Finite Group Databasebeta

← C2×#13068090 #14736367

Subgroups — C2×#13068090 #14736367

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3C2×#10622637C211yesmaximal, characteristic, complemented
4#13068090C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622185C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic
8C2×C11×#475C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4325—21no—
12C22×#4325—21no—
13C22×#4325—21no—
14C2×#66927C2211yescharacteristic
15C11×#475—22no—
16C11×#475C2214yescomplemented
17C2×C11×#106—21no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103—21no—
20#10622698—22no—
21#10622698C2214yes—
22#10622640—22no—
23#10622640C2214yes—
24#10622637—22no—
25#10622637C2214yescomplemented
26C2×#66873—21no—
27C2×C4⋊(C11⋊C8)—21no—
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×#66867—21no—
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622185C2214yescomplemented
33#10622123C2214yes—
34#10622117C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11D411yescharacteristic
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11D412yes—
48C4×Q8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4325—24no—
57C2×#4325—24no—
58C2×#4325—44no—
59C2×#4325—44no—
60C2×#4325—44no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—21no—
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65#66927—21no—
66#66927—21no—
67#66927—21no—
68#66927C2312yes—
69C11×#106—24no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×#103—24no—
73#66873—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—24no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2312yes—
79#66867—24no—
80C4×C11⋊C8D412yes—
81C4×C11⋊C8C2312yes—
82C2×#1686—111nomaximal, Sylow
83C23×D11—41no—
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—82no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4C2×D412yes—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4325—48no—
126#4325—48no—
127#4325—48no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8SD1614yescomplemented
134C2×C11⋊C8C2×D412yes—
135C2×C11⋊C8C2×D412yes—
136C2×#492—111no—
137C2×#475D1111yescharacteristic, complemented
138C2×#460—111no—
139C2×#446—111no—
140#1686—118no—
141C2×#335—111no—
142C2×#332—111no—
143C2×#331—111no—
144C23×C11#12111yescharacteristic
145C22×D11—42no—
146C22×D11—82no—
147C22×D11—82no—
148C22×D11—82no—
149Q8×C11—22no—
150Q8×C11—22no—
151Q8×C11—42no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—82no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11AGL(1,ℤ/8)12yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11#13712yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172D44—42no—
173D44—42no—
174D44—42no—
175D44—42no—
176D44—82no—
177D44—82no—
178D44—82no—
179D44—82no—
180C8×C11—42no—
181C11⋊C8—22no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8C2×SD1614yescomplemented
185C22×SD16—221no—
186C22×SD16—221no—
187C22×SD16—221no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×#127—111no—
190C2×C4×Q8C2×D1111yescharacteristic
191#492—114no—
192#492—222no—
193#475—22no—
194#475C2×D1114yescomplemented
195#460—114no—
196#460—222no—
197#446—114no—
198#446—222no—
199C2×#106—21no—
200C2×C4⋊C8—111no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8—221no—
203C2×C4⋊C8C2×D1111yescharacteristic
204C2×#103—21no—
205C2×#102—221no—
206C2×#97—221no—
207C2×C4×C8—111no—
208#335—114no—
209#332—114no—
210#331—114no—
211C22×C11#46012yes—
212C22×C11#46812yes—
213C22×C11#47112yes—
214C22×C11C2×#12111yescharacteristic
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—164no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—42no—
223C4×C11—82no—
224C4×C11#46012yes—
225C4×C11#46812yes—
226C4×C11C22×SD1611yescharacteristic
227C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C22×Q8—21no—
231C22×Q8C22⋊D1111yescharacteristic
232C22×D4—221no—
233C22×D4—221no—
234C22×D4—221no—
235C2×SD16—224no—
236C2×SD16—224no—
237C2×SD16—224no—
238C2×SD16—444no—
239C2×SD16—444no—
240C2×SD16—444no—
241C22×C8—21no—
242C22×C8—111no—
243C22×C8—111no—
244C22×C8—221no—
245C22×C8—221no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C22×D1112yes—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8C22⋊D1112yes—
257C4×Q8C22×D1112yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C42—21no—
263C2×C42C22×D1111yescharacteristic
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—224no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8C22×D1112yes—
272#103—24no—
273#102—224no—
274#97—224no—
275C4×C8—112no—
276C4×C8—112no—
277C2×C11#168614yescomplemented
278C2×C11C2×#46011yescharacteristic
279C2×C11C2×#46811yescharacteristic
280C2×C11C2×#47111yescharacteristic
281D11—162no—
282C24—441no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—42no—
289C2×Q8—42no—
290C2×Q8C2×C22⋊D1112yes—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—222no—
294C2×D4—442no—
295C2×D4—442no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—442no—
300C2×D4—442no—
301C2×D4—882no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—448no—
309SD16—448no—
310SD16—448no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—114no—
314C2×C8—112no—
315C2×C8—112no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—442no—
320C2×C8—442no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C2×C22⋊D1112yes—
329C42—22no—
330C42—22no—
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11C2×#168611yescharacteristic, complemented, Sylow
336C23—442no—
337C23—882no—
338C23—882no—
339C23—882no—
340C23#6699211yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—42no—
344Q8—42no—
345Q8—42no—
346Q8—82no—
347D4—442no—
348D4—442no—
349D4—442no—
350D4—442no—
351D4—882no—
352D4—882no—
353D4—882no—
354D4—882no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4SD16×D1112yes—
363C2×C4#6696712yes—
364C2×C4#6699211yescharacteristic
365C2×C4#6699211yescharacteristic
366C2×C4#6699211yescharacteristic
367C2×C4#6699512yes—
368C2×C4#6700212yes—
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4C2×#434111yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—42no—
373C8—114no—
374C8—222no—
375C8—442no—
376C8—442no—
377C22—882no—
378C22—882no—
379C22—882no—
380C22—1764no—
381C22#1062266212yes—
382C22#1062277612yes—
383C22#1062281612yes—
384C22C2×#6699211yescharacteristic
385C4—21no—
386C4—21no—
387C4—42no—
388C4—42no—
389C4—82no—
390C4#1062266212yes—
391C4#1062277612yes—
392C4C2×SD16×D1111yescharacteristic
393C4C2×#6696711yescharacteristic
394C4C2×#6699511yescharacteristic
395C4C2×#6700211yescharacteristic
396C2—1762no—
397C2#1306809014yesdirect product factor
398C2C2×#1062277611yescharacteristic
399C2C2×#1062266211yescharacteristic
400C2C2×#1062281611yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#475C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#475D11
hypocenterC11C2×#1686
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×#10622637C2semidirect
4. #13068090C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622185C2semidirect
8. C2×C11×#475C2semidirect
16. C11×#475C22semidirect
25. #10622637C22semidirect
32. #10622185C22semidirect
34. #10622117C22semidirect
133. C2×C11⋊C8SD16semidirect
137. C2×#475D11semidirect
184. C11⋊C8C2×SD16semidirect
194. #475C2×D11semidirect
277. C2×C11#1686semidirect
335. C11C2×#1686semidirect
397. C2#13068090direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226402
C2×#106226372
#130680902
C2×#106221172
C2×#106221852
C2×#106221232
C2×C11×#4752
C2×#168611