Finite Group Databasebeta

← C2×#13073807 #14925047

Subgroups — C2×#13073807 #14925047

Order 2816.

2486 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
1C22×#66923C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic
3#13073807C2116yesmaximal, direct product factor
4C2×#10622596C214yesmaximal
5C2×#10622542C211yesmaximal, characteristic
6C2×#10622542C211yesmaximal, characteristic
7C2×#10622266C214yesmaximal
8C2×#10622548C211yesmaximal, characteristic
9C2×#10622549C211yesmaximal, characteristic
10C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2214yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C2×#66923—28no—
25C2×#66923C2218yes—
26C2×C4×Dic22—28no—
27C2×C4×Dic22C2218yes—
28C4×C11×C4⋊C4C2218yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2214yes—
33#10622596C22132yes—
34#10622549C2218yes—
35#10622548C2218yes—
36#10622542C2218yes—
37#10622542C2218yes—
38#10622266C22132yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C22×Dic22—24no—
49C22×Dic22—24no—
50C22×Dic22Q818yes—
51C22×Dic22C2314yes—
52C2×C11×C4⋊C4—28no—
53C2×C11×C4⋊C4C2318yes—
54C2×C42×C11—24no—
55C2×C42×C11—24no—
56C2×C42×C11D418yes—
57C2×C42×C11C2314yes—
58C2×C42×C11C2314yes—
59C2×C42×C11C2314yes—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11—24no—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11—216no—
64C2×C4⋊Dic11C2314yes—
65C2×C4⋊Dic11C2314yes—
66C2×C4⋊Dic11C2314yes—
67C2×C4⋊Dic11C23116yes—
68C2×Dic11⋊C4—28no—
69C2×Dic11⋊C4—28no—
70C2×Dic11⋊C4—28no—
71C2×Dic11⋊C4C2318yes—
72C2×Dic11⋊C4C2318yes—
73C2×Dic11⋊C4C2318yes—
74C2×C4×Dic11—28no—
75C2×C4×Dic11C2318yes—
76#66923—232no—
77C4×Dic22—232no—
78C11×#95C2318yes—
79C11⋊#95C23116yes—
80C11⋊#95C23116yes—
81C11⋊#95C23116yes—
82C2×#2565—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2×D414yes—
94C22×C4×C11C2×Q814yes—
95C22×C4×C11#4118yes—
96C22×C4×C11#4114yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2414yes—
101C22×C4×C11C2412yes—
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—28no—
108C22×Dic11—28no—
109C22×Dic11—28no—
110C22×Dic11C2×Q818yes—
111C22×Dic11C2414yes—
112C22×Dic11C2414yes—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C2×Dic22—232no—
116C2×Dic22—28no—
117C2×Dic22—28no—
118C2×Dic22C2×Q8116yes—
119C11×C4⋊C4—216no—
120C42×C11—28no—
121C42×C11—28no—
122C42×C11C2×D4116yes—
123C4⋊Dic11—28no—
124C4⋊Dic11—28no—
125C4⋊Dic11—28no—
126C4⋊Dic11—232no—
127Dic11⋊C4—216no—
128Dic11⋊C4—216no—
129Dic11⋊C4—216no—
130C4×Dic11—216no—
131C22×#125—111no—
132C22×C4×Q8—111no—
133#2565—1116no—
134C2×#398—114no—
135C2×#391—111no—
136C2×#391—111no—
137C2×#387—114no—
138C2×#384—111no—
139C2×#382—111no—
140C2×C4×C4⋊C4D1111yescharacteristic
141C23×C11C22×D412yes—
142C23×C11C22×Q812yes—
143C23×C11C2×#4114yes—
144C23×C11C2×#4112yes—
145C23×C112−1+414yes—
146C23×C11C2511yescharacteristic
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11—216no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—48no—
158C2×C4×C11C22⋊Q8116yes—
159C2×C4×C11C22×D414yes—
160C2×C4×C11C22×D414yes—
161C2×C4×C11C22×D414yes—
162C2×C4×C11C22×Q814yes—
163C2×C4×C11C2×#4118yes—
164C2×C4×C11C2×#4114yes—
165C2×Dic11—216no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—28no—
172C2×Dic11—28no—
173C2×Dic11—28no—
174C2×Dic11—48no—
175C2×Dic11—48no—
176C2×Dic11—48no—
177C2×Dic11C22×Q818yes—
178Dic22—232no—
179C23×Q8—111no—
180C2×#125—118no—
181C2×#125—228no—
182C2×C4×Q8—118no—
183C2×C4×Q8—228no—
184C22×C4⋊C4—112no—
185C22×C4⋊C4—112no—
186C22×C4⋊C4—112no—
187C22×C4⋊C4—114no—
188C22×C4⋊C4—111no—
189C22×C4⋊C4—111no—
190C22×C4⋊C4—111no—
191C22×C4⋊C4C2×D1112yes—
192C22×C42—112no—
193C22×C42C2×D1111yescharacteristic
194C22×C42C2×D1111yescharacteristic
195C22×C42C2×D1111yescharacteristic
196#398—1132no—
197#391—118no—
198#391—118no—
199#387—1132no—
200#384—118no—
201#382—118no—
202C4×C4⋊C4C2×D1118yes—
203C2×#95—114no—
204C2×#95—114no—
205C2×#95—114no—
206C2×#95C2×D1112yes—
207C22×C11C2×C22⋊Q814yes—
208C22×C11#53214yes—
209C22×C11#53614yes—
210C22×C11#55218yes—
211C22×C11#55718yes—
212C22×C11C23×D411yescharacteristic
213C22×C11C23×Q811yescharacteristic
214C22×C11C22×#4112yes—
215C22×C11C22×#4111yescharacteristic
216C22×C11C2×2−1+412yes—
217C4×C11—24no—
218C4×C11—24no—
219C4×C11—28no—
220C4×C11—44no—
221C4×C11C2×C22⋊Q818yes—
222Dic11—28no—
223Dic11—44no—
224Dic11—44no—
225Dic11—44no—
226C22×Q8—118no—
227C22×Q8—114no—
228C22×Q8—224no—
229C22×Q8—224no—
230C23×C4—112no—
231C23×C4—112no—
232C23×C4—112no—
233C23×C4—112no—
234C23×C4C22×D1112yes—
235C23×C4C22×D1111yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C23×C4C22×D1112yes—
238C23×C4C22×D1111yescharacteristic
239#125—2232no—
240C4×Q8—2232no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—114no—
243C2×C4⋊C4—118no—
244C2×C4⋊C4—114no—
245C2×C4⋊C4—114no—
246C2×C4⋊C4—118no—
247C2×C4⋊C4—118no—
248C2×C4⋊C4—1116no—
249C2×C4⋊C4—228no—
250C2×C4⋊C4—224no—
251C2×C4⋊C4—228no—
252C2×C4⋊C4—228no—
253C2×C4⋊C4—224no—
254C2×C4⋊C4—224no—
255C2×C4⋊C4—2216no—
256C2×C4⋊C4C22×D1118yes—
257C2×C42—24no—
258C2×C42—24no—
259C2×C42—118no—
260C2×C42—228no—
261C2×C42D4418yes—
262C2×C42C22×D1114yes—
263C2×C42C22×D1114yes—
264C2×C42C22×D1114yes—
265#95—1116no—
266#95—1116no—
267#95—1116no—
268#95C22×D1118yes—
269C2×C11#256518yescomplemented
270C2×C11C22×C22⋊Q811yescharacteristic
271C2×C11C2×#53211yescharacteristic
272C2×C11C2×#53611yescharacteristic
273C2×C11C2×#55212yes—
274C2×C11C2×#55712yes—
275C24C23×D1111yescharacteristic
276C2×Q8—1116no—
277C2×Q8—2232no—
278C2×Q8—228no—
279C2×Q8—228no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—118no—
288C22×C4—114no—
289C22×C4—114no—
290C22×C4—114no—
291C22×C4—114no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—224no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—228no—
298C22×C4—228no—
299C22×C4—228no—
300C22×C4C2×D4414yes—
301C22×C4C2×D4414yes—
302C22×C4C2×D4414yes—
303C22×C4#433918yes—
304C22×C4#434114yes—
305C22×C4Q8×D1114yes—
306C22×C4C23×D1114yes—
307C22×C4C23×D1112yes—
308C22×C4C23×D1112yes—
309C22×C4C23×D1114yes—
310C22×C4C23×D1112yes—
311C4⋊C4—216no—
312C4⋊C4—2216no—
313C4⋊C4—228no—
314C4⋊C4—2216no—
315C4⋊C4—2216no—
316C4⋊C4—228no—
317C4⋊C4—228no—
318C4⋊C4—2232no—
319C42—28no—
320C42—28no—
321C42—2216no—
322C42C2×D44116yes—
323C11C2×#256511yescharacteristic, complemented, Sylow
324C23C22×D4412yes—
325C23C2×#433914yes—
326C23C2×#434112yes—
327C23C2×Q8×D1112yes—
328C23#6704314yes—
329C23C24×D1111yescharacteristic
330Q8—2232no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—216no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—48no—
342C2×C4—118no—
343C2×C4—2216no—
344C2×C4—224no—
345C2×C4—224no—
346C2×C4—224no—
347C2×C4—224no—
348C2×C4—224no—
349C2×C4—228no—
350C2×C4—228no—
351C2×C4—228no—
352C2×C4—448no—
353C2×C4—448no—
354C2×C4—448no—
355C2×C4#66950116yes—
356C2×C4C22×D4414yes—
357C2×C4C22×D4414yes—
358C2×C4C22×D4414yes—
359C2×C4C2×#433918yes—
360C2×C4C2×#434114yes—
361C2×C4C2×Q8×D1114yes—
362C22#1062300814yes—
363C22C2×#6695014yes—
364C22#1062305714yes—
365C22#1062307218yes—
366C22#1062309818yes—
367C22C23×D4411yescharacteristic
368C22C22×#433912yes—
369C22C22×#434111yescharacteristic
370C22C22×Q8×D1111yescharacteristic
371C22C2×#6704312yes—
372C4—28no—
373C4—24no—
374C4—24no—
375C4—44no—
376C4—228no—
377C4—444no—
378C4—444no—
379C4—444no—
380C4C2×#6695018yes—
381C2#1307380718yesdirect product factor
382C2C22×#6695011yescharacteristic
383C2C2×#1062300811yescharacteristic
384C2C2×#1062305711yescharacteristic
385C2C2×#1062307212yes—
386C2C2×#1062309812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2565
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13073807C2direct (N × H)
269. C2×C11#2565semidirect
323. C11C2×#2565semidirect
381. C2#13073807direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C22×C4×Dic222
#130738072
C2×#106225962
C2×#106225422
C2×#106222662
C2×#106225482
C2×#106225492
C2×C4×C11×C4⋊C42
C2×#256511