Finite Group Databasebeta

← C2×#20241508 #26131232

Subgroups — C2×#20241508 #26131232

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689097C211yesmaximal, characteristic
2C2×#15689090C211yesmaximal, characteristic
3#20241508C214yesmaximal, direct product factor
4C2×C47×#410C211yesmaximal, characteristic
5C22×#10625329C411yescharacteristic, complemented
6C23×C47⋊C8C411yescharacteristic, complemented
7C2×#13093983—21no—
8#15689097—21no—
9#15689097—21no—
10#15689097C412yescomplemented
11#15689097C2212yes—
12C2×#13093939—21no—
13C2×#13093939C412yescomplemented
14#15689090—21no—
15#15689090—21no—
16#15689090C412yescomplemented
17#15689090C2212yes—
18C2×C22⋊(C47⋊C8)—21no—
19C2×C22⋊(C47⋊C8)—21no—
20C22×#41×C47C2211yescharacteristic
21C2×#117×C47—21no—
22C47×#410—21no—
23C47×#410—21no—
24C47×#410C412yescomplemented
25C47×#410C2212yes—
26C2×#99×C47—21no—
27C2×#99×C47C412yescomplemented
28C2×#10625329—21no—
29C2×#10625329—41no—
30C2×#10625329—41no—
31C2×#10625329C2×C412yescomplemented
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—41no—
36C22×C47⋊C8—41no—
37C22×C47⋊C8C2×C412yescomplemented
38#13093983—22no—
39#13093983—22no—
40#13093983—41no—
41#13093983—41no—
42C2×C4⋊Dic47—41no—
43C2×C22⋊Dic47—22no—
44C2×C4×Dic47—41no—
45#13093939—22no—
46#13093939—22no—
47#13093939—22no—
48#13093939C2×C414yescomplemented
49C22⋊(C47⋊C8)—22no—
50C22⋊(C47⋊C8)—22no—
51C22⋊(C47⋊C8)—22no—
52C22⋊(C47⋊C8)—22no—
53C2×#41×C47—41no—
54C2×#41×C47—41no—
55C2×#41×C47—41no—
56C2×#41×C47—41no—
57C2×#41×C47C2×C411yescharacteristic
58C2×#41×C47C2×C411yescharacteristic
59C2×#41×C47C2×C411yescharacteristic
60C2×#41×C47D411yescharacteristic
61C2×#41×C47D411yescharacteristic
62C2×#41×C47D411yescharacteristic
63C2×#41×C47Q811yescharacteristic
64C2×#41×C47C2311yescharacteristic
65C22×Q8×C47Q811yescharacteristic
66C22×D4×C47C2×C411yescharacteristic
67C22×D4×C47C2×C411yescharacteristic
68C22×D4×C47D411yescharacteristic
69C23×C4×C47C2×C411yescharacteristic
70C23×C4×C47D411yescharacteristic
71C23×C4×C47D411yescharacteristic
72#117×C47—22no—
73#117×C47—22no—
74#117×C47—41no—
75#117×C47—41no—
76C2×C4⋊C4×C47—41no—
77C2×C22⋊C4×C47—22no—
78C2×C42×C47—41no—
79#99×C47—22no—
80#99×C47—22no—
81#99×C47—22no—
82#99×C47C2×C414yescomplemented
83C24×C47C4211yescharacteristic
84C24×C47C22⋊C411yescharacteristic
85C24×C47C22⋊C411yescharacteristic
86#41×C47—41no—
87#41×C47—41no—
88#41×C47—41no—
89#41×C47—41no—
90#41×C47—41no—
91#41×C47—41no—
92#41×C47—41no—
93#41×C47—41no—
94#41×C47—41no—
95#41×C47—41no—
96#41×C47—41no—
97#41×C47—41no—
98#41×C47—41no—
99#41×C47—41no—
100#41×C47—41no—
101#41×C47—41no—
102C2×Q8×C47—41no—
103C2×Q8×C47—41no—
104C2×Q8×C47C4⋊C411yescharacteristic
105C2×Q8×C47C4⋊C411yescharacteristic
106C2×Q8×C47C4⋊C411yescharacteristic
107C2×Q8×C47C2×Q811yescharacteristic
108C2×D4×C47—41no—
109C2×D4×C47—41no—
110C2×D4×C47—41no—
111C2×D4×C47—41no—
112C2×D4×C47—41no—
113C2×D4×C47—41no—
114C2×D4×C47C4211yescharacteristic
115C2×D4×C47C4211yescharacteristic
116C2×D4×C47C22⋊C411yescharacteristic
117C2×D4×C47C22⋊C411yescharacteristic
118C2×D4×C47C22⋊C411yescharacteristic
119C2×D4×C47C22⋊C411yescharacteristic
120C2×D4×C47C4⋊C411yescharacteristic
121C2×D4×C47C4⋊C411yescharacteristic
122C2×D4×C47C4⋊C411yescharacteristic
123C2×D4×C47C22×C411yescharacteristic
124C2×D4×C47C22×C411yescharacteristic
125C2×D4×C47C2×D411yescharacteristic
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—42no—
139C22×C4×C47C4211yescharacteristic
140C22×C4×C47C22⋊C411yescharacteristic
141C22×C4×C47C22⋊C411yescharacteristic
142C22×C4×C47C22⋊C411yescharacteristic
143C22×C4×C47C22⋊C411yescharacteristic
144C22×C4×C47C22⋊C411yescharacteristic
145C22×C4×C47C22⋊C411yescharacteristic
146C22×C4×C47C4⋊C411yescharacteristic
147C22×C4×C47C4⋊C411yescharacteristic
148C22×C4×C47C4⋊C411yescharacteristic
149C22×C4×C47C4⋊C411yescharacteristic
150C22×C4×C47C4⋊C411yescharacteristic
151C22×C4×C47C4⋊C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×Dic47—42no—
156C4⋊C4×C47—42no—
157C4⋊C4×C47—42no—
158C22⋊C4×C47—24no—
159C22⋊C4×C47—42no—
160C42×C47—42no—
161C42×C47—42no—
162C22⋊Dic47—24no—
163C22⋊Dic47—42no—
164C4⋊Dic47—42no—
165C4⋊Dic47—42no—
166C4×Dic47—42no—
167C4×Dic47—42no—
168#10625329—42no—
169#10625329—42no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—42no—
173C2×C47⋊C8—41no—
174C2×C47⋊C8—41no—
175C2×C47⋊C8—41no—
176C2×C47⋊C8—41no—
177C2×C47⋊C8—42no—
178C23×C47—21no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47—21no—
184C23×C47—42no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47#9511yescharacteristic
188C23×C47#9511yescharacteristic
189C23×C47#9511yescharacteristic
190C23×C47#9511yescharacteristic
191C23×C47C2×C4211yescharacteristic
192C23×C47C2×C22⋊C411yescharacteristic
193C23×C47C2×C22⋊C411yescharacteristic
194Q8×C47—41no—
195Q8×C47—41no—
196Q8×C47—41no—
197Q8×C47—41no—
198D4×C47—41no—
199D4×C47—41no—
200D4×C47—41no—
201D4×C47—41no—
202D4×C47—41no—
203D4×C47—41no—
204D4×C47—41no—
205D4×C47—41no—
206D4×C47—41no—
207D4×C47—41no—
208D4×C47—41no—
209D4×C47—41no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—44no—
241C2×C4×C47—84no—
242C2×C4×C47#9511yescharacteristic
243C2×C4×C47#9511yescharacteristic
244C2×C4×C47#9511yescharacteristic
245C2×C4×C47#9511yescharacteristic
246C2×C4×C47#9911yescharacteristic
247C2×C4×C47#9911yescharacteristic
248C2×C4×C47#9911yescharacteristic
249C2×C4×C47#9911yescharacteristic
250C2×C4×C47C2×C22⋊C411yescharacteristic
251C2×C4×C47C2×C4⋊C411yescharacteristic
252C2×C4×C47C2×C4⋊C411yescharacteristic
253C2×C4×C47C2×C4⋊C411yescharacteristic
254C2×Dic47—44no—
255C2×Dic47—84no—
256C47⋊C8—42no—
257C47⋊C8—42no—
258C2×#1391—471nomaximal, Sylow
259C22×C47—22no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47#34211yescharacteristic
279C22×C47#34211yescharacteristic
280C22×C47C2×#9511yescharacteristic
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—84no—
288C4×C47#34211yescharacteristic
289C4×C47#34211yescharacteristic
290C4×C47C2×#9911yescharacteristic
291C4×C47C2×#9911yescharacteristic
292Dic47—84no—
293C2×#410—471no—
294C2×#410D4711yescharacteristic
295C2×#408—471no—
296#1391—474no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—41no—
300C2×C47—41no—
301C2×C47—41no—
302C2×C47—41no—
303C2×C47—41no—
304C2×C47—41no—
305C2×C47#139112yescomplemented
306C2×C47C2×#34211yescharacteristic
307C22×#41C2×D4711yescharacteristic
308C22×M16—471no—
309C23×C8—471no—
310C2×#117—21no—
311C2×#117—941no—
312#410—21no—
313#410—21no—
314#410—472no—
315#410—472no—
316#410—941no—
317#410—941no—
318#410Dic4712yescomplemented
319#410C2×D4712yes—
320C2×#99—21no—
321C2×#99—472no—
322C2×#99—941no—
323C2×#99Dic4712yescomplemented
324#408—472no—
325#408—472no—
326#408—941no—
327#408—941no—
328C2×C22⋊C8—941no—
329C2×C22⋊C8—941no—
330C47C2×#139111yescharacteristic, complemented, Sylow
331C2×#41—41no—
332C2×#41—41no—
333C2×#41—41no—
334C2×#41—41no—
335C2×#41Dic9411yescharacteristic
336C2×#41C4×D4711yescharacteristic
337C2×#41C4×D4711yescharacteristic
338C2×#41D18811yescharacteristic
339C2×#41C2×Dic4711yescharacteristic
340C2×#41C22⋊D4711yescharacteristic
341C2×#41C22⋊D4711yescharacteristic
342C2×#41C22×D4711yescharacteristic
343C22×Q8Dic9411yescharacteristic
344C22×D4C4×D4711yescharacteristic
345C22×D4C2×Dic4711yescharacteristic
346C22×D4C22⋊D4711yescharacteristic
347C23×C4C4×D4711yescharacteristic
348C23×C4D18811yescharacteristic
349C23×C4C22⋊D4711yescharacteristic
350C2×M16—472no—
351C2×M16—941no—
352C2×M16—1881no—
353C2×M16—1881no—
354C22×C8—472no—
355C22×C8—941no—
356C22×C8—941no—
357C22×C8—941no—
358C22×C8—1881no—
359C22×C8—1881no—
360#117—22no—
361#117—22no—
362#117—41no—
363#117—41no—
364#117—942no—
365#117—942no—
366#117—1881no—
367#117—1881no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—1881no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—942no—
372C2×C42—41no—
373C2×C42—1881no—
374#99—22no—
375#99—22no—
376#99—22no—
377#99—474no—
378#99—942no—
379#99—942no—
380#99—942no—
381#99C2×Dic4714yescomplemented
382C22⋊C8—942no—
383C22⋊C8—942no—
384C22⋊C8—942no—
385C22⋊C8—942no—
386C24C4×Dic4711yescharacteristic
387C24(C2×D47)⋊C411yescharacteristic
388C24C22⋊Dic4711yescharacteristic
389#41—41no—
390#41—41no—
391#41—41no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8Dic47⋊C411yescharacteristic
408C2×Q8Dic47⋊C411yescharacteristic
409C2×Q8C4⋊Dic4711yescharacteristic
410C2×Q8C2×Dic9411yescharacteristic
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4C4×Dic4711yescharacteristic
418C2×D4C4×Dic4711yescharacteristic
419C2×D4Dic47⋊C411yescharacteristic
420C2×D4Dic47⋊C411yescharacteristic
421C2×D4C4⋊Dic4711yescharacteristic
422C2×D4(C2×D47)⋊C411yescharacteristic
423C2×D4(C2×D47)⋊C411yescharacteristic
424C2×D4C22⋊Dic4711yescharacteristic
425C2×D4C22⋊Dic4711yescharacteristic
426C2×D4C2×C4×D4711yescharacteristic
427C2×D4C22×Dic4711yescharacteristic
428C2×D4C2×C22⋊D4711yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—1882no—
443C22×C4C4×Dic4711yescharacteristic
444C22×C4Dic47⋊C411yescharacteristic
445C22×C4Dic47⋊C411yescharacteristic
446C22×C4Dic47⋊C411yescharacteristic
447C22×C4Dic47⋊C411yescharacteristic
448C22×C4C4⋊Dic4711yescharacteristic
449C22×C4C4⋊Dic4711yescharacteristic
450C22×C4(C2×D47)⋊C411yescharacteristic
451C22×C4(C2×D47)⋊C411yescharacteristic
452C22×C4(C2×D47)⋊C411yescharacteristic
453C22×C4(C2×D47)⋊C411yescharacteristic
454C22×C4(C2×D47)⋊C411yescharacteristic
455C22×C4C22⋊Dic4711yescharacteristic
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459M16—1882no—
460M16—1882no—
461C2×C8—942no—
462C2×C8—942no—
463C2×C8—1882no—
464C2×C8—1881no—
465C2×C8—1881no—
466C2×C8—1881no—
467C2×C8—1881no—
468C2×C8—1882no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—1882no—
472C4⋊C4—1882no—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—944no—
476C22⋊C4—1882no—
477C42—42no—
478C42—42no—
479C42—1882no—
480C42—1882no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23C47⋊#9511yescharacteristic
491C23C47⋊#9511yescharacteristic
492C23C47⋊#9511yescharacteristic
493C23C47⋊#9511yescharacteristic
494C23C2×C4×Dic4711yescharacteristic
495C23C2×(C2×D47)⋊C411yescharacteristic
496C23C2×C22⋊Dic4711yescharacteristic
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—84no—
545C2×C4—3764no—
546C2×C4—1884no—
547C2×C4C47⋊#9511yescharacteristic
548C2×C4C47⋊#9511yescharacteristic
549C2×C4C47⋊#9511yescharacteristic
550C2×C4C47⋊#9511yescharacteristic
551C2×C4#1309393811yescharacteristic
552C2×C4#1309393811yescharacteristic
553C2×C4#1309393811yescharacteristic
554C2×C4#1309393811yescharacteristic
555C2×C4C2×(C2×D47)⋊C411yescharacteristic
556C2×C4C2×Dic47⋊C411yescharacteristic
557C2×C4C2×Dic47⋊C411yescharacteristic
558C2×C4C2×C4⋊Dic4711yescharacteristic
559C8—1882no—
560C8—1882no—
561C22—22no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—81no—
579C22—81no—
580C22#1568888911yescharacteristic
581C22#1568888911yescharacteristic
582C22C2×C47⋊#9511yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—84no—
590C4—3764no—
591C4#1568888911yescharacteristic
592C4#1568888911yescharacteristic
593C4C2×#1309393811yescharacteristic
594C4C2×#1309393811yescharacteristic
595C2—21no—
596C2—21no—
597C2—41no—
598C2—41no—
599C2—41no—
600C2—41no—
601C2—41no—
602C2—41no—
603C2#2024150812yesdirect product factor
604C2C2×#1568888911yescharacteristic
subgroupG/H
centerC2×C4#13093938
commutatorC23×C47C2×C42
FrattiniC2×#41C22×D47
FittingC2×C47×#410C2
socleC22×C47#342
prime radicalC22×#41×C47C22
cosocleC2×#41×C47C23
hypercenterC2×#410D47
hypocenterC47C2×#1391
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #20241508C2direct (N × H)
5. C22×#10625329C4semidirect
6. C23×C47⋊C8C4semidirect
10. #15689097C4semidirect
13. C2×#13093939C4semidirect
16. #15689090C4semidirect
24. C47×#410C4semidirect
27. C2×#99×C47C4semidirect
31. C2×#10625329C2×C4semidirect
37. C22×C47⋊C8C2×C4semidirect
48. #13093939C2×C4semidirect
82. #99×C47C2×C4semidirect
305. C2×C47#1391semidirect
318. #410Dic47semidirect
323. C2×#99Dic47semidirect
330. C47C2×#1391semidirect
381. #99C2×Dic47semidirect
603. C2#20241508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890972
C2×#156890902
#202415082
C2×C47×#4102
C2×#139147