Finite Group Databasebeta

← C2×#13068188 #14736343

Subgroups — C2×#13068188 #14736343

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic
3C2×#10622301C211yesmaximal, characteristic
4#13068188C218yesmaximal, direct product factor
5C2×#10622095C211yesmaximal, characteristic, complemented
6C2×#10622184C211yesmaximal, characteristic, complemented
7C2×#10622185C211yesmaximal, characteristic, complemented
8C2×C11×#487C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4313—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#487—22no—
14C11×#487C2214yescomplemented
15C2×C11×#103—21no—
16C2×C11×#103—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C2×(C2×D11)⋊C8—21no—
19#10622700—22no—
20#10622700C2214yes—
21#10622697—22no—
22#10622697C2214yes—
23C2×#66873—21no—
24C2×#66873—21no—
25C2×#66872—21no—
26C2×#66871—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622301—22no—
31#10622301C2214yes—
32#10622185C2214yescomplemented
33#10622184C2214yescomplemented
34#10622095C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C2×#4313—24no—
60C2×#4313—44no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44D412yes—
64C4×D44C2312yes—
65C11×#103—24no—
66C11×#103—24no—
67C4×C8×C11D412yes—
68C4×C8×C11C2312yes—
69(C2×D11)⋊C8—24no—
70#66873—24no—
71#66873—24no—
72#66872—24no—
73#66871—24no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80C2×#1703—111nomaximal, Sylow
81C23×D11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—82no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44C2×D412yes—
99C2×C4×D11—22no—
100C2×C4×D11—22no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11C2×D412yes—
106C2×C8×C11C2×D412yes—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11C2×D412yes—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129#4313—48no—
130C2×#487D1111yescharacteristic, complemented
131C2×#476—111no—
132C2×#474—111no—
133C2×#436—111no—
134#1703—118no—
135C2×#334—111no—
136C2×#333—111no—
137C2×#332—111no—
138C23×C11#12111yescharacteristic
139C22×D11—22no—
140C22×D11—42no—
141C22×D11—42no—
142C22×D11—42no—
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—82no—
146Q8×C11—82no—
147Q8×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#13512yes—
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×C4×C11#13712yes—
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—42no—
165D44—22no—
166D44—22no—
167D44—42no—
168C4×D11—42no—
169C4×D11—42no—
170C4×D11—44no—
171C8×C11—22no—
172C8×C11—22no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176C22×M16—221no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×C4×D4—111no—
180#487—22no—
181#487C2×D1114yescomplemented
182#476—114no—
183#476—222no—
184#474—114no—
185#474—222no—
186#436—114no—
187#436—222no—
188C2×#107—221no—
189C2×#106—221no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8—111no—
193C2×#103—21no—
194C2×#103—21no—
195C2×#102—221no—
196C2×#102—221no—
197C2×C22⋊C8—221no—
198C2×C4×C8C2×D1111yescharacteristic
199#334—114no—
200#333—114no—
201#332—114no—
202C22×C11#46312yes—
203C22×C11#47012yes—
204C22×C11#47112yes—
205C22×C11C2×#12111yescharacteristic
206C2×D11—42no—
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—84no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11—82no—
214C4×C11#46312yes—
215C4×C11#47012yes—
216C4×C11C2×#13511yescharacteristic
217C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
218C4×C11C2×#13711yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—42no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×D4—111no—
224C23×C4—221no—
225C2×M16—224no—
226C2×M16—444no—
227C22×C8—221no—
228C22×C8—221no—
229C22×C8—221no—
230C22×C8C22⋊D1111yescharacteristic
231C22×C8C22⋊D1111yescharacteristic
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C22×D1112yes—
239C4⋊Q8C22×D1112yes—
240C4×D4—112no—
241C4×D4—112no—
242C4×D4—221no—
243C4×D4—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—111no—
249C2×C22⋊C4—221no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252#106—224no—
253C4⋊C8—112no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259#103—24no—
260#103—24no—
261#102—224no—
262#102—224no—
263C22⋊C8—224no—
264C4×C8C22⋊D1112yes—
265C4×C8C22×D1112yes—
266C2×C11#170314yescomplemented
267C2×C11C2×#46311yescharacteristic
268C2×C11C2×#47011yescharacteristic
269C2×C11C2×#47111yescharacteristic
270D11—82no—
271C24—221no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—82no—
279C2×D4—112no—
280C2×D4—222no—
281C2×D4—222no—
282C2×D4—221no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—221no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293M16—448no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8—442no—
300C2×C8—442no—
301C2×C8—442no—
302C2×C8C2×C22⋊D1112yes—
303C2×C8C2×C22⋊D1112yes—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—112no—
313C4⋊C4—221no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C42D4×D1111yescharacteristic
317C42#434111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C42C23×D1111yescharacteristic
320C11C2×#170311yescharacteristic, complemented, Sylow
321C23—222no—
322C23—442no—
323C23—442no—
324C23—442no—
325C23#6699111yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—82no—
330Q8—82no—
331D4—222no—
332D4—222no—
333D4—442no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—222no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—444no—
344C2×C4#6697112yes—
345C2×C4#6697112yes—
346C2×C4#6699111yescharacteristic
347C2×C4#6699111yescharacteristic
348C2×C4#6699111yescharacteristic
349C2×C4#6700212yes—
350C2×C4#6700312yes—
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4C2×#434111yescharacteristic
353C2×C4C22×C22⋊D1111yescharacteristic
354C8—22no—
355C8—22no—
356C8—442no—
357C8—442no—
358C8—442no—
359C22—442no—
360C22—442no—
361C22—442no—
362C22—884no—
363C22#1062267012yes—
364C22#1062279012yes—
365C22#1062280212yes—
366C22C2×#6699111yescharacteristic
367C4—21no—
368C4—21no—
369C4—82no—
370C4—82no—
371C4—442no—
372C4#1062267012yes—
373C4#1062280212yes—
374C4C2×#6697111yescharacteristic
375C4C2×#6697111yescharacteristic
376C4C2×#6700211yescharacteristic
377C4C2×#6700311yescharacteristic
378C2—882no—
379C2#1306818814yesdirect product factor
380C2C2×#1062267011yescharacteristic
381C2C2×#1062280211yescharacteristic
382C2C2×#1062279011yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#487D11
hypocenterC11C2×#1703
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #13068188C2direct (N × H)
5. C2×#10622095C2semidirect
6. C2×#10622184C2semidirect
7. C2×#10622185C2semidirect
8. C2×C11×#487C2semidirect
14. C11×#487C22semidirect
32. #10622185C22semidirect
33. #10622184C22semidirect
34. #10622095C22semidirect
130. C2×#487D11semidirect
181. #487C2×D11semidirect
266. C2×C11#1703semidirect
320. C11C2×#1703semidirect
379. C2#13068188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106227002
C2×#106223012
#130681882
C2×#106220952
C2×#106221842
C2×#106221852
C2×C11×#4872
C2×#170311