Finite Group Databasebeta

← C2×#13071591 #14913151

Subgroups — C2×#13071591 #14913151

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2#13071591C2116yesmaximal, direct product factor
3C2×#10622601C212yesmaximal
4C2×#10622283C214yesmaximal, complemented
5C2×#10622277C212yesmaximal, complemented
6C2×C4⋊C4×Dic11C212yesmaximal, complemented
7C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
8C2×#10622279C212yesmaximal, complemented
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2214yes—
15C22×(C2×D11)⋊C4C2214yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2214yes—
21C2×C4×D44C4116yescomplemented
22C2×C4×D44C2218yes—
23C11×#382C2218yescomplemented
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2214yes—
29#10622601C22116yes—
30C4⋊C4×Dic11C22116yescomplemented
31C4×C4⋊Dic11C2218yescomplemented
32#10622283C22132yescomplemented
33#10622279C22116yescomplemented
34#10622277C22116yescomplemented
35C24×D11C2312yes—
36C23×C4×C11C2314yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—24no—
44C22×D44—24no—
45C22×D44C2×C418yes—
46C22×D44C2314yes—
47C22×C4×D11—48no—
48C22×C4×D11C2×C4116yes—
49C22×C4×D11C2318yes—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4C2318yes—
52C2×C42×C11C2×C418yes—
53C2×C42×C11C2314yes—
54C2×(C2×D11)⋊C4—216no—
55C2×(C2×D11)⋊C4—48no—
56C2×(C2×D11)⋊C4C2×C4116yes—
57C2×(C2×D11)⋊C4C23116yes—
58C2×(C2×D11)⋊C4C23116yes—
59C2×(C2×D11)⋊C4C2318yes—
60C2×C4⋊Dic11—28no—
61C2×C4⋊Dic11C2×C418yes—
62C2×C4⋊Dic11C2318yes—
63C2×C4⋊Dic11C2314yes—
64C2×C4×Dic11—28no—
65C2×C4×Dic11—48no—
66C2×C4×Dic11C2318yes—
67C2×C4×Dic11C23116yes—
68C4×D44C2×C4164yescomplemented
69C11×#95C2318yes—
70C11×#95C2318yes—
71C11⋊#95C2314yes—
72C11⋊#95C23116yes—
73C11⋊#95C2314yes—
74C2×#2357—111nomaximal, Sylow
75C24×C11C2411yescharacteristic
76C23×D11—28no—
77C23×D11—24no—
78C23×D11—24no—
79C23×D11—28no—
80C23×D11C22×C418yes—
81C23×D11C2414yes—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—28no—
85C22×C4×C11—28no—
86C22×C4×C11—28no—
87C22×C4×C11C22×C414yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C22×C414yes—
90C22×C4×C11#4114yes—
91C22×C4×C11#4114yes—
92C22×C4×C11C2418yes—
93C22×C4×C11C2412yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2412yes—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—28no—
101C22×Dic11—24no—
102C22×Dic11C22×C418yes—
103C22×Dic11#4118yes—
104C22×Dic11C2414yes—
105C22×Dic11C2414yes—
106C22×Dic11C2414yes—
107C2×D44—232no—
108C2×D44—28no—
109C2×D44—28no—
110C2×D44C22×C4116yes—
111C2×C4×D11—432no—
112C2×C4×D11—416no—
113C2×C4×D11C22×C4132yes—
114C11×C4⋊C4—216no—
115C42×C11C22×C4116yes—
116(C2×D11)⋊C4—232no—
117(C2×D11)⋊C4—416no—
118(C2×D11)⋊C4C22×C4132yes—
119C4⋊Dic11—216no—
120C4⋊Dic11C22×C4116yes—
121C4×Dic11—216no—
122C4×Dic11—416no—
123C22×C4×D4—111no—
124#2357—1116no—
125C2×#390—112no—
126C2×#388—114no—
127C2×#382D1111yescharacteristic, complemented
128C2×#381—112no—
129C2×C4×C4⋊C4—111no—
130C2×C4×C4⋊C4—112no—
131C2×C4×C22⋊C4—112no—
132C23×C11C23×C412yes—
133C23×C11C2×#4112yes—
134C23×C11C2×#4112yes—
135C23×C11C2×#4114yes—
136C23×C11H(5,𝔽2)14yes—
137C23×C11C2511yescharacteristic
138C22×D11—216no—
139C22×D11—216no—
140C22×D11—216no—
141C22×D11—28no—
142C22×D11—24no—
143C22×D11—24no—
144C22×D11—28no—
145C22×D11—416no—
146C22×D11—416no—
147C22×D11C23×C418yes—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
154C2×C4×C11—28no—
155C2×C4×C11—416no—
156C2×C4×C11#117116yes—
157C2×C4×C11C23×C414yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C414yes—
160C2×C4×C11C2×#4114yes—
161C2×C4×C11C2×#4114yes—
162C2×Dic11—216no—
163C2×Dic11—216no—
164C2×Dic11—24no—
165C2×Dic11—24no—
166C2×Dic11—28no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—48no—
171C2×Dic11C23×C418yes—
172C2×Dic11C2×#4118yes—
173D44—232no—
174C4×D11—432no—
175C23×D4—111no—
176C24×C4—112no—
177C2×C4×D4—118no—
178C2×C4×D4—1116no—
179C22×C4⋊C4—111no—
180C22×C4⋊C4—112no—
181C22×C4⋊C4C2×D1112yes—
182C22×C22⋊C4—112no—
183C22×C22⋊C4—114no—
184C22×C22⋊C4—114no—
185C22×C42—112no—
186C22×C42—114no—
187C22×C42C2×D1111yescharacteristic
188#390—1116no—
189#388—1132no—
190#382C2×D1118yescomplemented
191#381—1116no—
192C4×C4⋊C4—1116no—
193C4×C4⋊C4—118no—
194C4×C22⋊C4—1116no—
195C2×#95—111no—
196C2×#95—111no—
197C2×#95—114no—
198C2×#95C2×D1112yes—
199C2×#95C2×D1112yes—
200C22×C11C2×#11714yes—
201C22×C11C4×#4114yes—
202C22×C11#51814yes—
203C22×C11#55318yes—
204C22×C11#55918yes—
205C22×C11C24×C411yescharacteristic
206C22×C11C22×#4111yescharacteristic
207C22×C11C22×#4111yescharacteristic
208C22×C11C22×#4112yes—
209C22×C11C2×H(5,𝔽2)12yes—
210C2×D11—28no—
211C2×D11—28no—
212C2×D11—28no—
213C2×D11—432no—
214C2×D11—48no—
215C2×D11—48no—
216C4×C11—24no—
217C4×C11—24no—
218C4×C11—48no—
219C4×C11C2×#11718yes—
220Dic11—28no—
221Dic11—28no—
222Dic11—44no—
223C25—112no—
224C22×D4—118no—
225C22×D4—114no—
226C22×D4—224no—
227C22×D4—224no—
228C23×C4—112no—
229C23×C4—112no—
230C23×C4—1116no—
231C23×C4—118no—
232C23×C4—112no—
233C23×C4—448no—
234C23×C4C22×D1114yes—
235C23×C4C22×D1111yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C23×C4C22×D1111yescharacteristic
238C4×D4—1164no—
239C2×C4⋊C4—28no—
240C2×C4⋊C4—118no—
241C2×C4⋊C4—114no—
242C2×C4⋊C4—118no—
243C2×C4⋊C4—228no—
244C2×C4⋊C4C22×D1118yes—
245C2×C22⋊C4—1116no—
246C2×C22⋊C4—118no—
247C2×C22⋊C4—1116no—
248C2×C22⋊C4—1116no—
249C2×C22⋊C4—2216no—
250C2×C22⋊C4—448no—
251C2×C42—118no—
252C2×C42—1116no—
253C2×C42—228no—
254C2×C42—448no—
255C2×C42C4×D1118yes—
256C2×C42C22×D1114yes—
257#95—114no—
258#95—114no—
259#95—1116no—
260#95C22×D1118yes—
261#95C22×D1118yes—
262C2×C11#235718yescomplemented
263C2×C11C22×#11711yescharacteristic
264C2×C11C2×C4×#4111yescharacteristic
265C2×C11C2×#51811yescharacteristic
266C2×C11C2×#55312yes—
267C2×C11C2×#55912yes—
268D11—48no—
269C24—118no—
270C24—114no—
271C24—224no—
272C24—224no—
273C24—228no—
274C24—228no—
275C24C23×D1111yescharacteristic
276C2×D4—1116no—
277C2×D4—2232no—
278C2×D4—228no—
279C2×D4—228no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—28no—
285C22×C4—118no—
286C22×C4—118no—
287C22×C4—114no—
288C22×C4—114no—
289C22×C4—1132no—
290C22×C4—114no—
291C22×C4—224no—
292C22×C4—224no—
293C22×C4—228no—
294C22×C4—224no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—4432no—
298C22×C4—4416no—
299C22×C4C2×C4×D1114yes—
300C22×C4C2×C4×D1114yes—
301C22×C4C2×C4×D1114yes—
302C22×C4#434114yes—
303C22×C4#434314yes—
304C22×C4C23×D1118yes—
305C22×C4C23×D1112yes—
306C22×C4C23×D1112yes—
307C22×C4C23×D1112yes—
308C4⋊C4—216no—
309C4⋊C4—1116no—
310C4⋊C4—2216no—
311C22⋊C4—1132no—
312C22⋊C4—2232no—
313C22⋊C4—4416no—
314C42—2216no—
315C42—4416no—
316C42C2×C4×D11116yes—
317C11C2×#235711yescharacteristic, complemented, Sylow
318C23—118no—
319C23—2216no—
320C23—2216no—
321C23—2216no—
322C23—224no—
323C23—224no—
324C23—228no—
325C23—228no—
326C23—4416no—
327C23—4416no—
328C23C22×C4×D1112yes—
329C23C2×#434112yes—
330C23C2×#434312yes—
331C23#41×D1114yes—
332C23#6704214yes—
333C23C24×D1111yescharacteristic
334D4—2232no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—28no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—416no—
343C2×C4—118no—
344C2×C4—118no—
345C2×C4—2216no—
346C2×C4—224no—
347C2×C4—224no—
348C2×C4—228no—
349C2×C4—2216no—
350C2×C4—224no—
351C2×C4—224no—
352C2×C4—224no—
353C2×C4—4432no—
354C2×C4—448no—
355C2×C4#66945116yes—
356C2×C4C22×C4×D1114yes—
357C2×C4C22×C4×D1114yes—
358C2×C4C22×C4×D1114yes—
359C2×C4C2×#434114yes—
360C2×C4C2×#434314yes—
361C22—228no—
362C22—228no—
363C22—228no—
364C22—448no—
365C22—448no—
366C22—4432no—
367C22C2×#6694514yes—
368C22#1062305214yes—
369C22#1062305314yes—
370C22#1062321218yes—
371C22#1062322618yes—
372C22C23×C4×D1111yescharacteristic
373C22C22×#434111yescharacteristic
374C22C22×#434311yescharacteristic
375C22C2×#41×D1112yes—
376C22C2×#6704212yes—
377C4—24no—
378C4—24no—
379C4—48no—
380C4—228no—
381C4—228no—
382C4—444no—
383C4C2×#6694518yes—
384C2—448no—
385C2#1307159118yesdirect product factor
386C2C22×#6694511yescharacteristic
387C2C2×#1062305311yescharacteristic
388C2C2×#1062305211yescharacteristic
389C2C2×#1062322612yes—
390C2C2×#1062321212yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#382C2
socleC24×C11C24
prime radicalC23×D44C22
cosocleC23×C11C25
hypercenterC2×#382D11
hypocenterC11C2×#2357
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #13071591C2direct (N × H)
4. C2×#10622283C2semidirect
5. C2×#10622277C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. C2×C4×C4⋊Dic11C2semidirect
8. C2×#10622279C2semidirect
9. C2×C11×#382C2semidirect
21. C2×C4×D44C4semidirect
23. C11×#382C22semidirect
30. C4⋊C4×Dic11C22semidirect
31. C4×C4⋊Dic11C22semidirect
32. #10622283C22semidirect
33. #10622279C22semidirect
34. #10622277C22semidirect
68. C4×D44C2×C4semidirect
127. C2×#382D11semidirect
190. #382C2×D11semidirect
262. C2×C11#2357semidirect
317. C11C2×#2357semidirect
385. C2#13071591direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
#130715912
C2×#106226012
C2×#106222832
C2×#106222772
C2×C4⋊C4×Dic112
C2×C4×C4⋊Dic112
C2×#106222792
C2×C11×#3822
C2×#235711