Finite Group Databasebeta

← C2×#21458566 #30559756

Subgroups — C2×#21458566 #30559756

Order 15616.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840472C211yesmaximal, characteristic, complemented
2#21458566C2116yesmaximal, direct product factor
3C2×#16840126C211yesmaximal, characteristic, complemented
4C2×#16840121C211yesmaximal, characteristic, complemented
5C2×#16840116C211yesmaximal, characteristic, complemented
6C2×#16840069C211yesmaximal, characteristic, complemented
7C2×#16840062C211yesmaximal, characteristic, complemented
8C2×#16840042C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839954C211yesmaximal, characteristic
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×C4×#11758199C211yesmaximal, characteristic, complemented
16C2×C61×#559C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20#16840472—24no—
21#16840472C2218yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519769C2211yescharacteristic
24C2×#14519769C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519755—21no—
27C2×#14519753—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×C4⋊C4×D61—21no—
32#16840126C2218yescomplemented
33#16840121C2218yescomplemented
34#16840116C2218yescomplemented
35#16840069C2218yescomplemented
36#16840062C2218yescomplemented
37#16840042C2218yescomplemented
38#16839974C2218yescomplemented
39#16839974C2218yescomplemented
40#16839954C2218yes—
41#16839893C2218yescomplemented
42#16839872C2218yescomplemented
43#16839860C2218yescomplemented
44C4×#11758199C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49C2×C4⋊#92418C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519698C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#559—24no—
65C61×#559C2218yescomplemented
66C2×#127×C61C2211yescharacteristic
67C2×#124×C61—21no—
68C2×#124×C61C2211yescharacteristic
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×#123×C61—21no—
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C2×C4×D4×C61—21no—
75C2×C4×D4×C61C2211yescharacteristic
76C2×C4×D4×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244C2311yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C2×#11758201—24no—
83C2×#11758201C2314yes—
84C2×#11758199—24no—
85C2×#11758199—24no—
86C2×#11758199C2314yes—
87C2×#11758199C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519777—22no—
93#14519777C2314yes—
94#14519769—22no—
95#14519769—22no—
96#14519769C2314yes—
97#14519769C2314yes—
98#14519755—28no—
99#14519755—28no—
100#14519753—28no—
101C4×D244—22no—
102C4×D244—22no—
103C4×D244—22no—
104C4×D244C2314yes—
105C4×D244C2314yes—
106C4×D244C2314yes—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C4⋊C4×D61—28no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119#14519710C2314yes—
120#14519710C2314yes—
121#14519708C2314yes—
122C4⋊#92418C2314yes—
123C4⋊#92418C2314yes—
124C4⋊#92418C2314yes—
125#14519701C2314yes—
126#14519701C2314yes—
127#14519701C2314yes—
128#14519698C2314yes—
129#14519698C2314yes—
130#14519698C2314yes—
131#14519698C2314yes—
132#14519698C2314yes—
133#14519698C2314yes—
134#14519697C2314yes—
135#14519688C2314yes—
136#14519688C2314yes—
137C4×#92418C2314yes—
138C22×Q8×C61D411yescharacteristic
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61—21no—
146#127×C61—22no—
147#127×C61C2314yes—
148#124×C61—28no—
149#124×C61—22no—
150#124×C61—22no—
151#124×C61C2314yes—
152#124×C61C2314yes—
153#123×C61—28no—
154#123×C61—28no—
155C4×Q8×C61—22no—
156C4×Q8×C61D414yes—
157C4×Q8×C61C2314yes—
158C4×Q8×C61C2314yes—
159C4×D4×C61—28no—
160C4×D4×C61—22no—
161C4×D4×C61—22no—
162C4×D4×C61C2314yes—
163C4×D4×C61C2314yes—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61D411yescharacteristic
166C2×C4⋊C4×C61D411yescharacteristic
167C2×C4⋊C4×C61D411yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C24×C61—21no—
180C24×C61—21no—
181C23×D61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—42no—
186C2×Q8×C61C2×D414yes—
187C2×Q8×C61C2412yes—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—44no—
197C2×D4×C61—82no—
198C2×D4×C61C2412yes—
199C2×D4×C61C2412yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—24no—
204C22×C4×C61—82no—
205C22×C4×C61—82no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C2×D244—21no—
217C2×D244—22no—
218C2×D244#4114yes—
219C2×D244C2412yes—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—44no—
224C2×C4×D61—82no—
225C2×C4×D61—82no—
226C2×Dic122—24no—
227C2×Dic122—82no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C2×D414yes—
231C4⋊C4×C61C2×D414yes—
232C4⋊C4×C61C2×D414yes—
233C4⋊C4×C61C2412yes—
234C22⋊C4×C61—24no—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C42×C61—24no—
241C42×C61C2×D412yes—
242C42×C61C2×D412yes—
243C42×C61C2×D412yes—
244C42×C61C2412yes—
245C42×C61C2412yes—
246C42×C61C2412yes—
247#11758201—28no—
248#11758199—28no—
249#11758199—28no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61C22×D411yescharacteristic
281C22×D61—24no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—44no—
288Q8×C61—42no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—48no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—84no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—84no—
308C2×C4×C61—84no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4112yes—
317C2×C4×C612−1+412yes—
318C2×C4×C61C2511yescharacteristic
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325D244—24no—
326D244—22no—
327D244C2×#4114yes—
328C4×D61—48no—
329C4×D61—84no—
330C4×D61—84no—
331Dic122—84no—
332#92418—22no—
333#92418—22no—
334#92418—22no—
335#92418—22no—
336C2×#3370—611nomaximal, Sylow
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—84no—
344C22×C61—84no—
345C22×C61#54812yes—
346C22×C61#57512yes—
347C22×C61#57612yes—
348C22×C61C23×D411yescharacteristic
349C2×D61—24no—
350C2×D61—48no—
351C2×D61—42no—
352C2×D61—42no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61#54812yes—
362C4×C61C22×#4111yescharacteristic
363C4×C61C2×2−1+411yescharacteristic
364Dic61—42no—
365Dic61—42no—
366Dic61—42no—
367C2×#559D6111yescharacteristic, complemented
368C2×#554—611no—
369#3370—6116no—
370C2×#490—611no—
371C2×#489—611no—
372C2×#488—611no—
373C2×#479—611no—
374C2×#478—611no—
375C2×#474—611no—
376C2×#463—611no—
377C2×#463—611no—
378C2×#459—611no—
379C2×#446—611no—
380C2×#442—611no—
381C2×#440—611no—
382C2×C4×D8—611no—
383C2×C61—82no—
384C2×C61—82no—
385C2×C61#337014yescomplemented
386C2×C61C2×#54811yescharacteristic
387C2×C61C2×#57511yescharacteristic
388C2×C61C2×#57611yescharacteristic
389D61—44no—
390C22×SD16—611no—
391C22×D8—611no—
392C22×D8—611no—
393#559—24no—
394#559C2×D6118yescomplemented
395#554—618no—
396#554—1224no—
397C2×C4⋊Q8—611no—
398C2×#127C2×D6111yescharacteristic
399C2×#125—611no—
400C2×#125—611no—
401C2×#124—21no—
402C2×#124C2×D6111yescharacteristic
403C2×#124C2×D6111yescharacteristic
404C2×#123—21no—
405C2×#123—21no—
406C2×C22⋊Q8—1221no—
407C2×C22⋊Q8—1221no—
408C2×C22⋊Q8—1221no—
409C2×C4×Q8C2×D6111yescharacteristic
410C2×C4×Q8C2×D6111yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4C2×D6111yescharacteristic
416C2×C4×D4C2×D6111yescharacteristic
417C22×C4⋊C4—1221no—
418#490—618no—
419#489—618no—
420#488—618no—
421#479—618no—
422#478—618no—
423#474—618no—
424#463—618no—
425#463—618no—
426#459—618no—
427#446—618no—
428#442—618no—
429#440—618no—
430C4×D8—618no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#97—611no—
448C2×#97—611no—
449C2×C4×C8—611no—
450C61C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—1221no—
452C22×Q8C22⋊D6111yescharacteristic
453C22×Q8C22×D6111yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—611no—
457C22×D4C22×D6111yescharacteristic
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C2×SD16—614no—
465C2×SD16—1224no—
466C2×D8—614no—
467C2×D8—614no—
468C2×D8—1224no—
469C2×D8—1224no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C4⋊Q8—614no—
475C4⋊Q8—1222no—
476#127—22no—
477#127C22×D6114yes—
478#125—614no—
479#125—614no—
480#125—1222no—
481#125—1222no—
482#124—28no—
483#124—22no—
484#124—22no—
485#124C22×D6114yes—
486#124C22×D6114yes—
487#123—28no—
488#123—28no—
489C22⋊Q8—1228no—
490C22⋊Q8—1228no—
491C22⋊Q8—1228no—
492C4×Q8—22no—
493C4×Q8C22⋊D6114yes—
494C4×Q8C22×D6114yes—
495C4×Q8C22×D6114yes—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—614no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4C22×D6114yes—
506C4×D4C22×D6114yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1228no—
517C2×C4⋊C4C22⋊D6111yescharacteristic
518C2×C4⋊C4C22⋊D6111yescharacteristic
519C2×C4⋊C4C22⋊D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—21no—
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533C2×C42C22×D6111yescharacteristic
534#107—614no—
535#107—614no—
536#106—614no—
537C4⋊C8—614no—
538C4⋊C8—614no—
539C4⋊C8—614no—
540#103—614no—
541#103—614no—
542#103—614no—
543#102—614no—
544#102—614no—
545#102—614no—
546#102—614no—
547#102—614no—
548#102—614no—
549#102—614no—
550#97—614no—
551#97—614no—
552C4×C8—614no—
553C24—21no—
554C24—21no—
555C24—1221no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—1224no—
561C2×Q8—4882no—
562C2×Q8C2×C22⋊D6114yes—
563C2×Q8C23×D6112yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—82no—
574C2×D4—614no—
575C2×D4—612no—
576C2×D4—1221no—
577C2×D4—1222no—
578C2×D4C23×D6112yes—
579C2×D4C23×D6112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1224no—
592C22×C4—4882no—
593C22×C4—4882no—
594C22×C4—2444no—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603D8—1228no—
604D8—1228no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—1222no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4C2×C22⋊D6114yes—
627C4⋊C4C2×C22⋊D6114yes—
628C4⋊C4C2×C22⋊D6114yes—
629C4⋊C4C23×D6112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—24no—
640C42C2×C22⋊D6112yes—
641C42C2×C22⋊D6112yes—
642C42C2×C22⋊D6112yes—
643C42C23×D6112yes—
644C42C23×D6112yes—
645C42C23×D6112yes—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1222no—
655C23—1224no—
656C23—2442no—
657C23—2442no—
658C23C22×C22⋊D6111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—4884no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—614no—
673D4—1222no—
674D4—1224no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—4884no—
691C2×C4—4884no—
692C2×C4—2448no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4C22×C22⋊D6112yes—
697C2×C4C22×C22⋊D6112yes—
698C2×C4C22×C22⋊D6112yes—
699C2×C4C22×C22⋊D6112yes—
700C2×C4C22×C22⋊D6112yes—
701C2×C4C22×C22⋊D6112yes—
702C2×C4C22×C22⋊D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4#1451982412yes—
705C2×C4C24×D6111yescharacteristic
706C8—1222no—
707C8—1222no—
708C8—1222no—
709C8—1222no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—1224no—
719C22—2442no—
720C22—2442no—
721C22—2448no—
722C22#1684041912yes—
723C22#1684056012yes—
724C22#1684056512yes—
725C22C23×C22⋊D6111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041912yes—
738C4C2×#41×D6111yescharacteristic
739C4C2×#1451982411yescharacteristic
740C2—82no—
741C2—82no—
742C2—2444no—
743C2#2145856614yesdirect product factor
744C2C2×#1684041911yescharacteristic
745C2C2×#1684056011yescharacteristic
746C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#559C2
socleC23×C61C22×D4
prime radicalC2×#16839954C2
hypercenterC2×#559D61
hypocenterC61C2×#3370
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16840472C2semidirect
2. #21458566C2direct (N × H)
3. C2×#16840126C2semidirect
4. C2×#16840121C2semidirect
5. C2×#16840116C2semidirect
6. C2×#16840069C2semidirect
7. C2×#16840062C2semidirect
8. C2×#16840042C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839974C2semidirect
12. C2×#16839893C2semidirect
13. C2×#16839872C2semidirect
14. C2×#16839860C2semidirect
15. C2×C4×#11758199C2semidirect
16. C2×C61×#559C2semidirect
21. #16840472C22semidirect
32. #16840126C22semidirect
33. #16840121C22semidirect
34. #16840116C22semidirect
35. #16840069C22semidirect
36. #16840062C22semidirect
37. #16840042C22semidirect
38. #16839974C22semidirect
39. #16839974C22semidirect
41. #16839893C22semidirect
42. #16839872C22semidirect
43. #16839860C22semidirect
44. C4×#11758199C22semidirect
65. C61×#559C22semidirect
367. C2×#559D61semidirect
385. C2×C61#3370semidirect
394. #559C2×D61semidirect
450. C61C2×#3370semidirect
743. C2#21458566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404722
#214585662
C2×#168401262
C2×#168401212
C2×#168401162
C2×#168400692
C2×#168400622
C2×#168400422
C2×#168399742
C2×#168399542
C2×#168398932
C2×#168398722
C2×#168398602
C2×C4×#117581992
C2×C61×#5592
C2×#337061