Finite Group Databasebeta

← C2×#13070499 #14907176

Subgroups — C2×#13070499 #14907176

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic
2C2×#10622809C211yesmaximal, characteristic, complemented
3C2×#10622508C211yesmaximal, characteristic, complemented
4#13070499C218yesmaximal, direct product factor
5C2×#10622131C211yesmaximal, characteristic, complemented
6C2×#10622148C211yesmaximal, characteristic, complemented
7C2×#10622140C211yesmaximal, characteristic, complemented
8C2×C11×#359C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C2×#67001—21no—
11C2×#66960—21no—
12C2×#66957C2211yescharacteristic
13C22×C11×C16C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C2×#66901—21no—
16#10622809—22no—
17#10622809C2214yescomplemented
18#10622807C414yescomplemented
19#10622807C2214yes—
20C2×#66893C411yescharacteristic, complemented
21C2×#66892C411yescharacteristic, complemented
22C2×#66891C411yescharacteristic, complemented
23C2×#66890C411yescharacteristic, complemented
24C2×#66889—21no—
25C2×#66883C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27C22×C11⋊C16C2211yescharacteristic
28#10622508—22no—
29#10622508C2214yescomplemented
30C11×#359C2214yescomplemented
31#10622148C2214yescomplemented
32#10622140C2214yescomplemented
33#10622131C2214yescomplemented
34C2×C11×#41—21no—
35C2×#4339—21no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135C2×C412yes—
39C11×#135C2312yes—
40C2×C11×Q16C2×C411yescharacteristic
41C2×C11×SD16—21no—
42C2×C11×D8C2×C411yescharacteristic
43C2×C11×M16—21no—
44C22×C8×C11C2311yescharacteristic
45#67001—24no—
46#67001—42no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4318—41no—
50C22×C11⋊C8—41no—
51C22×C11⋊C8D411yescharacteristic
52#66960—24no—
53#66960—42no—
54C2×Dic44C2×C411yescharacteristic
55#66957—21no—
56#66957—21no—
57#66957C2×C412yes—
58#66957C2312yes—
59C2×D88C2×C411yescharacteristic
60C2×#4314—21no—
61C2×#4313—41no—
62C2×C8×D11—41no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C2×C11×C16C2312yes—
66C11×#108—21no—
67C11×#108C2312yes—
68#66901—24no—
69#66893C2×C414yescomplemented
70#66892C2×C414yescomplemented
71#66891C2×C414yescomplemented
72#66890C2×C414yescomplemented
73#66889—24no—
74#66883—21no—
75#66883C2312yes—
76C8×Dic11D412yes—
77C8×Dic11C2312yes—
78C2×C11⋊C16C2×C411yescharacteristic
79C2×C11⋊C16C2×C411yescharacteristic
80C2×C11⋊C16C2×C412yes—
81C2×C11⋊C16C2312yes—
82C2×#2179—111nomaximal, Sylow
83C11×#41—22no—
84C11×#41—22no—
85C11×#41—41no—
86C11×#41—41no—
87C2×Q8×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—21no—
94#4339—22no—
95#4339—22no—
96#4339—41no—
97#4339—41no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×Q16—21no—
102C11×Q16C22×C412yes—
103C11×SD16—22no—
104C11×SD16—22no—
105C11×D8—21no—
106C11×D8C22×C412yes—
107C11×M16—22no—
108C11×M16—41no—
109C2×C8×C11—41no—
110C2×C8×C11C22×C411yescharacteristic
111C2×C8×C11C22×C411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4111yescharacteristic
114C2×C8×C11#4111yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C4×Dic11—21no—
117C4×Dic11C2×D412yes—
118#4318—22no—
119#4318—44no—
120#4318—41no—
121C2×C11⋊C8—44no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8D811yescharacteristic
124C2×C11⋊C8D811yescharacteristic
125C2×C11⋊C8D812yes—
126C2×C11⋊C8C2×D412yes—
127Dic44—21no—
128Dic44C22×C412yes—
129D88—21no—
130D88C22×C412yes—
131#4314—22no—
132#4314—22no—
133#4313—44no—
134C8×D11—44no—
135C11×C16—22no—
136C11⋊C16C22×C412yes—
137C11⋊C16C22×C412yes—
138C2×#508—111no—
139C2×#443—111no—
140C2×#443—111no—
141#2179—118no—
142C2×#368—111no—
143C2×#359—111no—
144C2×#359D1111yescharacteristic, complemented
145C2×#346—111no—
146C23×C11—41no—
147C23×C11#13511yescharacteristic
148C22×D11—41no—
149Q8×C11—22no—
150Q8×C11—41no—
151D4×C11—22no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C22⋊D11—42no—
165C22⋊D11—42no—
166C2×Dic11—22no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169D44—22no—
170D44—41no—
171C4×D11—42no—
172C4×D11—42no—
173Dic22—22no—
174Dic22—41no—
175C8×C11—42no—
176C8×C11C4×D411yescharacteristic
177C8×C11C4×D411yescharacteristic
178C8×C11C23×C411yescharacteristic
179C8×C11C2×#4111yescharacteristic
180C11⋊C8—42no—
181C11⋊C8C2×D812yes—
182C11⋊C8C2×D812yes—
183C2×#135—111no—
184C2×#135C2×D1111yescharacteristic
185C2×#131—221no—
186C2×#131—221no—
187#508—114no—
188#508—114no—
189C2×Q32—111no—
190C2×SD32—111no—
191C2×SD32—111no—
192C2×D16—111no—
193C22×C16—111no—
194C22×C16C2×D1111yescharacteristic
195#443—114no—
196#443—114no—
197#443—222no—
198#443—222no—
199C2×#108—111no—
200C2×#108C2×D1111yescharacteristic
201C2×#104—221no—
202C2×#104—221no—
203C2×C4×C8—111no—
204#368—114no—
205#359—114no—
206#359C2×D1114yescomplemented
207#346—114no—
208C22×C11—22no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11C4×D811yescharacteristic
212C22×C11C4×D811yescharacteristic
213C22×C11C2×#13511yescharacteristic
214C2×D11—42no—
215C2×D11—82no—
216C4×C11—42no—
217C4×C11C4×D811yescharacteristic
218C4×C11C4×D811yescharacteristic
219C4×C11C2×C4×D411yescharacteristic
220C4×C11C22×D811yescharacteristic
221Dic11—42no—
222Dic11—42no—
223C2×#41—21no—
224C2×#41—221no—
225#135—21no—
226#135—21no—
227#135—112no—
228#135—112no—
229#135—221no—
230#135—221no—
231#135C4×D1112yes—
232#135C22×D1112yes—
233C2×Q16—111no—
234C2×Q16C4×D1111yescharacteristic
235C2×SD16—21no—
236C2×SD16—221no—
237C2×D8—111no—
238C2×D8C4×D1111yescharacteristic
239#131—224no—
240#131—224no—
241#131—442no—
242#131—442no—
243C2×M16—21no—
244C2×M16—221no—
245C2×M16—441no—
246C2×M16—441no—
247C22×C8—111no—
248C22×C8—441no—
249C22×C8—441no—
250C22×C8C22×D1111yescharacteristic
251C2×C42—111no—
252Q32—114no—
253SD32—114no—
254SD32—114no—
255D16—114no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—111no—
259C2×C16—111no—
260C2×C16—112no—
261C2×C16—112no—
262C2×C16C22×D1112yes—
263#108—21no—
264#108—112no—
265#108—221no—
266#108C22×D1112yes—
267#104—224no—
268#104—224no—
269C4×C8—112no—
270C4×C8—112no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—82no—
274C2×C11#217912yescomplemented
275C2×C11C2×C4×D811yescharacteristic
276D11—82no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—222no—
282#41—222no—
283#41—441no—
284#41—441no—
285C2×Q8—21no—
286C2×Q8—221no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—221no—
290C2×D4—441no—
291C22×C4—41no—
292C22×C4—221no—
293C22×C4—441no—
294C22×C4D4×D1111yescharacteristic
295Q16—21no—
296Q16—112no—
297Q16—221no—
298Q16C2×C4×D1112yes—
299SD16—22no—
300SD16—22no—
301SD16—222no—
302SD16—222no—
303D8—21no—
304D8—112no—
305D8—221no—
306D8C2×C4×D1112yes—
307M16—22no—
308M16—41no—
309M16—222no—
310M16—444no—
311M16—444no—
312M16—441no—
313C2×C8—41no—
314C2×C8—112no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—112no—
318C2×C8—444no—
319C2×C8—444no—
320C2×C8—441no—
321C2×C8C2×C4×D1111yescharacteristic
322C2×C8C2×C4×D1111yescharacteristic
323C2×C8D4×D1111yescharacteristic
324C2×C8#434111yescharacteristic
325C2×C8#434111yescharacteristic
326C2×C8C23×D1111yescharacteristic
327C42—112no—
328C42—221no—
329C16—22no—
330C16—112no—
331C16—112no—
332C11C2×#217911yescharacteristic, complemented, Sylow
333C23—41no—
334C23—441no—
335C23#6696911yescharacteristic
336Q8—22no—
337Q8—41no—
338Q8—222no—
339Q8—441no—
340D4—22no—
341D4—42no—
342D4—42no—
343D4—41no—
344D4—222no—
345D4—442no—
346D4—442no—
347D4—441no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—222no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4(C22⋊D11)⋊C411yescharacteristic
357C2×C4(C22⋊D11)⋊C411yescharacteristic
358C2×C4D8×D1111yescharacteristic
359C2×C4D8×D1111yescharacteristic
360C2×C4#6696911yescharacteristic
361C2×C4C2×D4×D1111yescharacteristic
362C8—42no—
363C8—112no—
364C8—112no—
365C8—442no—
366C8(C22⋊D11)⋊C411yescharacteristic
367C8(C22⋊D11)⋊C411yescharacteristic
368C8C22×C4×D1111yescharacteristic
369C8C2×#434111yescharacteristic
370C22—22no—
371C22—42no—
372C22—82no—
373C22—442no—
374C22—882no—
375C22#1062236911yescharacteristic
376C22#1062236911yescharacteristic
377C22C2×#6696911yescharacteristic
378C4—42no—
379C4—442no—
380C4—442no—
381C4#1062236911yescharacteristic
382C4#1062236911yescharacteristic
383C4C2×(C22⋊D11)⋊C411yescharacteristic
384C4C2×D8×D1111yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2—882no—
389C2#1307049912yesdirect product factor
390C2C2×#1062236911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#359C2
socleC22×C11C4×D8
prime radicalC2×#10622807C2
cosocleC2×C8×C11C24
hypercenterC2×#359D11
hypocenterC11C2×#2179
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#10622809C2semidirect
3. C2×#10622508C2semidirect
4. #13070499C2direct (N × H)
5. C2×#10622131C2semidirect
6. C2×#10622148C2semidirect
7. C2×#10622140C2semidirect
8. C2×C11×#359C2semidirect
17. #10622809C22semidirect
18. #10622807C4semidirect
20. C2×#66893C4semidirect
21. C2×#66892C4semidirect
22. C2×#66891C4semidirect
23. C2×#66890C4semidirect
29. #10622508C22semidirect
30. C11×#359C22semidirect
31. #10622148C22semidirect
32. #10622140C22semidirect
33. #10622131C22semidirect
69. #66893C2×C4semidirect
70. #66892C2×C4semidirect
71. #66891C2×C4semidirect
72. #66890C2×C4semidirect
144. C2×#359D11semidirect
206. #359C2×D11semidirect
274. C2×C11#2179semidirect
332. C11C2×#2179semidirect
389. C2#13070499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228072
C2×#106228092
C2×#106225082
#130704992
C2×#106221312
C2×#106221482
C2×#106221402
C2×C11×#3592
C2×#217911