Finite Group Databasebeta

← C2×#13070505 #14907204

Subgroups — C2×#13070505 #14907204

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×#10622792C211yesmaximal, characteristic
2C2×#10622330C211yesmaximal, characteristic
3#13070505C218yesmaximal, direct product factor
4C2×#10622125C211yesmaximal, characteristic, complemented
5C2×#10622203C211yesmaximal, characteristic, complemented
6C2×#10622126C211yesmaximal, characteristic
7C2×#10622104C211yesmaximal, characteristic, complemented
8C2×C11×#441C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C2×C4×Q8×C11—21no—
11C2×#66957C2211yescharacteristic
12C2×#66954—21no—
13C11×#441—22no—
14C11×#441C2214yescomplemented
15C2×C11×#106C2211yescharacteristic
16C2×C11×#103—21no—
17C2×C11×#97C2211yescharacteristic
18C2×#66893C412yescomplemented
19#10622792C414yescomplemented
20#10622792C2214yes—
21C2×#66892C412yescomplemented
22C2×#66883C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C2×#66869—21no—
26#10622330—22no—
27#10622330C2214yes—
28#10622203C2214yescomplemented
29#10622126C2214yes—
30#10622125C2214yescomplemented
31#10622104C2214yescomplemented
32C22×Q8×C11—21no—
33C2×#4339—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2×C412yes—
38C2×C11×Q16C2×C412yes—
39C2×C11×Q16C2312yes—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C4×Q8×C11—24no—
43C4×Q8×C11—42no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—41no—
46C2×C42×C11—41no—
47C2×C42×C11D411yescharacteristic
48C2×#4318—21no—
49C2×Dic44C2×C411yescharacteristic
50#66957—21no—
51#66957—21no—
52#66957C2×C412yes—
53#66957C2312yes—
54C2×D88C2×C411yescharacteristic
55C2×#4314—21no—
56#66954—24no—
57#66954—42no—
58C2×#4313—41no—
59C2×C8×D11—41no—
60C11×#106—21no—
61C11×#106C2312yes—
62C11×#103—24no—
63C11×#97D412yes—
64C11×#97C2312yes—
65#66893C2×C418yescomplemented
66#66892C2×C418yescomplemented
67#66883—21no—
68#66883C2312yes—
69#66876—21no—
70#66876C2×C412yes—
71#66876C2312yes—
72#66876C2312yes—
73C2×C11⋊C16—21no—
74C2×C11⋊C16C2×C412yes—
75#66869—24no—
76C2×#2180—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88#4339—22no—
89#4339—22no—
90#4339—41no—
91#4339—41no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C11×Q16—22no—
96C11×Q16—22no—
97C11×Q16—22no—
98C11×Q16C22×C414yes—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—22no—
109C11×C4⋊C4—44no—
110C11×C4⋊C4—41no—
111C42×C11—21no—
112C42×C11—44no—
113C42×C11C2×D412yes—
114#4318—22no—
115#4318—41no—
116C2×C11⋊C8—41no—
117Dic44—21no—
118Dic44C22×C412yes—
119D88—21no—
120D88C22×C412yes—
121#4314—22no—
122#4314—22no—
123#4313—44no—
124C8×D11—44no—
125C11⋊C16—22no—
126C11⋊C16C22×C414yes—
127C2×#510—111no—
128C2×#444—111no—
129C2×#441D1111yescharacteristic, complemented
130#2180—118no—
131C2×#365—111no—
132C2×#362—111no—
133C2×#360—111no—
134C2×#347—111no—
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C22×D11—41no—
137Q8×C11—24no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—42no—
141C2×C4×C11—22no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—82no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—42no—
155C22⋊D11—42no—
156C2×Dic11—41no—
157D44—22no—
158D44—41no—
159C4×D11—42no—
160C4×D11—42no—
161Dic22—22no—
162Dic22—41no—
163C8×C11—22no—
164C8×C11C4×D411yescharacteristic
165C8×C11C4×D411yescharacteristic
166C8×C11C23×C411yescharacteristic
167C8×C11C2×#4111yescharacteristic
168C11⋊C8—42no—
169C2×#135—111no—
170C22×Q16C2×D1111yescharacteristic
171C2×#131—221no—
172C2×C4×Q8—21no—
173#510—114no—
174#510—114no—
175C2×Q32—112no—
176C2×SD32—112no—
177C2×M32—111no—
178C2×M32—111no—
179#444—114no—
180#444—222no—
181#441—22no—
182#441C2×D1114yescomplemented
183C2×#108—111no—
184C2×#106C2×D1111yescharacteristic
185C2×#104—221no—
186C2×#103—21no—
187C2×#97C2×D1111yescharacteristic
188#365—114no—
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—42no—
199C4×C11—44no—
200C4×C11—82no—
201C4×C11#44211yescharacteristic
202C4×C11#44211yescharacteristic
203C4×C11C2×C4×D411yescharacteristic
204C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
205Dic11—42no—
206C2×#41—221no—
207C22×Q8—21no—
208#135—112no—
209#135—112no—
210#135—221no—
211#135—221no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—111no—
216C2×Q16C4×D1112yes—
217C2×Q16C4×D1112yes—
218C2×Q16C22×D1112yes—
219C2×SD16—221no—
220C2×D8—111no—
221#131—224no—
222#131—442no—
223C2×M16—221no—
224C2×M16—441no—
225C22×C8—441no—
226C22×C8C22⋊D1111yescharacteristic
227C22×C8C22×D1111yescharacteristic
228C4×Q8—24no—
229C4×Q8—42no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—41no—
232C2×C42—41no—
233C2×C42C22⋊D1111yescharacteristic
234Q32—118no—
235SD32—118no—
236M32—112no—
237M32—112no—
238M32—112no—
239M32—221no—
240C2×C16—112no—
241C2×C16—221no—
242#108—112no—
243#108—221no—
244#106—21no—
245#106C22×D1112yes—
246#104—224no—
247#103—24no—
248#97C22⋊D1112yes—
249#97C22×D1112yes—
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—22no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—221no—
266C2×D4—221no—
267C2×D4—441no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—441no—
272C22×C4C2×C22⋊D1111yescharacteristic
273Q16—22no—
274Q16—22no—
275Q16—22no—
276Q16—112no—
277Q16—221no—
278Q16C2×C4×D1114yes—
279SD16—222no—
280SD16—222no—
281D8—112no—
282D8—221no—
283M16—222no—
284M16—444no—
285M16—441no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—444no—
289C2×C8—441no—
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8C2×C4×D1111yescharacteristic
292C2×C8#433911yescharacteristic
293C2×C8#433911yescharacteristic
294C2×C8C2×C22⋊D1112yes—
295C2×C8C2×C22⋊D1111yescharacteristic
296C2×C8C23×D1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—44no—
299C4⋊C4—41no—
300C42—21no—
301C42—44no—
302C42C2×C22⋊D1112yes—
303C16—114no—
304C16—222no—
305C11C2×#218011yescharacteristic, complemented, Sylow
306C23—441no—
307C23#6698511yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—222no—
313Q8—441no—
314D4—222no—
315D4—442no—
316D4—442no—
317D4—441no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4C4×C22⋊D1111yescharacteristic
329C2×C4C4×C22⋊D1111yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4#6700211yescharacteristic
332C2×C4#6700211yescharacteristic
333C2×C4C22×C22⋊D1111yescharacteristic
334C8—22no—
335C8—442no—
336C8C4×C22⋊D1111yescharacteristic
337C8C4×C22⋊D1111yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#433911yescharacteristic
340C22—22no—
341C22—442no—
342C22—882no—
343C22#1062262711yescharacteristic
344C22#1062262711yescharacteristic
345C22C2×#6698511yescharacteristic
346C4—42no—
347C4—44no—
348C4—82no—
349C4—442no—
350C4#1062262711yescharacteristic
351C4#1062262711yescharacteristic
352C4C2×C4×C22⋊D1111yescharacteristic
353C4C2×#6700211yescharacteristic
354C2—21no—
355C2—21no—
356C2—882no—
357C2#1307050512yesdirect product factor
358C2C2×#1062262711yescharacteristic
subgroupG/H
centerC22#10622627
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#441C2
socleC22×C11#442
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenterC2×#441D11
hypocenterC11C2×#2180
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #13070505C2direct (N × H)
4. C2×#10622125C2semidirect
5. C2×#10622203C2semidirect
7. C2×#10622104C2semidirect
8. C2×C11×#441C2semidirect
14. C11×#441C22semidirect
18. C2×#66893C4semidirect
19. #10622792C4semidirect
21. C2×#66892C4semidirect
28. #10622203C22semidirect
30. #10622125C22semidirect
31. #10622104C22semidirect
65. #66893C2×C4semidirect
66. #66892C2×C4semidirect
129. C2×#441D11semidirect
182. #441C2×D11semidirect
252. C2×C11#2180semidirect
305. C11C2×#2180semidirect
357. C2#13070505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106223302
#130705052
C2×#106221252
C2×#106222032
C2×#106221262
C2×#106221042
C2×C11×#4412
C2×#218011