Finite Group Databasebeta

← C2×#21455766 #30547818

Subgroups — C2×#21455766 #30547818

Order 15616.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic
3#21455766C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840104C211yesmaximal, characteristic, complemented
7C2×#16840103C211yesmaximal, characteristic, complemented
8C2×#16840100C211yesmaximal, characteristic, complemented
9C2×#16840094C211yesmaximal, characteristic, complemented
10C2×#16840091C211yesmaximal, characteristic, complemented
11C2×#16839803C211yesmaximal, characteristic, complemented
12C2×#16839801C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#16839724C211yesmaximal, characteristic
16C2×C61×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C2×#14519757C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519755—21no—
24C2×#14519754—21no—
25C2×#14519753C2211yescharacteristic
26C22⋊Q8×D61—24no—
27C22⋊Q8×D61C2218yes—
28C2×#14519736C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×#14519734—21no—
32C2×#14519733—21no—
33#117×D61—24no—
34#117×D61C2218yes—
35C2×C4⋊C4×D61—21no—
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C22⋊C4×D61—21no—
40C2×C22⋊C4×D61—21no—
41C2×C42×D61—21no—
42#16840104C2218yescomplemented
43#16840103C2218yescomplemented
44#16840100C2218yescomplemented
45#16840099C2218yescomplemented
46#16840096C2218yescomplemented
47#16840094C2218yescomplemented
48#16840091C2218yescomplemented
49#16839803C2218yescomplemented
50#16839801C2218yescomplemented
51C2×#14519711C2211yescharacteristic, complemented
52C2×#14519710C2211yescharacteristic, complemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519709C2211yescharacteristic, complemented
55C2×#14519708C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57#16839769C2218yescomplemented
58#16839769C2218yescomplemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519700C2211yescharacteristic, complemented
64C2×#14519700C2211yescharacteristic, complemented
65#16839724C2218yes—
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#485C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C24×D61D411yescharacteristic
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61—24no—
83C2×Q8×D61C2314yes—
84C23×Dic61D411yescharacteristic
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D414yes—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2314yes—
96C22×C4×D61C2311yescharacteristic
97C2×#11758189—24no—
98C2×#11758189—24no—
99C2×#11758189C2314yes—
100C2×#11758189C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519757—22no—
104#14519757C2314yes—
105#14519756—22no—
106#14519756C2314yes—
107#14519755—28no—
108#14519754—28no—
109#14519753—22no—
110#14519753C2314yes—
111#14519736—22no—
112#14519736C2314yes—
113#14519735—22no—
114#14519735—22no—
115#14519735C2314yes—
116#14519735C2314yes—
117#14519734—28no—
118#14519733—28no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C4⋊C4×D61—28no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C22⋊C4×D61—28no—
142C22⋊C4×D61—28no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C42×D61—28no—
147#14519711C2314yescomplemented
148#14519710C2314yescomplemented
149#14519710C2314yescomplemented
150#14519709C2314yescomplemented
151#14519708C2314yescomplemented
152#14519708C2314yescomplemented
153#14519702C2314yescomplemented
154#14519702C2314yescomplemented
155#14519701C2314yescomplemented
156#14519701C2314yescomplemented
157#14519700C2314yescomplemented
158#14519700C2314yescomplemented
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519689C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22⋊Q8×C61—22no—
167C22⋊Q8×C61C2314yes—
168#117×C61—22no—
169#117×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177#107×C61C2314yescomplemented
178#106×C61C2314yescomplemented
179#103×C61C2314yescomplemented
180#103×C61C2314yescomplemented
181C22⋊C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—24no—
184C23×D61—24no—
185C23×D61—42no—
186C23×D61C2×D414yes—
187C23×D61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—24no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D414yes—
210C22×Dic61C2×D411yescharacteristic
211Q8×D61—28no—
212Q8×D61—28no—
213Q8×D61—48no—
214C2×C4×D61—24no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—24no—
218C2×C4×D61—216no—
219C2×C4×D61—28no—
220C2×C4×D61—28no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61C2×D414yes—
230C2×C4×D61C2×D414yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61#4114yes—
234C2×C4×D61#4114yes—
235C2×C4×D61C2412yes—
236C2×C4×D61C2412yes—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—21no—
240C2×Dic122—24no—
241C2×Dic122—44no—
242C2×Dic122C2412yes—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61C2412yes—
246C2×C8×C61C2412yes—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C42×C61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—24no—
267C4⋊Dic61C2412yes—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275C4×Dic61—24no—
276C4×Dic61—24no—
277C4×Dic61—24no—
278C2×#92418—22no—
279C2×#92418—22no—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282#11758189—28no—
283#11758189—28no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—28no—
294C22×D61—28no—
295C22×D61—44no—
296C22×D61—416no—
297C22×D61#12314yes—
298C22×D61#13714yes—
299C22×D61C22×D412yes—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304C2×C4×C61—22no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2511yescharacteristic
321C2×Dic61—22no—
322C2×Dic61—28no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61#12314yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C4×D61—28no—
335C4×D61—24no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—28no—
339C4×D61—48no—
340C4×D61—48no—
341C4×D61—48no—
342C4×D61—48no—
343C4×D61#12318yes—
344C4×D61C2×#4114yes—
345C4×D61C2×#4114yes—
346Dic122—22no—
347Dic122—22no—
348Dic122—42no—
349Dic122—48no—
350C8×C61—22no—
351C8×C61—22no—
352#92418—22no—
353#92418—22no—
354C2×#3095—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—44no—
359C22×C61C2×#12312yes—
360C22×C61C2×#13712yes—
361C22×C61#57512yes—
362C22×C61C23×D411yescharacteristic
363C2×D61—28no—
364C2×D61—28no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—416no—
370C2×D61C2×#12314yes—
371C2×D61C2×#13714yes—
372C4×C61—22no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61C2×#12312yes—
378C4×C61C22×#4111yescharacteristic
379C4×C61C22×#4111yescharacteristic
380Dic61—22no—
381Dic61—42no—
382Dic61—42no—
383Dic61—42no—
384Dic61—42no—
385Dic61C2×#12314yes—
386C22×C22⋊Q8—611no—
387C22×#117—611no—
388#3095—6116no—
389C2×#484—611no—
390C2×#484—611no—
391C2×#485—611no—
392C2×#485—611no—
393C2×#485—611no—
394C2×#485D6111yescharacteristic, complemented
395C2×#483—611no—
396C2×#483—611no—
397C2×#428—611no—
398C2×#428—611no—
399C2×#419—611no—
400C2×#419—611no—
401C2×#407—611no—
402C2×C61—42no—
403C2×C61#309514yescomplemented
404C2×C61C22×#12311yescharacteristic
405C2×C61C22×#13711yescharacteristic
406C2×C61C2×#57511yescharacteristic
407D61—24no—
408D61—24no—
409C23×Q8—611no—
410C24×C4—611no—
411C22×M16—611no—
412C22×M16—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—618no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×C22⋊Q8—1224no—
420C2×C22⋊Q8C2×D6111yescharacteristic
421C2×#117—611no—
422C2×#117—618no—
423C2×#117—611no—
424C2×#117—611no—
425C2×#117—1221no—
426C2×#117—1221no—
427C2×#117—1224no—
428C2×#117C2×D6111yescharacteristic
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—1221no—
433C22×C22⋊C4—1221no—
434C22×C22⋊C4—1221no—
435C22×C42—1221no—
436#485—618no—
437#485—618no—
438#485—618no—
439#485C2×D6118yescomplemented
440#484—618no—
441#484—618no—
442#483—618no—
443#483—618no—
444#428—618no—
445#428—618no—
446C2×#107—611no—
447C2×#107—611no—
448C2×#107—611no—
449C2×#107C2×D6111yescharacteristic, complemented
450C2×#106—611no—
451C2×#106—611no—
452C2×#106—611no—
453C2×#106C2×D6111yescharacteristic, complemented
454#419—618no—
455#419—618no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic, complemented
463C2×#103C2×D6111yescharacteristic, complemented
464#407—618no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8C2×D6111yescharacteristic
469C61C2×#309511yescharacteristic, complemented, Sylow
470C25—611no—
471C22×Q8—614no—
472C22×Q8—611no—
473C22×Q8—1221no—
474C22×Q8—1222no—
475C22×Q8—1224no—
476C22×Q8—1224no—
477C22×Q8C22×D6111yescharacteristic
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—614no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—614no—
485C23×C4—1224no—
486C23×C4—1224no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×M16—614no—
493C2×M16—614no—
494C2×M16—1224no—
495C2×M16—1224no—
496C22×C8—611no—
497C22×C8—611no—
498C22×C8C22×D6111yescharacteristic
499C22×C8C22×D6111yescharacteristic
500C22⋊Q8—22no—
501C22⋊Q8—614no—
502C22⋊Q8—614no—
503C22⋊Q8—614no—
504C22⋊Q8—1228no—
505C22⋊Q8—1228no—
506C22⋊Q8—1222no—
507C22⋊Q8—1222no—
508C22⋊Q8—1222no—
509C22⋊Q8C22×D6114yes—
510#117—22no—
511#117—614no—
512#117—614no—
513#117—614no—
514#117—1228no—
515#117—1228no—
516#117—1222no—
517#117—1222no—
518#117—1222no—
519#117C22×D6114yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1222no—
529C2×C4⋊C4—1222no—
530C2×C4⋊C4—1228no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4C22×D6111yescharacteristic
538C2×C4⋊C4C22×D6111yescharacteristic
539C2×C4⋊C4C22×D6111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1228no—
543C2×C22⋊C4—1228no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C42—21no—
551C2×C42—1228no—
552C2×C42—1221no—
553C2×C42—1221no—
554C2×C42—1221no—
555#107—614no—
556#107—614no—
557#107—614no—
558#107C22×D6114yescomplemented
559#106—614no—
560#106—614no—
561#106—614no—
562#106C22×D6114yescomplemented
563#103—614no—
564#103—614no—
565#103—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103C22×D6114yescomplemented
570#103C22×D6114yescomplemented
571C22⋊C8—614no—
572C22⋊C8—614no—
573C22⋊C8—614no—
574C22⋊C8C22×D6114yes—
575C24—611no—
576C24—611no—
577C24—614no—
578C24—1224no—
579C24—1224no—
580C24—2442no—
581C24D4×D6111yescharacteristic
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—612no—
586C2×Q8—1224no—
587C2×Q8—1228no—
588C2×Q8—1228no—
589C2×Q8—1221no—
590C2×Q8—1222no—
591C2×Q8—1222no—
592C2×Q8—2444no—
593C2×Q8—2448no—
594C2×Q8C23×D6112yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—611no—
602C22×C4—612no—
603C22×C4—614no—
604C22×C4—614no—
605C22×C4—612no—
606C22×C4—614no—
607C22×C4—611no—
608C22×C4—614no—
609C22×C4—614no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—1224no—
613C22×C4—12216no—
614C22×C4—1228no—
615C22×C4—1228no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1224no—
621C22×C4—1224no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4D4×D6112yes—
633C22×C4D4×D6111yescharacteristic
634C22×C4C23×D6112yes—
635C22×C4C23×D6111yescharacteristic
636M16—1228no—
637M16—1228no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—612no—
641C2×C8—612no—
642C2×C8—1222no—
643C2×C8—1222no—
644C2×C8C23×D6112yes—
645C2×C8C23×D6112yes—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—612no—
653C4⋊C4—1224no—
654C4⋊C4—1224no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1224no—
662C4⋊C4C23×D6112yes—
663C4⋊C4C23×D6112yes—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C42—24no—
674C42—1224no—
675C42—1224no—
676C42—1224no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—614no—
681C23—614no—
682C23—612no—
683C23—612no—
684C23—1228no—
685C23—1228no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—2444no—
691C23—24416no—
692C23C2×D4×D6112yes—
693C23C2×D4×D6111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—1222no—
698Q8—1222no—
699Q8—2448no—
700Q8—2442no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—614no—
714C2×C4—612no—
715C2×C4—618no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—612no—
719C2×C4—1228no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1222no—
723C2×C4—1224no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—2448no—
731C2×C4—2448no—
732C2×C4—2448no—
733C2×C4—2448no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4C2×D4×D6112yes—
739C2×C4C2×D4×D6111yescharacteristic
740C2×C4#41×D6112yes—
741C2×C4#41×D6112yes—
742C2×C4C24×D6111yescharacteristic
743C8—22no—
744C8—22no—
745C8—1222no—
746C8—1222no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—614no—
752C22—614no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—1228no—
758C22—1228no—
759C22—24416no—
760C22#123×D6112yes—
761C22#137×D6112yes—
762C22#1684055912yes—
763C22C22×D4×D6111yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—614no—
770C4—1222no—
771C4—2442no—
772C4—2442no—
773C4—2442no—
774C4—2442no—
775C4#123×D6112yes—
776C4C2×#41×D6111yescharacteristic
777C4C2×#41×D6111yescharacteristic
778C2—42no—
779C2—1224no—
780C2—1224no—
781C2#2145576614yesdirect product factor
782C2C2×#123×D6111yescharacteristic
783C2C2×#137×D6111yescharacteristic
784C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenterC2×#485D61
hypocenterC61C2×#3095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #21455766C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840104C2semidirect
7. C2×#16840103C2semidirect
8. C2×#16840100C2semidirect
9. C2×#16840094C2semidirect
10. C2×#16840091C2semidirect
11. C2×#16839803C2semidirect
12. C2×#16839801C2semidirect
13. C2×#16839769C2semidirect
14. C2×#16839769C2semidirect
16. C2×C61×#485C2semidirect
42. #16840104C22semidirect
43. #16840103C22semidirect
44. #16840100C22semidirect
45. #16840099C22semidirect
46. #16840096C22semidirect
47. #16840094C22semidirect
48. #16840091C22semidirect
49. #16839803C22semidirect
50. #16839801C22semidirect
51. C2×#14519711C22semidirect
52. C2×#14519710C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519709C22semidirect
55. C2×#14519708C22semidirect
56. C2×#14519708C22semidirect
57. #16839769C22semidirect
58. #16839769C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519701C22semidirect
63. C2×#14519700C22semidirect
64. C2×#14519700C22semidirect
71. C61×#485C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#103×C61C22semidirect
147. #14519711C23semidirect
148. #14519710C23semidirect
149. #14519710C23semidirect
150. #14519709C23semidirect
151. #14519708C23semidirect
152. #14519708C23semidirect
153. #14519702C23semidirect
154. #14519702C23semidirect
155. #14519701C23semidirect
156. #14519701C23semidirect
157. #14519700C23semidirect
158. #14519700C23semidirect
177. #107×C61C23semidirect
178. #106×C61C23semidirect
179. #103×C61C23semidirect
180. #103×C61C23semidirect
394. C2×#485D61semidirect
403. C2×C61#3095semidirect
439. #485C2×D61semidirect
449. C2×#107C2×D61semidirect
453. C2×#106C2×D61semidirect
462. C2×#103C2×D61semidirect
463. C2×#103C2×D61semidirect
469. C61C2×#3095semidirect
558. #107C22×D61semidirect
562. #106C22×D61semidirect
569. #103C22×D61semidirect
570. #103C22×D61semidirect
781. C2#21455766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C2×#117×D612
#214557662
C2×#168400992
C2×#168400962
C2×#168401042
C2×#168401032
C2×#168401002
C2×#168400942
C2×#168400912
C2×#168398032
C2×#168398012
C2×#168397692
C2×#168397242
C2×C61×#4852
C2×#309561