Finite Group Databasebeta

← C2×#13067979 #14736006

Subgroups — C2×#13067979 #14736006

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3C2×D4×C11⋊C8C211yesmaximal, characteristic
4#13067979C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622185C211yesmaximal, characteristic, complemented
7C2×#10622124C211yesmaximal, characteristic, complemented
8C2×C11×#474C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4326—21no—
12C22×#4326—21no—
13C23×C11⋊C8—21no—
14C2×#66922C2211yescharacteristic
15C11×#474—22no—
16C11×#474C2214yes—
17C2×C11×#107—21no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×#66896—21no—
21C2×C22⋊(C11⋊C8)—21no—
22#10622705—22no—
23#10622705C2214yescomplemented
24D4×C11⋊C8—22no—
25D4×C11⋊C8C2214yes—
26#10622620—22no—
27#10622620C2214yes—
28C2×#66871—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622185C2214yescomplemented
33#10622124C2214yescomplemented
34#10622117C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C22×Dic22—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2312yes—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C4×D4×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—24no—
54C2×#4326—24no—
55C2×#4326—44no—
56C2×#4326—44no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—24no—
62C22×C11⋊C8—44no—
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922C2312yes—
69C11×#107—24no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×#102—24no—
73#66896—24no—
74C22⋊(C11⋊C8)—24no—
75#66871—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80C4×C11⋊C8D412yes—
81C4×C11⋊C8C2312yes—
82C2×#1669—111nomaximal, Sylow
83C24×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×D4×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11Q1614yescomplemented
91C2×D4×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×Dic11—41no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4C2×D412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4326—48no—
121#4326—48no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—48no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8D814yes—
133C2×C11⋊C8C2×D412yes—
134C2×C11⋊C8C2×D412yes—
135C2×#494—111no—
136C2×#474—111no—
137C2×#474D1111yescharacteristic
138C2×C8×D4—111no—
139#1669—118no—
140C2×#335—111no—
141C2×#332—111no—
142C2×#332—111no—
143C23×C11—22no—
144C23×C11—24no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11#12111yescharacteristic
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—24no—
153D4×C11C2×Q1614yescomplemented
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×D812yes—
166C2×C4×C11C2×Q1612yes—
167C2×C4×C11#13512yes—
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×Dic11—42no—
173C2×Dic11—82no—
174Dic22—42no—
175Dic22—42no—
176Dic22—82no—
177C8×C11—42no—
178C11⋊C8—22no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C11⋊C8C2×D814yes—
182C22×Q16—221no—
183C22×Q16—221no—
184C23×C8—221no—
185C2×C4⋊Q8—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×D4C2×D1111yescharacteristic
188#494—114no—
189#494—222no—
190#474—22no—
191#474—114no—
192#474—222no—
193#474C2×D1114yes—
194C8×D4—114no—
195C8×D4—222no—
196C2×#107—21no—
197C2×#107—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—21no—
202C2×#102—221no—
203C2×C22⋊C8—221no—
204C2×C4×C8—111no—
205#335—114no—
206#332—114no—
207#332—114no—
208C22×C11—24no—
209C22×C11—48no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11#45912yes—
213C22×C11#46712yes—
214C22×C11#47312yes—
215C22×C11C2×#12111yescharacteristic
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—82no—
220C4×C11#45912yes—
221C4×C11#46712yes—
222C4×C11C22×D811yescharacteristic
223C4×C11C22×Q1611yescharacteristic
224C4×C11C2×#13511yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226Dic11—82no—
227C22×Q8—21no—
228C22×Q8—221no—
229C22×D4C22⋊D1111yescharacteristic
230C23×C4—21no—
231C2×Q16—224no—
232C2×Q16—224no—
233C2×Q16—444no—
234C2×Q16—444no—
235C22×C8—21no—
236C22×C8—111no—
237C22×C8—111no—
238C22×C8—224no—
239C22×C8—221no—
240C22×C8—221no—
241C22×C8—444no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—112no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8C22×D1112yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C22⋊D1112yes—
253C4×D4C22×D1112yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#107—24no—
262#107—224no—
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269#102—24no—
270#102—224no—
271C22⋊C8—224no—
272C4×C8—112no—
273C4×C8—112no—
274C2×C11—44no—
275C2×C11#166914yescomplemented
276C2×C11C2×#45911yescharacteristic
277C2×C11C2×#46711yescharacteristic
278C2×C11C2×#47311yescharacteristic
279C24—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—222no—
285C2×Q8—441no—
286C2×Q8—442no—
287C2×Q8—442no—
288C2×D4—21no—
289C2×D4—22no—
290C2×D4#432614yescomplemented
291C2×D4C2×C22⋊D1112yes—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—441no—
299C22×C4D4×D1111yescharacteristic
300C22×C4#434111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—448no—
303Q16—448no—
304C2×C8—22no—
305C2×C8—42no—
306C2×C8—114no—
307C2×C8—112no—
308C2×C8—112no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—448no—
313C2×C8—442no—
314C2×C8—442no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4C2×C22⋊D1112yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C42D4×D1111yescharacteristic
328C42#434111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C42C23×D1111yescharacteristic
331C11C2×#166911yescharacteristic, complemented, Sylow
332C23—22no—
333C23—24no—
334C23—42no—
335C23—42no—
336C23#6699211yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—442no—
341Q8—442no—
342Q8—882no—
343D4—22no—
344D4—24no—
345D4C2×#432614yescomplemented
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4D8×D1112yes—
357C2×C4#6696412yes—
358C2×C4#6699211yescharacteristic
359C2×C4#6699211yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4C2×#432612yes—
362C2×C4#6700312yes—
363C2×C4C2×D4×D1111yescharacteristic
364C2×C4C2×#434111yescharacteristic
365C2×C4C22×C22⋊D1111yescharacteristic
366C8—42no—
367C8—114no—
368C8—222no—
369C8—442no—
370C8—442no—
371C22—24no—
372C22—42no—
373C22—42no—
374C22—48no—
375C22#1062266412yes—
376C22#1062276312yes—
377C22#1062281712yes—
378C22C2×#6699211yescharacteristic
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—882no—
384C4#1062266412yes—
385C4#1062276312yes—
386C4C2×D8×D1111yescharacteristic
387C4C2×#6696411yescharacteristic
388C4C22×#432611yescharacteristic
389C4C2×#6700311yescharacteristic
390C2—44no—
391C2#1306797914yesdirect product factor
392C2C2×#1062276311yescharacteristic
393C2C2×#1062266411yescharacteristic
394C2C2×#1062281711yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#474C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenterC2×#474D11
hypocenterC11C2×#1669
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
4. #13067979C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622185C2semidirect
7. C2×#10622124C2semidirect
23. #10622705C22semidirect
32. #10622185C22semidirect
33. #10622124C22semidirect
34. #10622117C22semidirect
90. C2×D4×C11Q16semidirect
153. D4×C11C2×Q16semidirect
275. C2×C11#1669semidirect
290. C2×D4#4326semidirect
331. C11C2×#1669semidirect
345. D4C2×#4326semidirect
391. C2#13067979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106226202
C2×D4×C11⋊C82
#130679792
C2×#106221172
C2×#106221852
C2×#106221242
C2×C11×#4742
C2×#166911