Finite Group Databasebeta

← C2×#13070506 #14907205

Subgroups — C2×#13070506 #14907205

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622522C211yesmaximal, characteristic
2C2×#10622507C211yesmaximal, characteristic
3C2×#10622466C211yesmaximal, characteristic, complemented
4#13070506C218yesmaximal, direct product factor
5C2×#10622134C211yesmaximal, characteristic, complemented
6C2×#10622126C211yesmaximal, characteristic
7C2×#10622150C211yesmaximal, characteristic, complemented
8C2×C11×#365C211yesmaximal, characteristic, complemented
9C2×#66960—21no—
10C22×Dic44C2211yescharacteristic
11C2×#66957C2211yescharacteristic
12C2×#66940—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C2×C11×#106C2211yescharacteristic
16C2×#66889—21no—
17C2×#66879C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19C2×#66874—21no—
20#10622522C414yescomplemented
21#10622522C2214yes—
22C2×Dic88C412yescomplemented
23C2×#66864C412yescomplemented
24#10622507—22no—
25#10622507C2214yes—
26#10622466—22no—
27#10622466C2214yescomplemented
28C11×#365C2214yescomplemented
29#10622150C2214yescomplemented
30#10622134C2214yescomplemented
31#10622126C2214yes—
32C2×#4339—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×Dic11⋊C4—41no—
38C2×C4×Dic11—41no—
39C2×C4×Dic11D411yescharacteristic
40C22×C11⋊C8D411yescharacteristic
41#66960—24no—
42#66960—42no—
43C2×Dic44—21no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44C2×C411yescharacteristic
47C2×Dic44C2×C412yes—
48C2×Dic44C2×C412yes—
49C2×Dic44C2312yes—
50#66957—21no—
51#66957—21no—
52#66957C2×C412yes—
53#66957C2312yes—
54C2×D88C2×C411yescharacteristic
55C2×#4314—21no—
56C2×#4313—41no—
57C2×C8×D11—41no—
58#66940—24no—
59#66940—42no—
60C11×M32C2×C412yes—
61C11×M32C2312yes—
62C2×C11×C16C2×C412yes—
63C11×#108—21no—
64C11×#108C2312yes—
65C11×#106—21no—
66C11×#106C2312yes—
67#66889—24no—
68#66879D412yes—
69#66879C2312yes—
70#66876—21no—
71#66876C2312yes—
72C2×C11⋊C16—21no—
73#66874—24no—
74Dic88C2×C418yescomplemented
75#66864C2×C418yescomplemented
76C2×#2180—111nomaximal, Sylow
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—41no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82#4339—22no—
83#4339—22no—
84#4339—41no—
85#4339—41no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×Dic22—22no—
90C2×Dic22—22no—
91C2×Dic22—22no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C11×M16—22no—
96C11×M16—41no—
97C2×C8×C11—41no—
98C2×C8×C11C22×C411yescharacteristic
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106Dic11⋊C4—44no—
107C4×Dic11—21no—
108C4×Dic11—44no—
109C4×Dic11C2×D412yes—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8C2×D412yes—
113Dic44—21no—
114Dic44—22no—
115Dic44—22no—
116Dic44—22no—
117Dic44C22×C414yes—
118Dic44C22×C412yes—
119D88—21no—
120D88C22×C412yes—
121#4314—22no—
122#4314—22no—
123#4313—44no—
124C8×D11—44no—
125C11×C16C22×C414yes—
126C11⋊C16—22no—
127C2×#510—111no—
128C2×#444—111no—
129C2×#441—111no—
130#2180—118no—
131C2×#365D1111yescharacteristic, complemented
132C2×#362—111no—
133C2×#360—111no—
134C2×#347—111no—
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C22×D11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C22⋊D11—42no—
146C22⋊D11—42no—
147C2×Dic11—22no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153D44—22no—
154D44—41no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—22no—
158Dic22—24no—
159Dic22—42no—
160Dic22—42no—
161Dic22—42no—
162Dic22—41no—
163C8×C11—42no—
164C8×C11C4×D411yescharacteristic
165C8×C11C4×D411yescharacteristic
166C8×C11C23×C411yescharacteristic
167C8×C11C2×#4111yescharacteristic
168C11⋊C8—22no—
169C2×#135—111no—
170C22×Q16—111no—
171C2×#131—221no—
172C2×C4×Q8—221no—
173#510—114no—
174#510—114no—
175C2×Q32—112no—
176C2×SD32—112no—
177C2×M32—111no—
178C2×M32C2×D1111yescharacteristic
179#444—114no—
180#444—222no—
181#441—114no—
182#441—222no—
183C2×#108C2×D1111yescharacteristic
184C2×#106C2×D1111yescharacteristic
185C2×#104—221no—
186C2×#103—221no—
187C2×#97—111no—
188#365C2×D1114yescomplemented
189#362—114no—
190#360—114no—
191#347—114no—
192C22×C11—22no—
193C22×C11#44211yescharacteristic
194C22×C11#44211yescharacteristic
195C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
196C2×D11—42no—
197C2×D11—82no—
198C4×C11—82no—
199C4×C11#44211yescharacteristic
200C4×C11#44211yescharacteristic
201C4×C11C2×C4×D411yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
203Dic11—42no—
204Dic11—44no—
205Dic11—42no—
206C2×#41—221no—
207C22×Q8—221no—
208#135—112no—
209#135—112no—
210#135—221no—
211#135—221no—
212C2×Q16—112no—
213C2×Q16—112no—
214C2×Q16—111no—
215C2×Q16—112no—
216C2×Q16—221no—
217C2×Q16—221no—
218C2×Q16—221no—
219C2×SD16—221no—
220C2×D8—111no—
221#131—224no—
222#131—442no—
223C2×M16—21no—
224C2×M16—441no—
225C22×C8—111no—
226C22×C8—441no—
227C22×C8C22×D1111yescharacteristic
228C4×Q8—224no—
229C4×Q8—442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—441no—
232C2×C42—111no—
233C2×C42—441no—
234Q32—118no—
235SD32—118no—
236M32—112no—
237M32—221no—
238M32C4×D1112yes—
239M32C22×D1112yes—
240C2×C16—221no—
241C2×C16C4×D1112yes—
242#108—21no—
243#108C22×D1112yes—
244#106—21no—
245#106C22×D1112yes—
246#104—224no—
247#103—224no—
248#97—112no—
249#97—112no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#218012yescomplemented
253C2×C11C2×#44211yescharacteristic
254D11—82no—
255#41—222no—
256#41—222no—
257#41—441no—
258#41—441no—
259C2×Q8—221no—
260C2×Q8—222no—
261C2×Q8—222no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—441no—
266C2×D4—221no—
267C2×D4—441no—
268C22×C4—41no—
269C22×C4—221no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4D4×D1111yescharacteristic
273Q16—114no—
274Q16—112no—
275Q16—222no—
276Q16—222no—
277Q16—221no—
278Q16—222no—
279SD16—222no—
280SD16—222no—
281D8—112no—
282D8—221no—
283M16—22no—
284M16—41no—
285M16—444no—
286C2×C8—41no—
287C2×C8—112no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—444no—
291C2×C8C2×C4×D1111yescharacteristic
292C2×C8C2×C4×D1111yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8#434311yescharacteristic
295C2×C8#434311yescharacteristic
296C2×C8C23×D1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—444no—
300C42—112no—
301C42—221no—
302C42—444no—
303C16—222no—
304C16C2×C4×D1114yes—
305C11C2×#218011yescharacteristic, complemented, Sylow
306C23—441no—
307C23#6696711yescharacteristic
308Q8—222no—
309Q8—224no—
310Q8—442no—
311Q8—442no—
312Q8—441no—
313Q8—442no—
314D4—222no—
315D4—442no—
316D4—442no—
317D4—441no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—222no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4#6694611yescharacteristic
329C2×C4#6694611yescharacteristic
330C2×C4#6696711yescharacteristic
331C2×C4#6696711yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C8—42no—
335C8—222no—
336C8#6694611yescharacteristic
337C8#6694611yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#434311yescharacteristic
340C22—22no—
341C22—442no—
342C22—882no—
343C22#1062248211yescharacteristic
344C22#1062248211yescharacteristic
345C22C2×#6696711yescharacteristic
346C4—82no—
347C4—442no—
348C4—442no—
349C4—444no—
350C4#1062248211yescharacteristic
351C4#1062248211yescharacteristic
352C4C2×#6694611yescharacteristic
353C4C2×#6696711yescharacteristic
354C2—21no—
355C2—21no—
356C2—882no—
357C2#1307050612yesdirect product factor
358C2C2×#1062248211yescharacteristic
subgroupG/H
centerC22#10622482
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#365C2
socleC22×C11#442
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenterC2×#365D11
hypocenterC11C2×#2180
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
3. C2×#10622466C2semidirect
4. #13070506C2direct (N × H)
5. C2×#10622134C2semidirect
7. C2×#10622150C2semidirect
8. C2×C11×#365C2semidirect
20. #10622522C4semidirect
22. C2×Dic88C4semidirect
23. C2×#66864C4semidirect
27. #10622466C22semidirect
28. C11×#365C22semidirect
29. #10622150C22semidirect
30. #10622134C22semidirect
74. Dic88C2×C4semidirect
75. #66864C2×C4semidirect
131. C2×#365D11semidirect
188. #365C2×D11semidirect
252. C2×C11#2180semidirect
305. C11C2×#2180semidirect
357. C2#13070506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225222
C2×#106225072
C2×#106224662
#130705062
C2×#106221342
C2×#106221262
C2×#106221502
C2×C11×#3652
C2×#218011