Finite Group Databasebeta

← C2×#13079017 #15623071

Subgroups — C2×#13079017 #15623071

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C22×#66923C211yesmaximal, characteristic, complemented
3#13079017C2116yesmaximal, direct product factor
4C2×#10622316C212yesmaximal, complemented
5C2×#10622326C212yesmaximal, complemented
6C2×#10622310C214yesmaximal, complemented
7C2×#10622746C214yesmaximal, complemented
8C2×C4×C11×M16C211yesmaximal, characteristic, complemented
9C22×#4339C2212yes—
10C22×C11×M16C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×#66983—22no—
13C22×C4⋊Dic11C2212yes—
14C22×Dic11⋊C4—22no—
15#10623008—24no—
16#10623008C2218yes—
17C2×#66928C2212yes—
18C2×#66927C2211yescharacteristic
19C2×C4×D44—22no—
20C2×#66923—24no—
21C2×#66923—22no—
22C2×#66923C2212yes—
23C2×#66923C2212yes—
24C2×#66923C2218yescomplemented
25C2×#66922C2211yescharacteristic
26C4×C11×M16C2218yescomplemented
27C2×C11×#97C2212yes—
28C2×C4×C8×C11C2212yes—
29#10622746C22132yescomplemented
30C2×#66885C2218yes—
31C2×#66880C2218yes—
32#10622326C22116yescomplemented
33#10622316C22116yescomplemented
34#10622310C22132yescomplemented
35C23×C4×C11D412yes—
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—22no—
38C23×Dic11—22no—
39C2×#4339—24no—
40C2×#4339—216no—
41C2×#4339C2318yes—
42C22×D44—22no—
43C22×D44C2312yes—
44C22×C4×D11—22no—
45C22×Dic22C2312yes—
46C2×C11×M16—28no—
47C2×C11×M16C2318yes—
48C22×C8×C11C2314yes—
49C2×C42×C11D412yes—
50C2×C42×C11D414yes—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2314yes—
54#66983—216no—
55C2×(C2×D11)⋊C4—24no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2318yes—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—216no—
64#66928—24no—
65#66928C2318yes—
66#66927—22no—
67#66927C2314yes—
68C4×D44—216no—
69#66923—24no—
70#66923—24no—
71#66923—216no—
72#66923C2318yes—
73#66923C2318yes—
74#66922—22no—
75#66922C2314yes—
76C11×#97C2318yes—
77C4×C8×C11C2318yes—
78#66885C23132yes—
79#66880C23132yes—
80C2×#3142—111nomaximal, Sylow
81C24×C11C2×D411yescharacteristic
82C23×D11—22no—
83C22×C4×C11—44no—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D418yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11#4118yes—
90C22×C4×C11C2411yescharacteristic
91C22×C4×C11C2412yes—
92C2×C22⋊D11—28no—
93C2×C22⋊D11—48no—
94C22×Dic11—28no—
95C22×Dic11—24no—
96C22×Dic11—22no—
97C22×Dic11—48no—
98#4339—232no—
99#4339—416no—
100C2×D44—28no—
101C2×D44—22no—
102C2×D44—28no—
103C2×D44—48no—
104C2×D44C2414yes—
105C2×C4×D11—28no—
106C2×C4×D11—48no—
107C2×Dic22—22no—
108C2×Dic22—28no—
109C2×Dic22C2414yes—
110C11×M16—216no—
111C2×C8×C11—28no—
112C2×C8×C11C2418yes—
113C42×C11C2×D412yes—
114C42×C11C2×D418yes—
115C42×C11C2×D412yes—
116C42×C11C2412yes—
117C42×C11C2412yes—
118(C2×D11)⋊C4—216no—
119C4⋊Dic11—28no—
120C4⋊Dic11—24no—
121C4⋊Dic11—28no—
122C4⋊Dic11C2418yes—
123Dic11⋊C4—216no—
124Dic11⋊C4—216no—
125C2×#532—111no—
126C22×#125—111no—
127#3142—1116no—
128C2×#491—112no—
129C2×#490—112no—
130C2×#488—114no—
131C2×#417—114no—
132C2×C4×M16D1111yescharacteristic, complemented
133C23×C11—24no—
134C23×C11#12414yes—
135C23×C11C22×D412yes—
136C23×C11C22×D411yescharacteristic
137C22×D11—24no—
138C22×D11—44no—
139C22×D11—48no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—48no—
143C2×C4×C11#12414yes—
144C2×C4×C11#12418yes—
145C2×C4×C11C22×D414yes—
146C2×C4×C11C22×D414yes—
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D412yes—
149C2×C4×C11C2×#4114yes—
150C2×C4×C11C2×#4118yes—
151C2×C4×C11C2511yescharacteristic
152C22⋊D11—416no—
153C2×Dic11—28no—
154C2×Dic11—24no—
155C2×Dic11—416no—
156C2×Dic11—44no—
157C2×Dic11—48no—
158D44—28no—
159D44—416no—
160D44—44no—
161C4×D11—416no—
162Dic22—28no—
163Dic22—44no—
164C8×C11—28no—
165C22×#41—112no—
166C22×M16C2×D1112yes—
167#532—118no—
168#532—224no—
169C2×C4⋊Q8—111no—
170C2×#127—111no—
171C2×#125—112no—
172C2×#125—112no—
173C2×#125—118no—
174C2×#125—222no—
175C2×#125—224no—
176C2×#124—112no—
177C2×#121—222no—
178C2×C4×D4—222no—
179C22×C4⋊C4—112no—
180C22×C4⋊C4—222no—
181C22×C42C2×D1111yescharacteristic
182#491—1116no—
183#490—1116no—
184#488—1132no—
185#417—1132no—
186C2×#103—118no—
187C2×#102—118no—
188C4×M16C2×D1118yescomplemented
189C2×#97C2×D1112yes—
190C2×C4×C8C2×D1112yes—
191C22×C11—28no—
192C22×C11—24no—
193C22×C11C2×#12414yes—
194C22×C11C2×#12412yes—
195C22×C11#57514yes—
196C22×C11C23×D411yescharacteristic
197C2×D11—44no—
198C2×D11—48no—
199C2×D11—88no—
200C4×C11—24no—
201C4×C11—24no—
202C4×C11C2×#12412yes—
203C4×C11C2×#12414yes—
204C4×C11C22×#4112yes—
205Dic11—44no—
206Dic11—48no—
207C2×#41—118no—
208C2×#41—224no—
209C2×#41—2216no—
210C22×Q8—112no—
211C22×D4—112no—
212C22×D4—222no—
213C22×D4—222no—
214C23×C4—222no—
215C23×C4—222no—
216C23×C4D4412yes—
217C23×C4C22×D1111yescharacteristic
218C2×M16—28no—
219C2×M16C22×D1118yes—
220C22×C8C22×D1114yes—
221C4⋊Q8—114no—
222C4⋊Q8—222no—
223#127—114no—
224#127—222no—
225#125—118no—
226#125—118no—
227#125—2216no—
228#125—224no—
229#125—224no—
230#124—118no—
231#124—224no—
232#121—2216no—
233C4×D4—2216no—
234C2×C4⋊C4—114no—
235C2×C4⋊C4—118no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—2216no—
239C2×C4⋊C4—224no—
240C2×C4⋊C4—224no—
241C2×C4⋊C4—222no—
242C2×C22⋊C4—224no—
243C2×C42D4412yes—
244C2×C42D4414yes—
245C2×C42C22×D1111yescharacteristic
246C2×C42C22×D1111yescharacteristic
247C2×C42C22×D1114yes—
248#103—1132no—
249#102—1132no—
250#97C22×D1118yes—
251C4×C8C22×D1118yes—
252C2×C11—24no—
253C2×C11#314214yescomplemented
254C2×C11C22×#12411yescharacteristic
255C2×C11C2×#57512yes—
256D11—84no—
257C24—222no—
258C24C2×D4411yescharacteristic
259#41—2232no—
260#41—4416no—
261C2×Q8—114no—
262C2×Q8—222no—
263C2×Q8—228no—
264C2×D4—114no—
265C2×D4—228no—
266C2×D4—228no—
267C2×D4—222no—
268C2×D4—228no—
269C2×D4—448no—
270C2×D4—448no—
271C22×C4—44no—
272C22×C4—228no—
273C22×C4—222no—
274C22×C4—224no—
275C22×C4—228no—
276C22×C4—448no—
277C22×C4—448no—
278C22×C4C2×D4412yes—
279C22×C4C2×D4412yes—
280C22×C4C2×D4418yes—
281C22×C4C2×D4412yes—
282C22×C4C2×D4411yescharacteristic
283C22×C4#433918yes—
284C22×C4C23×D1112yes—
285C22×C4C23×D1111yescharacteristic
286M16—216no—
287C2×C8—28no—
288C2×C8C23×D1118yes—
289C4⋊C4—118no—
290C4⋊C4—228no—
291C4⋊C4—224no—
292C4⋊C4—2216no—
293C4⋊C4—2216no—
294C4⋊C4—228no—
295C22⋊C4—2216no—
296C42C2×D4418yes—
297C42C2×D4412yes—
298C42C2×D4412yes—
299C42C23×D1112yes—
300C42C23×D1112yes—
301C11C2×#314211yescharacteristic, complemented, Sylow
302C23—24no—
303C23—224no—
304C23—444no—
305C23—448no—
306C23#6692814yes—
307C23C22×D4412yes—
308C23C22×D4411yescharacteristic
309Q8—228no—
310Q8—444no—
311D4—228no—
312D4—4416no—
313D4—4416no—
314D4—444no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—48no—
318C2×C4—224no—
319C2×C4—228no—
320C2×C4—4416no—
321C2×C4—444no—
322C2×C4—448no—
323C2×C4—4416no—
324C2×C4#6692814yes—
325C2×C4#6692818yes—
326C2×C4C22×D4414yes—
327C2×C4C22×D4414yes—
328C2×C4C22×D4412yes—
329C2×C4C22×D4411yescharacteristic
330C2×C4C2×#433914yes—
331C2×C4C2×#433918yes—
332C2×C4C24×D1111yescharacteristic
333C8—28no—
334C22—24no—
335C22—28no—
336C22—444no—
337C22—448no—
338C22—888no—
339C22C2×#6692814yes—
340C22C2×#6692812yes—
341C22#1062327914yes—
342C22C23×D4411yescharacteristic
343C4—24no—
344C4—24no—
345C4—444no—
346C4—448no—
347C4C2×#6692814yes—
348C4C2×#6692812yes—
349C4C22×#433912yes—
350C2—24no—
351C2—884no—
352C2#1307901714yesdirect product factor
353C2C22×#6692811yescharacteristic
354C2C2×#1062327912yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×M16C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenterC2×C4×M16D11
hypocenterC11C2×#3142
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C22×#66923C2semidirect
3. #13079017C2direct (N × H)
4. C2×#10622316C2semidirect
5. C2×#10622326C2semidirect
6. C2×#10622310C2semidirect
7. C2×#10622746C2semidirect
8. C2×C4×C11×M16C2semidirect
24. C2×#66923C22semidirect
26. C4×C11×M16C22semidirect
29. #10622746C22semidirect
32. #10622326C22semidirect
33. #10622316C22semidirect
34. #10622310C22semidirect
132. C2×C4×M16D11semidirect
188. C4×M16C2×D11semidirect
253. C2×C11#3142semidirect
301. C11C2×#3142semidirect
352. C2#13079017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
C22×#669232
#130790172
C2×#106223162
C2×#106223262
C2×#106223102
C2×#106227462
C2×C4×C11×M162
C2×#314211