Finite Group Databasebeta

← C2×#13072905 #14923594

Subgroups — C2×#13072905 #14923594

Order 2816.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic
3#13072905C2116yesmaximal, direct product factor
4C2×#10622272C212yesmaximal, complemented
5C2×#10622274C212yesmaximal, complemented
6C2×#10622266C214yesmaximal, complemented
7C2×#10622563C212yesmaximal
8C2×#10622556C212yesmaximal
9C2×C11×#381C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C2×#66979—28no—
16C2×#66979C2218yes—
17C22×C4⋊Dic11C2214yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—28no—
21C22×Dic11⋊C4C2218yes—
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C11×#381C2218yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31#10622563C22116yes—
32#10622556C22116yes—
33#10622274C22116yescomplemented
34#10622272C22116yescomplemented
35#10622266C22132yescomplemented
36C25×C11C2311yescharacteristic
37C23×C4×C11—28no—
38C23×C4×C11D418yes—
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2314yes—
43C23×Dic11—24no—
44C23×Dic11—28no—
45C23×Dic11—24no—
46C23×Dic11—28no—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2314yes—
50C23×Dic11C2314yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C2×C11×C22⋊C4—28no—
54C2×C11×C22⋊C4C2318yes—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11C2318yes—
57#66979—232no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11—24no—
60C2×C4⋊Dic11—216no—
61C2×C4⋊Dic11C23116yes—
62C2×C4⋊Dic11C2314yes—
63C2×C4⋊Dic11C2314yes—
64C2×Dic11⋊C4—28no—
65C2×Dic11⋊C4—28no—
66C2×Dic11⋊C4—232no—
67C2×Dic11⋊C4C2318yes—
68C2×Dic11⋊C4C2318yes—
69C2×C4×Dic11—28no—
70C2×C4×Dic11C2318yes—
71C11×#95C2318yes—
72C11×#95C2318yes—
73C11⋊#95C23116yes—
74C11⋊#95C23116yes—
75C11⋊#95C23116yes—
76C2×#2484—111nomaximal, Sylow
77C24×C11—24no—
78C24×C11—24no—
79C24×C11C2×D414yes—
80C24×C11#4118yes—
81C24×C11C2412yes—
82C24×C11C2411yescharacteristic
83C22×C4×C11—232no—
84C22×C4×C11—216no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—28no—
88C22×C4×C11—28no—
89C22×C4×C11—28no—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D4116yes—
93C22×C4×C11C2418yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2412yes—
96C22×Dic11—232no—
97C22×Dic11—216no—
98C22×Dic11—28no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—24no—
102C22×Dic11—28no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—28no—
106C22×Dic11—216no—
107C22×Dic11—28no—
108C22×Dic11—28no—
109C22×Dic11—416no—
110C22×Dic11#4118yes—
111C22×Dic11C2414yes—
112C22×Dic11C2414yes—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C11×C22⋊C4—216no—
116C22⋊Dic11—216no—
117C4⋊Dic11—232no—
118C4⋊Dic11—28no—
119C4⋊Dic11—28no—
120Dic11⋊C4—216no—
121Dic11⋊C4—216no—
122C4×Dic11—216no—
123C22×#117—111no—
124C23×C4⋊C4—111no—
125#2484—1116no—
126C2×#400—112no—
127C2×#398—112no—
128C2×#387—114no—
129C2×#385—112no—
130C2×#381—112no—
131C2×#381D1111yescharacteristic
132C23×C11—28no—
133C23×C11—28no—
134C23×C11—232no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11#123116yes—
138C23×C11C22×D414yes—
139C23×C11C22×D412yes—
140C23×C11C2×#4118yes—
141C23×C11C2×#4114yes—
142C23×C11C2×#4114yes—
143C23×C112−1+414yes—
144C23×C11C2511yescharacteristic
145C2×C4×C11—232no—
146C2×C4×C11—28no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—416no—
154C2×C4×C11C22×D414yes—
155C2×C4×C11C22×D414yes—
156C2×Dic11—232no—
157C2×Dic11—216no—
158C2×Dic11—24no—
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×Dic11—48no—
168C2×Dic11—48no—
169C2×Dic11—48no—
170C2×Dic11C2×#4118yes—
171C24×C4—111no—
172C24×C4—111no—
173C24×C4C2×D1111yescharacteristic
174C2×#117—118no—
175C2×#117—228no—
176C22×C4⋊C4—112no—
177C22×C4⋊C4—118no—
178C22×C4⋊C4—112no—
179C22×C4⋊C4—111no—
180C22×C4⋊C4—114no—
181C22×C4⋊C4—111no—
182C22×C4⋊C4—228no—
183C22×C22⋊C4—112no—
184C22×C22⋊C4C2×D1112yes—
185C22×C42—112no—
186#400—1116no—
187#398—1116no—
188#387—1132no—
189#385—1116no—
190#381—1116no—
191#381C2×D1118yes—
192C2×#95—114no—
193C2×#95—114no—
194C2×#95—114no—
195C2×#95C2×D1112yes—
196C2×#95C2×D1112yes—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—216no—
200C22×C11—232no—
201C22×C11C2×#12318yes—
202C22×C11C2×#12314yes—
203C22×C11#52514yes—
204C22×C11#53614yes—
205C22×C11#552116yes—
206C22×C11C23×D411yescharacteristic
207C22×C11C22×#4112yes—
208C22×C11C22×#4112yes—
209C22×C11C2×2−1+412yes—
210C4×C11—24no—
211C4×C11—24no—
212C4×C11—48no—
213Dic11—28no—
214Dic11—44no—
215Dic11—44no—
216Dic11—44no—
217C25C22×D1111yescharacteristic
218C23×C4—28no—
219C23×C4—112no—
220C23×C4—114no—
221C23×C4—114no—
222C23×C4—112no—
223C23×C4—112no—
224C23×C4—112no—
225C23×C4—228no—
226C23×C4—224no—
227C23×C4—224no—
228C23×C4—228no—
229C23×C4D4418yes—
230C23×C4C22×D1114yes—
231C23×C4C22×D1114yes—
232C23×C4C22×D1111yescharacteristic
233C23×C4C22×D1111yescharacteristic
234#117—2232no—
235C2×C4⋊C4—118no—
236C2×C4⋊C4—118no—
237C2×C4⋊C4—114no—
238C2×C4⋊C4—114no—
239C2×C4⋊C4—1116no—
240C2×C4⋊C4—2216no—
241C2×C4⋊C4—228no—
242C2×C4⋊C4—228no—
243C2×C4⋊C4—2232no—
244C2×C4⋊C4—224no—
245C2×C4⋊C4—224no—
246C2×C22⋊C4—28no—
247C2×C22⋊C4—118no—
248C2×C22⋊C4—228no—
249C2×C22⋊C4C22×D1118yes—
250C2×C42—118no—
251C2×C42—228no—
252#95—1116no—
253#95—1116no—
254#95—1116no—
255#95C22×D1118yes—
256#95C22×D1118yes—
257C2×C11—28no—
258C2×C11#248418yescomplemented
259C2×C11C22×#12311yescharacteristic
260C2×C11C2×#52511yescharacteristic
261C2×C11C2×#53611yescharacteristic
262C2×C11C2×#55214yes—
263C24—24no—
264C24—24no—
265C24C2×D4414yes—
266C24#434118yes—
267C24C23×D1112yes—
268C24C23×D1111yescharacteristic
269C22×C4—232no—
270C22×C4—216no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—118no—
277C22×C4—114no—
278C22×C4—114no—
279C22×C4—114no—
280C22×C4—114no—
281C22×C4—2216no—
282C22×C4—2232no—
283C22×C4—228no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—228no—
289C22×C4—224no—
290C22×C4—2216no—
291C22×C4—228no—
292C22×C4—228no—
293C22×C4—228no—
294C22×C4—4416no—
295C22×C4C2×D4414yes—
296C22×C4C2×D4414yes—
297C22×C4C2×D44116yes—
298C22×C4C23×D1118yes—
299C22×C4C23×D1112yes—
300C22×C4C23×D1112yes—
301C4⋊C4—2232no—
302C4⋊C4—2216no—
303C4⋊C4—2216no—
304C4⋊C4—228no—
305C4⋊C4—228no—
306C22⋊C4—216no—
307C22⋊C4—2216no—
308C42—2216no—
309C11C2×#248411yescharacteristic, complemented, Sylow
310C23—28no—
311C23—28no—
312C23—232no—
313C23—24no—
314C23—24no—
315C23#66939116yes—
316C23C22×D4414yes—
317C23C22×D4412yes—
318C23C2×#434118yes—
319C23C2×#434114yes—
320C23#41×D1114yes—
321C23#6704314yes—
322C23C24×D1111yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—416no—
332C2×C4—118no—
333C2×C4—2232no—
334C2×C4—2216no—
335C2×C4—224no—
336C2×C4—224no—
337C2×C4—224no—
338C2×C4—224no—
339C2×C4—224no—
340C2×C4—228no—
341C2×C4—228no—
342C2×C4—228no—
343C2×C4—4416no—
344C2×C4—448no—
345C2×C4—448no—
346C2×C4—448no—
347C2×C4C22×D4414yes—
348C2×C4C22×D4414yes—
349C22—24no—
350C22—232no—
351C22—216no—
352C22—24no—
353C22C2×#6693918yes—
354C22C2×#6693914yes—
355C22#1062305514yes—
356C22#1062305714yes—
357C22#10623181116yes—
358C22C23×D4411yescharacteristic
359C22C22×#434112yes—
360C22C2×#41×D1112yes—
361C22C2×#6704312yes—
362C4—24no—
363C4—24no—
364C4—48no—
365C4—228no—
366C4—444no—
367C4—444no—
368C4—444no—
369C2—28no—
370C2#1307290518yesdirect product factor
371C2C22×#6693911yescharacteristic
372C2C2×#1062305511yescharacteristic
373C2C2×#1062305711yescharacteristic
374C2C2×#1062318114yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#381C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11C2×#2484
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #13072905C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622274C2semidirect
6. C2×#10622266C2semidirect
33. #10622274C22semidirect
34. #10622272C22semidirect
35. #10622266C22semidirect
258. C2×C11#2484semidirect
309. C11C2×#2484semidirect
370. C2#13072905direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
C23×Dic11⋊C42
#130729052
C2×#106222722
C2×#106222742
C2×#106222662
C2×#106225632
C2×#106225562
C2×C11×#3812
C2×#248411