Finite Group Databasebeta

← C2×#13081496 #15634217

Subgroups — C2×#13081496 #15634217

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623261C211yesmaximal, characteristic
3#13081496C2116yesmaximal, direct product factor
4C2×#10622471C212yesmaximal, complemented
5C2×#10622470C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622484C212yesmaximal
8C2×#10622700C211yesmaximal, characteristic
9C2×C8×Dic22C211yesmaximal, characteristic, complemented
10C2×C4×#4314C211yesmaximal, characteristic
11C2×#10622465C212yesmaximal
12C2×C11×#498C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#66999—22no—
16C2×Q8×Dic11—21no—
17C2×#66997—21no—
18C22×#4314C2211yescharacteristic
19#10623261—24no—
20#10623261C2218yes—
21#10623252—24no—
22#10623252C2218yescomplemented
23C2×#66950—21no—
24C2×#66946C2212yes—
25C2×C4⋊C4×D11—21no—
26C2×#66943C2212yes—
27C2×#66943C2212yes—
28C2×#66942—22no—
29C2×#66940C2212yes—
30C2×C4×D44C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#498C2218yescomplemented
34C2×C11×#106C2212yes—
35C2×C11×#106C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622704C2218yescomplemented
43#10622700C2218yes—
44C2×#66874C2212yes—
45C2×#66873C2212yes—
46C2×#66871C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622484C22116yes—
50#10622471C22116yescomplemented
51#10622470C22116yescomplemented
52#10622465C22116yes—
53C4×#4314C2218yes—
54C8×Dic22C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×C4×D11—22no—
60C22×Dic22D411yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11C2311yescharacteristic
73#66999—216no—
74Q8×Dic11—28no—
75#66997—28no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4D412yes—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11C2312yes—
91C22×C11⋊C8C2312yes—
92C2×#4314Q818yescomplemented
93C2×#4314C2314yes—
94#66950—28no—
95#66946—24no—
96#66946C2318yes—
97C4⋊C4×D11—28no—
98#66943—24no—
99#66943—24no—
100#66943C2318yes—
101#66943C2318yes—
102#66942—216no—
103#66940—24no—
104#66940C2318yes—
105C4×D44—22no—
106C4×D44C2314yes—
107C4×Dic22—22no—
108C4×Dic22D414yes—
109C4×Dic22C2314yes—
110C4×Dic22C2314yes—
111C11×#106C2318yes—
112C11×#106C2318yes—
113C4×C8×C11C2314yes—
114#66885C2314yes—
115#66881C2314yes—
116#66880C2314yes—
117Dic11⋊C8C2318yes—
118C8×Dic11C2318yes—
119#66874C2318yes—
120#66873C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C2×#3381—111nomaximal, Sylow
125C23×D11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—24no—
128C2×Q8×C11—44no—
129C2×Q8×C11—82no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D412yes—
139C22×Dic11C2×D412yes—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44C2×Q814yes—
143C2×D44C2412yes—
144C2×C4×D11—28no—
145C2×C4×D11—24no—
146C2×C4×D11—44no—
147C2×C4×D11—84no—
148C2×Dic22—24no—
149C2×Dic22—21no—
150C2×Dic22—22no—
151C2×Dic22C2×D414yes—
152C2×Dic22C2×Q814yes—
153C2×Dic22C2412yes—
154C2×C8×C11—22no—
155C2×C8×C11C2×Q814yes—
156C2×C8×C11C2412yes—
157C2×C8×C11C2412yes—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4C2414yes—
163C11×C4⋊C4C2414yes—
164C42×C11C2×D412yes—
165C42×C11C2412yes—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—24no—
168C4⋊Dic11—28no—
169C4⋊Dic11—28no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11C2×D414yes—
173C4⋊Dic11C2412yes—
174C4⋊Dic11C2412yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—24no—
179Dic11⋊C4C2×D418yes—
180C4×Dic11—28no—
181C4×Dic11—24no—
182C4×Dic11C2×D414yes—
183C4×Dic11C2414yes—
184C2×C11⋊C8—24no—
185C2×C11⋊C8C2414yes—
186#4314C2×Q8116yescomplemented
187C2×#557—111no—
188C2×#554—111no—
189#3381—1116no—
190C2×#499—112no—
191C2×#498D1111yescharacteristic, complemented
192C2×#479—112no—
193C2×#477—111no—
194C2×#478—112no—
195C2×#474—111no—
196C2×C8×Q8—111no—
197C2×C4×SD16—112no—
198C2×C4×SD16—111no—
199C23×C11C22×D411yescharacteristic
200C22×D11—24no—
201C22×D11—22no—
202C22×D11—42no—
203C22×D11—42no—
204Q8×C11—48no—
205Q8×C11—84no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11#13514yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D412yes—
215C2×C4×C11C22×Q812yes—
216C2×C4×C112−1+412yes—
217C2×C4×C11C2511yescharacteristic
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11C22×D414yes—
227C2×Dic11C22×D414yes—
228D44—24no—
229D44—22no—
230D44C22×Q814yes—
231C4×D11—48no—
232C4×D11—88no—
233Dic22—24no—
234Dic22—28no—
235Dic22—22no—
236Dic22C22×Q814yes—
237C8×C11—22no—
238C8×C11C22×Q814yes—
239C11⋊C8—24no—
240C22×SD16—111no—
241#557—118no—
242#557—224no—
243#554—118no—
244#554—224no—
245C2×C4⋊Q8—221no—
246C2×C4⋊Q8C2×D1111yescharacteristic
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#125—112no—
249C2×#125—112no—
250C2×#125—222no—
251C2×C22⋊Q8—221no—
252C2×C22⋊Q8—222no—
253C2×C4×Q8—111no—
254C2×C4×Q8—112no—
255C2×C4×Q8—111no—
256C2×C4×Q8—221no—
257C2×C4×D4—112no—
258C2×C4×D4—111no—
259C22×C4⋊C4—221no—
260#499—1116no—
261#498C2×D1118yescomplemented
262#479—1116no—
263#478—1116no—
264#477—118no—
265#474—118no—
266C8×Q8—118no—
267C4×SD16—1116no—
268C4×SD16—118no—
269C2×#107—112no—
270C2×#107—112no—
271C2×#106—111no—
272C2×#106C2×D1112yes—
273C2×#106C2×D1112yes—
274C2×C4⋊C8—112no—
275C2×C4⋊C8—111no—
276C2×#103—111no—
277C2×#103—112no—
278C2×#102—111no—
279C2×#102—112no—
280C2×C4×C8—112no—
281C2×C4×C8C2×D1111yescharacteristic
282C22×C11D4×Q812yes—
283C22×C11C2×#13512yes—
284C22×C11#57712yes—
285C22×C11C23×D411yescharacteristic
286C2×D11—24no—
287C2×D11—48no—
288C2×D11—42no—
289C2×D11—42no—
290C4×C11—22no—
291C4×C11—44no—
292C4×C11—44no—
293C4×C11D4×Q812yes—
294C4×C11C2×#13514yes—
295C4×C11C23×Q811yescharacteristic
296C4×C11C2×2−1+411yescharacteristic
297Dic11—24no—
298Dic11—24no—
299Dic11—24no—
300Dic11—42no—
301Dic11—42no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×Q8—111no—
305C22×Q8—111no—
306C22×D4—111no—
307C23×C4—222no—
308C23×C4—221no—
309C2×SD16—118no—
310C2×SD16—114no—
311C22×C8—112no—
312C22×C8C22×D1111yescharacteristic
313C22×C8C22×D1111yescharacteristic
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—228no—
317C4⋊Q8C22×D1114yes—
318C4⋊Q8C22×D1114yes—
319#125—118no—
320#125—118no—
321#125—224no—
322#125—224no—
323#125—2216no—
324C22⋊Q8—228no—
325C22⋊Q8—2216no—
326C4×Q8—114no—
327C4×Q8—114no—
328C4×Q8—118no—
329C4×Q8—114no—
330C4×Q8—224no—
331C4×Q8—228no—
332C4×Q8—222no—
333C4×D4—118no—
334C4×D4—114no—
335C4×D4—224no—
336C4×D4—222no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22×D1112yes—
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—221no—
354C2×C42—112no—
355C2×C42—222no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358#107—118no—
359#107—118no—
360#106—114no—
361#106C22×D1118yes—
362#106C22×D1118yes—
363C4⋊C8—118no—
364C4⋊C8—114no—
365#103—114no—
366#103—118no—
367#102—114no—
368#102—118no—
369C4×C8—118no—
370C4×C8C22×D1114yes—
371C2×C11#338114yescomplemented
372C2×C11C2×D4×Q811yescharacteristic
373C2×C11C22×#13511yescharacteristic
374C2×C11C2×#57711yescharacteristic
375D11—44no—
376C24—221no—
377C2×Q8—24no—
378C2×Q8—24no—
379C2×Q8—44no—
380C2×Q8—82no—
381C2×Q8—114no—
382C2×Q8—114no—
383C2×Q8—112no—
384C2×Q8—224no—
385C2×Q8—221no—
386C2×Q8—222no—
387C2×D4—114no—
388C2×D4—112no—
389C2×D4—221no—
390C2×D4—222no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—228no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—224no—
400C22×C4—444no—
401C22×C4—884no—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—1116no—
406C2×C8—22no—
407C2×C8—114no—
408C2×C8—224no—
409C2×C8Q8×D1114yes—
410C2×C8C23×D1112yes—
411C2×C8C23×D1112yes—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—114no—
417C4⋊C4—118no—
418C4⋊C4—112no—
419C4⋊C4—112no—
420C4⋊C4—228no—
421C4⋊C4—228no—
422C4⋊C4—228no—
423C4⋊C4—228no—
424C4⋊C4—228no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—224no—
428C4⋊C4C23×D1114yes—
429C4⋊C4C23×D1114yes—
430C22⋊C4—228no—
431C22⋊C4—224no—
432C42—114no—
433C42—114no—
434C42—228no—
435C42—224no—
436C42D4×D1112yes—
437C42C23×D1112yes—
438C11C2×#338111yescharacteristic, complemented, Sylow
439C23—224no—
440C23—222no—
441C23—442no—
442C23—442no—
443C23C2×D4×D1111yescharacteristic
444Q8—48no—
445Q8—84no—
446Q8—114no—
447Q8—224no—
448Q8—228no—
449Q8—222no—
450D4—114no—
451D4—224no—
452D4—222no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—114no—
459C2×C4—114no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—448no—
469C2×C4—888no—
470C2×C4#6696914yes—
471C2×C4C2×D4×D1112yes—
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4C2×D4×D1112yes—
474C2×C4C2×Q8×D1112yes—
475C2×C4#6704012yes—
476C2×C4C24×D1111yescharacteristic
477C8—22no—
478C8—224no—
479C8C2×Q8×D1114yes—
480C22—224no—
481C22—448no—
482C22—442no—
483C22—442no—
484C22#1062325812yes—
485C22C2×#6696912yes—
486C22#1062329312yes—
487C22C22×D4×D1111yescharacteristic
488C4—22no—
489C4—44no—
490C4—44no—
491C4—224no—
492C4—224no—
493C4—224no—
494C4—442no—
495C4—442no—
496C4#1062325812yes—
497C4C2×#6696914yes—
498C4C22×Q8×D1111yescharacteristic
499C4C2×#6704011yescharacteristic
500C2—444no—
501C2#1308149614yesdirect product factor
502C2C2×#1062325811yescharacteristic
503C2C22×#6696911yescharacteristic
504C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#498D11
hypocenterC11C2×#3381
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081496C2direct (N × H)
4. C2×#10622471C2semidirect
5. C2×#10622470C2semidirect
6. C2×#10622704C2semidirect
9. C2×C8×Dic22C2semidirect
12. C2×C11×#498C2semidirect
22. #10623252C22semidirect
33. C11×#498C22semidirect
42. #10622704C22semidirect
50. #10622471C22semidirect
51. #10622470C22semidirect
54. C8×Dic22C22semidirect
92. C2×#4314Q8semidirect
186. #4314C2×Q8semidirect
191. C2×#498D11semidirect
261. #498C2×D11semidirect
371. C2×C11#3381semidirect
438. C11C2×#3381semidirect
501. C2#13081496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106232612
#130814962
C2×#106224712
C2×#106224702
C2×#106227042
C2×#106224842
C2×#106227002
C2×C8×Dic222
C2×C4×#43142
C2×#106224652
C2×C11×#4982
C2×#338111