Finite Group Databasebeta

← C2×#13070057 #14782664

Subgroups — C2×#13070057 #14782664

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622579C212yesmaximal
2C2×#10622723C211yesmaximal, characteristic
3#13070057C218yesmaximal, direct product factor
4C2×#10622168C212yesmaximal, complemented
5C2×#10622190C211yesmaximal, characteristic, complemented
6C22×C11×#107C211yesmaximal, characteristic, complemented
7C22×#4339C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×#4318C2212yes—
11C22×#4318C2211yescharacteristic
12C2×C11×#107—22no—
13C2×C11×#107—22no—
14C2×C11×#107C2214yescomplemented
15#10622723—22no—
16#10622723C2214yes—
17C2×(C2×D11)⋊C8—22no—
18C2×#66874—22no—
19#10622579—24no—
20#10622579C2218yes—
21C2×#66873—22no—
22#10622190C2214yescomplemented
23#10622168C2218yescomplemented
24C23×C4×C11—22no—
25C23×C4×C11C2311yescharacteristic
26C22×C22⋊D11—21no—
27C2×#4339—21no—
28C2×#4339—21no—
29C2×#4339—24no—
30C2×#4339—24no—
31C2×#4339D412yes—
32C2×#4339C2312yes—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×Dic22D411yescharacteristic
36C22×C8×C11—24no—
37C22×C8×C11D412yes—
38C22×C8×C11D412yes—
39C22×C8×C11C2312yes—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4C2314yes—
46C2×#4318—21no—
47C2×#4318—22no—
48C2×#4318—24no—
49C2×#4318—24no—
50C2×#4318—24no—
51C2×#4318C2312yes—
52C2×#4318C2314yes—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—22no—
55C11×#107—28no—
56(C2×D11)⋊C8—28no—
57#66874—28no—
58#66873—28no—
59C2×#2078—111nomaximal, Sylow
60C24×C11#4111yescharacteristic
61C23×D11—21no—
62C22×C4×C11—24no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—84no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4114yes—
72C22×C4×C11#4114yes—
73C22×C4×C11C2411yescharacteristic
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—44no—
77C22×Dic11—21no—
78#4339—28no—
79#4339—24no—
80#4339—24no—
81#4339—42no—
82#4339—42no—
83#4339—44no—
84C2×D44—21no—
85C2×D44—24no—
86C2×D44C2×D412yes—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×Dic22—21no—
92C2×Dic22—24no—
93C2×Dic22C2×D412yes—
94C2×C8×C11—24no—
95C2×C8×C11—24no—
96C2×C8×C11—24no—
97C2×C8×C11C2×D414yes—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102#4318—24no—
103#4318—24no—
104#4318—24no—
105#4318—44no—
106#4318—42no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—44no—
110C2×C11⋊C8—42no—
111C22×#107D1111yescharacteristic, complemented
112C2×#417—112no—
113C2×#408—111no—
114#2078—118no—
115C2×#343—112no—
116C2×#341—111no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11#12111yescharacteristic
120C23×C11#12111yescharacteristic
121C23×C11#12614yes—
122C23×C11C2×#4111yescharacteristic
123C22×D11—22no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—84no—
129C2×C4×C11—84no—
130C2×C4×C11—84no—
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12314yes—
134C2×C4×C11#12314yes—
135C2×C4×C11#12312yes—
136C2×C4×C11#12312yes—
137C2×C4×C11#12412yes—
138C2×C4×C11#12412yes—
139C2×C4×C11#12614yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×C4×C11C2×#4112yes—
143C2×C4×C11C2×#4112yes—
144C22⋊D11—44no—
145C22⋊D11—44no—
146C2×Dic11—22no—
147C2×Dic11—42no—
148D44—24no—
149D44—42no—
150C4×D11—42no—
151C4×D11—42no—
152C4×D11—44no—
153Dic22—24no—
154Dic22—42no—
155C8×C11—24no—
156C11⋊C8—44no—
157C11⋊C8—42no—
158C22×#41—111no—
159C22×M16—111no—
160C22×M16—112no—
161C23×C8C2×D1111yescharacteristic
162C22×C4⋊C4C2×D1112yes—
163C2×#107—22no—
164C2×#107—22no—
165C2×#107C2×D1114yescomplemented
166#417—118no—
167#417—224no—
168C2×#103—222no—
169C2×#102—222no—
170#408—114no—
171#408—222no—
172C2×C22⋊C8—222no—
173#343—118no—
174#341—114no—
175C22×C11—28no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39712yes—
181C22×C11#39712yes—
182C22×C11#47212yes—
183C22×C11#47312yes—
184C22×C11C2×#12111yescharacteristic
185C22×C11C2×#12612yes—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—84no—
190C4×C11—84no—
191C4×C11#39712yes—
192C4×C11#39712yes—
193C4×C11C2×#12312yes—
194C4×C11C2×#12311yescharacteristic
195C4×C11C2×#12411yescharacteristic
196Dic11—42no—
197C2×#41—112no—
198C2×#41—112no—
199C2×#41—221no—
200C2×#41—221no—
201C2×#41—224no—
202C2×#41—224no—
203C22×Q8—111no—
204C22×D4—111no—
205C22×D4—221no—
206C23×C4—22no—
207C23×C4—221no—
208C23×C4C22×D1111yescharacteristic
209C2×M16—114no—
210C2×M16—112no—
211C2×M16—222no—
212C2×M16—221no—
213C2×M16—224no—
214C2×M16—224no—
215C2×M16—224no—
216C22×C8—24no—
217C22×C8—222no—
218C22×C8—221no—
219C22×C8C22⋊D1112yes—
220C22×C8C22⋊D1112yes—
221C22×C8C22×D1112yes—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C22×D1114yes—
228#107—28no—
229#103—228no—
230#102—228no—
231C22⋊C8—228no—
232C2×C11—22no—
233C2×C11—22no—
234C2×C11#207814yescomplemented
235C2×C11C2×#39711yescharacteristic
236C2×C11C2×#47211yescharacteristic
237C2×C11C2×#47311yescharacteristic
238D11—82no—
239C24—221no—
240C24#434111yescharacteristic
241#41—228no—
242#41—224no—
243#41—224no—
244#41—444no—
245#41—442no—
246#41—442no—
247C2×Q8—112no—
248C2×Q8—221no—
249C2×Q8—224no—
250C2×D4—112no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—224no—
254C2×D4—221no—
255C2×D4—444no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—84no—
260C22×C4—221no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4#433914yes—
266C22×C4D4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4#434111yescharacteristic
269C22×C4#434314yes—
270C22×C4C2×C22⋊D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C23×D1111yescharacteristic
273M16—224no—
274M16—224no—
275M16—224no—
276M16—444no—
277M16—442no—
278C2×C8—24no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—224no—
282C2×C8—222no—
283C2×C8—444no—
284C2×C8—442no—
285C2×C8C2×C22⋊D1114yes—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C11C2×#207811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—222no—
294C23—442no—
295C23—442no—
296C23—442no—
297C23#6695114yes—
298C23#6699111yescharacteristic
299C23#6699111yescharacteristic
300C23C2×#434111yescharacteristic
301Q8—224no—
302Q8—442no—
303D4—224no—
304D4—444no—
305D4—444no—
306D4—442no—
307C2×C4—44no—
308C2×C4—84no—
309C2×C4—84no—
310C2×C4—84no—
311C2×C4—222no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—444no—
316C2×C4#6694714yes—
317C2×C4#6694714yes—
318C2×C4#6695114yes—
319C2×C4#6698212yes—
320C2×C4#6698212yes—
321C2×C4#6699111yescharacteristic
322C2×C4#6699111yescharacteristic
323C2×C4#6700012yes—
324C2×C4#6700012yes—
325C2×C4C2×#433912yes—
326C2×C4C2×D4×D1111yescharacteristic
327C2×C4C2×#434312yes—
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—24no—
330C8—444no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—28no—
337C22—442no—
338C22—442no—
339C22—442no—
340C22—884no—
341C22#1062260612yes—
342C22#1062260612yes—
343C22#1062277312yes—
344C22#1062280512yes—
345C22C2×#6695112yes—
346C22C2×#6699111yescharacteristic
347C4—84no—
348C4—442no—
349C4#1062260612yes—
350C4#1062260612yes—
351C4C2×#6694712yes—
352C4C2×#6698211yescharacteristic
353C4C2×#6700011yescharacteristic
354C2—22no—
355C2—22no—
356C2—882no—
357C2#1307005714yesdirect product factor
358C2C2×#1062260611yescharacteristic
359C2C2×#1062277311yescharacteristic
360C2C2×#1062280511yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#107C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC22×#107D11
hypocenterC11C2×#2078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #13070057C2direct (N × H)
4. C2×#10622168C2semidirect
5. C2×#10622190C2semidirect
6. C22×C11×#107C2semidirect
14. C2×C11×#107C22semidirect
22. #10622190C22semidirect
23. #10622168C22semidirect
111. C22×#107D11semidirect
165. C2×#107C2×D11semidirect
234. C2×C11#2078semidirect
290. C11C2×#2078semidirect
357. C2#13070057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225792
C2×#106227232
#130700572
C2×#106221682
C2×#106221902
C22×C11×#1072
C2×#207811