Finite Group Databasebeta

← C2×#13077182 #15617398

Subgroups — C2×#13077182 #15617398

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67001C211yesmaximal, characteristic
2C2×#41×Dic11C211yesmaximal, characteristic
3#13077182C2116yesmaximal, direct product factor
4C2×#10622732C213yesmaximal, complemented
5C2×#10622715C213yesmaximal, complemented
6C2×#10622731C213yesmaximal, complemented
7C22×Dic11⋊C8C213yesmaximal, complemented
8C22×C11×#131C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C2×C11×#131—28no—
11C2×C11×#131C2218yes—
12C22×C11×M16C2213yes—
13C23×C8×C11C2213yes—
14#41×Dic11C418yes—
15#41×Dic11C2218yes—
16C2×#67001—28no—
17C2×#67001C2218yes—
18C2×Q8×Dic11C411yescharacteristic
19C2×Q8×Dic11C411yescharacteristic
20C2×D4×Dic11C413yes—
21C2×D4×Dic11C413yes—
22C2×#66979C2213yes—
23C22×C4×Dic11C2213yes—
24C22×#4318C2213yes—
25C23×C11⋊C8C2213yes—
26#10622732C22124yescomplemented
27#10622731C22124yescomplemented
28#10622715C22124yescomplemented
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2213yes—
31C2×Dic11⋊C8C2213yes—
32C2×Dic11⋊C8C2213yes—
33C2×Dic11⋊C8C2216yes—
34C2×Dic11⋊C8C22124yescomplemented
35C2×C11×#41C2×C414yes—
36C2×C11×#41D418yes—
37C2×C11×#41Q818yes—
38C2×C11×#41C2314yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×D4×C11C2×C413yes—
41C23×C4×C11C2313yes—
42C23×Dic11C2×C413yes—
43C23×Dic11C2×C413yes—
44C11×#131—232no—
45C2×C11×M16—212no—
46C2×C11×M16C23112yes—
47C22×C8×C11—212no—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2313yes—
50C22×C8×C11C23112yes—
51C2×C22⋊Dic11C2×C416yes—
52#67001—232no—
53Q8×Dic11C2×C418yes—
54Q8×Dic11C2×C418yes—
55D4×Dic11C2×C4124yes—
56D4×Dic11C2×C4124yes—
57#66979C2×C4112yes—
58#66979C23112yes—
59C2×C4⋊Dic11C2×C413yes—
60C2×C4⋊Dic11C2×C413yes—
61C2×C4×Dic11C2×C413yes—
62C2×C4×Dic11C2×C413yes—
63C2×C4×Dic11C2×C4112yes—
64C2×C4×Dic11C23112yes—
65C2×C4×Dic11C2311yescharacteristic
66C2×C4×Dic11C2313yes—
67C2×#4318—212no—
68C2×#4318C23112yes—
69C22×C11⋊C8—212no—
70C22×C11⋊C8C23112yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2313yes—
73Dic11⋊C8C23112yes—
74Dic11⋊C8C23124yes—
75Dic11⋊C8C23112yes—
76Dic11⋊C8C2314yes—
77Dic11⋊C8C23112yes—
78C2×#2906—111nomaximal, Sylow
79C24×C11C22×C413yes—
80C11×#41C4⋊C4132yes—
81C11×#41C2×D4116yes—
82C11×#41C2×Q8116yes—
83C2×Q8×C11C4⋊C418yes—
84C2×Q8×C11C22×C414yes—
85C2×D4×C11C4⋊C4124yes—
86C2×D4×C11C22×C4112yes—
87C22×C4×C11C22×C413yes—
88C22×C4×C11C22×C416yes—
89C22×C4×C11C2×D4112yes—
90C22×C4×C11C2×Q8112yes—
91C22×C4×C11C2416yes—
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—212no—
94C22×Dic11—46no—
95C22×Dic11C22×C411yescharacteristic
96C22×Dic11C22×C413yes—
97C22×Dic11C22×C413yes—
98C22×Dic11C22×C4112yes—
99C22×Dic11C22×C4112yes—
100C22×Dic11C22×C411yescharacteristic
101C11×M16—224no—
102C2×C8×C11—22no—
103C2×C8×C11—26no—
104C2×C8×C11—224no—
105C2×C8×C11C2412yes—
106C2×C8×C11C2416yes—
107C22⋊Dic11C22×C4124yes—
108C4⋊Dic11C22×C4112yes—
109C4⋊Dic11C22×C4112yes—
110C4×Dic11C22×C412yes—
111C4×Dic11C22×C416yes—
112C4×Dic11C22×C4112yes—
113C4×Dic11C22×C4112yes—
114C4×Dic11C2412yes—
115C4×Dic11C2416yes—
116#4318—224no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—26no—
119C2×C11⋊C8—224no—
120C2×C11⋊C8C2412yes—
121C2×C11⋊C8C2416yes—
122C22×#131—111no—
123C22×#131D1111yescharacteristic
124C2×C4×#41—111no—
125#2906—1116no—
126C2×#424—113no—
127C2×#424—113no—
128C2×#423—113no—
129C22×C4⋊C8—113no—
130C23×C11—26no—
131C23×C11—26no—
132C23×C11C2×C4⋊C4112yes—
133C23×C11C23×C416yes—
134C23×C11C23×C411yescharacteristic
135Q8×C11C2×C4⋊C4116yes—
136D4×C11C2×C4⋊C4148yes—
137C2×C4×C11C2×C4⋊C4112yes—
138C2×C4×C11C2×C4⋊C4124yes—
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C23×C416yes—
141C2×C4×C11C22×D412yes—
142C2×C4×C11C22×D4112yes—
143C2×C4×C11C22×Q812yes—
144C2×C4×C11C22×Q8112yes—
145C2×C4×C11C2511yescharacteristic
146C2×Dic11—26no—
147C2×Dic11—22no—
148C2×Dic11—26no—
149C2×Dic11—224no—
150C2×Dic11—412no—
151C2×Dic11#13114yescomplemented
152C2×Dic11C23×C412yes—
153C2×Dic11C23×C416yes—
154C2×Dic11C23×C416yes—
155C2×Dic11C23×C412yes—
156C8×C11—22no—
157C8×C11—26no—
158C11⋊C8—22no—
159C11⋊C8—26no—
160C22×#41C2×D1111yescharacteristic
161C2×#131—28no—
162C2×#131—118no—
163C2×#131—228no—
164C2×#131C2×D1118yes—
165C22×M16—113no—
166C22×M16C2×D1113yes—
167C23×C8—113no—
168C23×C8C2×D1113yes—
169C4×#41—118no—
170C4×#41—118no—
171C2×C4×Q8—111no—
172C2×C4×Q8—111no—
173C2×C4×D4—113no—
174C2×C4×D4—113no—
175C2×#117—113no—
176C22×C42—113no—
177#424—1124no—
178#424—1124no—
179#423—1124no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8—113no—
182C2×C4⋊C8—113no—
183C2×C4⋊C8—113no—
184C2×C4⋊C8—1124no—
185C2×C4⋊C8—116no—
186C22×C11—224no—
187C22×C11—26no—
188C22×C11—26no—
189C22×C11C22×C4⋊C4112yes—
190C22×C11C22×C4⋊C412yes—
191C22×C11C2×#13112yes—
192C22×C11#56812yes—
193C22×C11C24×C411yescharacteristic
194C4×C11C22×C4⋊C412yes—
195C4×C11C22×C4⋊C4112yes—
196C4×C11C23×D411yescharacteristic
197C4×C11C23×Q811yescharacteristic
198Dic11—26no—
199Dic11—22no—
200Dic11—26no—
201Dic11C2×#13114yescomplemented
202C2×#41Dic2218yes—
203C2×#41C4×D1114yes—
204C2×#41C22⋊D1118yes—
205C2×#41C22×D1114yes—
206C22×Q8C4×D1111yescharacteristic
207C22×D4C4×D1113yes—
208C23×C4—113no—
209C23×C4—113no—
210C23×C4C22×D1113yes—
211#131—232no—
212#131—2232no—
213C2×M16—212no—
214C2×M16—1112no—
215C2×M16—2212no—
216C2×M16C22×D11112yes—
217C22×C8—212no—
218C22×C8—1112no—
219C22×C8—111no—
220C22×C8—113no—
221C22×C8—2212no—
222C22×C8C22×D11112yes—
223C22×C8C22×D1111yescharacteristic
224C22×C8C22×D1113yes—
225C4×Q8—118no—
226C4×Q8—118no—
227C4×D4—1124no—
228C4×D4—1124no—
229#117—1112no—
230#117—1112no—
231C2×C4⋊C4—113no—
232C2×C4⋊C4—113no—
233C2×C22⋊C4—116no—
234C2×C42—113no—
235C2×C42—113no—
236C2×C42—1112no—
237C2×C42—1112no—
238C2×C42—113no—
239C2×C42—111no—
240C4⋊C8—114no—
241C4⋊C8—1112no—
242C4⋊C8—1112no—
243C4⋊C8—1112no—
244C4⋊C8—1124no—
245C2×C11—212no—
246C2×C11#290614yescomplemented
247C2×C11C23×C4⋊C411yescharacteristic
248C2×C11C22×#13111yescharacteristic
249C2×C11C2×#56811yescharacteristic
250C24C2×C4×D1113yes—
251#41Dic11⋊C4132yes—
252#41C2×Dic22116yes—
253#41C2×C22⋊D11116yes—
254C2×Q8Dic11⋊C418yes—
255C2×Q8C2×C4×D1114yes—
256C2×D4Dic11⋊C4124yes—
257C2×D4C2×C4×D11112yes—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—113no—
261C22×C4—113no—
262C22×C4—1112no—
263C22×C4—1112no—
264C22×C4—2212no—
265C22×C4—446no—
266C22×C4C2×Dic22112yes—
267C22×C4C2×C4×D1113yes—
268C22×C4C2×C4×D1116yes—
269C22×C4C2×C22⋊D11112yes—
270C22×C4C23×D1116yes—
271C22×C4C23×D1111yescharacteristic
272M16—224no—
273M16—2224no—
274C2×C8—22no—
275C2×C8—26no—
276C2×C8—224no—
277C2×C8—112no—
278C2×C8—116no—
279C2×C8—222no—
280C2×C8—226no—
281C2×C8—2224no—
282C2×C8C23×D1112yes—
283C2×C8C23×D1116yes—
284C4⋊C4—1112no—
285C4⋊C4—1112no—
286C22⋊C4—1124no—
287C42—112no—
288C42—116no—
289C42—1112no—
290C42—1112no—
291C42—112no—
292C42—116no—
293C11C2×#290611yescharacteristic, complemented, Sylow
294C23—26no—
295C23—26no—
296C23C2×Dic11⋊C4112yes—
297C23C22×C4×D1116yes—
298C23C22×C4×D1111yescharacteristic
299Q8C2×Dic11⋊C4116yes—
300D4C2×Dic11⋊C4148yes—
301C2×C4—114no—
302C2×C4—112no—
303C2×C4—112no—
304C2×C4—116no—
305C2×C4—116no—
306C2×C4—2224no—
307C2×C4—226no—
308C2×C4—222no—
309C2×C4—226no—
310C2×C4—4412no—
311C2×C4C2×Dic11⋊C4112yes—
312C2×C4C2×Dic11⋊C4124yes—
313C2×C4C22×Dic2212yes—
314C2×C4C22×Dic22112yes—
315C2×C4C22×C4×D1111yescharacteristic
316C2×C4C22×C4×D1116yes—
317C2×C4C22×C22⋊D1112yes—
318C2×C4C22×C22⋊D11112yes—
319C2×C4C24×D1111yescharacteristic
320C8—22no—
321C8—26no—
322C8—222no—
323C8—226no—
324C22—26no—
325C22—26no—
326C22—224no—
327C22D11×#13112yes—
328C22#1062328112yes—
329C22C22×Dic11⋊C4112yes—
330C22C22×Dic11⋊C412yes—
331C22C23×C4×D1111yescharacteristic
332C4—114no—
333C4—226no—
334C4—222no—
335C4—226no—
336C4C22×Dic11⋊C412yes—
337C4C22×Dic11⋊C4112yes—
338C4C23×Dic2211yescharacteristic
339C4C23×C22⋊D1111yescharacteristic
340C2—212no—
341C2#1307718214yesdirect product factor
342C2C23×Dic11⋊C411yescharacteristic
343C2C2×D11×#13111yescharacteristic
344C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×#131C2
socleC23×C11C23×C4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC22×#131D11
hypocenterC11C2×#2906
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
3. #13077182C2direct (N × H)
4. C2×#10622732C2semidirect
5. C2×#10622715C2semidirect
6. C2×#10622731C2semidirect
7. C22×Dic11⋊C8C2semidirect
26. #10622732C22semidirect
27. #10622731C22semidirect
28. #10622715C22semidirect
34. C2×Dic11⋊C8C22semidirect
151. C2×Dic11#131semidirect
201. Dic11C2×#131semidirect
246. C2×C11#2906semidirect
293. C11C2×#2906semidirect
341. C2#13077182direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670012
C2×#41×Dic112
#130771822
C2×#106227322
C2×#106227152
C2×#106227312
C22×Dic11⋊C82
C22×C11×#1312
C2×#290611