Finite Group Databasebeta

← C2×#21459417 #30587071

Subgroups — C2×#21459417 #30587071

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#21459417C2132yesmaximal, direct product factor
2C2×#16840495C213yesmaximal, complemented
3C2×#16840488C211yesmaximal, characteristic, complemented
4C2×#16840480C213yesmaximal, complemented
5C2×#16840462C213yesmaximal, complemented
6C2×#16840456C213yesmaximal, complemented
7C2×#16840431C211yesmaximal, characteristic, complemented
8C2×#16840424C211yesmaximal, characteristic, complemented
9C2×#16840419C211yesmaximal, characteristic, complemented
10C2×#16840309C213yesmaximal, complemented
11C2×#16840296C213yesmaximal, complemented
12C2×#16840294C213yesmaximal, complemented
13C2×C4×#11758226C211yesmaximal, characteristic, complemented
14C2×C4×#11758222C213yesmaximal, complemented
15C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
16C2×C4×#41×C61C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2213yes—
19C22×Q8×D61C2211yescharacteristic
20#16840495C22148yescomplemented
21#16840488C22116yescomplemented
22#16840480C22148yescomplemented
23#16840462C22148yescomplemented
24#16840456C22148yescomplemented
25#16840431C22116yescomplemented
26#16840424C22116yescomplemented
27#16840419C22116yescomplemented
28#16840309C22148yescomplemented
29C2×#14519776C2213yes—
30C2×#14519773C2213yes—
31#16840296C22148yescomplemented
32#16840294C22148yescomplemented
33C2×#14519771C2216yes—
34C2×#14519770C2216yes—
35C2×#14519769C2213yes—
36C2×#14519768C2213yes—
37C2×#14519765C2213yes—
38C2×#14519764C2213yes—
39C2×#14519763C2216yes—
40C2×#14519760C2216yes—
41C2×#14519759C2216yes—
42C2×#14519757C2213yes—
43C2×#14519756C2213yes—
44C2×#14519752C2213yes—
45C2×#14519751C2213yes—
46C2×#14519750C2216yes—
47C2×#14519748C2213yes—
48C2×#14519748C2213yes—
49C4×#11758226C22116yescomplemented
50C4×#11758222C22148yescomplemented
51C2×Q8×Dic61C2211yescharacteristic
52C2×Q8×Dic61C2211yescharacteristic
53C2×C4×Dic122C2213yes—
54C2×C4×Dic122C2213yes—
55C2×C4×Dic122C2213yes—
56C2×#14519742C2213yes—
57C4×Q8×D61C22116yescomplemented
58C2×C4×D244C2213yes—
59C2×C4×D244C2213yes—
60C2×C4×D244C2213yes—
61C2×#14519739C2213yes—
62C2×C4×C22⋊D61C2213yes—
63C2×C4×C22⋊D61C2213yes—
64C2×C4×C22⋊D61C2213yes—
65C2×C4×C22⋊D61C2213yes—
66C2×C4×C22⋊D61C2216yes—
67C2×#14519736C2213yes—
68C2×#14519735C2213yes—
69C2×#14519734C2211yescharacteristic
70C2×#14519734C2213yes—
71C2×C4⋊C4×D61C2213yes—
72C2×C42×D61C2213yes—
73C2×C42×D61C2213yes—
74C22×#41×C61C2211yescharacteristic
75C4×#41×C61C22116yescomplemented
76C2×C4×Q8×C61C2211yescharacteristic
77C2×C4×Q8×C61C2211yescharacteristic
78C2×C4×D4×C61C2213yes—
79C2×C4×D4×C61C2213yes—
80C2×#117×C61C2213yes—
81C22×C42×C61C2213yes—
82C2×#11758226—28no—
83C2×#11758226C2318yes—
84C2×#11758222—224no—
85C2×#11758222C23124yes—
86C22×Dic122C2313yes—
87C22×Dic122C2313yes—
88C2×Q8×D61—28no—
89C2×Q8×D61C2318yes—
90C22×D244C2313yes—
91C22×D244C2313yes—
92C22×C22⋊D61C2313yes—
93C22×C22⋊D61C2313yes—
94C22×C22⋊D61C2316yes—
95C22×C4×D61C2313yes—
96C22×C4×D61C2313yes—
97C22×C4×D61C2313yes—
98C22×C4×D61C2313yes—
99C22×C4×D61C2313yes—
100C22×C4×D61C2311yescharacteristic
101#14519776C23124yes—
102#14519773C23124yes—
103#14519771C23148yes—
104#14519770C23148yes—
105#14519769C23124yes—
106#14519768C23124yes—
107#14519765C23124yes—
108#14519764C23124yes—
109#14519763C23148yes—
110#14519760C23148yes—
111#14519759C23148yes—
112#14519757C23124yes—
113#14519756C23124yes—
114#14519752C23124yes—
115#14519751C23124yes—
116#14519750C23148yes—
117#14519748C23124yes—
118#14519748C23124yes—
119Q8×Dic61C2318yes—
120Q8×Dic61C2318yes—
121C4×Dic122C23124yes—
122C4×Dic122C23124yes—
123C4×Dic122C23124yes—
124#14519742C23124yes—
125C4×D244C23124yes—
126C4×D244C23124yes—
127C4×D244C23124yes—
128#14519739C23124yes—
129C4×C22⋊D61C23124yes—
130C4×C22⋊D61C23124yes—
131C4×C22⋊D61C23124yes—
132C4×C22⋊D61C23124yes—
133C4×C22⋊D61C23148yes—
134#14519736C23124yes—
135#14519735C23124yes—
136#14519734C2318yes—
137#14519734C23124yes—
138C2×C4⋊Dic61C2313yes—
139C2×C4⋊Dic61C2313yes—
140C2×C4⋊Dic61C2313yes—
141C2×C4⋊Dic61C2313yes—
142C2×#11758196C2316yes—
143C2×#11758196C2311yescharacteristic
144C2×#11758196C2311yescharacteristic
145C2×#11758196C2313yes—
146C2×#11758196C2313yes—
147C2×#11758196C2316yes—
148C4⋊C4×D61C23124yes—
149C2×C22⋊Dic61C2313yes—
150C2×C22⋊Dic61C2313yes—
151C2×C22⋊Dic61C2316yes—
152C2×#11758198C2311yescharacteristic
153C2×#11758198C2311yescharacteristic
154C2×#11758198C2313yes—
155C2×#11758198C2313yes—
156C2×#11758198C2316yes—
157C2×#11758198C2316yes—
158C2×C4×Dic61C2311yescharacteristic
159C2×C4×Dic61C2313yes—
160C2×C4×Dic61C2313yes—
161C2×C4×Dic61C2313yes—
162C2×C4×Dic61C2313yes—
163C2×C4×Dic61C2313yes—
164C42×D61C23124yes—
165C42×D61C23124yes—
166C2×#41×C61—28no—
167C2×#41×C61C2318yes—
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61C2313yes—
170C23×C4×C61C2313yes—
171C23×C4×C61C2313yes—
172C23×C4×C61C2313yes—
173C4×Q8×C61C2318yes—
174C4×Q8×C61C2318yes—
175C4×D4×C61C23124yes—
176C4×D4×C61C23124yes—
177#117×C61C23124yes—
178C2×C4⋊C4×C61C2313yes—
179C2×C4⋊C4×C61C2313yes—
180C2×C22⋊C4×C61C2316yes—
181C2×C42×C61C2313yes—
182C2×C42×C61C2311yescharacteristic
183C2×C42×C61C2313yes—
184C2×C42×C61C2313yes—
185C2×C42×C61C23124yes—
186C24×C61C2413yes—
187C23×D61C2413yes—
188C23×D61C2411yescharacteristic
189#41×C61—232no—
190C2×Q8×C61#4118yescomplemented
191C2×Q8×C61C2414yes—
192C2×D4×C61—212no—
193C2×D4×C61C24112yes—
194C22×C4×C61—212no—
195C22×C4×C61—212no—
196C22×C4×C61—46no—
197C22×C4×C61C2413yes—
198C22×C4×C61C2413yes—
199C22×C4×C61C24112yes—
200C22×C4×C61C2411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C22×C4×C61C24112yes—
203C22×C4×C61C24112yes—
204C22×C4×C61C2413yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—212no—
207C2×C22⋊D61—212no—
208C2×C22⋊D61—412no—
209C2×C22⋊D61C24112yes—
210C2×C22⋊D61C24112yes—
211C2×C22⋊D61C24124yes—
212C22×Dic61C2411yescharacteristic
213C22×Dic61C2411yescharacteristic
214C22×Dic61C2413yes—
215C22×Dic61C2413yes—
216C22×Dic61C2413yes—
217C22×Dic61C2411yescharacteristic
218#11758226—232no—
219Q8×D61—232no—
220#11758222—296no—
221C2×D244—212no—
222C2×D244—212no—
223C2×D244C24112yes—
224C2×D244C24112yes—
225C2×C4×D61—212no—
226C2×C4×D61—212no—
227C2×C4×D61—212no—
228C2×C4×D61—46no—
229C2×C4×D61—46no—
230C2×C4×D61#4118yescomplemented
231C2×C4×D61C24112yes—
232C2×C4×D61C24112yes—
233C2×C4×D61C24112yes—
234C2×C4×D61C24112yes—
235C2×C4×D61C24112yes—
236C2×C4×D61C2414yes—
237C2×Dic122—212no—
238C2×Dic122—212no—
239C2×Dic122C24112yes—
240C2×Dic122C24112yes—
241C4⋊C4×C61C24112yes—
242C4⋊C4×C61C24112yes—
243C22⋊C4×C61C24124yes—
244C42×C61C2414yes—
245C42×C61C24112yes—
246C42×C61C24112yes—
247C42×C61C24112yes—
248C22⋊Dic61C24112yes—
249C22⋊Dic61C24112yes—
250C22⋊Dic61C24124yes—
251#11758198C2414yes—
252#11758198C2414yes—
253#11758198C24112yes—
254#11758198C24112yes—
255#11758198C24124yes—
256#11758198C24124yes—
257C4⋊Dic61C24112yes—
258C4⋊Dic61C24112yes—
259C4⋊Dic61C24112yes—
260C4⋊Dic61C24112yes—
261#11758196C24124yes—
262#11758196C2414yes—
263#11758196C2414yes—
264#11758196C24112yes—
265#11758196C24112yes—
266#11758196C24124yes—
267C4×Dic61C2414yes—
268C4×Dic61C24112yes—
269C4×Dic61C24112yes—
270C4×Dic61C24112yes—
271C4×Dic61C24112yes—
272C4×Dic61C24112yes—
273C23×C61—26no—
274C23×C61—26no—
275C23×C61—26no—
276C23×C61C2516yes—
277C23×C61C2511yescharacteristic
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—26no—
281C22×D61—26no—
282C22×D61—26no—
283C22×D61C2×#4114yes—
284C22×D61C2516yes—
285C22×D61C2512yes—
286Q8×C61C2×#41116yescomplemented
287D4×C61—224no—
288C2×C4×C61—26no—
289C2×C4×C61—22no—
290C2×C4×C61—26no—
291C2×C4×C61—22no—
292C2×C4×C61—224no—
293C2×C4×C61—224no—
294C2×C4×C61—412no—
295C2×C4×C61C2×#4114yes—
296C2×C4×C61C2×#41112yes—
297C2×C4×C61C2516yes—
298C2×C4×C61C2512yes—
299C2×C4×C61C2512yes—
300C2×C4×C61C2516yes—
301C2×C4×C61C2512yes—
302C2×C4×C61C2516yes—
303C22⋊D61—224no—
304C22⋊D61—224no—
305C22⋊D61—424no—
306C2×Dic61—26no—
307C2×Dic61—26no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—26no—
311C2×Dic61C2×#4114yes—
312C2×Dic61C2512yes—
313C2×Dic61C2512yes—
314C2×Dic61C2516yes—
315C2×Dic61C2516yes—
316C2×Dic61C2516yes—
317C2×Dic61C2512yes—
318D244—224no—
319D244—224no—
320C4×D61—224no—
321C4×D61—224no—
322C4×D61—224no—
323C4×D61—412no—
324C4×D61—412no—
325C4×D61C2×#41116yescomplemented
326Dic122—224no—
327Dic122—224no—
328C2×#3480—611nomaximal, Sylow
329C22×C61—26no—
330C22×C61—26no—
331C22×C61—26no—
332C22×C61—412no—
333C22×C61C22×#4112yes—
334C22×C61C22×#4112yes—
335C22×C61#58512yes—
336C22×C61C2611yescharacteristic
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—28no—
340C2×D61—26no—
341C2×D61—26no—
342C2×D61—26no—
343C2×D61—412no—
344C2×D61C22×#4114yes—
345C4×C61—26no—
346C4×C61—22no—
347C4×C61—26no—
348C4×C61—22no—
349C4×C61C22×#4114yes—
350C4×C61C22×#41112yes—
351Dic61—26no—
352Dic61—26no—
353Dic61—22no—
354Dic61—22no—
355Dic61—26no—
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×#548—611no—
366C2×#532—613no—
367C2×#529—613no—
368C2×#529—613no—
369C2×C4×#41—613no—
370C2×C4×#41—611no—
371C2×C4×#41D6111yescharacteristic, complemented
372C22×C4×Q8—611no—
373C2×C61—46no—
374C2×C61#348014yescomplemented
375C2×C61C23×#4111yescharacteristic
376C2×C61C23×#4111yescharacteristic
377C2×C61C2×#58511yescharacteristic
378D61—24no—
379D61—46no—
380C22×#41—611no—
381C22×#41—613no—
382C22×#41C2×D6111yescharacteristic
383C23×Q8—611no—
384#559—6148no—
385#557—6116no—
386#556—6148no—
387#553—6148no—
388#553—6148no—
389#550—6116no—
390#548—6116no—
391#548—6116no—
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×#124—613no—
404C2×#123—616no—
405C2×#123—616no—
406C2×C22⋊Q8—613no—
407C2×C22⋊Q8—613no—
408C2×#121—613no—
409C2×#121—613no—
410C2×#121—613no—
411C2×#121—613no—
412C2×#121—616no—
413C4×#41—6116no—
414C4×#41—6148no—
415C4×#41C2×D61116yescomplemented
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—6116no—
419C2×C4×Q8—613no—
420C2×C4×Q8—613no—
421C2×C4×Q8—613no—
422C2×C4×Q8—613no—
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×Q8C2×D6111yescharacteristic
425C2×C4×D4—613no—
426C2×C4×D4—613no—
427C2×C4×D4—613no—
428C2×C4×D4—613no—
429C2×C4×D4—616no—
430C2×C4×D4—613no—
431C2×C4×D4—613no—
432C2×C4×D4—613no—
433C2×C4×D4—613no—
434C2×C4×D4C2×D6113yes—
435C2×C4×D4C2×D6113yes—
436C2×#117—613no—
437C2×#117—613no—
438C2×#117—611no—
439C2×#117—613no—
440C2×#117C2×D6113yes—
441C22×C4⋊C4—613no—
442C22×C42—613no—
443C22×C42—613no—
444C22×C42C2×D6113yes—
445C61C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—618no—
448C2×#41—6124no—
449C2×#41—12224no—
450C2×#41—1228no—
451C2×#41C22×D6118yes—
452C22×Q8—618no—
453C22×Q8—613no—
454C22×Q8—613no—
455C22×Q8—1228no—
456C22×Q8C22×D6111yescharacteristic
457C22×D4—613no—
458C22×D4—613no—
459C22×D4—616no—
460C22×D4—613no—
461C22×D4—613no—
462C22×D4C22×D6113yes—
463C23×C4—611no—
464C23×C4—613no—
465C23×C4—613no—
466C23×C4—613no—
467C23×C4—613no—
468C23×C4—613no—
469C23×C4C22×D6113yes—
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#124—6124no—
481#123—6148no—
482#123—6148no—
483C22⋊Q8—6124no—
484C22⋊Q8—6124no—
485#121—6124no—
486#121—6124no—
487#121—6124no—
488#121—6124no—
489#121—6148no—
490C4×Q8—618no—
491C4×Q8—618no—
492C4×Q8—6124no—
493C4×Q8—6124no—
494C4×Q8—6124no—
495C4×Q8—6124no—
496C4×Q8C22×D6118yes—
497C4×Q8C22×D6118yes—
498C4×D4—6124no—
499C4×D4—6124no—
500C4×D4—6124no—
501C4×D4—6124no—
502C4×D4—6148no—
503C4×D4—6124no—
504C4×D4—6124no—
505C4×D4—6124no—
506C4×D4—6124no—
507C4×D4C22×D61124yes—
508C4×D4C22×D61124yes—
509#117—6124no—
510#117—6124no—
511#117—618no—
512#117—6124no—
513#117C22×D61124yes—
514C2×C4⋊C4—613no—
515C2×C4⋊C4—616no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—613no—
519C2×C4⋊C4—613no—
520C2×C4⋊C4—613no—
521C2×C4⋊C4—613no—
522C2×C4⋊C4—613no—
523C2×C4⋊C4—616no—
524C2×C4⋊C4—6124no—
525C2×C4⋊C4C22×D6113yes—
526C2×C4⋊C4C22×D6113yes—
527C2×C22⋊C4—613no—
528C2×C22⋊C4—613no—
529C2×C22⋊C4—616no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—613no—
533C2×C22⋊C4—616no—
534C2×C22⋊C4—613no—
535C2×C22⋊C4—616no—
536C2×C22⋊C4C22×D6116yes—
537C2×C42—613no—
538C2×C42—613no—
539C2×C42—613no—
540C2×C42—613no—
541C2×C42—611no—
542C2×C42—613no—
543C2×C42—6124no—
544C2×C42—6124no—
545C2×C42C22×D6113yes—
546C2×C42C22×D6113yes—
547C2×C42C22×D61124yes—
548C2×C42C22×D6111yescharacteristic
549C2×C42C22×D6113yes—
550C24—611no—
551C24—613no—
552C24C23×D6113yes—
553#41—232no—
554#41—12296no—
555#41—12232no—
556C2×Q8—6112no—
557C2×Q8—6112no—
558C2×Q8—12212no—
559C2×Q8—12232no—
560C2×Q8—12212no—
561C2×Q8#1175822218yescomplemented
562C2×Q8C23×D6114yes—
563C2×D4—212no—
564C2×D4—6112no—
565C2×D4—6112no—
566C2×D4—6124no—
567C2×D4—6112no—
568C2×D4—6112no—
569C2×D4—12212no—
570C2×D4—12212no—
571C2×D4—12212no—
572C2×D4—12212no—
573C2×D4—24412no—
574C2×D4C23×D61112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—611no—
579C22×C4—618no—
580C22×C4—614no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—613no—
584C22×C4—613no—
585C22×C4—613no—
586C22×C4—6112no—
587C22×C4—6112no—
588C22×C4—6112no—
589C22×C4—6112no—
590C22×C4—6112no—
591C22×C4—12212no—
592C22×C4—12212no—
593C22×C4—12212no—
594C22×C4—2446no—
595C22×C4—2446no—
596C22×C4C23×D6113yes—
597C22×C4C23×D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599C22×C4C23×D6113yes—
600C22×C4C23×D61112yes—
601C22×C4C23×D61112yes—
602C22×C4C23×D61112yes—
603C22×C4C23×D6113yes—
604C22×C4C23×D6111yescharacteristic
605C4⋊C4—6124no—
606C4⋊C4—6112no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4—6112no—
610C4⋊C4—6112no—
611C4⋊C4—6124no—
612C4⋊C4—6112no—
613C4⋊C4—6112no—
614C4⋊C4—6112no—
615C4⋊C4C23×D61112yes—
616C4⋊C4C23×D61112yes—
617C22⋊C4—6112no—
618C22⋊C4—6112no—
619C22⋊C4—6124no—
620C22⋊C4—614no—
621C22⋊C4—614no—
622C22⋊C4—6112no—
623C22⋊C4—6124no—
624C22⋊C4—6112no—
625C22⋊C4—6124no—
626C22⋊C4C23×D61124yes—
627C42—614no—
628C42—6112no—
629C42—6112no—
630C42—6112no—
631C42—6112no—
632C42—6112no—
633C42C23×D61112yes—
634C42C23×D6114yes—
635C42C23×D61112yes—
636C42C23×D61112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—614no—
641C23—612no—
642C23—616no—
643C23—1222no—
644C23—1222no—
645C23—1226no—
646C23—1226no—
647C23—1226no—
648C23C24×D6116yes—
649C23C24×D6111yescharacteristic
650Q8—12224no—
651Q8—12224no—
652Q8C2×#11758222116yescomplemented
653D4—224no—
654D4—12224no—
655D4—12224no—
656D4—12224no—
657D4—12224no—
658D4—24424no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—614no—
667C2×C4—612no—
668C2×C4—6116no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—616no—
672C2×C4—616no—
673C2×C4—616no—
674C2×C4—1226no—
675C2×C4—1222no—
676C2×C4—1226no—
677C2×C4—1222no—
678C2×C4—1226no—
679C2×C4—12224no—
680C2×C4—12224no—
681C2×C4—12224no—
682C2×C4—24412no—
683C2×C4—24412no—
684C2×C4#41×D6114yes—
685C2×C4C2×#11758222112yes—
686C2×C4C24×D6116yes—
687C2×C4C24×D6112yes—
688C2×C4C24×D6112yes—
689C2×C4C24×D6116yes—
690C2×C4C24×D6112yes—
691C2×C4C24×D6116yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—614no—
697C22—1222no—
698C22—1222no—
699C22—1228no—
700C22—1226no—
701C22—1226no—
702C22—1226no—
703C22—24412no—
704C22C2×#41×D6112yes—
705C22C22×#1175822212yes—
706C22#1684059812yes—
707C22C25×D6111yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—614no—
713C4—1226no—
714C4—1222no—
715C4—1226no—
716C4—1222no—
717C4—1226no—
718C4C2×#41×D6114yes—
719C4C22×#11758222112yes—
720C2—46no—
721C2—1224no—
722C2—2446no—
723C2#2145941714yesdirect product factor
724C2C22×#41×D6111yescharacteristic
725C2C23×#1175822211yescharacteristic
726C2C2×#1684059811yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C4×#41×C61C2
socleC23×C61C25
hypercenterC2×C4×#41D61
hypocenterC61C2×#3480
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21459417C2direct (N × H)
2. C2×#16840495C2semidirect
3. C2×#16840488C2semidirect
4. C2×#16840480C2semidirect
5. C2×#16840462C2semidirect
6. C2×#16840456C2semidirect
7. C2×#16840431C2semidirect
8. C2×#16840424C2semidirect
9. C2×#16840419C2semidirect
10. C2×#16840309C2semidirect
11. C2×#16840296C2semidirect
12. C2×#16840294C2semidirect
13. C2×C4×#11758226C2semidirect
14. C2×C4×#11758222C2semidirect
15. C2×C4×Q8×D61C2semidirect
16. C2×C4×#41×C61C2semidirect
20. #16840495C22semidirect
21. #16840488C22semidirect
22. #16840480C22semidirect
23. #16840462C22semidirect
24. #16840456C22semidirect
25. #16840431C22semidirect
26. #16840424C22semidirect
27. #16840419C22semidirect
28. #16840309C22semidirect
31. #16840296C22semidirect
32. #16840294C22semidirect
49. C4×#11758226C22semidirect
50. C4×#11758222C22semidirect
57. C4×Q8×D61C22semidirect
75. C4×#41×C61C22semidirect
190. C2×Q8×C61#41semidirect
230. C2×C4×D61#41semidirect
286. Q8×C61C2×#41semidirect
325. C4×D61C2×#41semidirect
371. C2×C4×#41D61semidirect
374. C2×C61#3480semidirect
415. C4×#41C2×D61semidirect
445. C61C2×#3480semidirect
561. C2×Q8#11758222semidirect
652. Q8C2×#11758222semidirect
723. C2#21459417direct (N × H)

Maximal subgroups

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

subgroupindex
#214594172
C2×#168404952
C2×#168404882
C2×#168404802
C2×#168404622
C2×#168404562
C2×#168404312
C2×#168404242
C2×#168404192
C2×#168403092
C2×#168402962
C2×#168402942
C2×C4×#117582262
C2×C4×#117582222
C2×C4×Q8×D612
C2×C4×#41×C612
C2×#348061