Finite Group Databasebeta

← C2×#13068083 #14736268

Subgroups — C2×#13068083 #14736268

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068083C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622185C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic, complemented
8C2×C11×#474C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4325—21no—
12C22×#4325—21no—
13C22×#4323—21no—
14C22×#4318—21no—
15C2×#66927C2211yescharacteristic
16C11×#474—22no—
17C11×#474C2214yescomplemented
18C2×C11×#107—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102—21no—
21C2×C22⋊(C11⋊C8)—21no—
22#10622698—22no—
23#10622698C2214yescomplemented
24#10622628—22no—
25#10622628C2214yes—
26#10622625—22no—
27#10622625C2214yescomplemented
28C2×#66873—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622185C2214yescomplemented
33#10622123C2214yescomplemented
34#10622117C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11D412yes—
49C4×D4×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4325—24no—
57C2×#4325—44no—
58C2×#4325—44no—
59C2×#4323—24no—
60C2×#4323—44no—
61C2×#4318—24no—
62C2×#4318—44no—
63C22×C11⋊C8—21no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8D411yescharacteristic
66C22×C11⋊C8D411yescharacteristic
67#66927—21no—
68#66927—21no—
69#66927—21no—
70#66927C2312yes—
71C11×#107—24no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8C2312yes—
74C11×#102—24no—
75C22⋊(C11⋊C8)—24no—
76#66873—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81C4×C11⋊C8D412yes—
82C4×C11⋊C8C2312yes—
83C2×#1685—111nomaximal, Sylow
84C24×C11—21no—
85C23×D11—41no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—42no—
110C2×D44—42no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—82no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#4325—48no—
129#4325—48no—
130#4323—48no—
131#4318—48no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—42no—
136C2×C11⋊C8—42no—
137C2×C11⋊C8D814yescomplemented
138C2×C11⋊C8C2×D412yes—
139C2×C11⋊C8C2×D412yes—
140C2×#492—111no—
141C2×#474D1111yescharacteristic, complemented
142C2×#459—111no—
143C2×#436—111no—
144#1685—118no—
145C2×#335—111no—
146C2×#332—111no—
147C2×#331—111no—
148C23×C11—22no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11#12111yescharacteristic
153C22×D11—42no—
154C22×D11—82no—
155C22×D11—82no—
156C22×D11—82no—
157Q8×C11—42no—
158Q8×C11—42no—
159Q8×C11—82no—
160D4×C11—22no—
161D4×C11—22no—
162D4×C11—42no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C2×D812yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11#13712yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181D44—42no—
182D44—42no—
183D44—42no—
184D44—42no—
185D44—82no—
186D44—82no—
187D44—82no—
188D44—82no—
189C8×C11—42no—
190C11⋊C8—22no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8C2×D814yescomplemented
194C22×SD16—221no—
195C22×SD16—221no—
196C22×D8—221no—
197C22×M16—221no—
198C2×C4⋊Q8C2×D1111yescharacteristic
199C2×#127—111no—
200C2×C4×D4C2×D1111yescharacteristic
201#492—114no—
202#492—222no—
203#474—22no—
204#474C2×D1114yescomplemented
205#459—114no—
206#459—222no—
207#436—114no—
208#436—222no—
209C2×#107—21no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—111no—
212C2×C4⋊C8C2×D1111yescharacteristic
213C2×#102—21no—
214C2×#102—221no—
215C2×C22⋊C8—221no—
216C2×C4×C8—111no—
217#335—114no—
218#332—114no—
219#331—114no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—84no—
224C22×C11#45912yes—
225C22×C11#46812yes—
226C22×C11#47112yes—
227C22×C11C2×#12111yescharacteristic
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—82no—
231C2×D11—164no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—42no—
235C4×C11—82no—
236C4×C11#45912yes—
237C4×C11#46812yes—
238C4×C11C22×D811yescharacteristic
239C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C4×C11C2×#13711yescharacteristic
242C22×Q8—21no—
243C22×D4—221no—
244C22×D4—221no—
245C22×D4—221no—
246C22×D4C22⋊D1111yescharacteristic
247C23×C4—21no—
248C2×SD16—224no—
249C2×SD16—224no—
250C2×SD16—444no—
251C2×SD16—444no—
252C2×D8—224no—
253C2×D8—444no—
254C2×M16—224no—
255C2×M16—444no—
256C22×C8—21no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—221no—
260C22×C8—221no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8C22×D1112yes—
265#127—112no—
266#127—221no—
267#127—221no—
268#127—221no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4C22⋊D1112yes—
272C4×D4C22×D1112yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4C22⋊D1111yescharacteristic
276C2×C22⋊C4—21no—
277C2×C42C22×D1111yescharacteristic
278#107—24no—
279C4⋊C8—21no—
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8C22×D1112yes—
285#102—24no—
286#102—224no—
287C22⋊C8—224no—
288C4×C8—112no—
289C4×C8—112no—
290C2×C11—82no—
291C2×C11#168514yescomplemented
292C2×C11C2×#45911yescharacteristic
293C2×C11C2×#46811yescharacteristic
294C2×C11C2×#47111yescharacteristic
295D11—162no—
296C24—21no—
297C24—441no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—222no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—442no—
309C2×D4—442no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—882no—
316C2×D4C2×C22⋊D1112yes—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4D4×D1111yescharacteristic
324C22×C4#434111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326SD16—448no—
327SD16—448no—
328D8—448no—
329M16—448no—
330C2×C8—22no—
331C2×C8—42no—
332C2×C8—114no—
333C2×C8—112no—
334C2×C8—112no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—442no—
339C2×C8—442no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C2×C22⋊D1112yes—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C42D4×D1111yescharacteristic
349C42#434111yescharacteristic
350C42C2×C22⋊D1111yescharacteristic
351C42C23×D1111yescharacteristic
352C11C2×#168511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—442no—
358C23—882no—
359C23—882no—
360C23—882no—
361C23#6699211yescharacteristic
362Q8—42no—
363Q8—42no—
364Q8—82no—
365D4—22no—
366D4—22no—
367D4—42no—
368D4—442no—
369D4—442no—
370D4—442no—
371D4—442no—
372D4—882no—
373D4—882no—
374D4—882no—
375D4—882no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4D8×D1112yes—
385C2×C4#6696412yes—
386C2×C4#6699211yescharacteristic
387C2×C4#6699211yescharacteristic
388C2×C4#6699211yescharacteristic
389C2×C4#6699512yes—
390C2×C4#6700212yes—
391C2×C4C2×D4×D1111yescharacteristic
392C2×C4C2×#434111yescharacteristic
393C2×C4C22×C22⋊D1111yescharacteristic
394C8—42no—
395C8—114no—
396C8—222no—
397C8—442no—
398C8—442no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22—882no—
404C22—882no—
405C22—882no—
406C22—1764no—
407C22#1062266212yes—
408C22#1062276312yes—
409C22#1062281612yes—
410C22C2×#6699211yescharacteristic
411C4—21no—
412C4—21no—
413C4—42no—
414C4—82no—
415C4#1062266212yes—
416C4#1062276312yes—
417C4C2×D8×D1111yescharacteristic
418C4C2×#6696411yescharacteristic
419C4C2×#6699511yescharacteristic
420C4C2×#6700211yescharacteristic
421C2—82no—
422C2—1762no—
423C2#1306808314yesdirect product factor
424C2C2×#1062276311yescharacteristic
425C2C2×#1062266211yescharacteristic
426C2C2×#1062281611yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#474C2
socleC23×C11#121
prime radicalC2×#10622628C2
hypercenterC2×#474D11
hypocenterC11C2×#1685
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622698C2semidirect
3. C2×#10622625C2semidirect
4. #13068083C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622185C2semidirect
7. C2×#10622123C2semidirect
8. C2×C11×#474C2semidirect
17. C11×#474C22semidirect
23. #10622698C22semidirect
27. #10622625C22semidirect
32. #10622185C22semidirect
33. #10622123C22semidirect
34. #10622117C22semidirect
137. C2×C11⋊C8D8semidirect
141. C2×#474D11semidirect
193. C11⋊C8C2×D8semidirect
204. #474C2×D11semidirect
291. C2×C11#1685semidirect
352. C11C2×#1685semidirect
423. C2#13068083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226282
C2×#106226252
#130680832
C2×#106221172
C2×#106221852
C2×#106221232
C2×C11×#4742
C2×#168511