Finite Group Databasebeta

← C2×#13076682 #14960313

Subgroups — C2×#13076682 #14960313

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C212yesmaximal
2#13076682C2116yesmaximal, direct product factor
3C2×#10622273C212yesmaximal
4C2×#10622271C212yesmaximal
5C2×#10622270C212yesmaximal
6C2×#10622597C212yesmaximal
7C2×#10622597C212yesmaximal
8C2×#10622596C211yesmaximal, characteristic
9C2×#10622590C211yesmaximal, characteristic
10C2×C11×#398C211yesmaximal, characteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66942—216no—
24C2×#66942C22116yes—
25C11×#398C2218yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622597C22116yes—
36#10622597C22116yes—
37#10622596C2218yes—
38#10622590C2218yes—
39#10622273C22116yes—
40#10622271C22116yes—
41#10622270C22116yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4—42no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4C2318yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C4⋊Dic11—28no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11—42no—
60C2×C4⋊Dic11C2318yes—
61C2×C4⋊Dic11C2314yes—
62C2×C4⋊Dic11C2314yes—
63C2×Dic11⋊C4—28no—
64C2×Dic11⋊C4—28no—
65C2×Dic11⋊C4—28no—
66C2×Dic11⋊C4—28no—
67C2×Dic11⋊C4—44no—
68C2×Dic11⋊C4C2318yes—
69C2×Dic11⋊C4C2318yes—
70C2×Dic11⋊C4C2318yes—
71C2×Dic11⋊C4C2318yes—
72C2×Dic11⋊C4C2318yes—
73C2×C4×Dic11D418yes—
74C2×C4×Dic11C2314yes—
75#66942—264no—
76C11×#95C2318yes—
77C11×#95C2314yes—
78C11⋊#95C2318yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2318yes—
82C11⋊#95C2318yes—
83C11⋊#95C2314yes—
84C11⋊#95C2318yes—
85C2×#2822—111nomaximal, Sylow
86C24×C11C2411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11C2×D414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2414yes—
103C22×C4×C11C2414yes—
104C22×C4×C11C2412yes—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—28no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11C2×D418yes—
116C22×Dic11C2414yes—
117C22×Dic11C2414yes—
118C22×Dic11C2414yes—
119C22×Dic11C2414yes—
120C11×C4⋊C4—216no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4—44no—
123C4⋊Dic11—216no—
124C4⋊Dic11—44no—
125C4⋊Dic11—44no—
126Dic11⋊C4—216no—
127Dic11⋊C4—216no—
128Dic11⋊C4—216no—
129Dic11⋊C4—216no—
130Dic11⋊C4—48no—
131C4×Dic11C2×D4116yes—
132C22×#125—112no—
133#2822—1116no—
134C2×#400—112no—
135C2×#400—112no—
136C2×#398—112no—
137C2×#398—111no—
138C2×#398—112no—
139C2×#398—112no—
140C2×#398D1111yescharacteristic
141C2×#382—111no—
142C23×C11C22×D412yes—
143C23×C11H(5,𝔽2)12yes—
144C23×C112−1+414yes—
145C23×C112−1+414yes—
146C23×C112−1+412yes—
147C23×C11C2511yescharacteristic
148C2×C4×C11—28no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—48no—
162C2×C4×C11—48no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11C22×D414yes—
166C2×Dic11—216no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—24no—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—28no—
175C2×Dic11—24no—
176C2×Dic11—24no—
177C2×Dic11—48no—
178C2×Dic11—48no—
179C2×Dic11—48no—
180C2×Dic11C22×D418yes—
181C2×#125—1116no—
182C2×#125—2216no—
183C22×C4⋊C4—112no—
184C22×C4⋊C4—112no—
185C22×C4⋊C4—112no—
186C22×C4⋊C4—112no—
187C22×C4⋊C4—112no—
188C22×C4⋊C4—112no—
189C22×C4⋊C4—111no—
190C22×C4⋊C4—111no—
191C22×C4⋊C4C2×D1112yes—
192C22×C4⋊C4C2×D1111yescharacteristic
193C22×C4⋊C4C2×D1111yescharacteristic
194C22×C42—111no—
195#400—1116no—
196#400—1116no—
197#398—118no—
198#398—1116no—
199#398—1116no—
200#398—1116no—
201#398C2×D1118yes—
202#382—118no—
203C2×#95—112no—
204C2×#95—112no—
205C2×#95—112no—
206C2×#95—111no—
207C2×#95—112no—
208C2×#95—112no—
209C2×#95—112no—
210C2×#95C2×D1112yes—
211C2×#95C2×D1111yescharacteristic
212C22×C11#53618yes—
213C22×C11#53714yes—
214C22×C11#56314yes—
215C22×C11#56314yes—
216C22×C11#56418yes—
217C22×C11C23×D411yescharacteristic
218C22×C11C2×H(5,𝔽2)11yescharacteristic
219C22×C11C2×2−1+412yes—
220C22×C11C2×2−1+412yes—
221C22×C11C2×2−1+411yescharacteristic
222C4×C11—24no—
223C4×C11—44no—
224C4×C11—44no—
225C4×C11—42no—
226C4×C11—42no—
227Dic11—28no—
228Dic11—44no—
229Dic11—44no—
230Dic11—44no—
231C23×C4—112no—
232C23×C4—112no—
233C23×C4—112no—
234C23×C4—112no—
235C23×C4C22×D1112yes—
236C23×C4C22×D1112yes—
237C23×C4C22×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C23×C4C22×D1111yescharacteristic
240#125—2264no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—118no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4—118no—
247C2×C4⋊C4—118no—
248C2×C4⋊C4—118no—
249C2×C4⋊C4—114no—
250C2×C4⋊C4—118no—
251C2×C4⋊C4—114no—
252C2×C4⋊C4—228no—
253C2×C4⋊C4—228no—
254C2×C4⋊C4—228no—
255C2×C4⋊C4—228no—
256C2×C4⋊C4—228no—
257C2×C4⋊C4—444no—
258C2×C4⋊C4—442no—
259C2×C4⋊C4—442no—
260C2×C4⋊C4C22×D1118yes—
261C2×C4⋊C4C22×D1114yes—
262C2×C4⋊C4C22×D1114yes—
263C2×C42—118no—
264C2×C42—114no—
265#95—118no—
266#95—118no—
267#95—118no—
268#95—118no—
269#95—118no—
270#95—118no—
271#95—114no—
272#95C22×D1118yes—
273#95C22×D1114yes—
274C2×C11#282218yescomplemented
275C2×C11C2×#53612yes—
276C2×C11C2×#53711yescharacteristic
277C2×C11C2×#56311yescharacteristic
278C2×C11C2×#56311yescharacteristic
279C2×C11C2×#56412yes—
280C24C23×D1111yescharacteristic
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—118no—
294C22×C4—114no—
295C22×C4—114no—
296C22×C4—114no—
297C22×C4—114no—
298C22×C4—224no—
299C22×C4—224no—
300C22×C4—224no—
301C22×C4—224no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—228no—
305C22×C4—224no—
306C22×C4—224no—
307C22×C4—224no—
308C22×C4D4×D1114yes—
309C22×C4C23×D1112yes—
310C22×C4C23×D1112yes—
311C22×C4C23×D1114yes—
312C22×C4C23×D1114yes—
313C22×C4C23×D1112yes—
314C4⋊C4—216no—
315C4⋊C4—44no—
316C4⋊C4—44no—
317C4⋊C4—2216no—
318C4⋊C4—2216no—
319C4⋊C4—2216no—
320C4⋊C4—2216no—
321C4⋊C4—2216no—
322C4⋊C4—448no—
323C4⋊C4—444no—
324C4⋊C4—444no—
325C42—1116no—
326C11C2×#282211yescharacteristic, complemented, Sylow
327C23C2×D4×D1112yes—
328C23#6703712yes—
329C23#6704014yes—
330C23#6704312yes—
331C23#6704314yes—
332C23C24×D1111yescharacteristic
333C2×C4—28no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—118no—
351C2×C4—2216no—
352C2×C4—224no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—224no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—224no—
359C2×C4—228no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—448no—
363C2×C4—448no—
364C2×C4—448no—
365C2×C4C2×D4×D1114yes—
366C22#1062312814yes—
367C22#1062315918yes—
368C22#1062318214yes—
369C22C11⋊#56418yes—
370C22#1062326614yes—
371C22C22×D4×D1111yescharacteristic
372C22C2×#6703711yescharacteristic
373C22C2×#6704012yes—
374C22C2×#6704312yes—
375C22C2×#6704311yescharacteristic
376C4—24no—
377C4—44no—
378C4—44no—
379C4—42no—
380C4—42no—
381C4—228no—
382C4—444no—
383C4—444no—
384C4—444no—
385C2#1307668218yesdirect product factor
386C2C2×#1062315912yes—
387C2C2×#1062312811yescharacteristic
388C2C2×#1062326611yescharacteristic
389C2C2×#1062318211yescharacteristic
390C2C2×C11⋊#56412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socle, prime radicalC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. #13076682C2direct (N × H)
274. C2×C11#2822semidirect
326. C11C2×#2822semidirect
385. C2#13076682direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
#130766822
C2×#106222732
C2×#106222712
C2×#106222702
C2×#106225972
C2×#106225962
C2×#106225902
C2×C11×#3982
C2×#282211