Finite Group Databasebeta

← C2×#20257498 #27124565

Subgroups — C2×#20257498 #27124565

Order 12032.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257498C2132yesmaximal, direct product factor
2C2×#15689855C213yesmaximal, complemented
3C2×#15689852C211yesmaximal, characteristic, complemented
4C2×#15689838C213yesmaximal, complemented
5C2×#15689820C213yesmaximal, complemented
6C2×#15689807C213yesmaximal, complemented
7C2×#15689792C211yesmaximal, characteristic, complemented
8C2×#15689784C211yesmaximal, characteristic, complemented
9C2×#15689742C213yesmaximal, complemented
10C2×#15689726C213yesmaximal, complemented
11C2×#15689659C213yesmaximal, complemented
12C2×#15689653C213yesmaximal, complemented
13C2×#15689605C211yesmaximal, characteristic, complemented
14C2×#15689601C211yesmaximal, characteristic, complemented
15C2×#41×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18#15689855C22148yescomplemented
19#15689852C22116yescomplemented
20#15689838C22148yescomplemented
21#15689820C22148yescomplemented
22#15689807C22148yescomplemented
23#15689792C22116yescomplemented
24#15689784C22116yescomplemented
25#15689742C22148yescomplemented
26#15689726C22148yescomplemented
27C2×#13094024C2213yes—
28C2×#13094020C2213yes—
29#15689659C22148yescomplemented
30#15689653C22148yescomplemented
31C2×#13094019C2213yes—
32C2×#13094017C2216yes—
33C2×#13094017C2211yescharacteristic
34C2×#13094015C2213yes—
35C2×#13094015C2213yes—
36C2×#13094014C2213yes—
37C2×#13094013C2213yes—
38C2×#13094010C2213yes—
39C2×#13094010C2216yes—
40C2×#13094008C2213yes—
41C2×#13094008C2216yes—
42C2×#13094006C2216yes—
43C2×#13094005C2213yes—
44C2×#13094001C2213yes—
45C2×#13094000C2213yes—
46C2×#13093998C2213yes—
47C2×#13093998C2213yes—
48C2×#13093996C2213yes—
49C2×#13093995C2213yes—
50C2×#13093995C2216yes—
51#15689605C22116yescomplemented
52#15689601C22116yescomplemented
53#41×Dic47C22116yescomplemented
54C2×Q8×Dic47C2211yescharacteristic
55C2×Q8×Dic47C2211yescharacteristic
56C2×Q8×Dic47C2211yescharacteristic
57C2×Q8×Dic47C2213yes—
58C2×Q8×Dic47C2213yes—
59C2×C4×Dic94C2213yes—
60C2×C4×D188C2213yes—
61C2×D4×Dic47C2213yes—
62C2×D4×Dic47C2213yes—
63C2×#13093986C2213yes—
64C2×C4×C22⋊D47C2213yes—
65C2×C4×C22⋊D47C2213yes—
66C2×(C22⋊D47)⋊C4C2216yes—
67C2×#13093983C2213yes—
68C2×#13093983C2213yes—
69C2×#13093983C2213yes—
70C2×#13093982C2216yes—
71C2×#13093981C2213yes—
72C2×C4⋊C4×D47C2213yes—
73C22×C4×Dic47C2213yes—
74C22×#41×C47C2211yescharacteristic
75C23×Q8×C47C2211yescharacteristic
76C47×#548C22116yescomplemented
77C2×#124×C47C2213yes—
78C2×C22⋊Q8×C47C2213yes—
79C2×#121×C47C2213yes—
80C2×C4×Q8×C47C2211yescharacteristic
81C2×C4×D4×C47C2213yes—
82C2×#10625354—28no—
83C2×#10625354C2318yes—
84C22×Dic94C2313yes—
85C22×D188C2313yes—
86C22×C22⋊D47C2316yes—
87C22×C22⋊D47C2313yes—
88C22×C22⋊D47C2313yes—
89C23×Dic47C2313yes—
90C23×Dic47C2313yes—
91C22×C4×D47C2313yes—
92C22×C4×D47C2316yes—
93#13094024C23124yes—
94#13094020C23124yes—
95#13094019C23124yes—
96#13094017C23148yes—
97#13094017C2318yes—
98#13094015C23124yes—
99#13094015C23124yes—
100#13094014C23124yes—
101#13094013C23124yes—
102#13094010C23148yes—
103#13094010C23124yes—
104#13094008C23148yes—
105#13094008C23124yes—
106#13094006C23148yes—
107#13094005C23124yes—
108#13094001C23124yes—
109#13094000C23124yes—
110#13093998C23124yes—
111#13093998C23124yes—
112#13093996C23124yes—
113#13093995C23124yes—
114#13093995C23148yes—
115Q8×Dic47C23124yes—
116Q8×Dic47C2318yes—
117Q8×Dic47C2318yes—
118Q8×Dic47C23124yes—
119Q8×Dic47C2318yes—
120C4×Dic94C23124yes—
121C4×D188C23124yes—
122D4×Dic47C23124yes—
123D4×Dic47C23124yes—
124#13093986C23124yes—
125C4×C22⋊D47C23124yes—
126C4×C22⋊D47C23124yes—
127(C22⋊D47)⋊C4C23148yes—
128#13093983C23124yes—
129#13093983C23124yes—
130#13093983C23124yes—
131#13093982C23148yes—
132#13093981C23124yes—
133C2×C4⋊Dic47C2313yes—
134C2×C4⋊Dic47C2316yes—
135C2×C4⋊Dic47C2313yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2313yes—
139C2×C4⋊Dic47C2311yescharacteristic
140C2×Dic47⋊C4C2313yes—
141C2×Dic47⋊C4C2311yescharacteristic
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2311yescharacteristic
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2313yes—
146C4⋊C4×D47C23124yes—
147C2×C22⋊Dic47C2313yes—
148C2×C22⋊Dic47C2311yescharacteristic
149C2×C22⋊Dic47C2316yes—
150C2×C22⋊Dic47C2311yescharacteristic
151C2×C22⋊Dic47C2313yes—
152C2×(C2×D47)⋊C4C2313yes—
153C2×(C2×D47)⋊C4C2313yes—
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2316yes—
156C2×(C2×D47)⋊C4C2313yes—
157C2×C4×Dic47C2311yescharacteristic
158C2×C4×Dic47C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C23124yes—
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C2×#41×C47—28no—
165C2×#41×C47C2318yes—
166C22×Q8×C47—28no—
167C22×Q8×C47C2318yes—
168C22×Q8×C47C2313yes—
169C22×Q8×C47C2311yescharacteristic
170C22×D4×C47C2313yes—
171C22×D4×C47C2313yes—
172C23×C4×C47C2313yes—
173C23×C4×C47C2313yes—
174#124×C47C23124yes—
175C22⋊Q8×C47C23124yes—
176#121×C47C23124yes—
177C4×Q8×C47C2318yes—
178C4×D4×C47C23124yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C4⋊C4×C47C2313yes—
181C2×C22⋊C4×C47C2311yescharacteristic
182C2×C22⋊C4×C47C2313yes—
183C2×C22⋊C4×C47C2316yes—
184C2×C42×C47C2313yes—
185C24×C47C2413yes—
186C24×C47C2411yescharacteristic
187C23×D47C2413yes—
188#41×C47—232no—
189C2×Q8×C47—232no—
190C2×Q8×C47—212no—
191C2×Q8×C47#4118yes—
192C2×Q8×C47C24112yes—
193C2×Q8×C47C2414yes—
194C2×D4×C47—212no—
195C2×D4×C47—46no—
196C2×D4×C47C24112yes—
197C2×D4×C47C24112yes—
198C22×C4×C47—212no—
199C22×C4×C47—212no—
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2413yes—
202C22×C4×C47C2413yes—
203C22×C4×C47C2411yescharacteristic
204C22×C4×C47C24112yes—
205C22×C4×C47C24112yes—
206C22×C4×C47C2413yes—
207C2×C22⋊D47—46no—
208C2×C22⋊D47—412no—
209C2×C22⋊D47—46no—
210C2×C22⋊D47C24124yes—
211C2×C22⋊D47C24112yes—
212C2×C22⋊D47C24112yes—
213C22×Dic47—46no—
214C22×Dic47—46no—
215C22×Dic47C2411yescharacteristic
216C22×Dic47C2411yescharacteristic
217C22×Dic47C2413yes—
218C22×Dic47C2413yes—
219C22×Dic47C2411yescharacteristic
220C22×Dic47C2413yes—
221C22×Dic47C2411yescharacteristic
222C22×Dic47C24112yes—
223C22×Dic47C24112yes—
224#10625354—232no—
225C2×D188—212no—
226C2×D188C24112yes—
227C2×C4×D47—212no—
228C2×C4×D47—412no—
229C2×C4×D47C24112yes—
230C2×C4×D47C24124yes—
231C2×Dic94—46no—
232C2×Dic94C24112yes—
233C4⋊C4×C47C24112yes—
234C4⋊C4×C47C24112yes—
235C22⋊C4×C47C2414yes—
236C22⋊C4×C47C24112yes—
237C22⋊C4×C47C24124yes—
238C42×C47C24112yes—
239C22⋊Dic47C24112yes—
240C22⋊Dic47C2414yes—
241C22⋊Dic47C24124yes—
242C22⋊Dic47C2414yes—
243C22⋊Dic47C24112yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C24112yes—
246(C2×D47)⋊C4C24112yes—
247(C2×D47)⋊C4C24124yes—
248(C2×D47)⋊C4C24112yes—
249C4⋊Dic47C24112yes—
250C4⋊Dic47C24124yes—
251C4⋊Dic47C24112yes—
252C4⋊Dic47C24112yes—
253C4⋊Dic47C24112yes—
254C4⋊Dic47C24112yes—
255C4⋊Dic47C2414yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C2414yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C2414yes—
260Dic47⋊C4C24112yes—
261Dic47⋊C4C24112yes—
262C4×Dic47C2414yes—
263C4×Dic47C24112yes—
264C4×Dic47C24112yes—
265C4×Dic47C24112yes—
266C4×Dic47C24124yes—
267C4×Dic47C24112yes—
268C23×C47—22no—
269C23×C47—26no—
270C23×C47—26no—
271C23×C47—26no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47C2512yes—
275C23×C47C2516yes—
276C23×C47C2511yescharacteristic
277C22×D47—26no—
278C22×D47—26no—
279C22×D47—26no—
280C22×D47C2516yes—
281Q8×C47—224no—
282Q8×C47C2×#41116yes—
283D4×C47—224no—
284D4×C47—412no—
285C2×C4×C47—22no—
286C2×C4×C47—26no—
287C2×C4×C47—22no—
288C2×C4×C47—26no—
289C2×C4×C47—224no—
290C2×C4×C47—224no—
291C2×C4×C47C2×#41112yes—
292C2×C4×C47C2512yes—
293C2×C4×C47C2516yes—
294C2×C4×C47C2516yes—
295C2×C4×C47C2512yes—
296C2×C4×C47C2516yes—
297C22⋊D47—412no—
298C22⋊D47—424no—
299C22⋊D47—412no—
300C2×Dic47—22no—
301C2×Dic47—26no—
302C2×Dic47—26no—
303C2×Dic47—26no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—412no—
308C2×Dic47—412no—
309C2×Dic47C2512yes—
310C2×Dic47C2512yes—
311C2×Dic47C2516yes—
312C2×Dic47C2512yes—
313C2×Dic47C2516yes—
314C2×Dic47C2516yes—
315C2×Dic47C2512yes—
316D188—224no—
317C4×D47—224no—
318C4×D47—424no—
319Dic94—412no—
320C2×#3524—471nomaximal, Sylow
321C22×C47—22no—
322C22×C47—26no—
323C22×C47—26no—
324C22×C47—26no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—44no—
328C22×C47—412no—
329C22×C47C22×#4112yes—
330C22×C47#58512yes—
331C22×C47#58512yes—
332C22×C47C2611yescharacteristic
333C2×D47—26no—
334C2×D47—26no—
335C2×D47—26no—
336C2×D47—412no—
337C4×C47—22no—
338C4×C47—26no—
339C4×C47—22no—
340C4×C47—26no—
341C4×C47C22×#41112yes—
342Dic47—22no—
343Dic47—26no—
344Dic47—26no—
345Dic47—26no—
346Dic47—22no—
347Dic47—22no—
348Dic47—22no—
349#3524—4732no—
350C2×#559—473no—
351C2×#557—471no—
352C2×#555—473no—
353C2×#553—473no—
354C2×#552—473no—
355C2×#550—471no—
356C2×#548—471no—
357C2×#548D4711yescharacteristic, complemented
358C2×#542—473no—
359C2×#540—473no—
360C2×#529—473no—
361C2×#529—473no—
362C2×#520—471no—
363C2×#519—471no—
364C2×C4×#41—471no—
365C2×C47—42no—
366C2×C47—46no—
367C2×C47#352414yescomplemented
368C2×C47C23×#4111yescharacteristic
369C2×C47C2×#58511yescharacteristic
370C2×C47C2×#58511yescharacteristic
371D47—46no—
372C22×#41—471no—
373C22×#41C2×D4711yescharacteristic
374C23×Q8C2×D4711yescharacteristic
375#559—4748no—
376#557—4716no—
377#555—4748no—
378#553—4748no—
379#552—4748no—
380#550—4716no—
381#548—4716no—
382#548C2×D47116yescomplemented
383#542—4748no—
384#540—4748no—
385C2×C4⋊Q8—473no—
386C2×#127—473no—
387#529—4748no—
388#529—4748no—
389C2×#126—473no—
390C2×#126—471no—
391C2×#126—476no—
392C2×#125—473no—
393C2×#125—473no—
394C2×#125—473no—
395C2×#124—473no—
396C2×#124—473no—
397C2×#124—476no—
398C2×#124C2×D4713yes—
399C2×#123—473no—
400C2×#123—476no—
401C2×#123—473no—
402C2×#123—476no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8C2×D4713yes—
406C2×#121—473no—
407C2×#121—476no—
408C2×#121—473no—
409C2×#121—473no—
410C2×#121—473no—
411C2×#121C2×D4713yes—
412#520—4716no—
413#519—4716no—
414C4×#41—4716no—
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8—473no—
418C2×C4×Q8—471no—
419C2×C4×Q8—473no—
420C2×C4×Q8—473no—
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×D4—473no—
423C2×C4×D4—473no—
424C2×C4×D4—473no—
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4—476no—
428C2×C4×D4—473no—
429C2×C4×D4C2×D4713yes—
430C2×#117—473no—
431C2×#117—473no—
432C2×#117—473no—
433C2×#117—476no—
434C2×#117—473no—
435C22×C4⋊C4—473no—
436C22×C42—473no—
437C47C2×#352411yescharacteristic, complemented, Sylow
438C2×#41—28no—
439C2×#41—478no—
440C2×#41—948no—
441C2×#41C22×D4718yes—
442C22×Q8—28no—
443C22×Q8—473no—
444C22×Q8C22×D4713yes—
445C22×Q8C22×D4718yes—
446C22×Q8C22×D4711yescharacteristic
447C22×D4—473no—
448C22×D4—476no—
449C22×D4—473no—
450C22×D4—473no—
451C22×D4C22×D4713yes—
452C22×D4C22×D4713yes—
453C23×C4—473no—
454C23×C4—473no—
455C23×C4—473no—
456C23×C4—476no—
457C23×C4C22×D4713yes—
458C23×C4C22×D4713yes—
459C4⋊Q8—4724no—
460#127—4724no—
461#126—4724no—
462#126—478no—
463#126—4748no—
464#125—4724no—
465#125—4724no—
466#125—4724no—
467#124—4724no—
468#124—4724no—
469#124—4748no—
470#124C22×D47124yes—
471#123—4724no—
472#123—4748no—
473#123—4724no—
474#123—4748no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477C22⋊Q8C22×D47124yes—
478#121—4724no—
479#121—4748no—
480#121—4724no—
481#121—4724no—
482#121—4724no—
483#121C22×D47124yes—
484C4×Q8—478no—
485C4×Q8—478no—
486C4×Q8—4724no—
487C4×Q8—478no—
488C4×Q8—4724no—
489C4×Q8—4724no—
490C4×Q8C22×D4718yes—
491C4×D4—4724no—
492C4×D4—4724no—
493C4×D4—4724no—
494C4×D4—4724no—
495C4×D4—4724no—
496C4×D4—4748no—
497C4×D4—4724no—
498C4×D4C22×D47124yes—
499#117—4724no—
500#117—4724no—
501#117—4724no—
502#117—4748no—
503#117—4724no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—473no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—476no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—473no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—473no—
517C2×C4⋊C4—4724no—
518C2×C4⋊C4C22×D4713yes—
519C2×C4⋊C4C22×D4713yes—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—476no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4—473no—
527C2×C22⋊C4—473no—
528C2×C22⋊C4—476no—
529C2×C22⋊C4—473no—
530C2×C22⋊C4C22×D4716yes—
531C2×C22⋊C4C22×D4711yescharacteristic
532C2×C22⋊C4C22×D4713yes—
533C2×C42—473no—
534C2×C42—473no—
535C2×C42—476no—
536C2×C42—473no—
537C2×C42—473no—
538C2×C42—4724no—
539C2×C42—471no—
540C2×C42C22×D4713yes—
541C24—473no—
542C24C23×D4711yescharacteristic
543C24C23×D4713yes—
544#41—232no—
545#41—9432no—
546C2×Q8—232no—
547C2×Q8—212no—
548C2×Q8—4712no—
549C2×Q8—1886no—
550C2×Q8#1062535218yes—
551C2×Q8C23×D47112yes—
552C2×Q8C23×D4714yes—
553C2×D4—212no—
554C2×D4—46no—
555C2×D4—4712no—
556C2×D4—4724no—
557C2×D4—4712no—
558C2×D4—4712no—
559C2×D4—9412no—
560C2×D4—1886no—
561C2×D4—1886no—
562C2×D4—18812no—
563C2×D4C23×D47112yes—
564C2×D4C23×D47112yes—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—471no—
568C22×C4—473no—
569C22×C4—471no—
570C22×C4—473no—
571C22×C4—471no—
572C22×C4—473no—
573C22×C4—471no—
574C22×C4—4712no—
575C22×C4—4712no—
576C22×C4—4712no—
577C22×C4—4724no—
578C22×C4—9412no—
579C22×C4—18812no—
580C22×C4—1886no—
581C22×C4—1886no—
582C22×C4C23×D47112yes—
583C22×C4C23×D47112yes—
584C22×C4C23×D4711yescharacteristic
585C22×C4C23×D4713yes—
586C22×C4C23×D4711yescharacteristic
587C22×C4C23×D4713yes—
588C22×C4C23×D4713yes—
589C4⋊C4—4712no—
590C4⋊C4—474no—
591C4⋊C4—474no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4712no—
595C4⋊C4—4712no—
596C4⋊C4—4712no—
597C4⋊C4—4712no—
598C4⋊C4—4712no—
599C4⋊C4—4712no—
600C4⋊C4—4724no—
601C4⋊C4—474no—
602C4⋊C4C23×D47112yes—
603C4⋊C4C23×D47112yes—
604C22⋊C4—474no—
605C22⋊C4—4712no—
606C22⋊C4—4724no—
607C22⋊C4—474no—
608C22⋊C4—4712no—
609C22⋊C4—4712no—
610C22⋊C4—4712no—
611C22⋊C4—4712no—
612C22⋊C4—4724no—
613C22⋊C4—4712no—
614C22⋊C4C23×D47124yes—
615C22⋊C4C23×D4714yes—
616C22⋊C4C23×D47112yes—
617C42—474no—
618C42—4712no—
619C42—4712no—
620C42—4712no—
621C42—4724no—
622C42—4712no—
623C42C23×D47112yes—
624C23—22no—
625C23—26no—
626C23—26no—
627C23—22no—
628C23—26no—
629C23—22no—
630C23—476no—
631C23—946no—
632C23—946no—
633C23—946no—
634C23C24×D4712yes—
635C23C24×D4716yes—
636C23C24×D4711yescharacteristic
637Q8—224no—
638Q8—18812no—
639Q8C2×#10625352116yes—
640D4—224no—
641D4—412no—
642D4—9424no—
643D4—18812no—
644D4—18812no—
645D4—18824no—
646C2×C4—22no—
647C2×C4—26no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—472no—
653C2×C4—476no—
654C2×C4—472no—
655C2×C4—476no—
656C2×C4—472no—
657C2×C4—476no—
658C2×C4—472no—
659C2×C4—942no—
660C2×C4—946no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—946no—
665C2×C4—946no—
666C2×C4—9424no—
667C2×C4—18824no—
668C2×C4—18812no—
669C2×C4—18812no—
670C2×C4C2×#10625352112yes—
671C2×C4C24×D4712yes—
672C2×C4C24×D4716yes—
673C2×C4C24×D4712yes—
674C2×C4C24×D4716yes—
675C2×C4C24×D4716yes—
676C22—22no—
677C22—26no—
678C22—26no—
679C22—22no—
680C22—26no—
681C22—22no—
682C22—44no—
683C22—412no—
684C22—946no—
685C22—946no—
686C22—946no—
687C22—18812no—
688C22C22×#1062535212yes—
689C22#1568995912yes—
690C22#1568996012yes—
691C22C25×D4711yescharacteristic
692C4—22no—
693C4—26no—
694C4—26no—
695C4—22no—
696C4—942no—
697C4—946no—
698C4—942no—
699C4—942no—
700C4—942no—
701C4—946no—
702C4—946no—
703C4C22×#10625352112yes—
704C2—42no—
705C2—46no—
706C2—1886no—
707C2#2025749814yesdirect product factor
708C2C23×#1062535211yescharacteristic
709C2C2×#1568995911yescharacteristic
710C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3524
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #20257498C2direct (N × H)
2. C2×#15689855C2semidirect
3. C2×#15689852C2semidirect
4. C2×#15689838C2semidirect
5. C2×#15689820C2semidirect
6. C2×#15689807C2semidirect
7. C2×#15689792C2semidirect
8. C2×#15689784C2semidirect
9. C2×#15689742C2semidirect
10. C2×#15689726C2semidirect
11. C2×#15689659C2semidirect
12. C2×#15689653C2semidirect
13. C2×#15689605C2semidirect
14. C2×#15689601C2semidirect
15. C2×#41×Dic47C2semidirect
16. C2×C47×#548C2semidirect
18. #15689855C22semidirect
19. #15689852C22semidirect
20. #15689838C22semidirect
21. #15689820C22semidirect
22. #15689807C22semidirect
23. #15689792C22semidirect
24. #15689784C22semidirect
25. #15689742C22semidirect
26. #15689726C22semidirect
29. #15689659C22semidirect
30. #15689653C22semidirect
51. #15689605C22semidirect
52. #15689601C22semidirect
53. #41×Dic47C22semidirect
76. C47×#548C22semidirect
357. C2×#548D47semidirect
367. C2×C47#3524semidirect
382. #548C2×D47semidirect
437. C47C2×#3524semidirect
707. C2#20257498direct (N × H)

Maximal subgroups

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

subgroupindex
#202574982
C2×#156898552
C2×#156898522
C2×#156898382
C2×#156898202
C2×#156898072
C2×#156897922
C2×#156897842
C2×#156897422
C2×#156897262
C2×#156896592
C2×#156896532
C2×#156896052
C2×#156896012
C2×#41×Dic472
C2×C47×#5482
C2×#352447