Finite Group Databasebeta

← C2×#21461779 #30615498

Subgroups — C2×#21461779 #30615498

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2C2×#16840773C211yesmaximal, characteristic, complemented
3C2×#16840753C211yesmaximal, characteristic
4C2×#16840706C211yesmaximal, characteristic, complemented
5#21461779C218yesmaximal, direct product factor
6C2×#16840641C211yesmaximal, characteristic, complemented
7C2×#16840633C211yesmaximal, characteristic, complemented
8C2×#104×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10#16840831—22no—
11#16840831—22no—
12#16840831—22no—
13#16840831C2214yes—
14C2×Q8×#6923—21no—
15C2×D4×#6923—22no—
16C2×D4×#6923—21no—
17C2×#14519856—21no—
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923—21no—
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22#16840773—22no—
23#16840773C2214yescomplemented
24C2×#14519846—21no—
25C2×#14519845—21no—
26#16840753—22no—
27#16840753C2214yes—
28C2×#14519840—21no—
29C2×#14519839—21no—
30#16840706—22no—
31#16840706C2214yescomplemented
32C2×(C2×#6923)⋊C4—22no—
33#16840641C2214yescomplemented
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—22no—
45C23×#6923—21no—
46C23×#6923D412yes—
47C2×#11758213—21no—
48D61⋊M16—21no—
49D61⋊M16—21no—
50D61⋊M16—21no—
51D61⋊M16C2312yes—
52C2×#11758217—21no—
53C2×D61⋊C8—21no—
54Q8×#6923—24no—
55Q8×#6923—24no—
56D4×#6923—28no—
57D4×#6923—24no—
58D4×#6923—28no—
59D4×#6923—24no—
60#14519856—24no—
61#14519856—21no—
62#14519856—21no—
63#14519856—24no—
64#14519856D412yes—
65#14519856C2312yes—
66C2×C4⋊#6923—22no—
67C2×C4⋊#6923—24no—
68C2×C4⋊#6923—21no—
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—24no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923D412yes—
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923C2312yes—
82C2×C4⋊#6923C2312yes—
83C2×C22⋊#6923—22no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—22no—
86C2×C4×#6923—21no—
87#14519846—24no—
88#14519845—24no—
89#14519840—24no—
90#14519839—24no—
91(C2×#6923)⋊C4—28no—
92C2×#11758226Q811yescharacteristic
93C2×#11758222—21no—
94C2×#11758222C2×C411yescharacteristic
95C2×#11758224—21no—
96C2×#11758224Q811yescharacteristic
97#41×D61—21no—
98#41×D61—21no—
99#41×D61—21no—
100#41×D61—21no—
101#41×D61C2×C412yes—
102#41×D61D412yes—
103#41×D61Q812yes—
104#41×D61C2312yes—
105C2×Q8×D61D411yescharacteristic
106C2×D4×D61—21no—
107C2×D4×D61D411yescharacteristic
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—21no—
134C22×#6923—22no—
135C22×#6923—21no—
136C22×#6923—28no—
137C22×#6923—22no—
138C22×#6923—22no—
139C22×#6923—44no—
140C22×#6923—44no—
141C22×#6923—41no—
142C22×#6923—41no—
143C22×#6923—84no—
144C22×#6923C2×D414yes—
145#41×C61—21no—
146#41×C61—21no—
147#41×C61C4⋊C412yes—
148#41×C61C22×C412yes—
149C2×Q8×C61C4⋊C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C4⋊C411yescharacteristic
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#11758226C4⋊C412yes—
164#11758226C2×Q812yes—
165Q8×D61—21no—
166Q8×D61—21no—
167Q8×D61C4⋊C412yes—
168Q8×D61C2×D412yes—
169#11758224—22no—
170#11758224—22no—
171#11758224—22no—
172#11758224—22no—
173#11758224—21no—
174#11758224—21no—
175#11758224C4⋊C412yes—
176#11758224C2×Q812yes—
177D4×D61—22no—
178D4×D61—22no—
179D4×D61—22no—
180D4×D61—22no—
181D4×D61—21no—
182D4×D61—21no—
183D4×D61C4⋊C412yes—
184D4×D61C2×D412yes—
185#11758222—21no—
186#11758222—21no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222C4⋊C412yes—
192#11758222C22×C412yes—
193C2×D244—21no—
194C2×D244C4⋊C411yescharacteristic
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—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×Q811yescharacteristic
213C2×C4×D61C2×Q811yescharacteristic
214C2×C4×D61#4111yescharacteristic
215C2×C4×D61#4111yescharacteristic
216C2×C4×D61#4111yescharacteristic
217C2×C4×D61C2411yescharacteristic
218C2×Dic122—21no—
219C2×Dic122C4⋊C411yescharacteristic
220C22⋊#6923—28no—
221C22⋊#6923—22no—
222C22⋊#6923—22no—
223#11758217—22no—
224#11758217—41no—
225C2×#92420—41no—
226C4⋊#6923—28no—
227C4⋊#6923—22no—
228C4⋊#6923—21no—
229C4⋊#6923—22no—
230C4⋊#6923—21no—
231C4⋊#6923—22no—
232C4⋊#6923—22no—
233C4⋊#6923—22no—
234C4⋊#6923—22no—
235C4⋊#6923—41no—
236C4⋊#6923—41no—
237C4⋊#6923C2×D412yes—
238C4⋊#6923C2×D412yes—
239C4×#6923—28no—
240C4×#6923—22no—
241C4×#6923—22no—
242#11758213—22no—
243#11758213—41no—
244D61⋊C8—22no—
245D61⋊C8—41no—
246M16×C61—21no—
247M16×C61C22×C412yescomplemented
248C2×C8×C61—21no—
249C42×C61—21no—
250C42×C61C22×C412yescomplemented
251C4×Dic61—21no—
252C4×Dic61—22no—
253C4×Dic61—22no—
254C4×Dic61C22×C412yescomplemented
255#11758194—21no—
256#11758194C22×C412yescomplemented
257C2×#92418—21no—
258#11758189—22no—
259#11758189—22no—
260C8×D61—22no—
261C8×D61—22no—
262C23×C61—21no—
263C23×C61C4×D411yescharacteristic
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—21no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61C4×D411yescharacteristic
272C22×D61#12011yescharacteristic
273C22×D61#12011yescharacteristic
274C22×D61C22⋊Q811yescharacteristic
275C22×D61C22⋊Q811yescharacteristic
276C22×D61C22×D411yescharacteristic
277C2×#6923—22no—
278C2×#6923—24no—
279C2×#6923—22no—
280C2×#6923—42no—
281C2×#6923—44no—
282C2×#6923—42no—
283C2×#6923—44no—
284C2×#6923—44no—
285C2×#6923—42no—
286C2×#6923—82no—
287C2×#6923—88no—
288C2×#6923—82no—
289C2×#6923—82no—
290Q8×C61—21no—
291Q8×C61C2×C4⋊C412yes—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—21no—
295D4×C61C2×C4⋊C412yes—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—42no—
301C2×C4×C61C2×C4⋊C411yescharacteristic
302C2×C4×C61C2×C4⋊C411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C23×C411yescharacteristic
307C22⋊D61—22no—
308C22⋊D61—22no—
309C22⋊D61—22no—
310C22⋊D61—22no—
311C22⋊D61—22no—
312C22⋊D61—22no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61C4×D411yescharacteristic
319C2×Dic61C22⋊Q811yescharacteristic
320C2×Dic61C22⋊Q811yescharacteristic
321C2×Dic61#12311yescharacteristic
322C2×Dic61#12311yescharacteristic
323C2×Dic61C2×#4111yescharacteristic
324D244—22no—
325D244—22no—
326D244—21no—
327D244C2×C4⋊C412yes—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—44no—
335C4×D61—42no—
336C4×D61—42no—
337C4×D61C2×C4⋊C411yescharacteristic
338C4×D61C2×C4⋊C411yescharacteristic
339C4×D61C4×D411yescharacteristic
340C4×D61C4×D411yescharacteristic
341C4×D61#12011yescharacteristic
342C4×D61#12011yescharacteristic
343C4×D61C22⋊Q811yescharacteristic
344C4×D61C22⋊Q811yescharacteristic
345C4×D61C22⋊Q811yescharacteristic
346C4×D61C22⋊Q811yescharacteristic
347C4×D61#12311yescharacteristic
348C4×D61#12311yescharacteristic
349C4×D61C22×D411yescharacteristic
350C4×D61C22×D411yescharacteristic
351C4×D61C22×Q811yescharacteristic
352C4×D61C2×#4111yescharacteristic
353Dic122—21no—
354Dic122—22no—
355Dic122—22no—
356Dic122C2×C4⋊C412yes—
357#92420—42no—
358C8×C61—22no—
359#92418—22no—
360C2×#1860—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—42no—
364C22×C61#38511yescharacteristic
365C22×C61#38511yescharacteristic
366C22×C61C2×C4×D411yescharacteristic
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—22no—
375C2×D61—42no—
376C2×D61—44no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61#38511yescharacteristic
380C2×D61#38511yescharacteristic
381C2×D61#45412yes—
382C2×D61#45512yes—
383C2×D61C2×#12011yescharacteristic
384C2×D61C2×C22⋊Q811yescharacteristic
385#6923—44no—
386#6923—42no—
387#6923—42no—
388#6923—82no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61#38511yescharacteristic
392C4×C61#38511yescharacteristic
393C4×C61C22×C4⋊C411yescharacteristic
394C4×C61C2×C4×D411yescharacteristic
395Dic61—22no—
396Dic61—42no—
397Dic61#38511yescharacteristic
398Dic61#38511yescharacteristic
399Dic61C2×C22⋊Q811yescharacteristic
400Dic61C2×#12311yescharacteristic
401C2×#520—611no—
402C2×#428—611no—
403C22×#104—611no—
404C2×#417—611no—
405C2×#382—611no—
406#1860—618no—
407C2×#343—611no—
408C2×#339—611no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—42no—
412C2×C61#186012yescomplemented
413C2×C61C2×#38511yescharacteristic
414D61—21no—
415D61—21no—
416D61—42no—
417D61#186012yescomplemented
418D61C2×#45511yescharacteristic
419D61C2×#45411yescharacteristic
420C22×#41—611no—
421C22×M16—611no—
422C22×M16—611no—
423#520—614no—
424#520—1222no—
425#520—1222no—
426#520—1222no—
427C2×C4×Q8—1221no—
428C2×C4×D4—1222no—
429C2×C4×D4—1221no—
430C2×#117—611no—
431C2×#117—1221no—
432C22×C4⋊C4—611no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—1221no—
435C22×C42—611no—
436#428—614no—
437#428—1222no—
438C2×#107—1221no—
439C2×#106—1221no—
440C2×#104—611no—
441C2×#104—611no—
442C2×#104—611no—
443C2×#104—614no—
444C2×#104—614no—
445C2×#104#692311yescharacteristic, complemented
446#417—614no—
447#417—1222no—
448C2×#103—1221no—
449C2×#102—1221no—
450#382—614no—
451#382—1222no—
452C2×#95—1222no—
453#343—614no—
454#339—614no—
455C61C2×#186011yescharacteristic, complemented, Sylow
456C2×#41—612no—
457C2×#41—612no—
458C2×#41—612no—
459C2×#41—612no—
460C2×#41—611no—
461C2×#41—611no—
462C2×#41—611no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41C2×#692311yescharacteristic
470C22×Q8—611no—
471C22×D4—611no—
472C22×D4—1221no—
473C23×C4—611no—
474C23×C4—612no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1222no—
478C23×C4—1221no—
479C2×M16—611no—
480C2×M16—612no—
481C2×M16—612no—
482C2×M16—612no—
483C2×M16—1221no—
484C2×M16—1221no—
485C2×M16—1221no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16C2×#692311yescharacteristic, complemented
492C22×C8—1221no—
493C22×C8—1221no—
494C4×Q8—1224no—
495C4×Q8—1224no—
496C4×D4—1228no—
497C4×D4—1224no—
498C4×D4—1224no—
499C4×D4—1228no—
500#117—612no—
501#117—612no—
502#117—1224no—
503#117—1221no—
504#117—1221no—
505#117—1224no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1224no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1224no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1222no—
525C2×C42—611no—
526C2×C42—612no—
527C2×C42—612no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1222no—
533C2×C42C2×#692311yescharacteristic, complemented
534#107—1224no—
535#106—1224no—
536#104—614no—
537#104—614no—
538#104—614no—
539#104C2×#692314yescomplemented
540#103—1224no—
541#102—1224no—
542#95—1228no—
543C24—611no—
544C24—1221no—
545#41—21no—
546#41—21no—
547#41—612no—
548#41—612no—
549#41—612no—
550#41—612no—
551#41—612no—
552#41—612no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1221no—
562#41—1221no—
563#41—1221no—
564#41—1221no—
565#41—1221no—
566#41—1221no—
567#41C4⋊#692312yes—
568#41C22×#692312yes—
569C2×Q8—612no—
570C2×Q8—612no—
571C2×Q8—611no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8C4⋊#692311yescharacteristic
576C2×D4—21no—
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—611no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4C4⋊#692311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—614no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1222no—
618C22×C4—1228no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—1222no—
624C22×C4—4884no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2441no—
628C22×C4—2441no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4C22×#692311yescharacteristic
632M16—21no—
633M16—612no—
634M16—1222no—
635M16—1222no—
636M16—1221no—
637M16—1222no—
638M16—1222no—
639M16—2441no—
640M16—2441no—
641M16C22×#692312yescomplemented
642C2×C8—21no—
643C2×C8—1222no—
644C2×C8—1222no—
645C2×C8—1221no—
646C2×C8—1222no—
647C2×C8—2441no—
648C2×C8—2441no—
649C4⋊C4—612no—
650C4⋊C4—612no—
651C4⋊C4—1221no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1221no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1228no—
660C4⋊C4—2441no—
661C4⋊C4—2441no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—1228no—
665C42—21no—
666C42—612no—
667C42—1222no—
668C42—1222no—
669C42—1222no—
670C42—1222no—
671C42—1228no—
672C42—1221no—
673C42C22×#692312yescomplemented
674C23—21no—
675C23—611no—
676C23—611no—
677C23—611no—
678C23—611no—
679C23—611no—
680C23—611no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1221no—
686C23—2442no—
687C23—2442no—
688C23D4×#692311yescharacteristic
689Q8—21no—
690Q8—612no—
691Q8—1222no—
692Q8—1222no—
693Q8—1221no—
694Q8C2×C4⋊#692312yes—
695D4—22no—
696D4—22no—
697D4—21no—
698D4—612no—
699D4—1222no—
700D4—1222no—
701D4—1222no—
702D4—1222no—
703D4—1222no—
704D4—1222no—
705D4—1222no—
706D4—1222no—
707D4—1221no—
708D4C2×C4⋊#692312yes—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
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—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1221no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1224no—
748C2×C4—1222no—
749C2×C4—4882no—
750C2×C4—4882no—
751C2×C4—4882no—
752C2×C4—4888no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2444no—
756C2×C4—2442no—
757C2×C4—2444no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2444no—
762C2×C4—2444no—
763C2×C4C2×C4⋊#692311yescharacteristic
764C2×C4C2×C4⋊#692311yescharacteristic
765C2×C4D4×#692311yescharacteristic
766C2×C4D4×#692311yescharacteristic
767C2×C4D4×#692311yescharacteristic
768C2×C4C23×#692311yescharacteristic
769C8—22no—
770C8—1222no—
771C8—2442no—
772C22—22no—
773C22—22no—
774C22—42no—
775C22—612no—
776C22—612no—
777C22—611no—
778C22—611no—
779C22—611no—
780C22—611no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—2442no—
790C22—2442no—
791C22—2444no—
792C22—2442no—
793C22#1684070911yescharacteristic
794C22#1684070911yescharacteristic
795C22C2×D4×#692311yescharacteristic
796C4—22no—
797C4—42no—
798C4—611no—
799C4—611no—
800C4—611no—
801C4—611no—
802C4—1222no—
803C4—4882no—
804C4—2442no—
805C4—2442no—
806C4—2444no—
807C4—2442no—
808C4#1684070911yescharacteristic
809C4#1684070911yescharacteristic
810C4C22×C4⋊#692311yescharacteristic
811C4C2×D4×#692311yescharacteristic
812C2—21no—
813C2—21no—
814C2—42no—
815C2—611no—
816C2—611no—
817C2—612no—
818C2—1221no—
819C2—1221no—
820C2—2442no—
821C2#2146177912yesdirect product factor
822C2C2×#1684070911yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#104×C61C4
socleC22×C61#385
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#104#6923
hypocenterC61C2×#1860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16840773C2semidirect
4. C2×#16840706C2semidirect
5. #21461779C2direct (N × H)
6. C2×#16840641C2semidirect
7. C2×#16840633C2semidirect
23. #16840773C22semidirect
31. #16840706C22semidirect
33. #16840641C22semidirect
34. #16840633C22semidirect
38. C2×#14519705C4semidirect
39. C2×#14519704C4semidirect
40. C2×#14519703C4semidirect
41. #104×D61C4semidirect
43. C2×#104×C61C4semidirect
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
247. M16×C61C22×C4semidirect
250. C42×C61C22×C4semidirect
254. C4×Dic61C22×C4semidirect
256. #11758194C22×C4semidirect
412. C2×C61#1860semidirect
417. D61#1860semidirect
445. C2×#104#6923semidirect
455. C61C2×#1860semidirect
491. C2×M16C2×#6923semidirect
533. C2×C42C2×#6923semidirect
539. #104C2×#6923semidirect
641. M16C22×#6923semidirect
673. C42C22×#6923semidirect
821. C2#21461779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168407732
C2×#168407532
C2×#168407062
#214617792
C2×#168406412
C2×#168406332
C2×#104×D612
C2×#186061