Finite Group Databasebeta

← C2×#13070500 #14907177

Subgroups — C2×#13070500 #14907177

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×#10622313C211yesmaximal, characteristic, complemented
3#13070500C218yesmaximal, direct product factor
4C2×#10622131C211yesmaximal, characteristic, complemented
5C2×#10622205C211yesmaximal, characteristic, complemented
6C2×#10622135C211yesmaximal, characteristic, complemented
7C2×#10622099C211yesmaximal, characteristic, complemented
8C2×C11×#443C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C2×C11×#131—21no—
11C2×#66957C2211yescharacteristic
12C2×#66954—21no—
13C11×#443—22no—
14C11×#443C2214yescomplemented
15C2×C11×#108C2211yescharacteristic
16C2×C11×#104—21no—
17C2×C4×C8×C11C2211yescharacteristic
18#10622807C414yescomplemented
19#10622807C2214yes—
20C2×#66893C411yescharacteristic, complemented
21C2×#66892C411yescharacteristic, complemented
22C2×#66891C411yescharacteristic, complemented
23C2×#66890C411yescharacteristic, complemented
24C2×#66883C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27C2×#66869—21no—
28#10622313—22no—
29#10622313C2214yescomplemented
30#10622205C2214yescomplemented
31#10622135C2214yescomplemented
32#10622131C2214yescomplemented
33#10622099C2214yescomplemented
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
43C11×#131—24no—
44C11×#131—42no—
45C2×C11×M16—21no—
46C2×C11×M16—41no—
47C22×C8×C11—41no—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×#4318—21no—
52C2×Dic44C2×C411yescharacteristic
53#66957—21no—
54#66957—21no—
55#66957C2×C412yes—
56#66957C2312yes—
57C2×D88C2×C411yescharacteristic
58C2×#4314—21no—
59#66954—24no—
60#66954—42no—
61C2×#4313—41no—
62C2×C8×D11—41no—
63C11×#108—21no—
64C11×#108C2312yes—
65C11×#104—24no—
66C4×C8×C11D412yes—
67C4×C8×C11C2312yes—
68#66893C2×C414yescomplemented
69#66892C2×C414yescomplemented
70#66891C2×C414yescomplemented
71#66890C2×C414yescomplemented
72#66883—21no—
73#66883C2312yes—
74C2×C11⋊C16—21no—
75C2×C11⋊C16—21no—
76C2×C11⋊C16C2×C411yescharacteristic
77C2×C11⋊C16C2×C411yescharacteristic
78C2×C11⋊C16C2×C412yes—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2312yes—
81#66869—24no—
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—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
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—44no—
109C11×M16—41no—
110C2×C8×C11—44no—
111C2×C8×C11—41no—
112C2×C8×C11D811yescharacteristic
113C2×C8×C11D811yescharacteristic
114C2×C8×C11D812yes—
115C2×C8×C11C22×C411yescharacteristic
116C2×C8×C11C22×C411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D412yes—
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C42×C11—21no—
123C42×C11C2×D412yes—
124#4318—22no—
125#4318—41no—
126C2×C11⋊C8—41no—
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×#443D1111yescharacteristic, complemented
141#2179—118no—
142C2×#368—111no—
143C2×#359—111no—
144C2×#359—111no—
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—22no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11#13511yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—42no—
167C22⋊D11—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×C11C2×D812yes—
179C8×C11C2×D812yes—
180C8×C11C23×C411yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C11⋊C8—42no—
183C2×#135—111no—
184C2×#135C2×D1111yescharacteristic
185C2×#131—21no—
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×C16—111no—
195#443—22no—
196#443—114no—
197#443—222no—
198#443C2×D1114yescomplemented
199C2×#108—111no—
200C2×#108C2×D1111yescharacteristic
201C2×#104—21no—
202C2×#104—221no—
203C2×C4×C8C2×D1111yescharacteristic
204#368—114no—
205#359—114no—
206#359—114no—
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×C11—42no—
218C4×C11C4×D811yescharacteristic
219C4×C11C4×D811yescharacteristic
220C4×C11C2×C4×D411yescharacteristic
221C4×C11C22×D811yescharacteristic
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—24no—
240#131—42no—
241#131—224no—
242#131—442no—
243C2×M16—21no—
244C2×M16—41no—
245C2×M16—221no—
246C2×M16—441no—
247C22×C8—41no—
248C22×C8—441no—
249C22×C8C22⋊D1111yescharacteristic
250C22×C8C22×D1111yescharacteristic
251C2×C42C22⋊D1111yescharacteristic
252Q32—114no—
253SD32—114no—
254SD32—114no—
255D16—114no—
256C2×C16—111no—
257C2×C16—111no—
258C2×C16—112no—
259C2×C16—112no—
260C2×C16—112no—
261C2×C16—221no—
262C2×C16—221no—
263#108—21no—
264#108—112no—
265#108—221no—
266#108C22×D1112yes—
267#104—24no—
268#104—224no—
269C4×C8C22⋊D1112yes—
270C4×C8C22×D1112yes—
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—21no—
292C22×C4—41no—
293C22×C4—441no—
294C22×C4C2×C22⋊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—44no—
310M16—222no—
311M16—441no—
312M16—444no—
313C2×C8—41no—
314C2×C8—44no—
315C2×C8—441no—
316C2×C8—444no—
317C2×C8#432312yes—
318C2×C8#432311yescharacteristic
319C2×C8#432311yescharacteristic
320C2×C8C2×C4×D1111yescharacteristic
321C2×C8C2×C4×D1111yescharacteristic
322C2×C8#433911yescharacteristic
323C2×C8#433911yescharacteristic
324C2×C8C2×C22⋊D1111yescharacteristic
325C2×C8C2×C22⋊D1112yes—
326C2×C8C23×D1111yescharacteristic
327C42—21no—
328C42C2×C22⋊D1112yes—
329C16—112no—
330C16—112no—
331C16—222no—
332C11C2×#217911yescharacteristic, complemented, Sylow
333C23—41no—
334C23—441no—
335C23#6700311yescharacteristic
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—22no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4C4×C22⋊D1111yescharacteristic
357C2×C4C4×C22⋊D1111yescharacteristic
358C2×C4C2×#432311yescharacteristic
359C2×C4C2×#432311yescharacteristic
360C2×C4#6700311yescharacteristic
361C2×C4C22×C22⋊D1111yescharacteristic
362C8—42no—
363C8—442no—
364C8C4×C22⋊D1111yescharacteristic
365C8C4×C22⋊D1111yescharacteristic
366C8C2×#432312yes—
367C8C2×#432312yes—
368C8C22×C4×D1111yescharacteristic
369C8C2×#433911yescharacteristic
370C22—22no—
371C22—42no—
372C22—82no—
373C22—442no—
374C22—882no—
375C22C4×#432311yescharacteristic
376C22C4×#432311yescharacteristic
377C22C2×#6700311yescharacteristic
378C4—42no—
379C4—42no—
380C4—442no—
381C4C4×#432311yescharacteristic
382C4C4×#432311yescharacteristic
383C4C2×C4×C22⋊D1111yescharacteristic
384C4C22×#432311yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2—882no—
389C2#1307050012yesdirect product factor
390C2C2×C4×#432311yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#443C2
socleC22×C11C4×D8
prime radicalC2×#10622807C2
cosocleC2×C8×C11C24
hypercenterC2×#443D11
hypocenterC11C2×#2179
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#10622313C2semidirect
3. #13070500C2direct (N × H)
4. C2×#10622131C2semidirect
5. C2×#10622205C2semidirect
6. C2×#10622135C2semidirect
7. C2×#10622099C2semidirect
8. C2×C11×#443C2semidirect
14. C11×#443C22semidirect
18. #10622807C4semidirect
20. C2×#66893C4semidirect
21. C2×#66892C4semidirect
22. C2×#66891C4semidirect
23. C2×#66890C4semidirect
29. #10622313C22semidirect
30. #10622205C22semidirect
31. #10622135C22semidirect
32. #10622131C22semidirect
33. #10622099C22semidirect
68. #66893C2×C4semidirect
69. #66892C2×C4semidirect
70. #66891C2×C4semidirect
71. #66890C2×C4semidirect
140. C2×#443D11semidirect
198. #443C2×D11semidirect
274. C2×C11#2179semidirect
332. C11C2×#2179semidirect
389. C2#13070500direct (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×#106223132
#130705002
C2×#106221312
C2×#106222052
C2×#106221352
C2×#106220992
C2×C11×#4432
C2×#217911