C411yescharacteristic, complemented
91C2×#11758190C2×C411yescharacteristic, complemented
92C2×#11758190C2×C411yescharacteristic, complemented
93C2×#11758190C2×C411yescharacteristic, complemented
94C2×D488C2×C411yescharacteristic, complemented
95C2×D488C2×C411yescharacteristic, complemented
96#14519783—22no—
97#14519783—22no—
98#14519783—22no—
99#14519783—41no—
100#14519783—41no—
101#14519783—41no—
102C2×#11758194—21no—
103C2×#11758194—22no—
104C2×#11758194—41no—
105C2×#11758194C2311yescharacteristic
106C2×#11758194C2311yescharacteristic
107C2×#11758194C2311yescharacteristic
108C2×#11758194C2311yescharacteristic
109C2×#11758189—21no—
110C2×#11758189—21no—
111C2×#11758189—21no—
112C22×#92418—21no—
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115C2×C8×D61—21no—
116#14519760—21no—
117#14519756C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic
119#14519751C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519746—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124#14519736C2311yescharacteristic
125#14519713—22no—
126#14519713—41no—
127#14519706—21no—
128#14519706—21no—
129#14519705—22no—
130#14519705—22no—
131#14519705—22no—
132#14519705—22no—
133#14519705—41no—
134#14519705D414yescomplemented
135#14519702C2×C411yescharacteristic, complemented
136#14519702C2×C411yescharacteristic, complemented
137#14519702C2×C411yescharacteristic, complemented
138#14519702C2×C411yescharacteristic, complemented
139#14519699C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic, complemented
142#14519699C2×C411yescharacteristic, complemented
143C22⋊#92418—21no—
144C22⋊#92418—21no—
145#14519689—21no—
146#14519689—21no—
147#14519689—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519687—21no—
152C8×Dic61—21no—
153C23×C4×C61—21no—
154C23×C4×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C22×C8×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C2×C42×C61—22no—
160C2×C42×C61—21no—
161C2×C42×C61—41no—
162C2×C42×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164C22⋊C8×C61C2×C411yescharacteristic
165C22⋊C8×C61C2×C411yescharacteristic
166C22⋊C8×C61C2×C411yescharacteristic
167C22⋊C8×C61C2×C411yescharacteristic
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172C4×C8×C61—22no—
173C4×C8×C61—41no—
174C24×C61#4111yescharacteristic
175C23×D61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61#4111yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C22×Dic61—21no—
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
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61C22×C411yescharacteristic
249C2×C8×C61C22×C411yescharacteristic
250C2×C8×C61C22×C411yescharacteristic
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61—42no—
260C42×C61C2×D412yes—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758198—21no—
265#11758198—21no—
266C4⋊Dic61C22×C411yescharacteristic
267C4⋊Dic61C22×C411yescharacteristic
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—42no—
279#11758194C2×D412yes—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—42no—
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—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
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×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—48no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61C4×D411yescharacteristic
330C2×C4×C61C4×D411yescharacteristic
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—22no—
338C22⋊D61—22no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C22⋊D61—41no—
345C22⋊D61—42no—
346C22⋊D61—81no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—42no—
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—21no—
380C8×C61—21no—
381C8×C61—21no—
382C8×C61—21no—
383#92418—22no—
384#92418—41no—
385#92418—41no—
386#92418—41no—
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—24no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—42no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—22no—
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#1855—611no—
437#1764—611no—
438C4×C22⋊C8D6111yescharacteristic, complemented
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×M16—611no—
456#525—611no—
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#443—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—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—611no—
489#407—1221no—
490C2×C22⋊C8—1221no—
491C2×C22⋊C8C2×D6111yescharacteristic
492C2×C22⋊C8C2×D6111yescharacteristic
493#405—611no—
494C2×C4×C8C2×D6111yescharacteristic, complemented
495C2×C4×C8C2×D6111yescharacteristic, complemented
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336C2×D6111yescharacteristic, complemented
501#336C2×D6111yescharacteristic, complemented
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—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—611no—
541C2×M16—611no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16—1222no—
547C2×M16—2441no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8—1221no—
551C22×C8—1221no—
552C22×C8C22×D6111yescharacteristic
553C22×C8C22×D6111yescharacteristic
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—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—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—1221no—
589C22⋊C8—1221no—
590C22⋊C8—1221no—
591C22⋊C8—1221no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8C4×D6111yescharacteristic
597C22⋊C8C4×D6111yescharacteristic
598C22⋊C8C4×D6111yescharacteristic
599C22⋊C8C4×D6111yescharacteristic
600C22⋊C8D24411yescharacteristic
601C22⋊C8D24411yescharacteristic
602C22⋊C8D24411yescharacteristic
603C22⋊C8D24411yescharacteristic
604#97—1221no—
605C4×C8—22no—
606C4×C8—41no—
607C4×C8—1221no—
608C24—1221no—
609C24#1175822211yescharacteristic
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—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1221no—
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×C4C2×D24411yescharacteristic
671C22×C4C2×D24411yescharacteristic
672C22×C4#1175822211yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—612no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
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—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8—2442no—
709C2×C8—2442no—
710C2×C8C2×C4×D6111yescharacteristic
711C2×C8C2×C4×D6111yescharacteristic
712C2×C8C2×C4×D6111yescharacteristic
713C2×C8C2×C4×D6111yescharacteristic
714C2×C8C2×D24411yescharacteristic
715C2×C8C2×D24411yescharacteristic
716C2×C8C2×D24411yescharacteristic
717C2×C8C2×D24411yescharacteristic
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—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1221no—
732C42D4×D6112yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—4881no—
741C23—2442no—
742C23—2442no—
743C23C4×D24411yescharacteristic
744C23C4×D24411yescharacteristic
745C23C2×#1175822211yescharacteristic
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—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C4×D24411yescharacteristic
802C2×C4C4×D24411yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×D24411yescharacteristic
806C2×C4#41×D6111yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—1222no—
818C8—2441no—
819C8—2441no—
820C8—2441no—
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#1683988012yescomplemented
841C22C2×C4×D24411yescharacteristic
842C22#1684040211yescharacteristic
843C22#1684043611yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—1222no—
849C4—2441no—
850C4—2441no—
851C4—2441no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023411yescharacteristic
855C4D4×D24411yescharacteristic
856C4#1684040711yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—4881no—
862C2—4881no—
863C2—2442no—
864C2#2144880111yescharacteristic
865C2C2×#1683988011yescharacteristic
866C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×C22⋊C8×C61C2
socleC22×C61C2×C4×D4
prime radical#21455041C2
cosocleC22×C4×C61C24
hypercenterC4×C22⋊C8D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16839880C2semidirect
3. #21454540C2semidirect
4. C22×#14519705C2semidirect
5. #21454265C2semidirect
6. #21446707C2semidirect
7. #21446523C2semidirect
8. #21446468C2semidirect
9. #21446262C2semidirect
10. #21446145C2semidirect
11. #21446145C2semidirect
12. #21446097C2semidirect
13. #21446026C2semidirect
14. #21445656C2semidirect
15. C4×C22⋊C8×C61C2semidirect
21. C2×#14519783C22semidirect
24. #16839926C4semidirect
25. #16839926C4semidirect
26. #16839920C4semidirect
27. #16839915C4semidirect
28. #16839909C4semidirect
29. #16839909C4semidirect
30. #16839903C4semidirect
31. #16839898C4semidirect
37. C2×#14519713C22semidirect
38. C2×#14519713C22semidirect
39. #16839788C22semidirect
45. C2×#14519705C22semidirect
46. C2×#14519705C22semidirect
51. #16839728C22semidirect
57. #16839717C22semidirect
58. #16839527C22semidirect
59. #16839527C22semidirect
60. #16839522C22semidirect
61. #16839522C22semidirect
65. C2×C4×C8×C61C22semidirect
66. C2×C4×C8×C61C22semidirect
67. C61×#336C22semidirect
68. C61×#336C22semidirect
88. C2×Dic244C2×C4semidirect
89. C2×Dic244C2×C4semidirect
90. C2×#11758190C2×C4semidirect
91. C2×#11758190C2×C4semidirect
92. C2×#11758190C2×C4semidirect
93. C2×#11758190C2×C4semidirect
94. C2×D488C2×C4semidirect
95. C2×D488C2×C4semidirect
134. #14519705D4semidirect
135. #14519702C2×C4semidirect
136. #14519702C2×C4semidirect
137. #14519702C2×C4semidirect
138. #14519702C2×C4semidirect
139. #14519699C2×C4semidirect
140. #14519699C2×C4semidirect
141. #14519699C2×C4semidirect
142. #14519699C2×C4semidirect
397. C22×C61#443semidirect
438. C4×C22⋊C8D61semidirect
494. C2×C4×C8C2×D61semidirect
495. C2×C4×C8C2×D61semidirect
500. #336C2×D61semidirect
501. #336C2×D61semidirect
502. C61#22888semidirect
840. C22#16839880semidirect

Maximal subgroups

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

subgroupindex
#214550412
C2×#168398802
#214545402
C22×#145197052
#214542652
#214467072
#214465232
#214464682
#214462622
#214461452
#214460972
#214460262
#214456562
C4×C22⋊C8×C612
#2288861