Finite Group Databasebeta

← C2×#20247226 #26384316

Subgroups — C2×#20247226 #26384316

Order 12032.

2702 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094023C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic
3#20247226C2116yesmaximal, direct product factor
4C2×#15689056C211yesmaximal, characteristic
5C2×#15689055C211yesmaximal, characteristic
6C2×#15689044C211yesmaximal, characteristic
7C2×#15689044C211yesmaximal, characteristic
8C2×#15689029C211yesmaximal, characteristic
9C2×#15689027C211yesmaximal, characteristic
10C2×#15689027C211yesmaximal, characteristic
11C2×#15689027C211yesmaximal, characteristic
12C2×#15689020C211yesmaximal, characteristic
13C2×#15689020C211yesmaximal, characteristic
14C2×#15689009C211yesmaximal, characteristic
15C2×C4⋊C4×Dic47C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C23×Dic94C2211yescharacteristic
20C2×#13094023—28no—
21C2×#13094023C2218yes—
22C2×C4×Dic94—28no—
23C2×C4×Dic94C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689056C2218yes—
40#15689055C2218yes—
41#15689044C2218yes—
42#15689044C2218yes—
43#15689029C2218yes—
44#15689027C2218yes—
45#15689027C2218yes—
46#15689027C2218yes—
47#15689020C2218yes—
48#15689020C2218yes—
49#15689009C2218yes—
50C4⋊C4×Dic47C2218yes—
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#387C2218yes—
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94—24no—
74C22×Dic94—24no—
75C22×Dic94—42no—
76C22×Dic94—42no—
77C22×Dic94Q818yescomplemented
78C22×Dic94C2314yes—
79C22×Dic94C2314yes—
80C22×Dic94C2314yes—
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89#13094023—232no—
90C4×Dic94—232no—
91C2×C4⋊Dic47—24no—
92C2×C4⋊Dic47—24no—
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47—42no—
95C2×C4⋊Dic47—42no—
96C2×C4⋊Dic47C2314yes—
97C2×C4⋊Dic47C2314yes—
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2314yes—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4D418yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×C4×Dic47—24no—
114C2×C4×Dic47—24no—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—24no—
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47—24no—
139C2×C4⋊C4×C47Q818yescomplemented
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C42×C47—24no—
143C2×C42×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148C24×C47C2411yescharacteristic
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47C2×D414yes—
166C22×C4×C47C2×Q814yes—
167C22×C4×C47C2×Q814yes—
168C22×C4×C47C2×Q814yes—
169C22×C4×C47C2×Q814yes—
170C22×C4×C47C2412yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47C2×D414yes—
196C22×Dic47C2×D414yes—
197C22×Dic47C2×Q814yes—
198C22×Dic47C2×Q814yes—
199C22×Dic47#4114yes—
200C22×Dic47#4114yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C2×Dic94—232no—
210C2×Dic94—28no—
211C2×Dic94—28no—
212C2×Dic94—28no—
213C2×Dic94—28no—
214C2×Dic94—28no—
215C2×Dic94—28no—
216C2×Dic94—44no—
217C2×Dic94—44no—
218C2×Dic94—416no—
219C2×Dic94—416no—
220C2×Dic94C2×Q8116yescomplemented
221C4⋊C4×C47—28no—
222C4⋊C4×C47C2×Q8116yescomplemented
223C42×C47—28no—
224C4⋊Dic47—28no—
225C4⋊Dic47—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—44no—
228C4⋊Dic47—44no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232Dic47⋊C4—44no—
233Dic47⋊C4—44no—
234Dic47⋊C4C2×D4116yes—
235C4×Dic47—28no—
236C4×Dic47—28no—
237C4×Dic47—28no—
238C4×Dic47—28no—
239C23×C47C22×D412yes—
240C23×C47C22×Q812yes—
241C23×C47C22×Q812yes—
242C23×C47C2×#4112yes—
243C23×C47C2×#4112yes—
244C23×C47H(5,𝔽2)12yes—
245C23×C472−1+412yes—
246C23×C47C2511yescharacteristic
247C2×C4×C47—28no—
248C2×C4×C47—28no—
249C2×C4×C47—28no—
250C2×C4×C47—28no—
251C2×C4×C47—28no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—44no—
269C2×C4×C47—44no—
270C2×C4×C47C22×D414yes—
271C2×C4×C47C22×Q814yes—
272C2×C4×C47C22×Q814yes—
273C2×C4×C47C22×Q814yes—
274C2×C4×C47C22×Q814yes—
275C2×Dic47—28no—
276C2×Dic47—28no—
277C2×Dic47—28no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—44no—
297C2×Dic47—44no—
298C2×Dic47—44no—
299C2×Dic47—44no—
300C2×Dic47C22⋊Q8116yes—
301C2×Dic47C22×D414yes—
302C2×Dic47C22×D414yes—
303C2×Dic47C22×Q814yes—
304C2×Dic47C22×Q814yes—
305C2×Dic47C2×#4114yes—
306C2×Dic47C2×#4114yes—
307Dic94—232no—
308Dic94—416no—
309Dic94—416no—
310C2×#2451—471nomaximal, Sylow
311C22×C47C2×C22⋊Q814yes—
312C22×C47#53314yes—
313C22×C47#54214yes—
314C22×C47#54614yes—
315C22×C47D4×Q814yes—
316C22×C47#55714yes—
317C22×C47Q8214yes—
318C22×C47C23×D411yescharacteristic
319C22×C47C23×Q811yescharacteristic
320C22×C47C23×Q811yescharacteristic
321C22×C47C22×#4111yescharacteristic
322C22×C47C22×#4111yescharacteristic
323C22×C47C2×H(5,𝔽2)11yescharacteristic
324C22×C47C2×2−1+411yescharacteristic
325C4×C47—24no—
326C4×C47—24no—
327C4×C47—24no—
328C4×C47—24no—
329C4×C47—24no—
330C4×C47—42no—
331C4×C47—42no—
332Dic47—24no—
333Dic47—24no—
334Dic47—24no—
335Dic47—42no—
336Dic47—42no—
337Dic47—42no—
338Dic47—42no—
339Dic47C2×C22⋊Q818yes—
340C22×C4⋊Q8—471no—
341C22×C4×Q8—471no—
342#2451—4716no—
343C2×#398—471no—
344C2×#398—471no—
345C2×#395—471no—
346C2×#395—471no—
347C2×#391—471no—
348C2×#391—471no—
349C2×#391—471no—
350C2×#391—471no—
351C2×#389—471no—
352C2×#389—471no—
353C2×#387—471no—
354C2×#387D4711yescharacteristic
355C2×C4×C4⋊C4—471no—
356C2×C47#245118yescomplemented
357C2×C47C22×C22⋊Q811yescharacteristic
358C2×C47C2×#53311yescharacteristic
359C2×C47C2×#54211yescharacteristic
360C2×C47C2×#54611yescharacteristic
361C2×C47C2×D4×Q811yescharacteristic
362C2×C47C2×#55711yescharacteristic
363C2×C47C2×Q8211yescharacteristic
364C23×Q8—471no—
365C23×Q8—471no—
366C23×Q8—471no—
367C2×C4⋊Q8—478no—
368C2×C4⋊Q8—948no—
369C2×C4×Q8—478no—
370C2×C4×Q8—948no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4—471no—
373C22×C4⋊C4—471no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C4⋊C4C2×D4711yescharacteristic
384C22×C42—471no—
385C22×C42—471no—
386C22×C42—471no—
387C22×C42—471no—
388C22×C42C2×D4711yescharacteristic
389#398—478no—
390#398—478no—
391#395—478no—
392#395—478no—
393#391—478no—
394#391—478no—
395#391—478no—
396#391—478no—
397#389—478no—
398#389—478no—
399#387—478no—
400#387C2×D4718yes—
401C4×C4⋊C4—478no—
402C2×#95—471no—
403C2×#95—471no—
404C2×#95—471no—
405C2×#95—471no—
406C2×#95—471no—
407C2×#95—471no—
408C2×#95—471no—
409C2×#95—471no—
410C2×#95—471no—
411C2×#95—471no—
412C2×#95C2×D4711yescharacteristic
413C2×#95C2×D4711yescharacteristic
414C2×#95C2×D4711yescharacteristic
415C2×#95C2×D4711yescharacteristic
416C47C2×#245111yescharacteristic, complemented, Sylow
417C22×Q8—478no—
418C22×Q8—474no—
419C22×Q8—474no—
420C22×Q8—474no—
421C22×Q8—944no—
422C22×Q8—944no—
423C22×Q8—944no—
424C22×Q8—944no—
425C22×Q8—944no—
426C22×Q8—944no—
427C22×Q8—1882no—
428C22×Q8—1882no—
429C23×C4—471no—
430C23×C4—471no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4C22×D4711yescharacteristic
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C23×C4C22×D4711yescharacteristic
441C23×C4C22×D4711yescharacteristic
442C23×C4C22×D4711yescharacteristic
443C23×C4C22×D4711yescharacteristic
444C4⋊Q8—9432no—
445C4×Q8—9432no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—478no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—474no—
451C2×C4⋊C4—474no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—474no—
454C2×C4⋊C4—474no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—944no—
460C2×C4⋊C4—944no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—944no—
463C2×C4⋊C4—944no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—1882no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4—1882no—
469C2×C4⋊C4Dic9418yescomplemented
470C2×C4⋊C4C22×D4714yes—
471C2×C4⋊C4C22×D4714yes—
472C2×C42—24no—
473C2×C42—474no—
474C2×C42—474no—
475C2×C42—474no—
476C2×C42—474no—
477C2×C42—944no—
478C2×C42—944no—
479C2×C42—944no—
480C2×C42—944no—
481C2×C42C22×D4714yes—
482#95—474no—
483#95—474no—
484#95—474no—
485#95—474no—
486#95—474no—
487#95—474no—
488#95—474no—
489#95—474no—
490#95—474no—
491#95—474no—
492#95C22×D4714yes—
493#95C22×D4714yes—
494#95C22×D4714yes—
495#95C22×D4714yes—
496C24C23×D4711yescharacteristic
497C2×Q8—4716no—
498C2×Q8—948no—
499C2×Q8—9432no—
500C2×Q8—948no—
501C2×Q8—948no—
502C2×Q8—948no—
503C2×Q8—948no—
504C2×Q8—948no—
505C2×Q8—1884no—
506C2×Q8—1884no—
507C2×Q8—18816no—
508C2×Q8—18816no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—474no—
528C22×C4—472no—
529C22×C4—474no—
530C22×C4—474no—
531C22×C4—474no—
532C22×C4—472no—
533C22×C4—472no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—472no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4C2×Dic9414yes—
558C22×C4C2×Dic9414yes—
559C22×C4C2×Dic9414yes—
560C22×C4D4×D4714yes—
561C22×C4Q8×D4714yes—
562C22×C4C23×D4712yes—
563C22×C4C23×D4712yes—
564C22×C4C23×D4712yes—
565C22×C4C23×D4712yes—
566C22×C4C23×D4712yes—
567C22×C4C23×D4712yes—
568C22×C4C23×D4712yes—
569C4⋊C4—28no—
570C4⋊C4—4716no—
571C4⋊C4—948no—
572C4⋊C4—948no—
573C4⋊C4—948no—
574C4⋊C4—948no—
575C4⋊C4—948no—
576C4⋊C4—948no—
577C4⋊C4—1884no—
578C4⋊C4—1884no—
579C4⋊C4—1884no—
580C4⋊C4—1884no—
581C4⋊C4C2×Dic94116yescomplemented
582C42—28no—
583C42—948no—
584C42—948no—
585C42—948no—
586C42—948no—
587C23C2×D4×D4712yes—
588C23C2×Q8×D4712yes—
589C23C22×Dic9412yes—
590C23#41×D4712yes—
591C23#41×D4712yes—
592C23#1309407012yes—
593C23#1309407112yes—
594C23C24×D4711yescharacteristic
595Q8—9432no—
596Q8—18816no—
597Q8—18816no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—28no—
601C2×C4—28no—
602C2×C4—28no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—4716no—
622C2×C4—474no—
623C2×C4—474no—
624C2×C4—474no—
625C2×C4—474no—
626C2×C4—474no—
627C2×C4—474no—
628C2×C4—948no—
629C2×C4—948no—
630C2×C4—948no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—1884no—
650C2×C4—1884no—
651C2×C4—1884no—
652C2×C4—1884no—
653C2×C4C2×D4×D4714yes—
654C2×C4C2×Q8×D4714yes—
655C2×C4C22×Dic9414yes—
656C2×C4C22×Dic9414yes—
657C2×C4C22×Dic9414yes—
658C22C22⋊Q8×D4714yes—
659C22#1568967614yes—
660C22#1568973914yes—
661C22#1568976514yes—
662C22D4×Dic9414yes—
663C22#1568985014yes—
664C22Q8×Dic9414yes—
665C22C22×D4×D4711yescharacteristic
666C22C22×Q8×D4711yescharacteristic
667C22C23×Dic9411yescharacteristic
668C22C2×#41×D4711yescharacteristic
669C22C2×#41×D4711yescharacteristic
670C22C2×#1309407011yescharacteristic
671C22C2×#1309407111yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—24no—
676C4—24no—
677C4—42no—
678C4—42no—
679C4—478no—
680C4—944no—
681C4—944no—
682C4—944no—
683C4—1882no—
684C4—1882no—
685C4—1882no—
686C4—1882no—
687C2#2024722618yesdirect product factor
688C2C2×C22⋊Q8×D4711yescharacteristic
689C2C2×#1568967611yescharacteristic
690C2C2×#1568973911yescharacteristic
691C2C2×#1568976511yescharacteristic
692C2C2×D4×Dic9411yescharacteristic
693C2C2×#1568985011yescharacteristic
694C2C2×Q8×Dic9411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socle, prime radicalC24×C47C24
hypercenterC2×#387D47
hypocenterC47C2×#2451
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #20247226C2direct (N × H)
77. C22×Dic94Q8semidirect
139. C2×C4⋊C4×C47Q8semidirect
220. C2×Dic94C2×Q8semidirect
222. C4⋊C4×C47C2×Q8semidirect
356. C2×C47#2451semidirect
416. C47C2×#2451semidirect
469. C2×C4⋊C4Dic94semidirect
581. C4⋊C4C2×Dic94semidirect
687. C2#20247226direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940232
C22×C4×Dic942
#202472262
C2×#156890562
C2×#156890552
C2×#156890442
C2×#156890292
C2×#156890272
C2×#156890202
C2×#156890092
C2×C4⋊C4×Dic472
C2×C47×#3872
C2×#245147