Finite Group Databasebeta

← C2×#21459409 #30587067

Subgroups — C2×#21459409 #30587067

Order 15616.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459409C2132yesmaximal, direct product factor
2C2×#16840494C213yesmaximal, complemented
3C2×#16840488C211yesmaximal, characteristic, complemented
4C2×#16840483C213yesmaximal, complemented
5C2×#16840464C213yesmaximal, complemented
6C2×#16840458C213yesmaximal, complemented
7C2×#16840431C211yesmaximal, characteristic, complemented
8C2×#16840423C211yesmaximal, characteristic, complemented
9C2×#16840307C213yesmaximal, complemented
10C2×#16840298C213yesmaximal, complemented
11C2×#16840291C213yesmaximal, complemented
12C2×#41×Dic61C211yesmaximal, characteristic, complemented
13C2×C4×#11758226C211yesmaximal, characteristic, complemented
14C2×C4×#11758224C213yesmaximal, complemented
15C22×Q8×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2213yes—
19#16840494C22148yescomplemented
20#16840488C22116yescomplemented
21#16840483C22148yescomplemented
22#16840464C22148yescomplemented
23#16840458C22148yescomplemented
24#16840431C22116yescomplemented
25#16840423C22116yescomplemented
26#16840307C22148yescomplemented
27C2×#14519776C2213yes—
28C2×#14519773C2213yes—
29#16840298C22148yescomplemented
30#16840291C22148yescomplemented
31C2×#14519772C2216yes—
32C2×#14519770C2216yes—
33C2×#14519769C2213yes—
34C2×#14519768C2213yes—
35C2×#14519766C2213yes—
36C2×#14519763C2216yes—
37C2×#14519761C2216yes—
38C2×#14519759C2216yes—
39C2×#14519753C2213yes—
40C2×#14519751C2213yes—
41C2×#14519751C2213yes—
42C2×#14519749C2216yes—
43C2×#14519748C2213yes—
44#41×Dic61C22116yescomplemented
45C4×#11758226C22116yescomplemented
46C4×#11758224C22148yescomplemented
47C2×Q8×Dic61C2211yescharacteristic
48C2×Q8×Dic61C2211yescharacteristic
49C2×Q8×Dic61C2213yes—
50C2×Q8×Dic61C2213yes—
51C2×Q8×Dic61C2211yescharacteristic
52C2×Q8×Dic61C22116yescomplemented
53C2×C4×Dic122C2213yes—
54C2×#14519742C2213yes—
55C2×C4×D244C2213yes—
56C2×D4×Dic61C2213yes—
57C2×D4×Dic61C2213yes—
58C2×D4×Dic61C2213yes—
59C2×#14519739C2213yes—
60C2×C4×C22⋊D61C2213yes—
61C2×C4×C22⋊D61C2213yes—
62C2×#14519737C2213yes—
63C2×#14519737C2213yes—
64C2×#14519737C2216yes—
65C2×#14519736C2213yes—
66C2×#14519735C2213yes—
67C2×#14519735C2213yes—
68C2×#14519733C2211yescharacteristic
69C2×#14519733C2213yes—
70C22×C4⋊Dic61C2213yes—
71C22×C4×Dic61C2213yes—
72C22×C4×Dic61C2213yes—
73C2×C42×D61C2213yes—
74C22×#41×C61C2211yescharacteristic
75C23×Q8×C61C2211yescharacteristic
76C61×#548C22116yescomplemented
77C2×#124×C61C2213yes—
78C2×C22⋊Q8×C61C2213yes—
79C2×#121×C61C2213yes—
80C2×C4×Q8×C61C2211yescharacteristic
81C2×C4×D4×C61C2213yes—
82C2×#11758226—28no—
83C2×#11758226C2318yes—
84C2×#11758224—224no—
85C2×#11758224C23124yes—
86C22×Dic122C2313yes—
87C22×D244C2313yes—
88C22×C22⋊D61C2313yes—
89C22×C22⋊D61C2313yes—
90C22×C22⋊D61C2316yes—
91C23×Dic61C2313yes—
92C23×Dic61C2313yes—
93C23×Dic61C2313yes—
94C23×Dic61C2311yescharacteristic
95C22×C4×D61C2313yes—
96C22×C4×D61C2313yes—
97C22×C4×D61C2313yes—
98#14519776C23124yes—
99#14519773C23124yes—
100#14519772C23148yes—
101#14519770C23148yes—
102#14519769C23124yes—
103#14519768C23124yes—
104#14519766C23124yes—
105#14519763C23148yes—
106#14519761C23148yes—
107#14519759C23148yes—
108#14519753C23124yes—
109#14519751C23124yes—
110#14519751C23124yes—
111#14519749C23148yes—
112#14519748C23124yes—
113Q8×Dic61C23124yes—
114Q8×Dic61C2318yes—
115Q8×Dic61C2318yes—
116Q8×Dic61C23124yes—
117Q8×Dic61C2318yes—
118C4×Dic122C23124yes—
119#14519742C23124yes—
120C4×D244C23124yes—
121D4×Dic61C23124yes—
122D4×Dic61C23124yes—
123D4×Dic61C23124yes—
124#14519739C23124yes—
125C4×C22⋊D61C23124yes—
126C4×C22⋊D61C23124yes—
127#14519737C23124yes—
128#14519737C23124yes—
129#14519737C23148yes—
130#14519736C23124yes—
131#14519735C23124yes—
132#14519735C23124yes—
133#14519733C2318yes—
134#14519733C23124yes—
135C2×C4⋊Dic61C23124yes—
136C2×C4⋊Dic61C2313yes—
137C2×C4⋊Dic61C2313yes—
138C2×C4⋊Dic61C2316yes—
139C2×C4⋊Dic61C2313yes—
140C2×C4⋊Dic61C2313yes—
141C2×#11758196C2311yescharacteristic
142C2×#11758196C2313yes—
143C2×#11758196C2311yescharacteristic
144C2×#11758196C2313yes—
145C2×#11758196C2316yes—
146C2×C22⋊Dic61C2311yescharacteristic
147C2×C22⋊Dic61C2313yes—
148C2×C22⋊Dic61C2316yes—
149C2×#11758198C2313yes—
150C2×#11758198C2313yes—
151C2×#11758198C2316yes—
152C2×#11758198C2316yes—
153C2×C4×Dic61C2311yescharacteristic
154C2×C4×Dic61C2313yes—
155C2×C4×Dic61C2313yes—
156C2×C4×Dic61C2311yescharacteristic
157C2×C4×Dic61C2313yes—
158C2×C4×Dic61C2313yes—
159C2×C4×Dic61C2313yes—
160C2×C4×Dic61C2313yes—
161C2×C4×Dic61C2313yes—
162C2×C4×Dic61C23124yes—
163C2×C4×Dic61C23124yes—
164C42×D61C23124yes—
165C2×#41×C61—28no—
166C2×#41×C61C2318yes—
167C22×Q8×C61—28no—
168C22×Q8×C61C2318yes—
169C22×Q8×C61C2313yes—
170C22×Q8×C61C2311yescharacteristic
171C22×D4×C61C2313yes—
172C22×D4×C61C2313yes—
173C23×C4×C61C2313yes—
174C23×C4×C61C2313yes—
175#124×C61C23124yes—
176C22⋊Q8×C61C23124yes—
177#121×C61C23124yes—
178C4×Q8×C61C2318yes—
179C4×D4×C61C23124yes—
180C2×C4⋊C4×C61C2313yes—
181C2×C4⋊C4×C61C2313yes—
182C2×C22⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61C2313yes—
184C2×C22⋊C4×C61C2316yes—
185C2×C42×C61C2313yes—
186C24×C61C2413yes—
187C24×C61C2411yescharacteristic
188C23×D61C2413yes—
189#41×C61—232no—
190C2×Q8×C61—232no—
191C2×Q8×C61—212no—
192C2×Q8×C61#4118yescomplemented
193C2×Q8×C61C24112yes—
194C2×Q8×C61C2414yes—
195C2×D4×C61—212no—
196C2×D4×C61—212no—
197C2×D4×C61C24112yes—
198C2×D4×C61C24112yes—
199C22×C4×C61—212no—
200C22×C4×C61—212no—
201C22×C4×C61C2411yescharacteristic
202C22×C4×C61C2413yes—
203C22×C4×C61C2413yes—
204C22×C4×C61C2411yescharacteristic
205C22×C4×C61C24112yes—
206C22×C4×C61C24112yes—
207C22×C4×C61C2413yes—
208C2×C22⋊D61—212no—
209C2×C22⋊D61—212no—
210C2×C22⋊D61—412no—
211C2×C22⋊D61C24112yes—
212C2×C22⋊D61C24112yes—
213C2×C22⋊D61C24124yes—
214C22×Dic61—212no—
215C22×Dic61—46no—
216C22×Dic61—46no—
217C22×Dic61#4118yescomplemented
218C22×Dic61C2411yescharacteristic
219C22×Dic61C2413yes—
220C22×Dic61C2411yescharacteristic
221C22×Dic61C2413yes—
222C22×Dic61C2413yes—
223C22×Dic61C24112yes—
224C22×Dic61C24112yes—
225C22×Dic61C24112yes—
226C22×Dic61C2411yescharacteristic
227C22×Dic61C2411yescharacteristic
228C22×Dic61C2414yes—
229#11758226—232no—
230#11758224—296no—
231C2×D244—212no—
232C2×D244C24112yes—
233C2×C4×D61—212no—
234C2×C4×D61—212no—
235C2×C4×D61—46no—
236C2×C4×D61C24112yes—
237C2×C4×D61C24112yes—
238C2×C4×D61C24112yes—
239C2×Dic122—212no—
240C2×Dic122C24112yes—
241C4⋊C4×C61C24112yes—
242C4⋊C4×C61C24112yes—
243C22⋊C4×C61C2414yes—
244C22⋊C4×C61C24112yes—
245C22⋊C4×C61C24124yes—
246C42×C61C24112yes—
247C22⋊Dic61C2414yes—
248C22⋊Dic61C24112yes—
249C22⋊Dic61C24124yes—
250#11758198C24112yes—
251#11758198C24112yes—
252#11758198C24124yes—
253#11758198C24124yes—
254C4⋊Dic61C24112yes—
255C4⋊Dic61C24112yes—
256C4⋊Dic61C24124yes—
257C4⋊Dic61C24112yes—
258C4⋊Dic61C24112yes—
259#11758196C2414yes—
260#11758196C24112yes—
261#11758196C2414yes—
262#11758196C24112yes—
263#11758196C24124yes—
264C4×Dic61C2414yes—
265C4×Dic61C24112yes—
266C4×Dic61C24112yes—
267C4×Dic61C2414yes—
268C4×Dic61C24112yes—
269C4×Dic61C24112yes—
270C4×Dic61C24112yes—
271C4×Dic61C24112yes—
272C4×Dic61C24112yes—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—26no—
276C23×C61—26no—
277C23×C61—26no—
278C23×C61C2×#4114yes—
279C23×C61C2516yes—
280C23×C61C2512yes—
281C23×C61C2511yescharacteristic
282C22×D61—26no—
283C22×D61—26no—
284C22×D61—26no—
285C22×D61C2516yes—
286Q8×C61—224no—
287Q8×C61C2×#41116yescomplemented
288D4×C61—224no—
289D4×C61—224no—
290C2×C4×C61—26no—
291C2×C4×C61—22no—
292C2×C4×C61—26no—
293C2×C4×C61—22no—
294C2×C4×C61—224no—
295C2×C4×C61—224no—
296C2×C4×C61C2×#41112yes—
297C2×C4×C61C2512yes—
298C2×C4×C61C2516yes—
299C2×C4×C61C2512yes—
300C2×C4×C61C2516yes—
301C2×C4×C61C2516yes—
302C22⋊D61—224no—
303C22⋊D61—224no—
304C22⋊D61—424no—
305C2×Dic61—26no—
306C2×Dic61—22no—
307C2×Dic61—26no—
308C2×Dic61—22no—
309C2×Dic61—26no—
310C2×Dic61—224no—
311C2×Dic61—412no—
312C2×Dic61—412no—
313C2×Dic61C2×#4114yes—
314C2×Dic61C2×#4114yes—
315C2×Dic61C2×#41116yescomplemented
316C2×Dic61C2512yes—
317C2×Dic61C2512yes—
318C2×Dic61C2516yes—
319C2×Dic61C2516yes—
320C2×Dic61C2516yes—
321C2×Dic61C2512yes—
322C2×Dic61C2512yes—
323D244—224no—
324C4×D61—224no—
325C4×D61—224no—
326C4×D61—412no—
327Dic122—224no—
328C2×#3480—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—28no—
332C22×C61—26no—
333C22×C61—26no—
334C22×C61—26no—
335C22×C61—412no—
336C22×C61C22×#4114yes—
337C22×C61C22×#4112yes—
338C22×C61C22×#4112yes—
339C22×C61#58512yes—
340C22×C61C2611yescharacteristic
341C2×D61—26no—
342C2×D61—26no—
343C2×D61—26no—
344C2×D61—412no—
345C4×C61—26no—
346C4×C61—22no—
347C4×C61—26no—
348C4×C61—22no—
349C4×C61C22×#41112yes—
350Dic61—26no—
351Dic61—22no—
352Dic61—26no—
353Dic61—22no—
354Dic61—26no—
355Dic61C22×#4114yes—
356Dic61C22×#4114yes—
357#3480—6132no—
358C2×#559—613no—
359C2×#557—611no—
360C2×#556—613no—
361C2×#553—613no—
362C2×#553—613no—
363C2×#550—611no—
364C2×#548—611no—
365C2×#548D6111yescharacteristic, complemented
366C2×#532—613no—
367C2×#529—613no—
368C2×#529—613no—
369C2×C4×#41—611no—
370C2×C4×#41—611no—
371C2×C4×#41—613no—
372C22×C4×Q8—611no—
373C2×C61—24no—
374C2×C61—46no—
375C2×C61#348014yescomplemented
376C2×C61C23×#4111yescharacteristic
377C2×C61C23×#4111yescharacteristic
378C2×C61C2×#58511yescharacteristic
379D61—46no—
380C22×#41—611no—
381C22×#41—613no—
382C22×#41C2×D6111yescharacteristic
383C23×Q8C2×D6111yescharacteristic
384#559—6148no—
385#557—6116no—
386#556—6148no—
387#553—6148no—
388#553—6148no—
389#550—6116no—
390#548—6116no—
391#548C2×D61116yescomplemented
392#532—6148no—
393C2×C4⋊Q8—613no—
394C2×#127—613no—
395#529—6148no—
396#529—6148no—
397C2×#126—616no—
398C2×#126—616no—
399C2×#125—613no—
400C2×#125—613no—
401C2×#124—613no—
402C2×#124—616no—
403C2×#124C2×D6113yes—
404C2×#123—616no—
405C2×#123—616no—
406C2×C22⋊Q8—613no—
407C2×C22⋊Q8C2×D6113yes—
408C2×#121—613no—
409C2×#121—616no—
410C2×#121—613no—
411C2×#121—613no—
412C2×#121C2×D6113yes—
413C4×#41—6116no—
414C4×#41—6116no—
415C4×#41—6148no—
416C2×C4×Q8—611no—
417C2×C4×Q8—613no—
418C2×C4×Q8—611no—
419C2×C4×Q8—613no—
420C2×C4×Q8—611no—
421C2×C4×Q8—6116no—
422C2×C4×Q8—613no—
423C2×C4×Q8—613no—
424C2×C4×Q8C2×D6111yescharacteristic
425C2×C4×D4—613no—
426C2×C4×D4—613no—
427C2×C4×D4—613no—
428C2×C4×D4—613no—
429C2×C4×D4—613no—
430C2×C4×D4—613no—
431C2×C4×D4—613no—
432C2×C4×D4—613no—
433C2×C4×D4—616no—
434C2×C4×D4—613no—
435C2×C4×D4C2×D6113yes—
436C2×#117—613no—
437C2×#117—613no—
438C2×#117—613no—
439C2×#117—611no—
440C2×#117—613no—
441C22×C4⋊C4—613no—
442C22×C42—613no—
443C22×C42—613no—
444C22×C42—613no—
445C61C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—618no—
448C2×#41—6124no—
449C2×#41—12224no—
450C2×#41—1228no—
451C2×#41C22×D6118yes—
452C22×Q8—28no—
453C22×Q8—613no—
454C22×Q8C22×D6113yes—
455C22×Q8C22×D6118yes—
456C22×Q8C22×D6111yescharacteristic
457C22×D4—613no—
458C22×D4—613no—
459C22×D4—616no—
460C22×D4—613no—
461C22×D4C22×D6113yes—
462C22×D4C22×D6113yes—
463C23×C4—611no—
464C23×C4—613no—
465C23×C4—613no—
466C23×C4—613no—
467C23×C4—613no—
468C23×C4—613no—
469C23×C4—613no—
470C23×C4C22×D6113yes—
471C23×C4C22×D6113yes—
472C4⋊Q8—6124no—
473#127—6124no—
474#126—6148no—
475#126—6148no—
476#125—6124no—
477#125—6124no—
478#124—6124no—
479#124—6148no—
480#124C22×D61124yes—
481#123—6148no—
482#123—6148no—
483C22⋊Q8—6124no—
484C22⋊Q8C22×D61124yes—
485#121—6124no—
486#121—6148no—
487#121—6124no—
488#121—6124no—
489#121C22×D61124yes—
490C4×Q8—618no—
491C4×Q8—6124no—
492C4×Q8—618no—
493C4×Q8—6124no—
494C4×Q8—618no—
495C4×Q8—6124no—
496C4×Q8—6124no—
497C4×Q8C22×D6118yes—
498C4×D4—6124no—
499C4×D4—6124no—
500C4×D4—6124no—
501C4×D4—6124no—
502C4×D4—6124no—
503C4×D4—6124no—
504C4×D4—6124no—
505C4×D4—6124no—
506C4×D4—6148no—
507C4×D4—6124no—
508C4×D4C22×D61124yes—
509#117—6124no—
510#117—6124no—
511#117—6124no—
512#117—618no—
513#117—6124no—
514C2×C4⋊C4—613no—
515C2×C4⋊C4—613no—
516C2×C4⋊C4—616no—
517C2×C4⋊C4—6124no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—613no—
521C2×C4⋊C4—613no—
522C2×C4⋊C4—613no—
523C2×C4⋊C4—613no—
524C2×C4⋊C4—616no—
525C2×C4⋊C4C22×D6113yes—
526C2×C4⋊C4C22×D6113yes—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—613no—
529C2×C22⋊C4—616no—
530C2×C22⋊C4—613no—
531C2×C22⋊C4—616no—
532C2×C22⋊C4—613no—
533C2×C22⋊C4—616no—
534C2×C22⋊C4C22×D6111yescharacteristic
535C2×C22⋊C4C22×D6113yes—
536C2×C22⋊C4C22×D6116yes—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—613no—
540C2×C42—613no—
541C2×C42—613no—
542C2×C42—613no—
543C2×C42—613no—
544C2×C42—613no—
545C2×C42—613no—
546C2×C42—6124no—
547C2×C42—6124no—
548C2×C42—6124no—
549C2×C42C22×D6113yes—
550C24—613no—
551C24C23×D6113yes—
552C24C23×D6111yescharacteristic
553#41—232no—
554#41—12296no—
555#41—12232no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—6112no—
559C2×Q8—12212no—
560C2×Q8#1175822418yescomplemented
561C2×Q8C23×D61112yes—
562C2×Q8C23×D6114yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—6112no—
566C2×D4—6112no—
567C2×D4—6124no—
568C2×D4—6112no—
569C2×D4—12212no—
570C2×D4—12212no—
571C2×D4—12212no—
572C2×D4—24412no—
573C2×D4C23×D61112yes—
574C2×D4C23×D61112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—618no—
578C22×C4—614no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—6112no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—613no—
585C22×C4—613no—
586C22×C4—613no—
587C22×C4—6112no—
588C22×C4—6112no—
589C22×C4—6112no—
590C22×C4—6112no—
591C22×C4—6112no—
592C22×C4—12212no—
593C22×C4—12212no—
594C22×C4—12212no—
595C22×C4—2446no—
596C22×C4—2446no—
597C22×C4—2446no—
598C22×C4C23×D61112yes—
599C22×C4C23×D61112yes—
600C22×C4C23×D6111yescharacteristic
601C22×C4C23×D6113yes—
602C22×C4C23×D6111yescharacteristic
603C22×C4C23×D6113yes—
604C22×C4C23×D6113yes—
605C4⋊C4—6112no—
606C4⋊C4—6112no—
607C4⋊C4—6124no—
608C4⋊C4—614no—
609C4⋊C4—614no—
610C4⋊C4—6112no—
611C4⋊C4—6112no—
612C4⋊C4—6124no—
613C4⋊C4—6112no—
614C4⋊C4—6112no—
615C4⋊C4C23×D61112yes—
616C4⋊C4C23×D61112yes—
617C22⋊C4—614no—
618C22⋊C4—6112no—
619C22⋊C4—6124no—
620C22⋊C4—6112no—
621C22⋊C4—6124no—
622C22⋊C4—6112no—
623C22⋊C4—6124no—
624C22⋊C4C23×D6114yes—
625C22⋊C4C23×D61112yes—
626C22⋊C4C23×D61124yes—
627C42—614no—
628C42—614no—
629C42—6112no—
630C42—6112no—
631C42—6112no—
632C42—6112no—
633C42—6112no—
634C42—6112no—
635C42—6112no—
636C42C23×D61112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—616no—
643C23—1226no—
644C23—1226no—
645C23—1226no—
646C23#41×D6114yes—
647C23C24×D6116yes—
648C23C24×D6112yes—
649C23C24×D6111yescharacteristic
650Q8—224no—
651Q8—12224no—
652Q8C2×#11758224116yescomplemented
653D4—224no—
654D4—224no—
655D4—12224no—
656D4—12224no—
657D4—12224no—
658D4—24424no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—6116no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—616no—
673C2×C4—616no—
674C2×C4—616no—
675C2×C4—12224no—
676C2×C4—12224no—
677C2×C4—1226no—
678C2×C4—1222no—
679C2×C4—1226no—
680C2×C4—1222no—
681C2×C4—1226no—
682C2×C4—12224no—
683C2×C4—24412no—
684C2×C4—24412no—
685C2×C4—24412no—
686C2×C4C2×#11758224112yes—
687C2×C4C24×D6112yes—
688C2×C4C24×D6116yes—
689C2×C4C24×D6112yes—
690C2×C4C24×D6116yes—
691C2×C4C24×D6116yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—1226no—
700C22—1226no—
701C22—1226no—
702C22—24412no—
703C22C2×#41×D6114yes—
704C22C2×#41×D6112yes—
705C22C22×#1175822412yes—
706C22#1684059912yes—
707C22C25×D6111yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—614no—
713C4—614no—
714C4—1226no—
715C4—1222no—
716C4—1226no—
717C4—1222no—
718C4—1226no—
719C4C22×#11758224112yes—
720C2—24no—
721C2—46no—
722C2—2446no—
723C2#2145940914yesdirect product factor
724C2C22×#41×D6111yescharacteristic
725C2C23×#1175822411yescharacteristic
726C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#548C2
socleC23×C61C25
hypercenterC2×#548D61
hypocenterC61C2×#3480
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #21459409C2direct (N × H)
2. C2×#16840494C2semidirect
3. C2×#16840488C2semidirect
4. C2×#16840483C2semidirect
5. C2×#16840464C2semidirect
6. C2×#16840458C2semidirect
7. C2×#16840431C2semidirect
8. C2×#16840423C2semidirect
9. C2×#16840307C2semidirect
10. C2×#16840298C2semidirect
11. C2×#16840291C2semidirect
12. C2×#41×Dic61C2semidirect
13. C2×C4×#11758226C2semidirect
14. C2×C4×#11758224C2semidirect
15. C22×Q8×Dic61C2semidirect
16. C2×C61×#548C2semidirect
19. #16840494C22semidirect
20. #16840488C22semidirect
21. #16840483C22semidirect
22. #16840464C22semidirect
23. #16840458C22semidirect
24. #16840431C22semidirect
25. #16840423C22semidirect
26. #16840307C22semidirect
29. #16840298C22semidirect
30. #16840291C22semidirect
44. #41×Dic61C22semidirect
45. C4×#11758226C22semidirect
46. C4×#11758224C22semidirect
52. C2×Q8×Dic61C22semidirect
76. C61×#548C22semidirect
192. C2×Q8×C61#41semidirect
217. C22×Dic61#41semidirect
287. Q8×C61C2×#41semidirect
315. C2×Dic61C2×#41semidirect
365. C2×#548D61semidirect
375. C2×C61#3480semidirect
391. #548C2×D61semidirect
445. C61C2×#3480semidirect
560. C2×Q8#11758224semidirect
652. Q8C2×#11758224semidirect
723. C2#21459409direct (N × H)

Maximal subgroups

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

subgroupindex
#214594092
C2×#168404942
C2×#168404882
C2×#168404832
C2×#168404642
C2×#168404582
C2×#168404312
C2×#168404232
C2×#168403072
C2×#168402982
C2×#168402912
C2×#41×Dic612
C2×C4×#117582262
C2×C4×#117582242
C22×Q8×Dic612
C2×C61×#5482
C2×#348061