Finite Group Databasebeta

← C2×#13071491 #14913016

Subgroups — C2×#13071491 #14913016

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic11C211yesmaximal, characteristic
2#13071491C2116yesmaximal, direct product factor
3C2×#10622541C212yesmaximal, complemented
4C2×#10622267C214yesmaximal, complemented
5C2×#10622825C211yesmaximal, characteristic
6C2×#10622555C212yesmaximal
7C2×C4×C4⋊Dic11C212yesmaximal, complemented
8C2×C22⋊C4×Dic11C212yesmaximal
9C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C4⋊Dic11C4116yescomplemented
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2218yes—
22C22×Dic11⋊C4C2214yes—
23C22×C4×Dic11C2214yes—
24C4×C11×C22⋊C4C2218yes—
25C2×C11×#95C2212yes—
26#10622825C2218yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622555C22116yes—
31C22⋊C4×Dic11C22116yes—
32C4×C4⋊Dic11C22116yescomplemented
33#10622541C22116yescomplemented
34#10622267C22132yescomplemented
35C25×C11C2311yescharacteristic
36C23×C4×C11—28no—
37C23×C4×C11C2×C418yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2314yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—48no—
44C23×Dic11C2×C4116yes—
45C23×Dic11C2314yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2318yes—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4Q818yes—
51C2×C11×C22⋊C4C2314yes—
52C2×C11×C22⋊C4C2314yes—
53C2×C42×C11—28no—
54C2×C42×C11C2318yes—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11C2318yes—
57C2×C4⋊Dic11—28no—
58C2×C4⋊Dic11C2×C4116yes—
59C2×C4⋊Dic11C2×C418yes—
60C2×C4⋊Dic11C2×C418yes—
61C2×C4⋊Dic11C2×C4164yescomplemented
62C2×C4⋊Dic11C2318yes—
63C2×C4⋊Dic11C2318yes—
64C2×C4⋊Dic11C2314yes—
65C2×C4⋊Dic11C2314yes—
66C2×Dic11⋊C4—48no—
67C2×Dic11⋊C4C23116yes—
68C2×C4×Dic11—48no—
69C2×C4×Dic11C23116yes—
70C11×#95C2318yes—
71C11⋊#95C2318yes—
72C11⋊#95C23116yes—
73C11⋊#95C23116yes—
74C2×#2345—111nomaximal, Sylow
75C24×C11—24no—
76C24×C11—24no—
77C24×C11C22×C414yes—
78C24×C11C2×Q814yes—
79C24×C11#4114yes—
80C24×C11C2412yes—
81C24×C11C2411yescharacteristic
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—232no—
86C22×C4×C11—216no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11C22×C414yes—
91C22×C4×C11C22×C4116yes—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C2×Q818yes—
94C22×C4×C11#4118yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2412yes—
99C22×Dic11—28no—
100C22×Dic11—28no—
101C22×Dic11—28no—
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11—432no—
105C22×Dic11—416no—
106C22×Dic11C22×C418yes—
107C22×Dic11C22×C418yes—
108C22×Dic11C22×C4132yes—
109C22×Dic11C2418yes—
110C22×Dic11C2414yes—
111C22×Dic11C2414yes—
112C11×C22⋊C4—28no—
113C11×C22⋊C4C2×Q8116yes—
114C42×C11—216no—
115C22⋊Dic11—216no—
116C4⋊Dic11—216no—
117C4⋊Dic11C22×C4132yes—
118C4⋊Dic11C22×C4116yes—
119C4⋊Dic11C22×C4116yes—
120Dic11⋊C4—416no—
121C4×Dic11—416no—
122C23×C4⋊C4—111no—
123#2345—1116no—
124C2×#389—112no—
125C2×#387—114no—
126C2×#380—111no—
127C2×#380—112no—
128C2×C4×C4⋊C4—112no—
129C2×C4×C22⋊C4—112no—
130C2×C4×C22⋊C4D1111yescharacteristic
131C23×C11—28no—
132C23×C11—28no—
133C23×C11—216no—
134C23×C11—216no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11C4×Q8116yes—
138C23×C11C23×C414yes—
139C23×C11C23×C412yes—
140C23×C11C22×Q814yes—
141C23×C11C22×Q812yes—
142C23×C11C2×#4114yes—
143C23×C11C2×#4112yes—
144C23×C11C2×#4114yes—
145C23×C11H(5,𝔽2)14yes—
146C23×C11C2511yescharacteristic
147C2×C4×C11—28no—
148C2×C4×C11—216no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—232no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—48no—
157C2×C4×C11#117116yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C414yes—
160C2×C4×C11C22×Q818yes—
161C2×C4×C11C2×#4118yes—
162C2×Dic11—216no—
163C2×Dic11—216no—
164C2×Dic11—28no—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—28no—
169C2×Dic11—432no—
170C2×Dic11—416no—
171C2×Dic11C23×C418yes—
172C2×Dic11C23×C418yes—
173C24×C4—112no—
174C24×C4C2×D1111yescharacteristic
175C22×C4⋊C4—118no—
176C22×C4⋊C4—111no—
177C22×C4⋊C4—112no—
178C22×C4⋊C4—111no—
179C22×C4⋊C4—1116no—
180C22×C4⋊C4—112no—
181C22×C4⋊C4—114no—
182C22×C22⋊C4—112no—
183C22×C22⋊C4C2×D1111yescharacteristic
184C22×C22⋊C4C2×D1111yescharacteristic
185C22×C42—114no—
186C22×C42C2×D1112yes—
187#389—1116no—
188#387—1132no—
189#380—118no—
190#380—1116no—
191C4×C4⋊C4—1116no—
192C4×C22⋊C4—1116no—
193C4×C22⋊C4C2×D1118yes—
194C2×#95—114no—
195C2×#95—114no—
196C2×#95—112no—
197C2×#95C2×D1112yes—
198C22×C11—232no—
199C22×C11—24no—
200C22×C11—24no—
201C22×C11—28no—
202C22×C11—28no—
203C22×C11C2×#11714yes—
204C22×C11C2×C4×Q818yes—
205C22×C11C2×C4×Q814yes—
206C22×C11#51814yes—
207C22×C11#55318yes—
208C22×C11#55418yes—
209C22×C11C24×C411yescharacteristic
210C22×C11C23×Q811yescharacteristic
211C22×C11C22×#4111yescharacteristic
212C22×C11C22×#4112yes—
213C22×C11C2×H(5,𝔽2)12yes—
214C4×C11—24no—
215C4×C11—28no—
216C4×C11—44no—
217C4×C11C2×#11718yes—
218Dic11—28no—
219Dic11—28no—
220Dic11—48no—
221C25C22×D1111yescharacteristic
222C23×C4—28no—
223C23×C4—112no—
224C23×C4—112no—
225C23×C4—1116no—
226C23×C4—118no—
227C23×C4—114no—
228C23×C4—448no—
229C23×C4C4×D1118yes—
230C23×C4C22×D1112yes—
231C23×C4C22×D1112yes—
232C23×C4C22×D1114yes—
233C23×C4C22×D1111yescharacteristic
234C23×C4C22×D1111yescharacteristic
235C2×C4⋊C4—1116no—
236C2×C4⋊C4—118no—
237C2×C4⋊C4—118no—
238C2×C4⋊C4—1164no—
239C2×C4⋊C4—114no—
240C2×C4⋊C4—118no—
241C2×C4⋊C4—114no—
242C2×C4⋊C4—118no—
243C2×C4⋊C4—1116no—
244C2×C4⋊C4—228no—
245C2×C4⋊C4—448no—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—118no—
248C2×C22⋊C4—228no—
249C2×C22⋊C4Dic2218yes—
250C2×C22⋊C4C22×D1114yes—
251C2×C22⋊C4C22×D1114yes—
252C2×C42—28no—
253C2×C42—1116no—
254C2×C42—448no—
255C2×C42C22×D1118yes—
256#95—1116no—
257#95—1116no—
258#95—118no—
259#95C22×D1118yes—
260C2×C11—28no—
261C2×C11#234518yescomplemented
262C2×C11C22×#11711yescharacteristic
263C2×C11C22×C4×Q811yescharacteristic
264C2×C11C2×#51811yescharacteristic
265C2×C11C2×#55312yes—
266C2×C11C2×#55412yes—
267C24—24no—
268C24—24no—
269C24C2×Dic2214yes—
270C24C2×C4×D1114yes—
271C24#433914yes—
272C24C23×D1112yes—
273C24C23×D1111yescharacteristic
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—232no—
278C22×C4—216no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—118no—
283C22×C4—118no—
284C22×C4—114no—
285C22×C4—114no—
286C22×C4—1132no—
287C22×C4—118no—
288C22×C4—228no—
289C22×C4—228no—
290C22×C4—228no—
291C22×C4—228no—
292C22×C4—228no—
293C22×C4—4432no—
294C22×C4—4416no—
295C22×C4C2×Dic2218yes—
296C22×C4C2×C4×D1114yes—
297C22×C4C2×C4×D11116yes—
298C22×C4C2×C4×D1114yes—
299C22×C4#434118yes—
300C22×C4C23×D1114yes—
301C22×C4C23×D1114yes—
302C22×C4C23×D1112yes—
303C22×C4C23×D1112yes—
304C4⋊C4—1132no—
305C4⋊C4—1116no—
306C4⋊C4—1116no—
307C4⋊C4—2216no—
308C4⋊C4—4416no—
309C22⋊C4—28no—
310C22⋊C4—2216no—
311C22⋊C4C2×Dic22116yes—
312C42—216no—
313C42—4416no—
314C11C2×#234511yescharacteristic, complemented, Sylow
315C23—28no—
316C23—28no—
317C23—216no—
318C23—216no—
319C23—24no—
320C23—24no—
321C23C4×Dic22116yes—
322C23C22×Dic2214yes—
323C23C22×Dic2212yes—
324C23C22×C4×D1114yes—
325C23C22×C4×D1112yes—
326C23C2×#433914yes—
327C23C2×#433912yes—
328C23C2×#434114yes—
329C23#6704214yes—
330C23C24×D1111yescharacteristic
331C2×C4—28no—
332C2×C4—216no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—232no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—48no—
341C2×C4—118no—
342C2×C4—118no—
343C2×C4—2216no—
344C2×C4—2216no—
345C2×C4—228no—
346C2×C4—228no—
347C2×C4—228no—
348C2×C4—228no—
349C2×C4—228no—
350C2×C4—4432no—
351C2×C4—4416no—
352C2×C4#66930116yes—
353C2×C4C22×Dic2218yes—
354C2×C4C22×C4×D1114yes—
355C2×C4C22×C4×D1114yes—
356C2×C4C2×#434118yes—
357C22—28no—
358C22—28no—
359C22—232no—
360C22—24no—
361C22—24no—
362C22C2×C4×Dic2218yes—
363C22C2×C4×Dic2214yes—
364C22C2×#6693014yes—
365C22#1062305214yes—
366C22#1062307418yes—
367C22#1062309618yes—
368C22C23×Dic2211yescharacteristic
369C22C23×C4×D1111yescharacteristic
370C22C22×#433911yescharacteristic
371C22C22×#434112yes—
372C22C2×#6704212yes—
373C4—28no—
374C4—24no—
375C4—44no—
376C4—228no—
377C4—228no—
378C4—448no—
379C4C2×#6693018yes—
380C2—28no—
381C2#1307149118yesdirect product factor
382C2C22×#6693011yescharacteristic
383C2C22×C4×Dic2211yescharacteristic
384C2C2×#1062305211yescharacteristic
385C2C2×#1062309612yes—
386C2C2×#1062307412yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2345
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071491C2direct (N × H)
3. C2×#10622541C2semidirect
4. C2×#10622267C2semidirect
7. C2×C4×C4⋊Dic11C2semidirect
16. C22×C4⋊Dic11C4semidirect
32. C4×C4⋊Dic11C22semidirect
33. #10622541C22semidirect
34. #10622267C22semidirect
61. C2×C4⋊Dic11C2×C4semidirect
261. C2×C11#2345semidirect
314. C11C2×#2345semidirect
381. C2#13071491direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic112
#130714912
C2×#106225412
C2×#106222672
C2×#106228252
C2×#106225552
C2×C4×C4⋊Dic112
C2×C22⋊C4×Dic112
C2×C4×C11×C22⋊C42
C2×#234511