Finite Group Databasebeta

← C2×#13070062 #14782670

Subgroups — C2×#13070062 #14782670

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622579C212yesmaximal
2C2×#10622723C211yesmaximal, characteristic
3#13070062C218yesmaximal, direct product factor
4C2×#10622168C212yesmaximal, complemented
5C2×#10622190C211yesmaximal, characteristic, complemented
6C22×C11×#106C211yesmaximal, characteristic, complemented
7C22×#4339C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×#4318C2212yes—
11C22×#4318C2211yescharacteristic
12C2×C11×#106—22no—
13C2×C11×#106—22no—
14C2×C11×#106C2214yescomplemented
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×#106—28no—
56(C2×D11)⋊C8—28no—
57#66874—28no—
58#66873—28no—
59C2×#2079—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×#106D1111yescharacteristic, complemented
112C2×#417—112no—
113C2×#408—111no—
114#2079—118no—
115C2×#343—112no—
116C2×#341—111no—
117C23×C11—24no—
118C23×C11#12111yescharacteristic
119C23×C11#12111yescharacteristic
120C23×C11#12614yes—
121C23×C11C2×#4111yescharacteristic
122C22×D11—22no—
123C22×D11—42no—
124C22×D11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—84no—
127C2×C4×C11—84no—
128C2×C4×C11—84no—
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12314yes—
132C2×C4×C11#12314yes—
133C2×C4×C11#12312yes—
134C2×C4×C11#12312yes—
135C2×C4×C11#12412yes—
136C2×C4×C11#12412yes—
137C2×C4×C11#12614yes—
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C2×#4112yes—
141C2×C4×C11C2×#4112yes—
142C22⋊D11—44no—
143C22⋊D11—44no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146D44—24no—
147D44—42no—
148C4×D11—42no—
149C4×D11—42no—
150C4×D11—44no—
151Dic22—24no—
152Dic22—42no—
153C8×C11—24no—
154C11⋊C8—44no—
155C11⋊C8—42no—
156C22×#41—111no—
157C22×M16—111no—
158C22×M16—112no—
159C23×C8C2×D1111yescharacteristic
160C22×C4⋊C4C2×D1112yes—
161C2×#106—22no—
162C2×#106—22no—
163C2×#106C2×D1114yescomplemented
164#417—118no—
165#417—224no—
166C2×#103—222no—
167C2×#102—222no—
168#408—114no—
169#408—222no—
170C2×C22⋊C8—222no—
171#343—118no—
172#341—114no—
173C22×C11—28no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11#39712yes—
177C22×C11#39712yes—
178C22×C11#47114yes—
179C22×C11C2×#12111yescharacteristic
180C22×C11C2×#12612yes—
181C2×D11—42no—
182C2×D11—44no—
183C2×D11—84no—
184C4×C11—84no—
185C4×C11#39712yes—
186C4×C11#39712yes—
187C4×C11C2×#12312yes—
188C4×C11C2×#12311yescharacteristic
189C4×C11C2×#12411yescharacteristic
190Dic11—42no—
191C2×#41—112no—
192C2×#41—112no—
193C2×#41—221no—
194C2×#41—221no—
195C2×#41—224no—
196C2×#41—224no—
197C22×Q8—111no—
198C22×D4—111no—
199C22×D4—221no—
200C23×C4—22no—
201C23×C4—221no—
202C23×C4C22×D1111yescharacteristic
203C2×M16—114no—
204C2×M16—112no—
205C2×M16—222no—
206C2×M16—221no—
207C2×M16—224no—
208C2×M16—224no—
209C2×M16—224no—
210C22×C8—24no—
211C22×C8—222no—
212C22×C8—221no—
213C22×C8C22⋊D1112yes—
214C22×C8C22⋊D1112yes—
215C22×C8C22×D1112yes—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4C22×D1114yes—
222#106—28no—
223#103—228no—
224#102—228no—
225C22⋊C8—228no—
226C2×C11—22no—
227C2×C11—22no—
228C2×C11#207914yescomplemented
229C2×C11C2×#39711yescharacteristic
230C2×C11C2×#47112yes—
231D11—82no—
232C24—221no—
233C24#434111yescharacteristic
234#41—228no—
235#41—224no—
236#41—224no—
237#41—444no—
238#41—442no—
239#41—442no—
240C2×Q8—112no—
241C2×Q8—221no—
242C2×Q8—224no—
243C2×D4—112no—
244C2×D4—222no—
245C2×D4—222no—
246C2×D4—224no—
247C2×D4—221no—
248C2×D4—444no—
249C22×C4—24no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—84no—
253C22×C4—221no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4#433914yes—
259C22×C4D4×D1111yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4#434314yes—
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C23×D1111yescharacteristic
266M16—224no—
267M16—224no—
268M16—224no—
269M16—444no—
270M16—442no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—224no—
275C2×C8—222no—
276C2×C8—444no—
277C2×C8—442no—
278C2×C8C2×C22⋊D1114yes—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C11C2×#207911yescharacteristic, complemented, Sylow
284C23—24no—
285C23—222no—
286C23—444no—
287C23—442no—
288C23#6695114yes—
289C23#6699111yescharacteristic
290C23#6699111yescharacteristic
291C23C2×#434111yescharacteristic
292Q8—224no—
293Q8—442no—
294D4—224no—
295D4—444no—
296D4—444no—
297D4—442no—
298C2×C4—44no—
299C2×C4—84no—
300C2×C4—84no—
301C2×C4—84no—
302C2×C4—222no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—444no—
307C2×C4#6694714yes—
308C2×C4#6694714yes—
309C2×C4#6695114yes—
310C2×C4#6698212yes—
311C2×C4#6698212yes—
312C2×C4#6699111yescharacteristic
313C2×C4#6699111yescharacteristic
314C2×C4#6700012yes—
315C2×C4#6700012yes—
316C2×C4C2×#433912yes—
317C2×C4C2×D4×D1111yescharacteristic
318C2×C4C2×#434312yes—
319C2×C4C22×C22⋊D1111yescharacteristic
320C8—24no—
321C8—444no—
322C8—442no—
323C22—22no—
324C22—22no—
325C22—28no—
326C22—444no—
327C22—442no—
328C22—884no—
329C22#1062260612yes—
330C22#1062260612yes—
331C22#1062279014yes—
332C22C2×#6695112yes—
333C22C2×#6699111yescharacteristic
334C4—84no—
335C4—442no—
336C4#1062260612yes—
337C4#1062260612yes—
338C4C2×#6694712yes—
339C4C2×#6698211yescharacteristic
340C4C2×#6700011yescharacteristic
341C2—22no—
342C2—22no—
343C2—882no—
344C2#1307006214yesdirect product factor
345C2C2×#1062260611yescharacteristic
346C2C2×#1062279012yes—
subgroupG/H
centerC23#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#106C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC22×#106D11
hypocenterC11C2×#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #13070062C2direct (N × H)
4. C2×#10622168C2semidirect
5. C2×#10622190C2semidirect
6. C22×C11×#106C2semidirect
14. C2×C11×#106C22semidirect
22. #10622190C22semidirect
23. #10622168C22semidirect
111. C22×#106D11semidirect
163. C2×#106C2×D11semidirect
228. C2×C11#2079semidirect
283. C11C2×#2079semidirect
344. C2#13070062direct (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
#130700622
C2×#106221682
C2×#106221902
C22×C11×#1062
C2×#207911