Finite Group Databasebeta

← C2×#21461584 #30614114

Subgroups — C2×#21461584 #30614114

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#6923C211yesmaximal, characteristic
2C2×D61⋊#104C211yesmaximal, characteristic
3C2×M16×#6923C211yesmaximal, characteristic, complemented
4C2×#16840698C211yesmaximal, characteristic, complemented
5#21461584C218yesmaximal, direct product factor
6C2×#16840634C211yesmaximal, characteristic, complemented
7C2×#16840633C211yesmaximal, characteristic, complemented
8C2×#104×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10#41×#6923—22no—
11#41×#6923—22no—
12#41×#6923C414yescomplemented
13#41×#6923C2214yes—
14C2×Q8×#6923C412yescomplemented
15C2×D4×#6923—22no—
16C2×D4×#6923C412yescomplemented
17C2×#14519856—21no—
18C2×#14519856C2211yescharacteristic
19C22×C4×#6923—21no—
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C2×#14519842C412yescomplemented
23D61⋊#104C414yescomplemented
24D61⋊#104C2214yes—
25C2×#14519841C412yescomplemented
26M16×#6923—22no—
27M16×#6923C2214yescomplemented
28C2×#14519831—21no—
29C2×C8×#6923—21no—
30#16840698—22no—
31#16840698C2214yescomplemented
32C2×(C2×#6923)⋊C4—22no—
33#16840634C2214yescomplemented
34#16840633C2214yescomplemented
35C2×#41×D61C2211yescharacteristic
36C2×M16×D61C2211yescharacteristic
37C2×C42×D61C2211yescharacteristic
38C2×#14519705C411yescharacteristic, complemented
39C2×#14519704C411yescharacteristic, complemented
40C2×#14519703C411yescharacteristic, complemented
41#104×D61C414yescomplemented
42#104×D61C2214yes—
43C2×#104×C61C411yescharacteristic, complemented
44C23×#6923—21no—
45C23×#6923—22no—
46C23×#6923D412yes—
47C2×#11758213C2×C412yescomplemented
48D61⋊M16—21no—
49D61⋊M16—21no—
50D61⋊M16C2×C412yescomplemented
51D61⋊M16C2312yes—
52C2×#11758217—21no—
53C2×D61⋊C8—21no—
54Q8×#6923—24no—
55Q8×#6923C2×C418yescomplemented
56D4×#6923—28no—
57D4×#6923—28no—
58D4×#6923—24no—
59D4×#6923C2×C418yescomplemented
60#14519856—21no—
61#14519856—21no—
62#14519856—24no—
63#14519856—24no—
64#14519856C2×C412yes—
65#14519856C2312yes—
66C2×C4⋊#6923—22no—
67C2×C4⋊#6923C2×C412yes—
68C2×C22⋊#6923—21no—
69C2×C22⋊#6923—22no—
70C2×C4×#6923—22no—
71C2×C4×#6923—21no—
72C2×C4×#6923—21no—
73C2×C4×#6923—21no—
74C2×C4×#6923—21no—
75C2×C4×#6923—24no—
76C2×C4×#6923—24no—
77C2×C4×#6923C2×C412yes—
78C2×C4×#6923C2×C412yes—
79C2×C4×#6923C2×C412yescomplemented
80C2×C4×#6923C2×C412yescomplemented
81C2×C4×#6923D412yes—
82C2×C4×#6923D411yescharacteristic
83C2×C4×#6923D411yescharacteristic
84C2×C4×#6923D412yes—
85C2×C4×#6923C2312yes—
86C2×C4×#6923C2312yes—
87#14519842C2×C418yescomplemented
88#14519841C2×C418yescomplemented
89#14519831—24no—
90C8×#6923—24no—
91(C2×#6923)⋊C4—28no—
92C2×#11758226C2×C411yescharacteristic
93C2×#11758222—21no—
94C2×#11758222C2×C411yescharacteristic
95C2×#11758224—21no—
96C2×#11758224C2×C411yescharacteristic
97#41×D61—21no—
98#41×D61—21no—
99#41×D61—21no—
100#41×D61—21no—
101#41×D61C2×C412yes—
102#41×D61C2×C412yes—
103#41×D61C2×C412yes—
104#41×D61C2312yes—
105C2×Q8×D61C2×C411yescharacteristic
106C2×D4×D61—21no—
107C2×D4×D61C2×C411yescharacteristic
108C22×C4×D61—21no—
109C22×C4×D61—21no—
110C22×C4×D61C2311yescharacteristic
111C2×#11758194C2×C411yescharacteristic, complemented
112C2×#11758189—21no—
113M16×D61—21no—
114M16×D61—21no—
115M16×D61C2×C412yescomplemented
116M16×D61C2312yes—
117C2×C8×D61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61C2×C411yescharacteristic, complemented
120C42×D61—21no—
121C42×D61—21no—
122C42×D61C2×C412yescomplemented
123C42×D61C2312yes—
124#14519705C2×C414yescomplemented
125#14519704C2×C414yescomplemented
126#14519703C2×C414yescomplemented
127C2×#41×C61C2×C411yescharacteristic
128C2×M16×C61C2×C411yescharacteristic, complemented
129C2×C42×C61C2×C411yescharacteristic, complemented
130#104×C61C2×C414yescomplemented
131C23×D61—21no—
132C23×D61C2×D411yescharacteristic
133C22×#6923—22no—
134C22×#6923—22no—
135C22×#6923—22no—
136C22×#6923—22no—
137C22×#6923—28no—
138C22×#6923—44no—
139C22×#6923—48no—
140C22×#6923—44no—
141C22×#6923C22⋊C412yes—
142C22×#6923C22⋊C412yes—
143C22×#6923C22⋊C414yes—
144C22×#6923C2×D414yes—
145#41×C61—21no—
146#41×C61—21no—
147#41×C61C4212yes—
148#41×C61C22×C412yes—
149C2×Q8×C61C4211yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C4211yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C411yescharacteristic
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157C2×C22⋊D61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61#4111yescharacteristic
161#11758226—21no—
162#11758226—21no—
163#11758226C4212yes—
164#11758226C22×C412yes—
165Q8×D61—21no—
166Q8×D61—21no—
167Q8×D61C4212yes—
168Q8×D61C22×C412yes—
169#11758224—22no—
170#11758224—22no—
171#11758224—22no—
172#11758224—22no—
173#11758224—21no—
174#11758224—21no—
175#11758224C4212yes—
176#11758224C22×C412yes—
177D4×D61—22no—
178D4×D61—22no—
179D4×D61—22no—
180D4×D61—22no—
181D4×D61—21no—
182D4×D61—21no—
183D4×D61C4212yes—
184D4×D61C22×C412yes—
185#11758222—21no—
186#11758222—21no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222C4212yes—
192#11758222C22×C412yes—
193C2×D244—21no—
194C2×D244C4211yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—44no—
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C22×C411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61#4111yescharacteristic
214C2×C4×D61#4111yescharacteristic
215C2×C4×D61#4111yescharacteristic
216C2×C4×D61C2411yescharacteristic
217C2×Dic122—21no—
218C2×Dic122C4211yescharacteristic
219C22⋊#6923—22no—
220C22⋊#6923—22no—
221C22⋊#6923—28no—
222#11758217—22no—
223#11758217—22no—
224C2×#92420—22no—
225C4⋊#6923—28no—
226C4⋊#6923—22no—
227C4⋊#6923C22×C414yes—
228C4×#6923—28no—
229C4×#6923—22no—
230C4×#6923—22no—
231C4×#6923—22no—
232C4×#6923—22no—
233C4×#6923—22no—
234C4×#6923C22⋊C412yes—
235C4×#6923C22⋊C412yes—
236C4×#6923C22⋊C414yes—
237C4×#6923C22×C414yes—
238C4×#6923C22×C414yescomplemented
239C4×#6923C2×D412yes—
240C4×#6923C2×D412yes—
241#11758213—22no—
242#11758213C22×C414yescomplemented
243D61⋊C8—22no—
244D61⋊C8—22no—
245M16×C61—21no—
246M16×C61C22×C412yescomplemented
247C2×C8×C61—21no—
248C42×C61—21no—
249C42×C61C22×C412yescomplemented
250C4×Dic61—21no—
251C4×Dic61—22no—
252C4×Dic61—22no—
253C4×Dic61C22×C412yescomplemented
254#11758194—21no—
255#11758194C22×C412yescomplemented
256C2×#92418—21no—
257#11758189—22no—
258#11758189—22no—
259C8×D61—22no—
260C8×D61—22no—
261C23×C61—21no—
262C23×C61C4×D411yescharacteristic
263C22×D61—24no—
264C22×D61—21no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—44no—
268C22×D61C2×C22⋊C411yescharacteristic
269C22×D61C2×C22⋊C411yescharacteristic
270C22×D61C4×D411yescharacteristic
271C22×D61C4×D411yescharacteristic
272C22×D61C4×D411yescharacteristic
273C22×D61C22×D411yescharacteristic
274C2×#6923—24no—
275C2×#6923—24no—
276C2×#6923—24no—
277C2×#6923—24no—
278C2×#6923—44no—
279C2×#6923—44no—
280C2×#6923—416no—
281C2×#6923—44no—
282C2×#6923—44no—
283C2×#6923—44no—
284C2×#6923—44no—
285C2×#6923C2×C22⋊C414yes—
286C2×#6923C2×C22⋊C414yes—
287Q8×C61—21no—
288Q8×C61C2×C4212yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—21no—
292D4×C61C2×C4212yes—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—42no—
298C2×C4×C61C2×C4211yescharacteristic
299C2×C4×C61C2×C4211yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C23×C411yescharacteristic
304C22⋊D61—22no—
305C22⋊D61—22no—
306C22⋊D61—22no—
307C22⋊D61—22no—
308C22⋊D61—22no—
309C22⋊D61—22no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61#11711yescharacteristic
316C2×Dic61#11711yescharacteristic
317C2×Dic61C4×D411yescharacteristic
318C2×Dic61C4×D411yescharacteristic
319C2×Dic61C4×D411yescharacteristic
320C2×Dic61C2×#4111yescharacteristic
321D244—22no—
322D244—22no—
323D244—21no—
324D244C2×C4212yes—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—44no—
332C4×D61—44no—
333C4×D61C2×C4211yescharacteristic
334C4×D61C2×C4211yescharacteristic
335C4×D61C2×C22⋊C411yescharacteristic
336C4×D61C2×C22⋊C411yescharacteristic
337C4×D61#11711yescharacteristic
338C4×D61#11711yescharacteristic
339C4×D61C4×D411yescharacteristic
340C4×D61C4×D411yescharacteristic
341C4×D61C4×D411yescharacteristic
342C4×D61C4×D411yescharacteristic
343C4×D61C4×D411yescharacteristic
344C4×D61C4×D411yescharacteristic
345C4×D61C23×C411yescharacteristic
346C4×D61C23×C411yescharacteristic
347C4×D61C22×D411yescharacteristic
348C4×D61C2×#4111yescharacteristic
349Dic122—21no—
350Dic122—22no—
351Dic122—22no—
352Dic122C2×C4212yes—
353#92420—24no—
354C8×C61—22no—
355#92418—22no—
356C2×#1759—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—42no—
360C22×C61C4×C22⋊C411yescharacteristic
361C22×C61C4×C22⋊C411yescharacteristic
362C22×C61C2×C4×D411yescharacteristic
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—42no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61C4×C22⋊C411yescharacteristic
373C2×D61C4×C22⋊C411yescharacteristic
374C2×D61#42114yes—
375C2×D61C22×C22⋊C411yescharacteristic
376C2×D61C2×C4×D411yescharacteristic
377#6923—24no—
378#6923—24no—
379#6923—44no—
380#6923—44no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61C4×C22⋊C411yescharacteristic
384C4×C61C4×C22⋊C411yescharacteristic
385C4×C61C22×C4211yescharacteristic
386C4×C61C2×C4×D411yescharacteristic
387Dic61—22no—
388Dic61—42no—
389Dic61C4×C22⋊C411yescharacteristic
390Dic61C4×C22⋊C411yescharacteristic
391Dic61C2×#11711yescharacteristic
392Dic61C2×C4×D411yescharacteristic
393C2×C4×#41—611no—
394C22×#104—611no—
395C22×#104—611no—
396C2×C4×M16—611no—
397C2×#376—611no—
398#1759—618no—
399C2×#339—611no—
400C2×#339—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—42no—
404C2×C61#175912yescomplemented
405C2×C61C2×C4×C22⋊C411yescharacteristic
406D61—21no—
407D61—21no—
408D61—42no—
409D61#175912yescomplemented
410D61C2×#42112yes—
411C22×#41—611no—
412C22×M16—611no—
413C22×M16—611no—
414C4×#41—614no—
415C4×#41—614no—
416C4×#41—1222no—
417C4×#41—1222no—
418C2×C4×Q8—612no—
419C2×C4×D4—612no—
420C2×C4×D4—1222no—
421C2×#117—611no—
422C2×#117—1221no—
423C22×C42—611no—
424C22×C42—611no—
425C22×C42—611no—
426C22×C42—1221no—
427C2×#104—612no—
428C2×#104—614no—
429C2×#104—614no—
430C2×#104—612no—
431C2×#104—611no—
432C2×#104—611no—
433C2×#104—611no—
434C2×#104—614no—
435C2×#104—614no—
436C2×#104#692311yescharacteristic, complemented
437C4×M16—614no—
438C4×M16—1222no—
439C2×#97—1221no—
440C2×C4×C8—1221no—
441#376—614no—
442#376—1222no—
443C2×#95—1222no—
444#339—614no—
445#339—614no—
446C61C2×#175911yescharacteristic, complemented, Sylow
447C2×#41—612no—
448C2×#41—612no—
449C2×#41—612no—
450C2×#41—612no—
451C2×#41—611no—
452C2×#41—611no—
453C2×#41—611no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1221no—
459C2×#41—1221no—
460C2×#41C2×#692311yescharacteristic
461C22×Q8—611no—
462C22×D4—611no—
463C22×D4—1221no—
464C23×C4—611no—
465C23×C4—612no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1222no—
469C23×C4—1221no—
470C2×M16—612no—
471C2×M16—612no—
472C2×M16—612no—
473C2×M16—611no—
474C2×M16—612no—
475C2×M16—612no—
476C2×M16—1221no—
477C2×M16—1221no—
478C2×M16—1221no—
479C2×M16—1221no—
480C2×M16—1221no—
481C2×M16—1221no—
482C2×M16C2×#692311yescharacteristic, complemented
483C22×C8—1221no—
484C22×C8—1221no—
485C4×Q8—618no—
486C4×Q8—1224no—
487C4×D4—618no—
488C4×D4—1224no—
489C4×D4—1228no—
490C4×D4—1228no—
491#117—612no—
492#117—612no—
493#117—1224no—
494#117—1224no—
495#117—1221no—
496#117—1221no—
497C2×C4⋊C4—612no—
498C2×C4⋊C4—1222no—
499C2×C22⋊C4—1222no—
500C2×C22⋊C4—1221no—
501C2×C42—611no—
502C2×C42—612no—
503C2×C42—612no—
504C2×C42—612no—
505C2×C42—612no—
506C2×C42—612no—
507C2×C42—611no—
508C2×C42—612no—
509C2×C42—612no—
510C2×C42—612no—
511C2×C42—611no—
512C2×C42—612no—
513C2×C42—612no—
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—1224no—
517C2×C42—1224no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1222no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42C2×#692311yescharacteristic, complemented
525#104—618no—
526#104—618no—
527#104—614no—
528#104—614no—
529#104—614no—
530#104C2×#692314yescomplemented
531#97—1224no—
532C4×C8—1224no—
533#95—1228no—
534C24—611no—
535C24—1221no—
536#41—21no—
537#41—21no—
538#41—612no—
539#41—612no—
540#41—612no—
541#41—612no—
542#41—612no—
543#41—612no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—1221no—
553#41—1221no—
554#41—1221no—
555#41—1221no—
556#41—1221no—
557#41—1221no—
558#41C4×#692312yes—
559#41C22×#692312yes—
560C2×Q8—612no—
561C2×Q8—612no—
562C2×Q8—611no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8C4×#692311yescharacteristic
567C2×D4—21no—
568C2×D4—612no—
569C2×D4—612no—
570C2×D4—611no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4C4×#692311yescharacteristic
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—614no—
600C22×C4—614no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1221no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1228no—
611C22×C4—1221no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1221no—
617C22×C4—2444no—
618C22×C4—2444no—
619C22×C4—2448no—
620C22×C4—2444no—
621C22×C4C22×#692311yescharacteristic
622M16—21no—
623M16—614no—
624M16—612no—
625M16—1222no—
626M16—1222no—
627M16—1222no—
628M16—1222no—
629M16—1222no—
630M16—1221no—
631M16C22×#692312yescomplemented
632C2×C8—21no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1222no—
636C2×C8—1222no—
637C2×C8—1222no—
638C2×C8—1221no—
639C4⋊C4—614no—
640C4⋊C4—1222no—
641C4⋊C4—1228no—
642C22⋊C4—1228no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C42—21no—
646C42—612no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—614no—
651C42—614no—
652C42—614no—
653C42—612no—
654C42—1222no—
655C42—1222no—
656C42—1222no—
657C42—1222no—
658C42—1222no—
659C42—1222no—
660C42—1222no—
661C42—1228no—
662C42—1221no—
663C42C22×#692312yescomplemented
664C23—21no—
665C23—611no—
666C23—611no—
667C23—611no—
668C23—611no—
669C23—611no—
670C23—611no—
671C23—1224no—
672C23—1222no—
673C23—1222no—
674C23—1221no—
675C23—2444no—
676C23D4×#692311yescharacteristic
677Q8—21no—
678Q8—612no—
679Q8—1222no—
680Q8—1222no—
681Q8—1221no—
682Q8C2×C4×#692312yes—
683D4—22no—
684D4—22no—
685D4—21no—
686D4—612no—
687D4—1222no—
688D4—1222no—
689D4—1222no—
690D4—1222no—
691D4—1222no—
692D4—1222no—
693D4—1222no—
694D4—1222no—
695D4—1221no—
696D4C2×C4×#692312yes—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1221no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1222no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4—2444no—
743C2×C4—2444no—
744C2×C4—24416no—
745C2×C4—2442no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4—2444no—
750C2×C4C2×C4×#692311yescharacteristic
751C2×C4C2×C4×#692311yescharacteristic
752C2×C4D4×#692311yescharacteristic
753C2×C4D4×#692311yescharacteristic
754C2×C4D4×#692311yescharacteristic
755C2×C4C23×#692311yescharacteristic
756C8—22no—
757C8—1224no—
758C8—1222no—
759C22—22no—
760C22—22no—
761C22—42no—
762C22—614no—
763C22—611no—
764C22—611no—
765C22—611no—
766C22—611no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—2444no—
774C22—2444no—
775C22—2442no—
776C22C22⋊C4×#692311yescharacteristic
777C22C22⋊C4×#692311yescharacteristic
778C22C2×D4×#692311yescharacteristic
779C4—22no—
780C4—42no—
781C4—611no—
782C4—611no—
783C4—611no—
784C4—611no—
785C4—1224no—
786C4—1224no—
787C4—1222no—
788C4—2442no—
789C4—2444no—
790C4—2444no—
791C4C22⋊C4×#692311yescharacteristic
792C4C22⋊C4×#692311yescharacteristic
793C4C22×C4×#692311yescharacteristic
794C4C2×D4×#692311yescharacteristic
795C2—21no—
796C2—21no—
797C2—42no—
798C2—612no—
799C2—612no—
800C2—1221no—
801C2—1221no—
802C2—2442no—
803C2#2146158412yesdirect product factor
804C2C2×C22⋊C4×#692311yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC2×#104×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#104#6923
hypocenterC61C2×#1759
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×M16×#6923C2semidirect
4. C2×#16840698C2semidirect
5. #21461584C2direct (N × H)
6. C2×#16840634C2semidirect
7. C2×#16840633C2semidirect
12. #41×#6923C4semidirect
14. C2×Q8×#6923C4semidirect
16. C2×D4×#6923C4semidirect
22. C2×#14519842C4semidirect
23. D61⋊#104C4semidirect
25. C2×#14519841C4semidirect
27. M16×#6923C22semidirect
31. #16840698C22semidirect
33. #16840634C22semidirect
34. #16840633C22semidirect
38. C2×#14519705C4semidirect
39. C2×#14519704C4semidirect
40. C2×#14519703C4semidirect
41. #104×D61C4semidirect
43. C2×#104×C61C4semidirect
47. C2×#11758213C2×C4semidirect
50. D61⋊M16C2×C4semidirect
55. Q8×#6923C2×C4semidirect
59. D4×#6923C2×C4semidirect
79. C2×C4×#6923C2×C4semidirect
80. C2×C4×#6923C2×C4semidirect
87. #14519842C2×C4semidirect
88. #14519841C2×C4semidirect
111. C2×#11758194C2×C4semidirect
115. M16×D61C2×C4semidirect
119. C2×C4×Dic61C2×C4semidirect
122. C42×D61C2×C4semidirect
124. #14519705C2×C4semidirect
125. #14519704C2×C4semidirect
126. #14519703C2×C4semidirect
128. C2×M16×C61C2×C4semidirect
129. C2×C42×C61C2×C4semidirect
130. #104×C61C2×C4semidirect
238. C4×#6923C22×C4semidirect
242. #11758213C22×C4semidirect
246. M16×C61C22×C4semidirect
249. C42×C61C22×C4semidirect
253. C4×Dic61C22×C4semidirect
255. #11758194C22×C4semidirect
404. C2×C61#1759semidirect
409. D61#1759semidirect
436. C2×#104#6923semidirect
446. C61C2×#1759semidirect
482. C2×M16C2×#6923semidirect
524. C2×C42C2×#6923semidirect
530. #104C2×#6923semidirect
631. M16C22×#6923semidirect
663. C42C22×#6923semidirect
803. C2#21461584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×#69232
C2×D61⋊#1042
C2×M16×#69232
C2×#168406982
#214615842
C2×#168406342
C2×#168406332
C2×#104×D612
C2×#175961