Finite Group Databasebeta

← C2×#13068186 #14736439

Subgroups — C2×#13068186 #14736439

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3C2×#10622637C211yesmaximal, characteristic, complemented
4#13068186C218yesmaximal, direct product factor
5C2×#10622118C211yesmaximal, characteristic, complemented
6C2×#10622185C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic
8C2×C11×#462C211yesmaximal, characteristic, complemented
9C22×C11×Q16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C22×#4325—21no—
13C2×#66927C2211yescharacteristic
14C11×#462—22no—
15C11×#462C2214yescomplemented
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18#10622701—22no—
19#10622701C2214yes—
20#10622640—22no—
21#10622640C2214yes—
22#10622637—22no—
23#10622637C2214yescomplemented
24C2×#66873—21no—
25C2×#66873—21no—
26C2×#66873—21no—
27C2×C4⋊(C11⋊C8)—21no—
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×#66867—21no—
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622185C2214yescomplemented
33#10622123C2214yes—
34#10622118C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11D411yescharacteristic
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C2×C11×Q16—24no—
41C2×C11×Q16—44no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8C2312yes—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4325—24no—
58C2×#4325—44no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×#103—24no—
70#66873—24no—
71#66873—24no—
72#66873—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—24no—
76C4⋊(C11⋊C8)C2312yes—
77C4⋊(C11⋊C8)C2312yes—
78#66867—24no—
79C4×C11⋊C8D412yes—
80C4×C11⋊C8C2312yes—
81C2×#1702—111nomaximal, Sylow
82C23×D11—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11C2×D412yes—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—42no—
107C2×D44—82no—
108C11×Q16—48no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4C2×D412yes—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4325—48no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8C2×D412yes—
133C2×C11⋊C8C2×D412yes—
134C2×#486—111no—
135C2×#462D1111yescharacteristic, complemented
136C2×#460—111no—
137C2×#446—111no—
138#1702—118no—
139C2×#334—111no—
140C2×#332—111no—
141C2×#331—111no—
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—82no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C2×C4×C11AGL(1,ℤ/8)12yes—
166C2×C4×C11#13712yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170D44—42no—
171D44—42no—
172D44—42no—
173D44—42no—
174D44—82no—
175D44—82no—
176D44—82no—
177D44—82no—
178C8×C11—42no—
179C11⋊C8—22no—
180C11⋊C8—22no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C22×Q16—21no—
184C22×SD16—221no—
185C2×C4⋊Q8C2×D1111yescharacteristic
186C2×#127—111no—
187C2×C4×Q8C2×D1111yescharacteristic
188#486—114no—
189#486—222no—
190#462—22no—
191#462C2×D1114yescomplemented
192#460—114no—
193#460—222no—
194#446—114no—
195#446—222no—
196C2×C4⋊C8—111no—
197C2×C4⋊C8—111no—
198C2×C4⋊C8—221no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×#103—21no—
201C2×#102—221no—
202C2×#102—221no—
203C2×#102—221no—
204C2×#97—221no—
205C2×C4×C8—111no—
206#334—114no—
207#332—114no—
208#331—114no—
209C22×C11#46412yes—
210C22×C11#46912yes—
211C22×C11#47112yes—
212C22×C11C2×#12111yescharacteristic
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—164no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—42no—
221C4×C11—82no—
222C4×C11#46412yes—
223C4×C11#46912yes—
224C4×C11C2×#13511yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11C2×#13711yescharacteristic
228C22×Q8—21no—
229C22×Q8C22⋊D1111yescharacteristic
230C22×D4—221no—
231C22×D4—221no—
232C22×D4—221no—
233C2×Q16—24no—
234C2×Q16—44no—
235C2×SD16—224no—
236C2×SD16—444no—
237C22×C8—21no—
238C22×C8—111no—
239C22×C8—111no—
240C22×C8—221no—
241C22×C8—221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22×D1112yes—
246#127—112no—
247#127—221no—
248#127—221no—
249#127—221no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C22⋊D1112yes—
253C4×Q8C22×D1112yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D1111yescharacteristic
258C2×C42—21no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—112no—
263C4⋊C8—224no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C4⋊C8C22×D1112yes—
267#103—24no—
268#102—224no—
269#102—224no—
270#102—224no—
271#97—224no—
272C4×C8—112no—
273C4×C8—112no—
274C2×C11#170214yescomplemented
275C2×C11C2×#46411yescharacteristic
276C2×C11C2×#46911yescharacteristic
277C2×C11C2×#47111yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8C2×C22⋊D1112yes—
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—442no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—442no—
298C2×D4—882no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4D4×D1111yescharacteristic
303C22×C4#434111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305Q16—48no—
306SD16—448no—
307C2×C8—22no—
308C2×C8—42no—
309C2×C8—112no—
310C2×C8—112no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—442no—
316C2×C8—442no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C2×C22⋊D1112yes—
325C42—22no—
326C42—22no—
327C42D4×D1111yescharacteristic
328C42#434111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C42C23×D1111yescharacteristic
331C11C2×#170211yescharacteristic, complemented, Sylow
332C23—442no—
333C23—882no—
334C23—882no—
335C23—882no—
336C23#6699211yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—82no—
343D4—442no—
344D4—442no—
345D4—442no—
346D4—442no—
347D4—882no—
348D4—882no—
349D4—882no—
350D4—882no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4#6697112yes—
359C2×C4#6697212yes—
360C2×C4#6698512yes—
361C2×C4#6699211yescharacteristic
362C2×C4#6699211yescharacteristic
363C2×C4#6699211yescharacteristic
364C2×C4#6700212yes—
365C2×C4C2×D4×D1111yescharacteristic
366C2×C4C2×#434111yescharacteristic
367C2×C4C22×C22⋊D1111yescharacteristic
368C8—42no—
369C8—222no—
370C8—222no—
371C8—442no—
372C8—442no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22—1764no—
377C22#1062265212yes—
378C22#1062279812yes—
379C22#1062281612yes—
380C22C2×#6699211yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4#1062265212yes—
387C4#1062279812yes—
388C4C2×#6697111yescharacteristic
389C4C2×#6697211yescharacteristic
390C4C2×#6698511yescharacteristic
391C4C2×#6700211yescharacteristic
392C2—1762no—
393C2#1306818614yesdirect product factor
394C2C2×#1062279811yescharacteristic
395C2C2×#1062265211yescharacteristic
396C2C2×#1062281611yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#462C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#462D11
hypocenterC11C2×#1702
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×#10622637C2semidirect
4. #13068186C2direct (N × H)
5. C2×#10622118C2semidirect
6. C2×#10622185C2semidirect
8. C2×C11×#462C2semidirect
15. C11×#462C22semidirect
23. #10622637C22semidirect
32. #10622185C22semidirect
34. #10622118C22semidirect
135. C2×#462D11semidirect
191. #462C2×D11semidirect
274. C2×C11#1702semidirect
331. C11C2×#1702semidirect
393. C2#13068186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
C2×#106226372
#130681862
C2×#106221182
C2×#106221852
C2×#106221232
C2×C11×#4622
C2×#170211