Finite Group Databasebeta

← C2×#13073651 #14925595

Subgroups — C2×#13073651 #14925595

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C212yesmaximal
2#13073651C2116yesmaximal, direct product factor
3C2×#10622270C214yesmaximal
4C2×#10622541C212yesmaximal
5C2×#10622586C212yesmaximal
6C2×#10622548C211yesmaximal, characteristic
7C2×#10622589C212yesmaximal
8C2×C4×C4⋊Dic11C211yesmaximal, characteristic
9C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2214yes—
20C22×Dic11⋊C4C2214yes—
21C22×Dic11⋊C4C2214yes—
22C22×C4×Dic11C2212yes—
23C2×#66923—216no—
24C2×#66923C22116yes—
25C4×C11×C4⋊C4C2218yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29#10622589C22116yes—
30#10622586C22116yes—
31#10622548C2218yes—
32C4×C4⋊Dic11C2218yes—
33#10622541C22116yes—
34#10622270C22132yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2314yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4C2314yes—
46C2×C11×C4⋊C4C2314yes—
47C2×C42×C11—28no—
48C2×C42×C11Q818yes—
49C2×C42×C11C2318yes—
50C2×C42×C11C2314yes—
51C2×C4⋊Dic11—28no—
52C2×C4⋊Dic11—28no—
53C2×C4⋊Dic11—44no—
54C2×C4⋊Dic11D418yes—
55C2×C4⋊Dic11Q818yes—
56C2×C4⋊Dic11C2318yes—
57C2×C4⋊Dic11C2318yes—
58C2×C4⋊Dic11C2318yes—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2314yes—
61C2×Dic11⋊C4—216no—
62C2×Dic11⋊C4—216no—
63C2×Dic11⋊C4—48no—
64C2×Dic11⋊C4C23116yes—
65C2×Dic11⋊C4C23116yes—
66C2×Dic11⋊C4C23116yes—
67C2×C4×Dic11—28no—
68C2×C4×Dic11C2318yes—
69#66923—264no—
70C11×#95C2318yes—
71C11⋊#95C2318yes—
72C11⋊#95C23116yes—
73C2×#2552—111nomaximal, Sylow
74C24×C11C2411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11C2×D414yes—
84C22×C4×C11C2×Q814yes—
85C22×C4×C11C2×Q814yes—
86C22×C4×C11C2×Q814yes—
87C22×C4×C11C2×Q814yes—
88C22×C4×C11#4114yes—
89C22×C4×C11#4114yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2414yes—
92C22×C4×C11C2412yes—
93C22×C4×C11C2412yes—
94C22×C4×C11C2412yes—
95C22×Dic11—28no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—28no—
99C22×Dic11—24no—
100C22×Dic11—28no—
101C22×Dic11—24no—
102C22×Dic11C2×D418yes—
103C22×Dic11C2×Q818yes—
104C22×Dic11C2418yes—
105C22×Dic11C2414yes—
106C22×Dic11C2414yes—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—28no—
109C42×C11—216no—
110C42×C11C2×Q8116yes—
111C4⋊Dic11—216no—
112C4⋊Dic11—216no—
113C4⋊Dic11—48no—
114C4⋊Dic11C2×D4116yes—
115C4⋊Dic11C2×Q8116yes—
116Dic11⋊C4—232no—
117Dic11⋊C4—232no—
118Dic11⋊C4—416no—
119C4×Dic11—216no—
120C22×#125—112no—
121#2552—1116no—
122C2×#398—114no—
123C2×#389—112no—
124C2×#389—112no—
125C2×#384—111no—
126C2×#384—112no—
127C2×C4×C4⋊C4—111no—
128C2×C4×C4⋊C4D1111yescharacteristic
129C23×C11C22×D412yes—
130C23×C11C22×Q812yes—
131C23×C11C22×Q812yes—
132C23×C11C2×#4112yes—
133C23×C11C2×#4112yes—
134C23×C11H(5,𝔽2)12yes—
135C23×C112−1+412yes—
136C23×C11C2511yescharacteristic
137C2×C4×C11—28no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—48no—
147C2×C4×C11—48no—
148C2×C4×C11#125116yescomplemented
149C2×C4×C11C4⋊Q8116yes—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C22×Q814yes—
152C2×C4×C11C22×Q814yes—
153C2×C4×C11C22×Q814yes—
154C2×C4×C11C22×Q814yes—
155C2×C4×C11C2×#4114yes—
156C2×C4×C11C2×#4114yes—
157C2×Dic11—216no—
158C2×Dic11—216no—
159C2×Dic11—24no—
160C2×Dic11—24no—
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—28no—
164C2×Dic11—28no—
165C2×Dic11—28no—
166C2×Dic11—416no—
167C2×Dic11C22×D418yes—
168C2×Dic11C22×Q818yes—
169C2×#125—1116no—
170C2×#125—2216no—
171C22×C4⋊C4—111no—
172C22×C4⋊C4—111no—
173C22×C4⋊C4—114no—
174C22×C4⋊C4—114no—
175C22×C4⋊C4—112no—
176C22×C4⋊C4—112no—
177C22×C4⋊C4—114no—
178C22×C4⋊C4—112no—
179C22×C4⋊C4C2×D1111yescharacteristic
180C22×C4⋊C4C2×D1111yescharacteristic
181C22×C42—112no—
182C22×C42C2×D1112yes—
183C22×C42C2×D1111yescharacteristic
184#398—1132no—
185#389—1116no—
186#389—1116no—
187#384—1116no—
188#384—118no—
189C4×C4⋊C4—118no—
190C4×C4⋊C4C2×D1118yes—
191C2×#95—112no—
192C2×#95—114no—
193C2×#95C2×D1112yes—
194C22×C11C2×#12514yes—
195C22×C11C2×C4⋊Q814yes—
196C22×C11#54414yes—
197C22×C11#54714yes—
198C22×C11#55014yes—
199C22×C11#55414yes—
200C22×C11#55714yes—
201C22×C11C23×D411yescharacteristic
202C22×C11C23×Q811yescharacteristic
203C22×C11C23×Q811yescharacteristic
204C22×C11C22×#4111yescharacteristic
205C22×C11C22×#4111yescharacteristic
206C22×C11C2×H(5,𝔽2)11yescharacteristic
207C22×C11C2×2−1+411yescharacteristic
208C4×C11—24no—
209C4×C11—44no—
210C4×C11—44no—
211C4×C11C2×#12518yescomplemented
212C4×C11C2×C4⋊Q818yes—
213Dic11—28no—
214Dic11—28no—
215Dic11—48no—
216C23×C4—112no—
217C23×C4—112no—
218C23×C4—114no—
219C23×C4C22×D1112yes—
220C23×C4C22×D1112yes—
221C23×C4C22×D1111yescharacteristic
222C23×C4C22×D1111yescharacteristic
223C23×C4C22×D1111yescharacteristic
224#125—2264no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—118no—
228C2×C4⋊C4—118no—
229C2×C4⋊C4—114no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—118no—
232C2×C4⋊C4—1116no—
233C2×C4⋊C4—1116no—
234C2×C4⋊C4—118no—
235C2×C4⋊C4—1116no—
236C2×C4⋊C4—118no—
237C2×C4⋊C4—2216no—
238C2×C4⋊C4—2216no—
239C2×C4⋊C4—228no—
240C2×C4⋊C4—228no—
241C2×C4⋊C4—448no—
242C2×C4⋊C4—444no—
243C2×C4⋊C4C22×D1114yes—
244C2×C4⋊C4C22×D1114yes—
245C2×C42—28no—
246C2×C42—118no—
247C2×C42—228no—
248C2×C42Dic2218yes—
249C2×C42C22×D1118yes—
250C2×C42C22×D1114yes—
251#95—118no—
252#95—1116no—
253#95C22×D1118yes—
254C2×C11#255218yescomplemented
255C2×C11C22×#12511yescharacteristic
256C2×C11C22×C4⋊Q811yescharacteristic
257C2×C11C2×#54411yescharacteristic
258C2×C11C2×#54711yescharacteristic
259C2×C11C2×#55011yescharacteristic
260C2×C11C2×#55411yescharacteristic
261C2×C11C2×#55711yescharacteristic
262C24C23×D1111yescharacteristic
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—118no—
272C22×C4—118no—
273C22×C4—114no—
274C22×C4—114no—
275C22×C4—118no—
276C22×C4—224no—
277C22×C4—224no—
278C22×C4—224no—
279C22×C4—224no—
280C22×C4—228no—
281C22×C4—228no—
282C22×C4—228no—
283C22×C4C2×Dic2214yes—
284C22×C4C2×Dic2214yes—
285C22×C4C2×Dic2214yes—
286C22×C4#433914yes—
287C22×C4#433914yes—
288C22×C4D4×D1114yes—
289C22×C4Q8×D1114yes—
290C22×C4C23×D1114yes—
291C22×C4C23×D1114yes—
292C22×C4C23×D1112yes—
293C22×C4C23×D1112yes—
294C22×C4C23×D1112yes—
295C4⋊C4—28no—
296C4⋊C4—28no—
297C4⋊C4—1116no—
298C4⋊C4—1116no—
299C4⋊C4—2232no—
300C4⋊C4—2232no—
301C4⋊C4—2216no—
302C4⋊C4—2216no—
303C4⋊C4—4416no—
304C4⋊C4—448no—
305C42—216no—
306C42—2216no—
307C42C2×Dic22116yes—
308C11C2×#255211yescharacteristic, complemented, Sylow
309C23C22×Dic2212yes—
310C23C2×#433912yes—
311C23C2×#433912yes—
312C23C2×D4×D1112yes—
313C23C2×Q8×D1112yes—
314C23#6704212yes—
315C23#6704312yes—
316C23C24×D1111yescharacteristic
317C2×C4—28no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—118no—
329C2×C4—118no—
330C2×C4—2216no—
331C2×C4—2216no—
332C2×C4—224no—
333C2×C4—224no—
334C2×C4—224no—
335C2×C4—224no—
336C2×C4—228no—
337C2×C4—228no—
338C2×C4—228no—
339C2×C4—4416no—
340C2×C4#66923116yescomplemented
341C2×C4#66941116yes—
342C2×C4C22×Dic2214yes—
343C2×C4C22×Dic2214yes—
344C2×C4C22×Dic2214yes—
345C2×C4C2×#433914yes—
346C2×C4C2×#433914yes—
347C2×C4C2×D4×D1114yes—
348C2×C4C2×Q8×D1114yes—
349C22C2×#6692314yes—
350C22C2×#6694114yes—
351C22#1062305014yes—
352C22#1062308214yes—
353C22#1062308414yes—
354C22#1062309814yes—
355C22#1062311014yes—
356C22C23×Dic2211yescharacteristic
357C22C22×#433911yescharacteristic
358C22C22×#433911yescharacteristic
359C22C22×D4×D1111yescharacteristic
360C22C22×Q8×D1111yescharacteristic
361C22C2×#6704211yescharacteristic
362C22C2×#6704311yescharacteristic
363C4—24no—
364C4—44no—
365C4—44no—
366C4—228no—
367C4—228no—
368C4—448no—
369C4C2×#6692318yescomplemented
370C4C2×#6694118yes—
371C2#1307365118yesdirect product factor
372C2C22×#6692311yescharacteristic
373C2C22×#6694111yescharacteristic
374C2C2×#1062305011yescharacteristic
375C2C2×#1062308211yescharacteristic
376C2C2×#1062308411yescharacteristic
377C2C2×#1062311011yescharacteristic
378C2C2×#1062309811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2552
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13073651C2direct (N × H)
148. C2×C4×C11#125semidirect
211. C4×C11C2×#125semidirect
254. C2×C11#2552semidirect
308. C11C2×#2552semidirect
340. C2×C4#66923semidirect
369. C4C2×#66923semidirect
371. C2#13073651direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
#130736512
C2×#106222702
C2×#106225412
C2×#106225862
C2×#106225482
C2×#106225892
C2×C4×C4⋊Dic112
C2×C4×C11×C4⋊C42
C2×#255211