Finite Group Databasebeta

← C2×#13071090 #14912145

Subgroups — C2×#13071090 #14912145

Order 2816.

2750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2#13071090C2116yesmaximal, direct product factor
3C2×#10622587C212yesmaximal
4C2×#10622586C212yesmaximal
5C2×#10622265C214yesmaximal
6C2×C4×Dic11⋊C4C212yesmaximal
7C2×#10622545C212yesmaximal
8C2×C42×Dic11C211yesmaximal, characteristic
9C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2214yes—
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C4×Dic22C4116yescomplemented
23C2×C4×Dic22C2218yes—
24C4×C11×C4⋊C4C2218yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29#10622587C22116yes—
30#10622586C22116yes—
31#10622545C22116yes—
32C4×Dic11⋊C4C22116yes—
33C42×Dic11C2218yes—
34#10622265C22132yes—
35C23×C4×C11C2314yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×Dic22—28no—
44C22×Dic22C2×C418yes—
45C22×Dic22C2314yes—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4C2318yes—
48C2×C42×C11—28no—
49C2×C42×C11C2×C418yes—
50C2×C42×C11C2318yes—
51C2×C42×C11C2314yes—
52C2×C4⋊Dic11C2×C418yes—
53C2×C4⋊Dic11C2314yes—
54C2×Dic11⋊C4—216no—
55C2×Dic11⋊C4C2×C4116yes—
56C2×Dic11⋊C4C23116yes—
57C2×Dic11⋊C4C2318yes—
58C2×C4×Dic11—28no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—28no—
61C2×C4×Dic11C2×C4116yes—
62C2×C4×Dic11Q818yescomplemented
63C2×C4×Dic11C2318yes—
64C2×C4×Dic11C2314yes—
65C2×C4×Dic11C2318yes—
66C2×C4×Dic11C2318yes—
67C2×C4×Dic11C2314yes—
68C4×Dic22C2×C4164yescomplemented
69C11×#95C2318yes—
70C11⋊#95C23116yes—
71C11⋊#95C23116yes—
72C11⋊#95C23116yes—
73C2×#2295—111nomaximal, Sylow
74C24×C11C2411yescharacteristic
75C22×C4×C11—24no—
76C22×C4×C11—28no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C414yes—
81C22×C4×C11C22×C414yes—
82C22×C4×C11C2×Q814yes—
83C22×C4×C11#4118yes—
84C22×C4×C11#4114yes—
85C22×C4×C11C2418yes—
86C22×C4×C11C2412yes—
87C22×C4×C11C2412yes—
88C22×C4×C11C2412yes—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—28no—
94C22×Dic11—28no—
95C22×Dic11C22×C418yes—
96C22×Dic11C22×C418yes—
97C22×Dic11C2×Q818yes—
98C22×Dic11#4118yes—
99C22×Dic11C2414yes—
100C22×Dic11C2414yes—
101C22×Dic11C2414yes—
102C22×Dic11C2414yes—
103C2×Dic22—232no—
104C2×Dic22—216no—
105C2×Dic22C22×C4116yes—
106C11×C4⋊C4—216no—
107C42×C11—216no—
108C42×C11C22×C4116yes—
109C4⋊Dic11C22×C4116yes—
110Dic11⋊C4—232no—
111Dic11⋊C4C22×C4132yes—
112C4×Dic11—216no—
113C4×Dic11—216no—
114C4×Dic11—28no—
115C4×Dic11C22×C4132yes—
116C4×Dic11C2×Q8116yescomplemented
117C22×C4×Q8—111no—
118#2295—1116no—
119C2×#391—112no—
120C2×#389—112no—
121C2×#387—114no—
122C2×C4×C4⋊C4—112no—
123C2×C4×C4⋊C4D1111yescharacteristic
124C2×#376—112no—
125C2×C43—111no—
126C23×C11C23×C412yes—
127C23×C11C22×Q812yes—
128C23×C11C2×#4114yes—
129C23×C11C2×#4112yes—
130C23×C11C2×#4114yes—
131C23×C11C2511yescharacteristic
132C2×C4×C11—28no—
133C2×C4×C11—24no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—416no—
138C2×C4×C11#117116yes—
139C2×C4×C11C4×Q8116yes—
140C2×C4×C11C23×C414yes—
141C2×C4×C11C23×C414yes—
142C2×C4×C11C23×C414yes—
143C2×C4×C11C22×Q814yes—
144C2×C4×C11C2×#4118yes—
145C2×C4×C11C2×#4114yes—
146C2×Dic11—216no—
147C2×Dic11—216no—
148C2×Dic11—216no—
149C2×Dic11—216no—
150C2×Dic11—24no—
151C2×Dic11—24no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11C23×C418yes—
157C2×Dic11C23×C418yes—
158C2×Dic11C22×Q818yes—
159C2×Dic11C2×#4118yes—
160Dic22—232no—
161C23×Q8—111no—
162C2×C4×Q8—118no—
163C2×C4×Q8—1116no—
164C22×C4⋊C4—112no—
165C22×C4⋊C4—111no—
166C22×C4⋊C4—114no—
167C22×C4⋊C4C2×D1112yes—
168C22×C42—112no—
169C22×C42—111no—
170C22×C42—112no—
171C22×C42—112no—
172C22×C42—111no—
173C22×C42C2×D1112yes—
174C22×C42C2×D1111yescharacteristic
175#391—1116no—
176#389—1116no—
177#387—1132no—
178C4×C4⋊C4—1116no—
179C4×C4⋊C4C2×D1118yes—
180#376—1116no—
181C2×#95—114no—
182C2×#95—114no—
183C2×#95—114no—
184C2×#95C2×D1112yes—
185C43—118no—
186C22×C11C2×#11714yes—
187C22×C11C2×C4×Q814yes—
188C22×C11C4×#4114yes—
189C22×C11#52918yes—
190C22×C11#53318yes—
191C22×C11C24×C411yescharacteristic
192C22×C11C23×Q811yescharacteristic
193C22×C11C22×#4112yes—
194C22×C11C22×#4111yescharacteristic
195C22×C11C22×#4112yes—
196C4×C11—24no—
197C4×C11—48no—
198C4×C11C2×#11718yes—
199C4×C11C2×C4×Q818yes—
200Dic11—28no—
201Dic11—28no—
202Dic11—28no—
203Dic11—28no—
204C22×Q8—118no—
205C22×Q8—114no—
206C22×Q8—228no—
207C23×C4—112no—
208C23×C4—112no—
209C23×C4—112no—
210C23×C4—112no—
211C23×C4C22×D1114yes—
212C23×C4C22×D1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C4×Q8—1164no—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—1116no—
218C2×C4⋊C4—118no—
219C2×C4⋊C4—118no—
220C2×C4⋊C4—114no—
221C2×C4⋊C4—1116no—
222C2×C4⋊C4—2216no—
223C2×C4⋊C4C22×D1118yes—
224C2×C42—28no—
225C2×C42—1116no—
226C2×C42—118no—
227C2×C42—118no—
228C2×C42—114no—
229C2×C42—114no—
230C2×C42—118no—
231C2×C42—118no—
232C2×C42—228no—
233C2×C42—228no—
234C2×C42—224no—
235C2×C42C4×D1118yes—
236C2×C42C22×D1118yes—
237C2×C42C22×D1114yes—
238#95—1116no—
239#95—1116no—
240#95—1116no—
241#95C22×D1118yes—
242C2×C11#229518yescomplemented
243C2×C11C22×#11711yescharacteristic
244C2×C11C22×C4×Q811yescharacteristic
245C2×C11C2×C4×#4111yescharacteristic
246C2×C11C2×#52912yes—
247C2×C11C2×#53312yes—
248C24C23×D1111yescharacteristic
249C2×Q8—1116no—
250C2×Q8—2232no—
251C2×Q8—2216no—
252C22×C4—24no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—28no—
256C22×C4—118no—
257C22×C4—118no—
258C22×C4—118no—
259C22×C4—118no—
260C22×C4—114no—
261C22×C4—114no—
262C22×C4—114no—
263C22×C4—114no—
264C22×C4—224no—
265C22×C4—224no—
266C22×C4—228no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—228no—
270C22×C4C2×C4×D1114yes—
271C22×C4C2×C4×D1114yes—
272C22×C4C2×C4×D1114yes—
273C22×C4#433918yes—
274C22×C4#434114yes—
275C22×C4Q8×D1114yes—
276C22×C4C23×D1118yes—
277C22×C4C23×D1112yes—
278C22×C4C23×D1112yes—
279C22×C4C23×D1112yes—
280C4⋊C4—216no—
281C4⋊C4—1132no—
282C4⋊C4—1116no—
283C4⋊C4—2232no—
284C42—216no—
285C42—1132no—
286C42—1116no—
287C42—2216no—
288C42—2216no—
289C42—228no—
290C42C2×C4×D11116yes—
291C11C2×#229511yescharacteristic, complemented, Sylow
292C23C22×C4×D1112yes—
293C23C2×#433914yes—
294C23C2×#434112yes—
295C23C2×Q8×D1112yes—
296C23#41×D1114yes—
297C23C24×D1111yescharacteristic
298Q8—2232no—
299C2×C4—28no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—416no—
305C2×C4—118no—
306C2×C4—118no—
307C2×C4—118no—
308C2×C4—118no—
309C2×C4—2216no—
310C2×C4—2216no—
311C2×C4—2216no—
312C2×C4—2216no—
313C2×C4—224no—
314C2×C4—224no—
315C2×C4—228no—
316C2×C4—224no—
317C2×C4—224no—
318C2×C4—228no—
319C2×C4#66925116yes—
320C2×C4#66940116yes—
321C2×C4C22×C4×D1114yes—
322C2×C4C22×C4×D1114yes—
323C2×C4C22×C4×D1114yes—
324C2×C4C2×#433918yes—
325C2×C4C2×#434114yes—
326C2×C4C2×Q8×D1114yes—
327C22C2×#6692514yes—
328C22C2×#6694014yes—
329C22#1062305314yes—
330C22#1062308818yes—
331C22#1062310918yes—
332C22C23×C4×D1111yescharacteristic
333C22C22×#433912yes—
334C22C22×#434111yescharacteristic
335C22C22×Q8×D1111yescharacteristic
336C22C2×#41×D1112yes—
337C4—24no—
338C4—48no—
339C4—228no—
340C4—228no—
341C4—228no—
342C4—228no—
343C4C2×#6692518yes—
344C4C2×#6694018yes—
345C2#1307109018yesdirect product factor
346C2C22×#6692511yescharacteristic
347C2C22×#6694011yescharacteristic
348C2C2×#1062305311yescharacteristic
349C2C2×#1062308812yes—
350C2C2×#1062310912yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2295
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071090C2direct (N × H)
22. C2×C4×Dic22C4semidirect
62. C2×C4×Dic11Q8semidirect
68. C4×Dic22C2×C4semidirect
116. C4×Dic11C2×Q8semidirect
242. C2×C11#2295semidirect
291. C11C2×#2295semidirect
345. C2#13071090direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
#130710902
C2×#106225872
C2×#106225862
C2×#106222652
C2×C4×Dic11⋊C42
C2×#106225452
C2×C42×Dic112
C2×C4×C11×C4⋊C42
C2×#229511