Finite Group Databasebeta

← C2×#20246395 #26375797

Subgroups — C2×#20246395 #26375797

Order 12032.

3614 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094004C211yesmaximal, characteristic
2C22×#13093989C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic
4#20246395C2116yesmaximal, direct product factor
5C2×#15689029C211yesmaximal, characteristic, complemented
6C2×#15689022C211yesmaximal, characteristic, complemented
7C2×#15689021C212yesmaximal, complemented
8C2×#15689008C212yesmaximal, complemented
9C2×#15688997C212yesmaximal
10C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
11C2×C4×(C2×D47)⋊C4C212yesmaximal
12C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
13C23×Dic94C2211yescharacteristic
14C23×C4×D47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C2×#13094004C4116yescomplemented
17C2×#13094004C2218yes—
18C2×#13093989—28no—
19C2×#13093989C2218yescomplemented
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2212yes—
22C22×C4⋊Dic47C2212yes—
23C22×Dic47⋊C4C2212yes—
24C22×Dic47⋊C4C2212yes—
25C2×C4⋊C4×D47—28no—
26C2×C4⋊C4×D47C2218yes—
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2212yes—
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×C4×Dic47C2212yes—
31C22×C4×Dic47C2211yescharacteristic
32#15689029C2218yescomplemented
33#15689022C2218yescomplemented
34#15689021C22116yescomplemented
35#15689008C22116yescomplemented
36#15688997C22116yes—
37C4×(C2×D47)⋊C4C2218yes—
38C4×(C2×D47)⋊C4C22116yes—
39C2×C47⋊#95C2212yes—
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2212yes—
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2212yes—
44C22×C4⋊C4×C47C2211yescharacteristic
45C22×C4⋊C4×C47C2211yescharacteristic
46C22×C42×C47C2211yescharacteristic
47C22×C42×C47C2212yes—
48C4×C4⋊C4×C47C2218yescomplemented
49C2×#95×C47C2212yes—
50C24×D47C2311yescharacteristic
51C22×Dic94—24no—
52C22×Dic94—24no—
53C22×Dic94C2×C418yescomplemented
54C22×Dic94C2314yes—
55C23×Dic47C2312yes—
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2312yes—
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—28no—
63C22×C4×D47—28no—
64C22×C4×D47—44no—
65C22×C4×D47C2×C418yes—
66C22×C4×D47C2318yes—
67C22×C4×D47C2314yes—
68#13094004C2×C4164yescomplemented
69#13093989—232no—
70C2×C4⋊Dic47—24no—
71C2×C4⋊Dic47—44no—
72C2×C4⋊Dic47C2×C4116yescomplemented
73C2×C4⋊Dic47C2314yes—
74C2×C4⋊Dic47C2318yes—
75C2×C4⋊Dic47C2318yes—
76C2×Dic47⋊C4—28no—
77C2×Dic47⋊C4—28no—
78C2×Dic47⋊C4C2318yes—
79C2×Dic47⋊C4C2318yes—
80C4⋊C4×D47—232no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4C2×C4116yes—
83C2×(C2×D47)⋊C4Q818yescomplemented
84C2×(C2×D47)⋊C4C2314yes—
85C2×(C2×D47)⋊C4C2318yes—
86C2×(C2×D47)⋊C4C2314yes—
87C2×C4×Dic47—28no—
88C2×C4×Dic47—24no—
89C2×C4×Dic47C2318yes—
90C2×C4×Dic47C2314yes—
91C47⋊#95C2314yes—
92C47⋊#95C2318yes—
93C47⋊#95C2314yes—
94C47⋊#95C2318yes—
95C47⋊#95C2318yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2312yes—
98C23×C4×C47C2312yes—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2×C418yescomplemented
102C2×C4⋊C4×C47D418yes—
103C2×C4⋊C4×C47C2314yes—
104C2×C4⋊C4×C47C2314yes—
105C2×C42×C47—24no—
106C2×C42×C47—44no—
107C2×C42×C47C2314yes—
108C2×C42×C47C2318yes—
109#95×C47C2318yes—
110C24×C47C2411yescharacteristic
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47—22no—
115C23×D47C22×C414yes—
116C23×D47C2×Q814yes—
117C23×D47#4114yes—
118C23×D47C2412yes—
119C22×C4×C47—22no—
120C22×C4×C47—24no—
121C22×C4×C47—22no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—24no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47C22×C418yes—
129C22×C4×C47C22×C414yes—
130C22×C4×C47C2×D418yes—
131C22×C4×C47C2×D414yes—
132C22×C4×C47C2×Q814yes—
133C22×C4×C47#4114yes—
134C22×C4×C47C2412yes—
135C22×C4×C47C2414yes—
136C22×C4×C47C2414yes—
137C22×C4×C47C2412yes—
138C22×C4×C47C2412yes—
139C22×Dic47—22no—
140C22×Dic47—24no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—24no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—24no—
147C22×Dic47—22no—
148C22×Dic47—24no—
149C22×Dic47—22no—
150C22×Dic47—24no—
151C22×Dic47C22×C418yes—
152C22×Dic47C22×C414yes—
153C22×Dic47C2×Q814yes—
154C22×Dic47C2414yes—
155C22×Dic47C2412yes—
156C22×Dic47C2414yes—
157C22×Dic47C2412yes—
158C22×Dic47C2412yes—
159C2×C4×D47—232no—
160C2×C4×D47—28no—
161C2×C4×D47—28no—
162C2×C4×D47—216no—
163C2×C4×D47—216no—
164C2×C4×D47—48no—
165C2×C4×D47—432no—
166C2×C4×D47C22×C4116yes—
167C2×Dic94—232no—
168C2×Dic94—28no—
169C2×Dic94—28no—
170C2×Dic94C22×C4116yescomplemented
171C4⋊C4×C47C22×C4116yescomplemented
172C4⋊C4×C47C2×D4116yes—
173C42×C47—28no—
174C42×C47—48no—
175(C2×D47)⋊C4—28no—
176(C2×D47)⋊C4C22×C4132yes—
177(C2×D47)⋊C4C2×Q8116yescomplemented
178C4⋊Dic47—28no—
179C4⋊Dic47—48no—
180C4⋊Dic47C22×C4132yescomplemented
181Dic47⋊C4—216no—
182Dic47⋊C4—216no—
183C4×Dic47—216no—
184C4×Dic47—28no—
185C23×C47C23×C412yes—
186C23×C47C22×D412yes—
187C23×C47C22×Q812yes—
188C23×C47C2×#4112yes—
189C23×C47C2×#4112yes—
190C23×C47H(5,𝔽2)12yes—
191C23×C472−1+412yes—
192C23×C47C2511yescharacteristic
193C22×D47—28no—
194C22×D47—28no—
195C22×D47—28no—
196C22×D47—28no—
197C22×D47—28no—
198C22×D47—28no—
199C22×D47—22no—
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47C4×Q8116yescomplemented
204C22×D47C23×C414yes—
205C22×D47C22×Q814yes—
206C22×D47C2×#4114yes—
207C2×C4×C47—216no—
208C2×C4×C47—216no—
209C2×C4×C47—28no—
210C2×C4×C47—22no—
211C2×C4×C47—24no—
212C2×C4×C47—24no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—44no—
220C2×C4×C47C4×D4116yes—
221C2×C4×C47C23×C418yes—
222C2×C4×C47C23×C414yes—
223C2×C4×C47C22×D418yes—
224C2×C4×C47C22×D414yes—
225C2×C4×C47C22×Q814yes—
226C2×C4×C47C2×#4114yes—
227C2×Dic47—216no—
228C2×Dic47—28no—
229C2×Dic47—28no—
230C2×Dic47—22no—
231C2×Dic47—24no—
232C2×Dic47—22no—
233C2×Dic47—24no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—22no—
241C2×Dic47—24no—
242C2×Dic47—48no—
243C2×Dic47—44no—
244C2×Dic47C23×C414yes—
245C2×Dic47C23×C418yes—
246C2×Dic47C22×Q814yes—
247C4×D47—232no—
248C4×D47—432no—
249Dic94—232no—
250C2×#2360—471nomaximal, Sylow
251C22×C47C2×C4×D414yes—
252C22×C47C2×C4×Q814yes—
253C22×C47#52014yes—
254C22×C47#54614yes—
255C22×C47D4×Q814yes—
256C22×C47#55214yes—
257C22×C47#55414yes—
258C22×C47C24×C411yescharacteristic
259C22×C47C23×D411yescharacteristic
260C22×C47C23×Q811yescharacteristic
261C22×C47C22×#4111yescharacteristic
262C22×C47C22×#4111yescharacteristic
263C22×C47C2×H(5,𝔽2)11yescharacteristic
264C22×C47C2×2−1+411yescharacteristic
265C2×D47—232no—
266C2×D47—24no—
267C2×D47—24no—
268C2×D47—24no—
269C2×D47—24no—
270C2×D47—24no—
271C2×D47—24no—
272C2×D47C2×C4×Q818yescomplemented
273C4×C47—28no—
274C4×C47—28no—
275C4×C47—24no—
276C4×C47—42no—
277C4×C47C2×C4×D418yes—
278Dic47—28no—
279Dic47—24no—
280Dic47—24no—
281Dic47—44no—
282Dic47—42no—
283C22×C22⋊Q8—471no—
284C22×C4×Q8—471no—
285C23×C4⋊C4—471no—
286#2360—4716no—
287C2×#391—471no—
288C2×#389—472no—
289C2×#389—471no—
290C2×#387—472no—
291C2×#385—472no—
292C2×C4×C4⋊C4D4711yescharacteristic, complemented
293C2×C4×C22⋊C4—472no—
294C2×C4×C22⋊C4—471no—
295C2×C47#236018yescomplemented
296C2×C47C22×C4×D411yescharacteristic
297C2×C47C22×C4×Q811yescharacteristic
298C2×C47C2×#52011yescharacteristic
299C2×C47C2×#54611yescharacteristic
300C2×C47C2×D4×Q811yescharacteristic
301C2×C47C2×#55211yescharacteristic
302C2×C47C2×#55411yescharacteristic
303D47—28no—
304C23×Q8—471no—
305C24×C4—471no—
306C24×C4—472no—
307C2×C22⋊Q8—4716no—
308C2×C22⋊Q8—478no—
309C2×C4×Q8—478no—
310C2×C4×Q8—948no—
311C22×C4⋊C4—472no—
312C22×C4⋊C4—472no—
313C22×C4⋊C4—471no—
314C22×C4⋊C4—472no—
315C22×C4⋊C4—472no—
316C22×C4⋊C4—478no—
317C22×C4⋊C4—948no—
318C22×C4⋊C4C2×D4711yescharacteristic
319C22×C4⋊C4C2×D4711yescharacteristic
320C22×C22⋊C4—472no—
321C22×C22⋊C4—471no—
322C22×C22⋊C4—471no—
323C22×C42—472no—
324C22×C42—471no—
325C22×C42C2×D4711yescharacteristic
326C22×C42C2×D4712yes—
327#391—478no—
328#389—478no—
329#389—4716no—
330#387—4716no—
331#385—4716no—
332C4×C4⋊C4C2×D4718yescomplemented
333C4×C22⋊C4—478no—
334C4×C22⋊C4—4716no—
335C2×#95—471no—
336C2×#95—472no—
337C2×#95—471no—
338C2×#95—472no—
339C2×#95—472no—
340C2×#95C2×D4712yes—
341C47C2×#236011yescharacteristic, complemented, Sylow
342C25—471no—
343C22×Q8—478no—
344C22×Q8—474no—
345C22×Q8—944no—
346C22×Q8—944no—
347C23×C4—472no—
348C23×C4—471no—
349C23×C4—471no—
350C23×C4—478no—
351C23×C4—474no—
352C23×C4—471no—
353C23×C4—472no—
354C23×C4—478no—
355C23×C4—948no—
356C23×C4—944no—
357C23×C4—944no—
358C23×C4—948no—
359C23×C4—1884no—
360C23×C4C22×D4711yescharacteristic
361C23×C4C22×D4712yes—
362C23×C4C22×D4712yes—
363C23×C4C22×D4711yescharacteristic
364C23×C4C22×D4711yescharacteristic
365C22⋊Q8—4764no—
366C4×Q8—9432no—
367C2×C4⋊C4—4716no—
368C2×C4⋊C4—478no—
369C2×C4⋊C4—478no—
370C2×C4⋊C4—474no—
371C2×C4⋊C4—478no—
372C2×C4⋊C4—478no—
373C2×C4⋊C4—948no—
374C2×C4⋊C4—944no—
375C2×C4⋊C4—948no—
376C2×C4⋊C4—9432no—
377C2×C4⋊C4—1884no—
378C2×C4⋊C4C4×D4718yescomplemented
379C2×C4⋊C4D18818yes—
380C2×C4⋊C4C22×D4714yes—
381C2×C4⋊C4C22×D4714yes—
382C2×C22⋊C4—4716no—
383C2×C22⋊C4—478no—
384C2×C22⋊C4—478no—
385C2×C22⋊C4—474no—
386C2×C22⋊C4—474no—
387C2×C22⋊C4—944no—
388C2×C42—24no—
389C2×C42—44no—
390C2×C42—478no—
391C2×C42—474no—
392C2×C42—948no—
393C2×C42—944no—
394C2×C42C22×D4714yes—
395C2×C42C22×D4718yes—
396#95—474no—
397#95—478no—
398#95—474no—
399#95—478no—
400#95—478no—
401#95C22×D4718yes—
402C24—474no—
403C24—474no—
404C24—474no—
405C24—472no—
406C24—942no—
407C24—942no—
408C24—942no—
409C24—942no—
410C24C23×D4711yescharacteristic
411C2×Q8—4716no—
412C2×Q8—9432no—
413C2×Q8—948no—
414C2×Q8—948no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—478no—
425C22×C4—474no—
426C22×C4—474no—
427C22×C4—472no—
428C22×C4—474no—
429C22×C4—472no—
430C22×C4—4716no—
431C22×C4—474no—
432C22×C4—472no—
433C22×C4—9416no—
434C22×C4—942no—
435C22×C4—944no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—944no—
439C22×C4—942no—
440C22×C4—9432no—
441C22×C4—948no—
442C22×C4—948no—
443C22×C4—942no—
444C22×C4—944no—
445C22×C4—942no—
446C22×C4—944no—
447C22×C4—942no—
448C22×C4—944no—
449C22×C4—9416no—
450C22×C4—1888no—
451C22×C4—18832no—
452C22×C4C2×C4×D4718yes—
453C22×C4C2×C4×D4714yes—
454C22×C4C2×D18818yes—
455C22×C4C2×D18814yes—
456C22×C4#1062535014yes—
457C22×C4Q8×D4714yes—
458C22×C4C23×D4712yes—
459C22×C4C23×D4714yes—
460C22×C4C23×D4714yes—
461C22×C4C23×D4712yes—
462C22×C4C23×D4712yes—
463C4⋊C4—4732no—
464C4⋊C4—9416no—
465C4⋊C4—9416no—
466C4⋊C4—948no—
467C4⋊C4—1888no—
468C4⋊C4C2×C4×D47116yescomplemented
469C4⋊C4C2×D188116yes—
470C22⋊C4—4732no—
471C22⋊C4—4716no—
472C22⋊C4—948no—
473C42—28no—
474C42—48no—
475C42—9416no—
476C42—948no—
477C23—4716no—
478C23—474no—
479C23—474no—
480C23—474no—
481C23—948no—
482C23—948no—
483C23—948no—
484C23—948no—
485C23—948no—
486C23—948no—
487C23—942no—
488C23—942no—
489C23—942no—
490C23—942no—
491C23C22×C4×D4712yes—
492C23C22×D18812yes—
493C23C2×Q8×D4712yes—
494C23#41×D4712yes—
495C23C2×#1062535012yes—
496C23#1309406912yes—
497C23#1309407112yes—
498C23C24×D4711yescharacteristic
499Q8—9432no—
500C2×C4—216no—
501C2×C4—28no—
502C2×C4—216no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—478no—
514C2×C4—474no—
515C2×C4—474no—
516C2×C4—948no—
517C2×C4—948no—
518C2×C4—9416no—
519C2×C4—942no—
520C2×C4—944no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—9432no—
526C2×C4—942no—
527C2×C4—944no—
528C2×C4—942no—
529C2×C4—944no—
530C2×C4—942no—
531C2×C4—944no—
532C2×C4—18832no—
533C2×C4—1884no—
534C2×C4—1888no—
535C2×C4C4×D188116yes—
536C2×C4C22×C4×D4718yes—
537C2×C4C22×C4×D4714yes—
538C2×C4C22×D18818yes—
539C2×C4C22×D18814yes—
540C2×C4C2×Q8×D4714yes—
541C2×C4C2×#1062535014yes—
542C22—478no—
543C22—944no—
544C22—944no—
545C22—944no—
546C22—944no—
547C22—9432no—
548C22—944no—
549C22—944no—
550C22C2×C4×D18814yes—
551C22C4×Q8×D4714yes—
552C22#1568960214yes—
553C22#1568976814yes—
554C22Q8×D18814yes—
555C22#1568981214yes—
556C22#1568982814yes—
557C22C23×C4×D4711yescharacteristic
558C22C23×D18811yescharacteristic
559C22C22×Q8×D4711yescharacteristic
560C22C2×#41×D4711yescharacteristic
561C22C22×#1062535011yescharacteristic
562C22C2×#1309406911yescharacteristic
563C22C2×#1309407111yescharacteristic
564C4—28no—
565C4—28no—
566C4—24no—
567C4—42no—
568C4—944no—
569C4—948no—
570C4—944no—
571C4—1884no—
572C4—1882no—
573C4C2×C4×D18818yes—
574C2—948no—
575C2#2024639518yesdirect product factor
576C2C22×C4×D18811yescharacteristic
577C2C2×C4×Q8×D4711yescharacteristic
578C2C2×#1568960211yescharacteristic
579C2C2×#1568976811yescharacteristic
580C2C2×Q8×D18811yescharacteristic
581C2C2×#1568981211yescharacteristic
582C2C2×#1568982811yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C2×#2360
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#13093989C2semidirect
4. #20246395C2direct (N × H)
5. C2×#15689029C2semidirect
6. C2×#15689022C2semidirect
7. C2×#15689021C2semidirect
8. C2×#15689008C2semidirect
12. C2×C4×C4⋊C4×C47C2semidirect
16. C2×#13094004C4semidirect
19. C2×#13093989C22semidirect
32. #15689029C22semidirect
33. #15689022C22semidirect
34. #15689021C22semidirect
35. #15689008C22semidirect
48. C4×C4⋊C4×C47C22semidirect
53. C22×Dic94C2×C4semidirect
68. #13094004C2×C4semidirect
72. C2×C4⋊Dic47C2×C4semidirect
83. C2×(C2×D47)⋊C4Q8semidirect
101. C2×C4⋊C4×C47C2×C4semidirect
170. C2×Dic94C22×C4semidirect
171. C4⋊C4×C47C22×C4semidirect
177. (C2×D47)⋊C4C2×Q8semidirect
180. C4⋊Dic47C22×C4semidirect
203. C22×D47C4×Q8semidirect
272. C2×D47C2×C4×Q8semidirect
292. C2×C4×C4⋊C4D47semidirect
295. C2×C47#2360semidirect
332. C4×C4⋊C4C2×D47semidirect
341. C47C2×#2360semidirect
378. C2×C4⋊C4C4×D47semidirect
468. C4⋊C4C2×C4×D47semidirect
575. C2#20246395direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940042
C22×#130939892
C22×C4⋊C4×D472
#202463952
C2×#156890292
C2×#156890222
C2×#156890212
C2×#156890082
C2×#156889972
C2×C4×(C2×D47)⋊C42
C2×C4×C4⋊C4×C472
C2×#236047