Finite Group Databasebeta

← C2×#20256978 #27123332

Subgroups — C2×#20256978 #27123332

Order 12032.

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#20256978C2132yesmaximal, direct product factor
2C2×#15689855C213yesmaximal, complemented
3C2×#15689849C211yesmaximal, characteristic, complemented
4C2×#15689844C213yesmaximal, complemented
5C2×#15689825C213yesmaximal, complemented
6C2×#15689819C213yesmaximal, complemented
7C2×#15689792C211yesmaximal, characteristic, complemented
8C2×#15689784C211yesmaximal, characteristic, complemented
9C2×#15689668C213yesmaximal, complemented
10C2×#15689659C213yesmaximal, complemented
11C2×#15689652C213yesmaximal, complemented
12C2×#41×Dic47C211yesmaximal, characteristic, complemented
13C2×C4×#10625354C211yesmaximal, characteristic, complemented
14C2×C4×#10625352C213yesmaximal, complemented
15C22×Q8×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2213yes—
19#15689855C22148yescomplemented
20#15689849C22116yescomplemented
21#15689844C22148yescomplemented
22#15689825C22148yescomplemented
23#15689819C22148yescomplemented
24#15689792C22116yescomplemented
25#15689784C22116yescomplemented
26#15689668C22148yescomplemented
27C2×#13094023C2213yes—
28C2×#13094020C2213yes—
29#15689659C22148yescomplemented
30#15689652C22148yescomplemented
31C2×#13094019C2216yes—
32C2×#13094017C2216yes—
33C2×#13094016C2213yes—
34C2×#13094015C2213yes—
35C2×#13094013C2213yes—
36C2×#13094010C2216yes—
37C2×#13094008C2216yes—
38C2×#13094006C2216yes—
39C2×#13094000C2213yes—
40C2×#13093998C2213yes—
41C2×#13093998C2213yes—
42C2×#13093996C2216yes—
43C2×#13093995C2213yes—
44#41×Dic47C22116yescomplemented
45C4×#10625354C22116yescomplemented
46C4×#10625352C22148yescomplemented
47C2×Q8×Dic47C2211yescharacteristic
48C2×Q8×Dic47C2211yescharacteristic
49C2×Q8×Dic47C2213yes—
50C2×Q8×Dic47C2213yes—
51C2×Q8×Dic47C2211yescharacteristic
52C2×Q8×Dic47C22116yescomplemented
53C2×C4×Dic94C2213yes—
54C2×#13093989C2213yes—
55C2×C4×D188C2213yes—
56C2×D4×Dic47C2213yes—
57C2×D4×Dic47C2213yes—
58C2×D4×Dic47C2213yes—
59C2×#13093986C2213yes—
60C2×C4×C22⋊D47C2213yes—
61C2×C4×C22⋊D47C2213yes—
62C2×(C22⋊D47)⋊C4C2213yes—
63C2×(C22⋊D47)⋊C4C2213yes—
64C2×(C22⋊D47)⋊C4C2216yes—
65C2×#13093983C2213yes—
66C2×#13093982C2213yes—
67C2×#13093982C2213yes—
68C2×#13093980C2211yescharacteristic
69C2×#13093980C2213yes—
70C22×C4⋊Dic47C2213yes—
71C22×C4×Dic47C2213yes—
72C22×C4×Dic47C2213yes—
73C2×C42×D47C2213yes—
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—
84C2×#10625352—224no—
85C2×#10625352C23124yes—
86C22×Dic94C2313yes—
87C22×D188C2313yes—
88C22×C22⋊D47C2313yes—
89C22×C22⋊D47C2313yes—
90C22×C22⋊D47C2316yes—
91C23×Dic47C2313yes—
92C23×Dic47C2313yes—
93C23×Dic47C2313yes—
94C23×Dic47C2311yescharacteristic
95C22×C4×D47C2313yes—
96C22×C4×D47C2313yes—
97C22×C4×D47C2313yes—
98#13094023C23124yes—
99#13094020C23124yes—
100#13094019C23148yes—
101#13094017C23148yes—
102#13094016C23124yes—
103#13094015C23124yes—
104#13094013C23124yes—
105#13094010C23148yes—
106#13094008C23148yes—
107#13094006C23148yes—
108#13094000C23124yes—
109#13093998C23124yes—
110#13093998C23124yes—
111#13093996C23148yes—
112#13093995C23124yes—
113Q8×Dic47C2318yes—
114Q8×Dic47C2318yes—
115Q8×Dic47C23124yes—
116Q8×Dic47C2318yes—
117Q8×Dic47C23124yes—
118C4×Dic94C23124yes—
119#13093989C23124yes—
120C4×D188C23124yes—
121D4×Dic47C23124yes—
122D4×Dic47C23124yes—
123D4×Dic47C23124yes—
124#13093986C23124yes—
125C4×C22⋊D47C23124yes—
126C4×C22⋊D47C23124yes—
127(C22⋊D47)⋊C4C23124yes—
128(C22⋊D47)⋊C4C23124yes—
129(C22⋊D47)⋊C4C23148yes—
130#13093983C23124yes—
131#13093982C23124yes—
132#13093982C23124yes—
133#13093980C2318yes—
134#13093980C23124yes—
135C2×C4⋊Dic47C23124yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2316yes—
139C2×C4⋊Dic47C2313yes—
140C2×C4⋊Dic47C2313yes—
141C2×Dic47⋊C4C2311yescharacteristic
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2311yescharacteristic
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2316yes—
146C2×C22⋊Dic47C2311yescharacteristic
147C2×C22⋊Dic47C2313yes—
148C2×C22⋊Dic47C2316yes—
149C2×(C2×D47)⋊C4C2313yes—
150C2×(C2×D47)⋊C4C2313yes—
151C2×(C2×D47)⋊C4C2316yes—
152C2×(C2×D47)⋊C4C2316yes—
153C2×C4×Dic47C2311yescharacteristic
154C2×C4×Dic47C2313yes—
155C2×C4×Dic47C2313yes—
156C2×C4×Dic47C2311yescharacteristic
157C2×C4×Dic47C2313yes—
158C2×C4×Dic47C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C23124yes—
163C2×C4×Dic47C23124yes—
164C42×D47C23124yes—
165C2×#41×C47—28no—
166C2×#41×C47C2318yes—
167C22×Q8×C47—28no—
168C22×Q8×C47C2318yes—
169C22×Q8×C47C2313yes—
170C22×Q8×C47C2311yescharacteristic
171C22×D4×C47C2313yes—
172C22×D4×C47C2313yes—
173C23×C4×C47C2313yes—
174C23×C4×C47C2313yes—
175#124×C47C23124yes—
176C22⋊Q8×C47C23124yes—
177#121×C47C23124yes—
178C4×Q8×C47C2318yes—
179C4×D4×C47C23124yes—
180C2×C4⋊C4×C47C2313yes—
181C2×C4⋊C4×C47C2313yes—
182C2×C22⋊C4×C47C2311yescharacteristic
183C2×C22⋊C4×C47C2313yes—
184C2×C22⋊C4×C47C2316yes—
185C2×C42×C47C2313yes—
186C24×C47C2413yes—
187C24×C47C2411yescharacteristic
188C23×D47C2413yes—
189#41×C47—232no—
190C2×Q8×C47—232no—
191C2×Q8×C47—212no—
192C2×Q8×C47#4118yescomplemented
193C2×Q8×C47C24112yes—
194C2×Q8×C47C2414yes—
195C2×D4×C47—212no—
196C2×D4×C47—212no—
197C2×D4×C47C24112yes—
198C2×D4×C47C24112yes—
199C22×C4×C47—212no—
200C22×C4×C47—212no—
201C22×C4×C47C2411yescharacteristic
202C22×C4×C47C2413yes—
203C22×C4×C47C2413yes—
204C22×C4×C47C2411yescharacteristic
205C22×C4×C47C24112yes—
206C22×C4×C47C24112yes—
207C22×C4×C47C2413yes—
208C2×C22⋊D47—212no—
209C2×C22⋊D47—212no—
210C2×C22⋊D47—412no—
211C2×C22⋊D47C24112yes—
212C2×C22⋊D47C24112yes—
213C2×C22⋊D47C24124yes—
214C22×Dic47—212no—
215C22×Dic47—46no—
216C22×Dic47—46no—
217C22×Dic47#4118yescomplemented
218C22×Dic47C2411yescharacteristic
219C22×Dic47C2413yes—
220C22×Dic47C2411yescharacteristic
221C22×Dic47C2413yes—
222C22×Dic47C2413yes—
223C22×Dic47C24112yes—
224C22×Dic47C24112yes—
225C22×Dic47C24112yes—
226C22×Dic47C2411yescharacteristic
227C22×Dic47C2411yescharacteristic
228C22×Dic47C2414yes—
229#10625354—232no—
230#10625352—296no—
231C2×D188—212no—
232C2×D188C24112yes—
233C2×C4×D47—212no—
234C2×C4×D47—212no—
235C2×C4×D47—46no—
236C2×C4×D47C24112yes—
237C2×C4×D47C24112yes—
238C2×C4×D47C24112yes—
239C2×Dic94—212no—
240C2×Dic94C24112yes—
241C4⋊C4×C47C24112yes—
242C4⋊C4×C47C24112yes—
243C22⋊C4×C47C2414yes—
244C22⋊C4×C47C24112yes—
245C22⋊C4×C47C24124yes—
246C42×C47C24112yes—
247C22⋊Dic47C2414yes—
248C22⋊Dic47C24112yes—
249C22⋊Dic47C24124yes—
250(C2×D47)⋊C4C24112yes—
251(C2×D47)⋊C4C24112yes—
252(C2×D47)⋊C4C24124yes—
253(C2×D47)⋊C4C24124yes—
254C4⋊Dic47C24112yes—
255C4⋊Dic47C24112yes—
256C4⋊Dic47C24124yes—
257C4⋊Dic47C24112yes—
258C4⋊Dic47C24112yes—
259Dic47⋊C4C2414yes—
260Dic47⋊C4C24112yes—
261Dic47⋊C4C2414yes—
262Dic47⋊C4C24112yes—
263Dic47⋊C4C24124yes—
264C4×Dic47C2414yes—
265C4×Dic47C24112yes—
266C4×Dic47C24112yes—
267C4×Dic47C2414yes—
268C4×Dic47C24112yes—
269C4×Dic47C24112yes—
270C4×Dic47C24112yes—
271C4×Dic47C24112yes—
272C4×Dic47C24112yes—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—26no—
276C23×C47—26no—
277C23×C47—26no—
278C23×C47C2×#4114yes—
279C23×C47C2516yes—
280C23×C47C2512yes—
281C23×C47C2511yescharacteristic
282C22×D47—26no—
283C22×D47—26no—
284C22×D47—26no—
285C22×D47C2516yes—
286Q8×C47—224no—
287Q8×C47C2×#41116yescomplemented
288D4×C47—224no—
289D4×C47—224no—
290C2×C4×C47—26no—
291C2×C4×C47—22no—
292C2×C4×C47—26no—
293C2×C4×C47—22no—
294C2×C4×C47—224no—
295C2×C4×C47—224no—
296C2×C4×C47C2×#41112yes—
297C2×C4×C47C2512yes—
298C2×C4×C47C2516yes—
299C2×C4×C47C2512yes—
300C2×C4×C47C2516yes—
301C2×C4×C47C2516yes—
302C22⋊D47—224no—
303C22⋊D47—224no—
304C22⋊D47—424no—
305C2×Dic47—26no—
306C2×Dic47—22no—
307C2×Dic47—26no—
308C2×Dic47—22no—
309C2×Dic47—26no—
310C2×Dic47—224no—
311C2×Dic47—412no—
312C2×Dic47—412no—
313C2×Dic47C2×#4114yes—
314C2×Dic47C2×#4114yes—
315C2×Dic47C2×#41116yescomplemented
316C2×Dic47C2512yes—
317C2×Dic47C2512yes—
318C2×Dic47C2516yes—
319C2×Dic47C2516yes—
320C2×Dic47C2516yes—
321C2×Dic47C2512yes—
322C2×Dic47C2512yes—
323D188—224no—
324C4×D47—224no—
325C4×D47—224no—
326C4×D47—412no—
327Dic94—224no—
328C2×#3480—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—28no—
332C22×C47—26no—
333C22×C47—26no—
334C22×C47—26no—
335C22×C47—412no—
336C22×C47C22×#4114yes—
337C22×C47C22×#4112yes—
338C22×C47C22×#4112yes—
339C22×C47#58512yes—
340C22×C47C2611yescharacteristic
341C2×D47—26no—
342C2×D47—26no—
343C2×D47—26no—
344C2×D47—412no—
345C4×C47—26no—
346C4×C47—22no—
347C4×C47—26no—
348C4×C47—22no—
349C4×C47C22×#41112yes—
350Dic47—26no—
351Dic47—22no—
352Dic47—26no—
353Dic47—22no—
354Dic47—26no—
355Dic47C22×#4114yes—
356Dic47C22×#4114yes—
357#3480—4732no—
358C2×#559—473no—
359C2×#557—471no—
360C2×#556—473no—
361C2×#553—473no—
362C2×#553—473no—
363C2×#550—471no—
364C2×#548—471no—
365C2×#548D4711yescharacteristic, complemented
366C2×#532—473no—
367C2×#529—473no—
368C2×#529—473no—
369C2×C4×#41—471no—
370C2×C4×#41—471no—
371C2×C4×#41—473no—
372C22×C4×Q8—471no—
373C2×C47—24no—
374C2×C47—46no—
375C2×C47#348014yescomplemented
376C2×C47C23×#4111yescharacteristic
377C2×C47C23×#4111yescharacteristic
378C2×C47C2×#58511yescharacteristic
379D47—46no—
380C22×#41—471no—
381C22×#41—473no—
382C22×#41C2×D4711yescharacteristic
383C23×Q8C2×D4711yescharacteristic
384#559—4748no—
385#557—4716no—
386#556—4748no—
387#553—4748no—
388#553—4748no—
389#550—4716no—
390#548—4716no—
391#548C2×D47116yescomplemented
392#532—4748no—
393C2×C4⋊Q8—473no—
394C2×#127—473no—
395#529—4748no—
396#529—4748no—
397C2×#126—476no—
398C2×#126—476no—
399C2×#125—473no—
400C2×#125—473no—
401C2×#124—473no—
402C2×#124—476no—
403C2×#124C2×D4713yes—
404C2×#123—476no—
405C2×#123—476no—
406C2×C22⋊Q8—473no—
407C2×C22⋊Q8C2×D4713yes—
408C2×#121—473no—
409C2×#121—476no—
410C2×#121—473no—
411C2×#121—473no—
412C2×#121C2×D4713yes—
413C4×#41—4716no—
414C4×#41—4716no—
415C4×#41—4748no—
416C2×C4×Q8—471no—
417C2×C4×Q8—473no—
418C2×C4×Q8—471no—
419C2×C4×Q8—473no—
420C2×C4×Q8—4716no—
421C2×C4×Q8—471no—
422C2×C4×Q8—473no—
423C2×C4×Q8—473no—
424C2×C4×Q8C2×D4711yescharacteristic
425C2×C4×D4—473no—
426C2×C4×D4—473no—
427C2×C4×D4—473no—
428C2×C4×D4—473no—
429C2×C4×D4—473no—
430C2×C4×D4—473no—
431C2×C4×D4—473no—
432C2×C4×D4—473no—
433C2×C4×D4—476no—
434C2×C4×D4—473no—
435C2×C4×D4C2×D4713yes—
436C2×#117—473no—
437C2×#117—473no—
438C2×#117—473no—
439C2×#117—471no—
440C2×#117—473no—
441C22×C4⋊C4—473no—
442C22×C42—473no—
443C22×C42—473no—
444C22×C42—473no—
445C47C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—478no—
448C2×#41—4724no—
449C2×#41—9424no—
450C2×#41—948no—
451C2×#41C22×D4718yes—
452C22×Q8—28no—
453C22×Q8—473no—
454C22×Q8C22×D4713yes—
455C22×Q8C22×D4718yes—
456C22×Q8C22×D4711yescharacteristic
457C22×D4—473no—
458C22×D4—473no—
459C22×D4—476no—
460C22×D4—473no—
461C22×D4C22×D4713yes—
462C22×D4C22×D4713yes—
463C23×C4—471no—
464C23×C4—473no—
465C23×C4—473no—
466C23×C4—473no—
467C23×C4—473no—
468C23×C4—473no—
469C23×C4—473no—
470C23×C4C22×D4713yes—
471C23×C4C22×D4713yes—
472C4⋊Q8—4724no—
473#127—4724no—
474#126—4748no—
475#126—4748no—
476#125—4724no—
477#125—4724no—
478#124—4724no—
479#124—4748no—
480#124C22×D47124yes—
481#123—4748no—
482#123—4748no—
483C22⋊Q8—4724no—
484C22⋊Q8C22×D47124yes—
485#121—4724no—
486#121—4748no—
487#121—4724no—
488#121—4724no—
489#121C22×D47124yes—
490C4×Q8—478no—
491C4×Q8—4724no—
492C4×Q8—478no—
493C4×Q8—4724no—
494C4×Q8—478no—
495C4×Q8—4724no—
496C4×Q8—4724no—
497C4×Q8C22×D4718yes—
498C4×D4—4724no—
499C4×D4—4724no—
500C4×D4—4724no—
501C4×D4—4724no—
502C4×D4—4724no—
503C4×D4—4724no—
504C4×D4—4724no—
505C4×D4—4724no—
506C4×D4—4748no—
507C4×D4—4724no—
508C4×D4C22×D47124yes—
509#117—4724no—
510#117—4724no—
511#117—4724no—
512#117—478no—
513#117—4724no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—473no—
516C2×C4⋊C4—476no—
517C2×C4⋊C4—4724no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—473no—
521C2×C4⋊C4—473no—
522C2×C4⋊C4—473no—
523C2×C4⋊C4—473no—
524C2×C4⋊C4—476no—
525C2×C4⋊C4C22×D4713yes—
526C2×C4⋊C4C22×D4713yes—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—473no—
529C2×C22⋊C4—476no—
530C2×C22⋊C4—473no—
531C2×C22⋊C4—476no—
532C2×C22⋊C4—473no—
533C2×C22⋊C4—476no—
534C2×C22⋊C4C22×D4711yescharacteristic
535C2×C22⋊C4C22×D4713yes—
536C2×C22⋊C4C22×D4716yes—
537C2×C42—471no—
538C2×C42—471no—
539C2×C42—473no—
540C2×C42—473no—
541C2×C42—473no—
542C2×C42—473no—
543C2×C42—473no—
544C2×C42—473no—
545C2×C42—473no—
546C2×C42—4724no—
547C2×C42—4724no—
548C2×C42—4724no—
549C2×C42C22×D4713yes—
550C24—473no—
551C24C23×D4713yes—
552C24C23×D4711yescharacteristic
553#41—232no—
554#41—9496no—
555#41—9432no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—4712no—
559C2×Q8—9412no—
560C2×Q8#1062535218yescomplemented
561C2×Q8C23×D47112yes—
562C2×Q8C23×D4714yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—4712no—
566C2×D4—4712no—
567C2×D4—4724no—
568C2×D4—4712no—
569C2×D4—9412no—
570C2×D4—9412no—
571C2×D4—9412no—
572C2×D4—18812no—
573C2×D4C23×D47112yes—
574C2×D4C23×D47112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—478no—
578C22×C4—474no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—4712no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—473no—
585C22×C4—473no—
586C22×C4—473no—
587C22×C4—4712no—
588C22×C4—4712no—
589C22×C4—4712no—
590C22×C4—4712no—
591C22×C4—4712no—
592C22×C4—9412no—
593C22×C4—9412no—
594C22×C4—9412no—
595C22×C4—1886no—
596C22×C4—1886no—
597C22×C4—1886no—
598C22×C4C23×D47112yes—
599C22×C4C23×D47112yes—
600C22×C4C23×D4711yescharacteristic
601C22×C4C23×D4713yes—
602C22×C4C23×D4711yescharacteristic
603C22×C4C23×D4713yes—
604C22×C4C23×D4713yes—
605C4⋊C4—474no—
606C4⋊C4—474no—
607C4⋊C4—4712no—
608C4⋊C4—4712no—
609C4⋊C4—4724no—
610C4⋊C4—4712no—
611C4⋊C4—4712no—
612C4⋊C4—4724no—
613C4⋊C4—4712no—
614C4⋊C4—4712no—
615C4⋊C4C23×D47112yes—
616C4⋊C4C23×D47112yes—
617C22⋊C4—474no—
618C22⋊C4—4712no—
619C22⋊C4—4724no—
620C22⋊C4—4712no—
621C22⋊C4—4724no—
622C22⋊C4—4712no—
623C22⋊C4—4724no—
624C22⋊C4C23×D4714yes—
625C22⋊C4C23×D47112yes—
626C22⋊C4C23×D47124yes—
627C42—474no—
628C42—474no—
629C42—4712no—
630C42—4712no—
631C42—4712no—
632C42—4712no—
633C42—4712no—
634C42—4712no—
635C42—4712no—
636C42C23×D47112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—476no—
643C23—946no—
644C23—946no—
645C23—946no—
646C23#41×D4714yes—
647C23C24×D4716yes—
648C23C24×D4712yes—
649C23C24×D4711yescharacteristic
650Q8—224no—
651Q8—9424no—
652Q8C2×#10625352116yescomplemented
653D4—224no—
654D4—224no—
655D4—9424no—
656D4—9424no—
657D4—9424no—
658D4—18824no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—474no—
666C2×C4—474no—
667C2×C4—4716no—
668C2×C4—472no—
669C2×C4—472no—
670C2×C4—472no—
671C2×C4—472no—
672C2×C4—476no—
673C2×C4—476no—
674C2×C4—476no—
675C2×C4—9424no—
676C2×C4—9424no—
677C2×C4—946no—
678C2×C4—942no—
679C2×C4—946no—
680C2×C4—942no—
681C2×C4—946no—
682C2×C4—9424no—
683C2×C4—18812no—
684C2×C4—18812no—
685C2×C4—18812no—
686C2×C4C2×#10625352112yes—
687C2×C4C24×D4712yes—
688C2×C4C24×D4716yes—
689C2×C4C24×D4712yes—
690C2×C4C24×D4716yes—
691C2×C4C24×D4716yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—946no—
700C22—946no—
701C22—946no—
702C22—18812no—
703C22C2×#41×D4714yes—
704C22C2×#41×D4712yes—
705C22C22×#1062535212yes—
706C22#1568996012yes—
707C22C25×D4711yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—474no—
713C4—474no—
714C4—946no—
715C4—942no—
716C4—946no—
717C4—942no—
718C4—946no—
719C4C22×#10625352112yes—
720C2—24no—
721C2—46no—
722C2—1886no—
723C2#2025697814yesdirect product factor
724C2C22×#41×D4711yescharacteristic
725C2C23×#1062535211yescharacteristic
726C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3480
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #20256978C2direct (N × H)
2. C2×#15689855C2semidirect
3. C2×#15689849C2semidirect
4. C2×#15689844C2semidirect
5. C2×#15689825C2semidirect
6. C2×#15689819C2semidirect
7. C2×#15689792C2semidirect
8. C2×#15689784C2semidirect
9. C2×#15689668C2semidirect
10. C2×#15689659C2semidirect
11. C2×#15689652C2semidirect
12. C2×#41×Dic47C2semidirect
13. C2×C4×#10625354C2semidirect
14. C2×C4×#10625352C2semidirect
15. C22×Q8×Dic47C2semidirect
16. C2×C47×#548C2semidirect
19. #15689855C22semidirect
20. #15689849C22semidirect
21. #15689844C22semidirect
22. #15689825C22semidirect
23. #15689819C22semidirect
24. #15689792C22semidirect
25. #15689784C22semidirect
26. #15689668C22semidirect
29. #15689659C22semidirect
30. #15689652C22semidirect
44. #41×Dic47C22semidirect
45. C4×#10625354C22semidirect
46. C4×#10625352C22semidirect
52. C2×Q8×Dic47C22semidirect
76. C47×#548C22semidirect
192. C2×Q8×C47#41semidirect
217. C22×Dic47#41semidirect
287. Q8×C47C2×#41semidirect
315. C2×Dic47C2×#41semidirect
365. C2×#548D47semidirect
375. C2×C47#3480semidirect
391. #548C2×D47semidirect
445. C47C2×#3480semidirect
560. C2×Q8#10625352semidirect
652. Q8C2×#10625352semidirect
723. C2#20256978direct (N × H)

Maximal subgroups

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

subgroupindex
#202569782
C2×#156898552
C2×#156898492
C2×#156898442
C2×#156898252
C2×#156898192
C2×#156897922
C2×#156897842
C2×#156896682
C2×#156896592
C2×#156896522
C2×#41×Dic472
C2×C4×#106253542
C2×C4×#106253522
C22×Q8×Dic472
C2×C47×#5482
C2×#348047