Finite Group Databasebeta

← C2×#13068158 #14736423

Subgroups — C2×#13068158 #14736423

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3C2×#10622637C211yesmaximal, characteristic, complemented
4#13068158C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622184C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic
8C2×C11×#477C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4325—21no—
12C2×#66927C2211yescharacteristic
13C11×#477—22no—
14C11×#477C2214yescomplemented
15C2×C11×#107—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18#10622701—22no—
19#10622701C2214yes—
20#10622640—22no—
21#10622640C2214yes—
22#10622637—22no—
23#10622637C2214yescomplemented
24C2×#66873—21no—
25C2×#66873—21no—
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#10622184C2214yescomplemented
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—44no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8D411yescharacteristic
60C22×C11⋊C8D411yescharacteristic
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927C2312yes—
65C11×#107—24no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×#103—24no—
69#66873—24no—
70#66873—24no—
71#66873—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—24no—
75C4⋊(C11⋊C8)C2312yes—
76C4⋊(C11⋊C8)C2312yes—
77#66867—24no—
78C4×C11⋊C8D412yes—
79C4×C11⋊C8C2312yes—
80C2×#1698—111nomaximal, Sylow
81C23×D11—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—82no—
88C2×Q8×C11C2×D412yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—42no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—82no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4C2×D412yes—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122#4325—48no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8C2×D412yes—
130C2×C11⋊C8C2×D412yes—
131C2×#486—111no—
132C2×#477D1111yescharacteristic, complemented
133C2×#460—111no—
134C2×#446—111no—
135#1698—118no—
136C2×#335—111no—
137C2×#333—111no—
138C2×#331—111no—
139C23×C11#12111yescharacteristic
140C22×D11—42no—
141C22×D11—82no—
142C22×D11—82no—
143C22×D11—82no—
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—42no—
147Q8×C11—82no—
148Q8×C11—82no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#13512yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×C4×C11#13712yes—
162C2×C4×C11#13712yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166D44—42no—
167D44—42no—
168D44—42no—
169D44—42no—
170D44—82no—
171D44—82no—
172D44—82no—
173D44—82no—
174C8×C11—42no—
175C11⋊C8—22no—
176C11⋊C8—22no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C22×SD16—221no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×#127—111no—
182C2×C4×Q8C2×D1111yescharacteristic
183#486—114no—
184#486—222no—
185#477—22no—
186#477C2×D1114yescomplemented
187#460—114no—
188#460—222no—
189#446—114no—
190#446—222no—
191C2×#107—21no—
192C2×C4⋊C8—111no—
193C2×C4⋊C8—111no—
194C2×C4⋊C8—221no—
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×#103—21no—
197C2×#102—221no—
198C2×#102—221no—
199C2×#102—221no—
200C2×#97—221no—
201C2×C4×C8—111no—
202#335—114no—
203#333—114no—
204#331—114no—
205C22×C11#46412yes—
206C22×C11#46812yes—
207C22×C11#47212yes—
208C22×C11C2×#12111yescharacteristic
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—164no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—82no—
218C4×C11#46412yes—
219C4×C11#46812yes—
220C4×C11C2×#13511yescharacteristic
221C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C11C2×#13711yescharacteristic
223C4×C11C2×#13711yescharacteristic
224C22×Q8—21no—
225C22×Q8C22⋊D1111yescharacteristic
226C22×D4—221no—
227C22×D4—221no—
228C22×D4—221no—
229C2×SD16—224no—
230C2×SD16—444no—
231C22×C8—21no—
232C22×C8—111no—
233C22×C8—111no—
234C22×C8—221no—
235C22×C8—221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C22×D1112yes—
240#127—112no—
241#127—221no—
242#127—221no—
243#127—221no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8C22⋊D1112yes—
247C4×Q8C22×D1112yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1111yescharacteristic
254#107—24no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—224no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22×D1112yes—
262#103—24no—
263#102—224no—
264#102—224no—
265#102—224no—
266#97—224no—
267C4×C8—112no—
268C4×C8—112no—
269C2×C11#169814yescomplemented
270C2×C11C2×#46411yescharacteristic
271C2×C11C2×#46811yescharacteristic
272C2×C11C2×#47211yescharacteristic
273D11—162no—
274C24—441no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—82no—
281C2×Q8C2×C22⋊D1112yes—
282C2×D4—222no—
283C2×D4—222no—
284C2×D4—222no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—882no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4D4×D1111yescharacteristic
297C22×C4#434111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—112no—
303C2×C8—112no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—442no—
309C2×C8—442no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4C2×C22⋊D1112yes—
318C42—22no—
319C42—22no—
320C42D4×D1111yescharacteristic
321C42#434111yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C42C23×D1111yescharacteristic
324C11C2×#169811yescharacteristic, complemented, Sylow
325C23—442no—
326C23—882no—
327C23—882no—
328C23—882no—
329C23#6699211yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333Q8—82no—
334Q8—82no—
335D4—442no—
336D4—442no—
337D4—442no—
338D4—442no—
339D4—882no—
340D4—882no—
341D4—882no—
342D4—882no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4#6697112yes—
351C2×C4#6697212yes—
352C2×C4#6699211yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699211yescharacteristic
355C2×C4#6699512yes—
356C2×C4#6700212yes—
357C2×C4C2×D4×D1111yescharacteristic
358C2×C4C2×#434111yescharacteristic
359C2×C4C22×C22⋊D1111yescharacteristic
360C8—42no—
361C8—222no—
362C8—222no—
363C8—442no—
364C8—442no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—1764no—
369C22#1062266212yes—
370C22#1062279812yes—
371C22#1062281212yes—
372C22C2×#6699211yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4#1062266212yes—
379C4#1062279812yes—
380C4C2×#6697111yescharacteristic
381C4C2×#6697211yescharacteristic
382C4C2×#6699511yescharacteristic
383C4C2×#6700211yescharacteristic
384C2—1762no—
385C2#1306815814yesdirect product factor
386C2C2×#1062279811yescharacteristic
387C2C2×#1062266211yescharacteristic
388C2C2×#1062281211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#477C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#477D11
hypocenterC11C2×#1698
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×#10622637C2semidirect
4. #13068158C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622184C2semidirect
8. C2×C11×#477C2semidirect
14. C11×#477C22semidirect
23. #10622637C22semidirect
32. #10622184C22semidirect
34. #10622117C22semidirect
132. C2×#477D11semidirect
186. #477C2×D11semidirect
269. C2×C11#1698semidirect
324. C11C2×#1698semidirect
385. C2#13068158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
C2×#106226372
#130681582
C2×#106221172
C2×#106221842
C2×#106221232
C2×C11×#4772
C2×#169811