Finite Group Databasebeta

← C2×#20248766 #26386505

Subgroups — C2×#20248766 #26386505

Order 12032.

3094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic
2C22×C4⋊C4×D47C211yesmaximal, characteristic
3#20248766C2116yesmaximal, direct product factor
4C2×#15689057C211yesmaximal, characteristic, complemented
5C2×#15689056C211yesmaximal, characteristic, complemented
6C2×#15689044C211yesmaximal, characteristic, complemented
7C2×#15689043C211yesmaximal, characteristic, complemented
8C2×#15689021C211yesmaximal, characteristic, complemented
9C2×#15689018C211yesmaximal, characteristic, complemented
10C2×#15689018C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic
12C2×#15688997C211yesmaximal, characteristic
13C2×#15688994C211yesmaximal, characteristic
14C2×#15688994C211yesmaximal, characteristic
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
16C2×C47×#389C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094002—28no—
22C2×#13094002C2218yes—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C2×C4⋊C4×D47—28no—
35C2×C4⋊C4×D47C2218yes—
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689057C2218yescomplemented
42#15689056C2218yescomplemented
43#15689044C2218yescomplemented
44#15689043C2218yescomplemented
45#15689021C2218yescomplemented
46#15689018C2218yescomplemented
47#15689018C2218yescomplemented
48#15688997C2218yes—
49#15688997C2218yes—
50#15688994C2218yes—
51#15688994C2218yes—
52C4×(C2×D47)⋊C4C2218yes—
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×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C47×#389C2218yescomplemented
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C22×Dic94—24no—
71C22×Dic94—42no—
72C22×Dic94—42no—
73C22×Dic94C2314yes—
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C22×C4×D47—24no—
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47—42no—
88C22×C4×D47—42no—
89C22×C4×D47D418yes—
90C22×C4×D47C2314yes—
91C22×C4×D47C2314yes—
92C22×C4×D47C2314yes—
93#13094002—232no—
94C2×C4⋊Dic47—24no—
95C2×C4⋊Dic47—24no—
96C2×C4⋊Dic47—42no—
97C2×C4⋊Dic47C2314yes—
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—42no—
107C2×Dic47⋊C4—42no—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C4⋊C4×D47—232no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4Q818yescomplemented
120C2×(C2×D47)⋊C4Q818yescomplemented
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×C4×Dic47—42no—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47—24no—
143C2×C4⋊C4×C47—24no—
144C2×C4⋊C4×C47—24no—
145C2×C4⋊C4×C47—42no—
146C2×C4⋊C4×C47C2314yes—
147C2×C4⋊C4×C47C2314yes—
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C42×C47—42no—
151C2×C42×C47C2314yes—
152#95×C47C2314yes—
153#95×C47C2314yes—
154C24×C47C2411yescharacteristic
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—22no—
159C23×D47C2×D414yes—
160C23×D47C2×Q814yes—
161C23×D47C2×Q814yes—
162C23×D47C2412yes—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47C2×D414yes—
181C22×C4×C47C2×Q814yes—
182C22×C4×C47C2×Q814yes—
183C22×C4×C47#4114yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47C2×D414yes—
209C22×Dic47C2×Q814yes—
210C22×Dic47C2×Q814yes—
211C22×Dic47#4114yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C2×C4×D47—232no—
220C2×C4×D47—28no—
221C2×C4×D47—28no—
222C2×C4×D47—28no—
223C2×C4×D47—28no—
224C2×C4×D47—416no—
225C2×C4×D47—44no—
226C2×C4×D47—44no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C2×C4×D47—416no—
230C2×C4×D47C2×D4116yes—
231C2×Dic94—28no—
232C2×Dic94—44no—
233C2×Dic94—44no—
234C2×Dic94—416no—
235C4⋊C4×C47—28no—
236C4⋊C4×C47—28no—
237C4⋊C4×C47—28no—
238C4⋊C4×C47—44no—
239C42×C47—44no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—28no—
242(C2×D47)⋊C4C2×Q8116yescomplemented
243(C2×D47)⋊C4C2×Q8116yescomplemented
244C4⋊Dic47—28no—
245C4⋊Dic47—28no—
246C4⋊Dic47—44no—
247Dic47⋊C4—28no—
248Dic47⋊C4—28no—
249Dic47⋊C4—28no—
250Dic47⋊C4—28no—
251Dic47⋊C4—28no—
252Dic47⋊C4—28no—
253Dic47⋊C4—44no—
254Dic47⋊C4—44no—
255C4×Dic47—44no—
256C23×C47C22×D412yes—
257C23×C47C22×Q812yes—
258C23×C47C22×Q812yes—
259C23×C47C2×#4112yes—
260C23×C47C2×#4112yes—
261C23×C47H(5,𝔽2)12yes—
262C23×C47H(5,𝔽2)12yes—
263C23×C47C2511yescharacteristic
264C22×D47—28no—
265C22×D47—28no—
266C22×D47—28no—
267C22×D47—28no—
268C22×D47—28no—
269C22×D47—28no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47C4⋊Q8116yes—
275C22×D47C22×D414yes—
276C22×D47C22×Q814yes—
277C22×D47C22×Q814yes—
278C2×C4×C47—28no—
279C2×C4×C47—28no—
280C2×C4×C47—28no—
281C2×C4×C47—28no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—44no—
300C2×C4×C47—44no—
301C2×C4×C47—44no—
302C2×C4×C47C22×D414yes—
303C2×C4×C47C22×Q814yes—
304C2×C4×C47C22×Q814yes—
305C2×C4×C47C2×#4114yes—
306C2×Dic47—28no—
307C2×Dic47—28no—
308C2×Dic47—28no—
309C2×Dic47—28no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—44no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47C22×D414yes—
331C2×Dic47C22×Q814yes—
332C2×Dic47C22×Q814yes—
333C2×Dic47C2×#4114yes—
334C4×D47—232no—
335C4×D47—416no—
336C4×D47—416no—
337Dic94—416no—
338C2×#2583—471nomaximal, Sylow
339C22×C47#52514yes—
340C22×C47C2×C4⋊Q814yes—
341C22×C47#53414yes—
342C22×C47#55414yes—
343C22×C47#55414yes—
344C22×C47#55414yes—
345C22×C47#55414yes—
346C22×C47C23×D411yescharacteristic
347C22×C47C23×Q811yescharacteristic
348C22×C47C23×Q811yescharacteristic
349C22×C47C22×#4111yescharacteristic
350C22×C47C22×#4111yescharacteristic
351C22×C47C2×H(5,𝔽2)11yescharacteristic
352C22×C47C2×H(5,𝔽2)11yescharacteristic
353C2×D47—232no—
354C2×D47—24no—
355C2×D47—24no—
356C2×D47—24no—
357C2×D47—24no—
358C2×D47—24no—
359C2×D47—24no—
360C2×D47C2×C4⋊Q818yes—
361C4×C47—24no—
362C4×C47—24no—
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—42no—
366C4×C47—42no—
367C4×C47—42no—
368Dic47—24no—
369Dic47—24no—
370Dic47—24no—
371Dic47—24no—
372Dic47—42no—
373Dic47—42no—
374Dic47—42no—
375C22×C22⋊Q8—471no—
376C23×C4⋊C4—471no—
377#2583—4716no—
378C2×#398—471no—
379C2×#398—471no—
380C2×#395—471no—
381C2×#395—471no—
382C2×#389—471no—
383C2×#389—471no—
384C2×#389—471no—
385C2×#389D4711yescharacteristic, complemented
386C2×#385—471no—
387C2×#385—471no—
388C2×#385—471no—
389C2×#385—471no—
390C2×C4×C22⋊C4—471no—
391C2×C47#258318yescomplemented
392C2×C47C2×#52511yescharacteristic
393C2×C47C22×C4⋊Q811yescharacteristic
394C2×C47C2×#53411yescharacteristic
395C2×C47C2×#55411yescharacteristic
396C2×C47C2×#55411yescharacteristic
397C2×C47C2×#55411yescharacteristic
398C2×C47C2×#55411yescharacteristic
399D47—28no—
400C23×Q8—471no—
401C24×C4—471no—
402C24×C4—471no—
403C24×C4—471no—
404C2×C22⋊Q8—478no—
405C2×C22⋊Q8—948no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4—471no—
408C22×C4⋊C4—471no—
409C22×C4⋊C4—471no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4—471no—
412C22×C4⋊C4—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—478no—
418C22×C4⋊C4—948no—
419C22×C4⋊C4C2×D4711yescharacteristic
420C22×C4⋊C4C2×D4711yescharacteristic
421C22×C4⋊C4C2×D4711yescharacteristic
422C22×C4⋊C4C2×D4711yescharacteristic
423C22×C22⋊C4—471no—
424C22×C22⋊C4—471no—
425C22×C22⋊C4—471no—
426C22×C22⋊C4—471no—
427C22×C42—471no—
428C22×C42C2×D4711yescharacteristic
429#398—478no—
430#398—478no—
431#395—478no—
432#395—478no—
433#389—478no—
434#389—478no—
435#389—478no—
436#389C2×D4718yescomplemented
437#385—478no—
438#385—478no—
439#385—478no—
440#385—478no—
441C4×C22⋊C4—478no—
442C2×#95—471no—
443C2×#95—471no—
444C2×#95—471no—
445C2×#95—471no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95—471no—
450C2×#95C2×D4711yescharacteristic
451C2×#95C2×D4711yescharacteristic
452C47C2×#258311yescharacteristic, complemented, Sylow
453C25—471no—
454C22×Q8—474no—
455C22×Q8—944no—
456C22×Q8—1882no—
457C22×Q8—1882no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—478no—
463C23×C4—474no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—474no—
468C23×C4—474no—
469C23×C4—944no—
470C23×C4—944no—
471C23×C4—944no—
472C23×C4—944no—
473C23×C4—1882no—
474C23×C4—1882no—
475C23×C4—1882no—
476C23×C4—1882no—
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C22⋊Q8—9432no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—474no—
495C2×C4⋊C4—474no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—9432no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—944no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4—1882no—
510C2×C4⋊C4—1882no—
511C2×C4⋊C4—1882no—
512C2×C4⋊C4C22×D4714yes—
513C2×C4⋊C4C22×D4714yes—
514C2×C4⋊C4C22×D4714yes—
515C2×C4⋊C4C22×D4714yes—
516C2×C22⋊C4—478no—
517C2×C22⋊C4—478no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C42—42no—
525C2×C42—474no—
526C2×C42—1882no—
527C2×C42C22×D4714yes—
528#95—474no—
529#95—474no—
530#95—474no—
531#95—474no—
532#95—474no—
533#95—474no—
534#95—474no—
535#95—474no—
536#95C22×D4714yes—
537#95C22×D4714yes—
538C24—474no—
539C24—474no—
540C24—474no—
541C24—472no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24C23×D4711yescharacteristic
547C2×Q8—948no—
548C2×Q8—1884no—
549C2×Q8—1884no—
550C2×Q8—18816no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—474no—
569C22×C4—474no—
570C22×C4—474no—
571C22×C4—474no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—4716no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—948no—
581C22×C4—948no—
582C22×C4—9432no—
583C22×C4—948no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—948no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—18816no—
603C22×C4—1884no—
604C22×C4—1884no—
605C22×C4—1884no—
606C22×C4—1884no—
607C22×C4—18816no—
608C22×C4#1062535014yes—
609C22×C4D4×D4714yes—
610C22×C4Q8×D4714yes—
611C22×C4Q8×D4714yes—
612C22×C4C23×D4712yes—
613C22×C4C23×D4712yes—
614C22×C4C23×D4712yes—
615C22×C4C23×D4712yes—
616C22×C4C23×D4712yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—948no—
624C4⋊C4—948no—
625C4⋊C4—948no—
626C4⋊C4—948no—
627C4⋊C4—948no—
628C4⋊C4—948no—
629C4⋊C4—948no—
630C4⋊C4—948no—
631C4⋊C4—1884no—
632C4⋊C4—1884no—
633C4⋊C4—1884no—
634C22⋊C4—4716no—
635C22⋊C4—4716no—
636C22⋊C4—948no—
637C22⋊C4—948no—
638C42—44no—
639C42—1884no—
640C23—4716no—
641C23—474no—
642C23—474no—
643C23—474no—
644C23—948no—
645C23—948no—
646C23—948no—
647C23—948no—
648C23—948no—
649C23—948no—
650C23—942no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23C2×D4×D4712yes—
655C23C2×Q8×D4712yes—
656C23C2×Q8×D4712yes—
657C23#41×D4712yes—
658C23C2×#1062535012yes—
659C23#1309406912yes—
660C23#1309407012yes—
661C23C24×D4711yescharacteristic
662Q8—18816no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—474no—
688C2×C4—474no—
689C2×C4—474no—
690C2×C4—474no—
691C2×C4—9432no—
692C2×C4—948no—
693C2×C4—948no—
694C2×C4—948no—
695C2×C4—948no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—18816no—
714C2×C4—18816no—
715C2×C4—1884no—
716C2×C4—1884no—
717C2×C4—1884no—
718C2×C4C2×D4×D4714yes—
719C2×C4C2×Q8×D4714yes—
720C2×C4C2×Q8×D4714yes—
721C2×C4C2×#1062535014yes—
722C22—478no—
723C22—944no—
724C22—944no—
725C22—944no—
726C22—944no—
727C22—944no—
728C22—944no—
729C22—9432no—
730C22#1568963214yes—
731C22C4⋊Q8×D4714yes—
732C22#1568968114yes—
733C22#1568982714yes—
734C22#1568982814yes—
735C22#1568982914yes—
736C22#1568983314yes—
737C22C22×D4×D4711yescharacteristic
738C22C22×Q8×D4711yescharacteristic
739C22C22×Q8×D4711yescharacteristic
740C22C2×#41×D4711yescharacteristic
741C22C22×#1062535011yescharacteristic
742C22C2×#1309406911yescharacteristic
743C22C2×#1309407011yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—944no—
752C4—944no—
753C4—944no—
754C4—944no—
755C4—1882no—
756C4—1882no—
757C4—1882no—
758C2—948no—
759C2#2024876618yesdirect product factor
760C2C2×#1568963211yescharacteristic
761C2C2×C4⋊Q8×D4711yescharacteristic
762C2C2×#1568968111yescharacteristic
763C2C2×#1568982711yescharacteristic
764C2C2×#1568982811yescharacteristic
765C2C2×#1568982911yescharacteristic
766C2C2×#1568983311yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#389C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#389D47
hypocenterC47C2×#2583
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #20248766C2direct (N × H)
4. C2×#15689057C2semidirect
5. C2×#15689056C2semidirect
6. C2×#15689044C2semidirect
7. C2×#15689043C2semidirect
8. C2×#15689021C2semidirect
9. C2×#15689018C2semidirect
10. C2×#15689018C2semidirect
16. C2×C47×#389C2semidirect
41. #15689057C22semidirect
42. #15689056C22semidirect
43. #15689044C22semidirect
44. #15689043C22semidirect
45. #15689021C22semidirect
46. #15689018C22semidirect
47. #15689018C22semidirect
66. C47×#389C22semidirect
119. C2×(C2×D47)⋊C4Q8semidirect
120. C2×(C2×D47)⋊C4Q8semidirect
242. (C2×D47)⋊C4C2×Q8semidirect
243. (C2×D47)⋊C4C2×Q8semidirect
385. C2×#389D47semidirect
391. C2×C47#2583semidirect
436. #389C2×D47semidirect
452. C47C2×#2583semidirect
759. C2#20248766direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×C4⋊C4×D472
#202487662
C2×#156890572
C2×#156890562
C2×#156890442
C2×#156890432
C2×#156890212
C2×#156890182
C2×#156889972
C2×#156889942
C2×C4×(C2×D47)⋊C42
C2×C47×#3892
C2×#258347