Finite Group Databasebeta

← C2×#13067660 #14726010

Subgroups — C2×#13067660 #14726010

Order 2816.

984 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic
2C2×#10622335C212yesmaximal
3C2×#10622599C211yesmaximal, characteristic
4#13067660C218yesmaximal, direct product factor
5C2×#10622105C212yesmaximal
6C2×C11×#324C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66979—21no—
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66977—21no—
11C2×#66977C2212yes—
12#10623031—22no—
13#10623031—24no—
14#10623031C2214yes—
15C2×#66943—22no—
16C2×#66941—22no—
17C2×C11×C22⋊C8C2212yes—
18C2×C11⋊#95—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×#66882—22no—
22C2×#66880—22no—
23#10622599—22no—
24#10622599C2214yes—
25#10622335—24no—
26#10622335C2218yes—
27C11×#324C2214yes—
28#10622105C2218yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11—21no—
34C22×Dic22—21no—
35C22×Dic22D412yes—
36C22×C8×C11—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4D412yes—
40C2×C11×C4⋊C4C2312yes—
41C2×C22⋊Dic11—22no—
42#66979—24no—
43#66979—24no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D412yes—
51C2×C4⋊Dic11C2312yes—
52#66977—24no—
53#66977—22no—
54#66977—22no—
55#66977—24no—
56#66977D414yes—
57#66977C2314yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61#66943—28no—
62#66943—28no—
63#66941—28no—
64#66941—28no—
65C11×C22⋊C8—22no—
66C11×C22⋊C8C2314yes—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—21no—
70C11⋊#95C2312yes—
71#66882—28no—
72#66880—28no—
73C2×#1617—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11Q1614yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—42no—
94C22×Dic11—44no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—42no—
99C2×Dic22—24no—
100C2×Dic22—22no—
101C2×Dic22—44no—
102C2×Dic22—82no—
103C2×Dic22C2×D414yes—
104C2×C8×C11—24no—
105C2×C8×C11—44no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C22⋊Dic11—24no—
109C22⋊Dic11—24no—
110C4⋊Dic11—24no—
111C4⋊Dic11—24no—
112C4⋊Dic11—24no—
113C4⋊Dic11—22no—
114C4⋊Dic11—24no—
115C4⋊Dic11—42no—
116C4⋊Dic11C2×D414yes—
117Dic11⋊C4—28no—
118Dic11⋊C4—24no—
119Dic11⋊C4—24no—
120C4×Dic11—28no—
121C2×#544—111no—
122C2×#484—112no—
123C2×#400—111no—
124#1617—118no—
125C2×#328—112no—
126C2×#324D1111yescharacteristic
127C23×C11—22no—
128C23×C11—22no—
129C23×C11#12011yescharacteristic
130C23×C11#12011yescharacteristic
131C23×C11C2×Q1612yes—
132C23×C11#13712yes—
133C23×C11C22×D411yescharacteristic
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—81no—
146C2×C4×C11#12012yes—
147C2×C4×C11C2×Q1614yes—
148C2×C4×C11C22×D412yes—
149C2×Dic11—24no—
150C2×Dic11—24no—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—44no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—84no—
159C2×Dic11—82no—
160C2×Dic11—82no—
161Dic22—44no—
162Dic22—82no—
163Dic22—84no—
164C8×C11—44no—
165#544—114no—
166#544—224no—
167#544—222no—
168C2×C4⋊Q8—222no—
169C2×#125—222no—
170C2×C22⋊Q8—112no—
171C2×C22⋊Q8—221no—
172C2×#117—221no—
173C22×C4⋊C4—111no—
174C22×C4⋊C4C2×D1111yescharacteristic
175#484—118no—
176#484—224no—
177C2×#107—222no—
178C2×#103—222no—
179C2×C22⋊C8C2×D1112yes—
180#400—114no—
181#400—222no—
182C2×#95—111no—
183C2×#95—221no—
184C2×#95—221no—
185#328—118no—
186#324C2×D1114yes—
187C22×C11—24no—
188C22×C11—24no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#45112yes—
194C22×C11#45112yes—
195C22×C11#45412yes—
196C22×C11#45812yes—
197C22×C11C2×#12011yescharacteristic
198C22×C11C22×Q1611yescharacteristic
199C22×C11C2×#13711yescharacteristic
200C4×C11—24no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—42no—
204Dic11—44no—
205Dic11—44no—
206Dic11—82no—
207Dic11—82no—
208C22×Q8—112no—
209C22×Q8—221no—
210C23×C4—221no—
211C23×C4—221no—
212C23×C4D4411yescharacteristic
213C23×C4D4411yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C22×C8—22no—
216C4⋊Q8—228no—
217C4⋊Q8—228no—
218#125—228no—
219#125—228no—
220C22⋊Q8—114no—
221C22⋊Q8—114no—
222C22⋊Q8—224no—
223C22⋊Q8—222no—
224C22⋊Q8—224no—
225C22⋊Q8—222no—
226#117—224no—
227#117—224no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—222no—
236C2×C4⋊C4—222no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4D4412yes—
241C2×C4⋊C4C22×D1112yes—
242C2×C22⋊C4—222no—
243C2×C42—222no—
244#107—228no—
245#103—228no—
246C22⋊C8—22no—
247C22⋊C8C22×D1114yes—
248#95—112no—
249#95—221no—
250#95—224no—
251#95—224no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—22no—
255C2×C11#161714yescomplemented
256C2×C11C2×#45111yescharacteristic
257C2×C11C2×#45411yescharacteristic
258C2×C11C2×#45811yescharacteristic
259C24C2×D4411yescharacteristic
260C2×Q8—114no—
261C2×Q8—224no—
262C2×Q8—222no—
263C2×Q8—444no—
264C2×Q8—882no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—222no—
276C22×C4—442no—
277C22×C4—442no—
278C22×C4—444no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—442no—
282C22×C4Dic4414yes—
283C22×C4C2×D4412yes—
284C22×C4C2×D4412yes—
285C22×C4C2×D4411yescharacteristic
286C22×C4D4×D1112yes—
287C22×C4D4×D1112yes—
288C22×C4C23×D1111yescharacteristic
289C2×C8—24no—
290C2×C8—44no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—114no—
294C4⋊C4—224no—
295C4⋊C4—224no—
296C4⋊C4—224no—
297C4⋊C4—228no—
298C4⋊C4—222no—
299C4⋊C4—224no—
300C4⋊C4—224no—
301C4⋊C4—224no—
302C4⋊C4—442no—
303C22⋊C4—224no—
304C22⋊C4—224no—
305C42—228no—
306C11C2×#161711yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23#6693511yescharacteristic
310C23#6693511yescharacteristic
311C23C2×Dic4412yes—
312C23#6696212yes—
313C23C22×D4411yescharacteristic
314Q8—444no—
315Q8—882no—
316Q8—884no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—224no—
330C2×C4—224no—
331C2×C4—444no—
332C2×C4—444no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—444no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—884no—
339C2×C4—882no—
340C2×C4—882no—
341C2×C4#6693512yes—
342C2×C4C2×Dic4414yes—
343C2×C4C2×D4×D1112yes—
344C8—44no—
345C22—24no—
346C22—24no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22#1062235212yes—
352C22#1062235212yes—
353C22#1062235512yes—
354C22#1062236612yes—
355C22C2×#6693511yescharacteristic
356C22C22×Dic4411yescharacteristic
357C22C2×#6696211yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—444no—
363C4—444no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—21no—
368C2—22no—
369C2#1306766014yesdirect product factor
370C2C2×#1062235211yescharacteristic
371C2C2×#1062236611yescharacteristic
372C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#324D11
hypocenterC11C2×#1617
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #13067660C2direct (N × H)
255. C2×C11#1617semidirect
306. C11C2×#1617semidirect
369. C2#13067660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230312
C2×#106223352
C2×#106225992
#130676602
C2×#106221052
C2×C11×#3242
C2×#161711