Finite Group Databasebeta

← C2×#13068138 #14736307

Subgroups — C2×#13068138 #14736307

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3C2×#10622697C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic
5#13068138C218yesmaximal, direct product factor
6C2×#10622118C211yesmaximal, characteristic, complemented
7C2×#10622119C211yesmaximal, characteristic, complemented
8C2×C11×#333C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4313—21no—
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66885—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66881—21no—
18#10622697—22no—
19#10622697C2214yes—
20#10622691—22no—
21#10622691C2214yescomplemented
22C2×#66873—21no—
23C2×#66872—21no—
24C2×#66871—21no—
25C2×#66871—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622455—22no—
29#10622455C2214yes—
30#10622451—22no—
31#10622451C2214yes—
32C11×#333C2214yescomplemented
33#10622119C2214yescomplemented
34#10622118C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×Dic22—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8D411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55C2×#4313—24no—
56C2×#4313—44no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44D412yes—
60C4×D44C2312yes—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922C2312yes—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×C4⋊C8C2312yes—
69#66885—24no—
70(C2×D11)⋊C8—24no—
71#66881—24no—
72#66873—24no—
73#66872—24no—
74#66871—24no—
75#66871—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4×C11⋊C8D412yes—
79C4×C11⋊C8C2312yes—
80C2×#1695—111nomaximal, Sylow
81C23×D11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—41no—
91C2×D44—21no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44C2×D412yes—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×Dic22—22no—
100C2×Dic22—41no—
101C2×Dic22—82no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11C2411yescharacteristic
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11C2×D412yes—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—42no—
125C2×C11⋊C8SD1614yes—
126C2×C11⋊C8C2×D412yes—
127C2×C11⋊C8C2×D412yes—
128#4313—48no—
129C2×#500—111no—
130C2×#476—111no—
131C2×#476—111no—
132C2×#436—111no—
133#1695—118no—
134C2×#334—111no—
135C2×#333—111no—
136C2×#333D1111yescharacteristic, complemented
137C23×C11#12111yescharacteristic
138C22×D11—22no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—42no—
142Q8×C11—82no—
143Q8×C11—82no—
144C2×C4×C11—22no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C2×SD1612yes—
151C2×C4×C11#13712yes—
152C2×C4×C11#13712yes—
153C2×C4×C11#13712yes—
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161D44—22no—
162D44—22no—
163D44—42no—
164C4×D11—42no—
165C4×D11—42no—
166C4×D11—44no—
167Dic22—82no—
168Dic22—82no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—22no—
172C11⋊C8—42no—
173C11⋊C8C2×SD1614yes—
174C22×M16—221no—
175C2×C4⋊Q8—111no—
176C2×C4⋊Q8C2×D1111yescharacteristic
177C2×C4×D4—111no—
178#500—114no—
179#500—222no—
180#476—114no—
181#476—114no—
182#476—222no—
183#476—222no—
184#436—114no—
185#436—222no—
186C2×#107—221no—
187C2×#107—221no—
188C2×#106—221no—
189C2×#106—221no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8C2×D1111yescharacteristic
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×#102—221no—
194C2×#102—221no—
195C2×C22⋊C8—221no—
196C2×C4×C8—111no—
197#334—114no—
198#333—114no—
199#333C2×D1114yescomplemented
200C22×C11#46112yes—
201C22×C11#47012yes—
202C22×C11#47212yes—
203C22×C11C2×#12111yescharacteristic
204C2×D11—42no—
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—84no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—82no—
211C4×C11#46112yes—
212C4×C11#47012yes—
213C4×C11C22×SD1611yescharacteristic
214C4×C11C2×#13711yescharacteristic
215C4×C11C2×#13711yescharacteristic
216C4×C11C2×#13711yescharacteristic
217Dic11—42no—
218Dic11—82no—
219C22×Q8—21no—
220C22×Q8—221no—
221C22×D4—111no—
222C23×C4—221no—
223C2×M16—224no—
224C2×M16—444no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—111no—
228C22×C8—111no—
229C22×C8—221no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—112no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237C4⋊Q8C22×D1112yes—
238C4×D4—112no—
239C4×D4—112no—
240C4×D4—221no—
241C4×D4—221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C42C22×D1111yescharacteristic
249#107—224no—
250#107—224no—
251#106—224no—
252#106—224no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8C22×D1112yes—
258C4⋊C8C22×D1112yes—
259#102—224no—
260#102—224no—
261C22⋊C8—224no—
262C4×C8—112no—
263C4×C8—112no—
264C2×C11#169514yescomplemented
265C2×C11C2×#46111yescharacteristic
266C2×C11C2×#47011yescharacteristic
267C2×C11C2×#47211yescharacteristic
268D11—82no—
269C24—221no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×Q8—222no—
274C2×Q8—441no—
275C2×Q8—882no—
276C2×D4—112no—
277C2×D4—221no—
278C2×D4—222no—
279C2×D4—222no—
280C22×C4—41no—
281C22×C4—221no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—441no—
287C22×C4#433911yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290M16—448no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—114no—
296C2×C8—112no—
297C2×C8—112no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—442no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—112no—
306C4⋊C4—221no—
307C4⋊C4—222no—
308C4⋊C4—222no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—222no—
312C22⋊C4—222no—
313C42#433911yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C42C23×D1111yescharacteristic
317C11C2×#169511yescharacteristic, complemented, Sylow
318C23—222no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23#6693711yescharacteristic
323Q8—82no—
324Q8—82no—
325Q8—882no—
326Q8—882no—
327D4—222no—
328D4—222no—
329D4—442no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—222no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—444no—
338C2×C4—442no—
339C2×C4—882no—
340C2×C4#6693711yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4SD16×D1112yes—
344C2×C4#6696812yes—
345C2×C4#6697112yes—
346C2×C4#6697112yes—
347C2×C4C2×#433911yescharacteristic
348C2×C4C2×D4×D1111yescharacteristic
349C2×C4C2×D4×D1111yescharacteristic
350C8—42no—
351C8—42no—
352C8—114no—
353C8—222no—
354C8—442no—
355C22—442no—
356C22—442no—
357C22—442no—
358C22—884no—
359C22#1062236212yes—
360C22#1062242912yes—
361C22#1062243112yes—
362C22C2×#6693711yescharacteristic
363C4—21no—
364C4—21no—
365C4—82no—
366C4—442no—
367C4—882no—
368C4#1062242912yes—
369C4#1062243112yes—
370C4C2×SD16×D1111yescharacteristic
371C4C2×#6696811yescharacteristic
372C4C2×#6697111yescharacteristic
373C4C2×#6697111yescharacteristic
374C2—882no—
375C2#1306813814yesdirect product factor
376C2C2×#1062243111yescharacteristic
377C2C2×#1062242911yescharacteristic
378C2C2×#1062236211yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#333C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#333D11
hypocenterC11C2×#1695
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. #13068138C2direct (N × H)
6. C2×#10622118C2semidirect
7. C2×#10622119C2semidirect
8. C2×C11×#333C2semidirect
21. #10622691C22semidirect
32. C11×#333C22semidirect
33. #10622119C22semidirect
34. #10622118C22semidirect
136. C2×#333D11semidirect
199. #333C2×D11semidirect
264. C2×C11#1695semidirect
317. C11C2×#1695semidirect
375. C2#13068138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106224552
C2×#106226972
C2×#106224512
#130681382
C2×#106221182
C2×#106221192
C2×C11×#3332
C2×#169511