Finite Group Databasebeta

← C2×#13079167 #15623428

Subgroups — C2×#13079167 #15623428

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic
3#13079167C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622315C211yesmaximal, characteristic, complemented
6C2×#10622693C211yesmaximal, characteristic, complemented
7C2×#10622491C212yesmaximal, complemented
8C2×#10622471C212yesmaximal, complemented
9C2×#10622494C212yesmaximal
10C2×#10622474C212yesmaximal
11C2×#10622320C211yesmaximal, characteristic
12C2×C11×#501C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C2×#66999—21no—
16C2×Q8×Dic11—21no—
17C22×#4313C2212yes—
18#10623259—24no—
19#10623259C2218yes—
20D11×#125—24no—
21D11×#125C2218yes—
22C2×#66950—21no—
23C2×#66945C2212yes—
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×#66943C2211yescharacteristic
29C2×#66943C2211yescharacteristic
30C2×#66943C2212yes—
31C2×#66942—21no—
32C2×#66942—21no—
33C2×#66940—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66923C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C11×#501C2218yescomplemented
38C2×C11×#107C2212yes—
39C2×C11×#106C2212yes—
40C2×C11×#97C2211yescharacteristic
41C2×#66882C2212yes—
42C2×#66881C2212yes—
43C2×C8×Dic11C2212yes—
44#10622693C2218yescomplemented
45#10622678C2218yescomplemented
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622494C22116yes—
52#10622491C22116yescomplemented
53#10622474C22116yes—
54#10622471C22116yescomplemented
55#10622320C2218yes—
56#10622315C2218yescomplemented
57C22×Q8×C11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—21no—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—21no—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×#125—22no—
68C11×#125C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—28no—
77Q8×Dic11—28no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2312yes—
98C2×#4313Q8116yescomplemented
99C2×#4313C2318yes—
100#66950—28no—
101#66945—24no—
102#66945C2318yes—
103C4⋊C4×D11—28no—
104C4⋊C4×D11—28no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11C2314yes—
108C4⋊C4×D11C2314yes—
109#66943—24no—
110#66943—22no—
111#66943—22no—
112#66943C2314yes—
113#66943C2318yes—
114#66943C2314yes—
115#66942—28no—
116#66942—28no—
117#66940—28no—
118C42×D11D414yes—
119C42×D11C2314yes—
120#66923—22no—
121#66923C2314yes—
122#66922—22no—
123#66922C2314yes—
124C11×#107C2318yes—
125C11×#106C2318yes—
126C11×#97C2314yes—
127#66882C2318yes—
128#66881C2318yes—
129C8×Dic11C2318yes—
130#66872C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133#66871C2318yes—
134#66867C2314yes—
135C2×#3166—111nomaximal, Sylow
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—24no—
138C2×Q8×C11—44no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×C4×D11—24no—
152C2×C4×D11—24no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2×D414yes—
159C2×C4×D11C2×D412yes—
160C2×C4×D11C2×Q818yes—
161C2×C4×D11C2412yes—
162C2×Dic22—24no—
163C2×Dic22—44no—
164C2×C8×C11C2×Q818yes—
165C2×C8×C11C2414yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2412yes—
173C11×C4⋊C4C2414yes—
174C11×C4⋊C4C2412yes—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C2412yes—
186C4⋊Dic11C2414yes—
187C4⋊Dic11C2412yes—
188Dic11⋊C4—28no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195C4×Dic11—28no—
196C4×Dic11C2×D412yes—
197C4×Dic11C2×D414yes—
198C4×Dic11C2×D414yes—
199C4×Dic11C2412yes—
200C2×C11⋊C8C2×Q818yes—
201C2×C11⋊C8C2414yes—
202#4313C2×Q8132yescomplemented
203C2×#533—111no—
204C22×#125—111no—
205#3166—1116no—
206C2×#501—111no—
207C2×#501—111no—
208C2×#501—111no—
209C2×#501D1111yescharacteristic, complemented
210C2×#499—112no—
211C2×#499—112no—
212C2×#428—112no—
213C2×#428—112no—
214C2×C4×M16—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11C4⋊Q814yes—
219C22×D11C22×D412yes—
220Q8×C11—48no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×Q814yes—
233C2×C4×C11C2511yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11C4⋊Q814yes—
243C2×Dic11C22×D412yes—
244C2×Dic11C22×D412yes—
245C2×Dic11C22×D412yes—
246C4×D11—44no—
247C4×D11—44no—
248C4×D11—48no—
249C4×D11—48no—
250C4×D11C4⋊Q818yes—
251C4×D11C22×Q818yes—
252Dic22—48no—
253C8×C11C22×Q818yes—
254C11⋊C8C22×Q818yes—
255C22×M16—112no—
256#533—118no—
257#533—224no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#125—118no—
261C2×#125—111no—
262C2×#125—111no—
263C2×#125—112no—
264C2×#125—111no—
265C2×#125—221no—
266C2×#125—221no—
267C2×#125—224no—
268C2×#125C2×D1111yescharacteristic
269C2×C22⋊Q8—221no—
270C2×C22⋊Q8—221no—
271C2×C4×Q8—221no—
272C2×C4×Q8—221no—
273C2×#117—112no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—221no—
277C22×C4⋊C4—221no—
278C22×C42—111no—
279#501—118no—
280#501—118no—
281#501—118no—
282#501C2×D1118yescomplemented
283#499—1116no—
284#499—1116no—
285#428—1116no—
286#428—1116no—
287C2×#107—112no—
288C2×#107—112no—
289C2×#107—112no—
290C2×#107C2×D1112yes—
291C2×#106—112no—
292C2×#106—112no—
293C2×#106—112no—
294C2×#106C2×D1112yes—
295C4×M16—118no—
296C2×#97—111no—
297C2×#97C2×D1111yescharacteristic
298C2×C4×C8—112no—
299C22×C11C2×C4⋊Q812yes—
300C22×C11#57512yes—
301C22×C11#57512yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—28no—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11C2×C4⋊Q814yes—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11C2×C4⋊Q812yes—
313C4×C11C23×Q812yes—
314Dic11—22no—
315Dic11—22no—
316Dic11—44no—
317Dic11—42no—
318Dic11—42no—
319Dic11C2×C4⋊Q814yes—
320C22×Q8—21no—
321C22×Q8—221no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—221no—
326C23×C4—221no—
327C2×M16—1116no—
328C2×M16—118no—
329C22×C8—112no—
330C22×C8C22×D1112yes—
331C4⋊Q8—22no—
332C4⋊Q8—114no—
333C4⋊Q8—222no—
334C4⋊Q8C22×D1114yes—
335#125—22no—
336#125—114no—
337#125—114no—
338#125—118no—
339#125—114no—
340#125—228no—
341#125—228no—
342#125—222no—
343#125—222no—
344#125—224no—
345#125—222no—
346#125C22×D1114yes—
347C22⋊Q8—228no—
348C22⋊Q8—228no—
349C4×Q8—228no—
350C4×Q8—228no—
351#117—118no—
352#117—224no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1112yes—
379C2×C22⋊C4—222no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—114no—
384C2×C42—114no—
385C2×C42—222no—
386C2×C42C22×D1111yescharacteristic
387#107—118no—
388#107—118no—
389#107—118no—
390#107C22×D1118yes—
391#106—118no—
392#106—118no—
393#106—118no—
394#106C22×D1118yes—
395#97—114no—
396#97C22×D1114yes—
397C4×C8—118no—
398C2×C11#316614yescomplemented
399C2×C11C22×C4⋊Q811yescharacteristic
400C2×C11C2×#57511yescharacteristic
401C2×C11C2×#57511yescharacteristic
402D11—24no—
403C24—111no—
404C2×Q8—24no—
405C2×Q8—44no—
406C2×Q8—224no—
407C2×Q8—444no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—118no—
414C22×C4—112no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431M16—1132no—
432C2×C8—118no—
433C2×C8—114no—
434C2×C8Q8×D1118yes—
435C2×C8C23×D1114yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—112no—
443C4⋊C4—112no—
444C4⋊C4—114no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—222no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4C23×D1112yes—
460C4⋊C4C23×D1114yes—
461C4⋊C4C23×D1112yes—
462C22⋊C4—228no—
463C42—114no—
464C42—114no—
465C42—112no—
466C42—112no—
467C42—228no—
468C42D4×D1112yes—
469C42C23×D1112yes—
470C11C2×#316611yescharacteristic, complemented, Sylow
471C23—114no—
472C23—112no—
473C23—222no—
474C23—222no—
475C23C2×D4×D1111yescharacteristic
476Q8—48no—
477Q8—448no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—114no—
487C2×C4—112no—
488C2×C4—118no—
489C2×C4—118no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—444no—
498C2×C4—444no—
499C2×C4—448no—
500C2×C4—448no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—444no—
504C2×C4C2×D4×D1112yes—
505C2×C4C2×D4×D1112yes—
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×Q8×D1114yes—
508C2×C4C24×D1111yescharacteristic
509C8—118no—
510C8C2×Q8×D1118yes—
511C22—114no—
512C22—228no—
513C22—222no—
514C22—222no—
515C22D11×C4⋊Q812yes—
516C22#1062330412yes—
517C22#1062330812yes—
518C22C22×D4×D1111yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—114no—
525C4—222no—
526C4—222no—
527C4—442no—
528C4—442no—
529C4—444no—
530C4D11×C4⋊Q812yes—
531C4C22×Q8×D1112yes—
532C2—224no—
533C2#1307916714yesdirect product factor
534C2C2×D11×C4⋊Q811yescharacteristic
535C2C2×#1062330411yescharacteristic
536C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#501D11
hypocenterC11C2×#3166
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13079167C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622315C2semidirect
6. C2×#10622693C2semidirect
7. C2×#10622491C2semidirect
8. C2×#10622471C2semidirect
12. C2×C11×#501C2semidirect
37. C11×#501C22semidirect
44. #10622693C22semidirect
45. #10622678C22semidirect
52. #10622491C22semidirect
54. #10622471C22semidirect
56. #10622315C22semidirect
98. C2×#4313Q8semidirect
202. #4313C2×Q8semidirect
209. C2×#501D11semidirect
282. #501C2×D11semidirect
398. C2×C11#3166semidirect
470. C11C2×#3166semidirect
533. C2#13079167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×D11×#1252
#130791672
C2×#106226782
C2×#106223152
C2×#106226932
C2×#106224912
C2×#106224712
C2×#106224942
C2×#106224742
C2×#106223202
C2×C11×#5012
C2×#316611