Finite Group Databasebeta

← #13082703

Subgroups — #13082703

Order 1408.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×C11C211yesmaximal, characteristic, complemented
2Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3Q8×C22⋊D11C211yesmaximal, characteristic, complemented
4#10623343C211yesmaximal, characteristic, complemented
5C2×Q8×Dic11C211yesmaximal, characteristic, complemented
6#10623262C213yesmaximal, complemented
7#10623252C213yesmaximal, complemented
8#10623173C213yesmaximal, complemented
9#10623172C213yesmaximal, complemented
10#10623156C213yesmaximal, complemented
11#10623153C213yesmaximal, complemented
12#10623103C211yesmaximal, characteristic, complemented
13#10623100C211yesmaximal, characteristic, complemented
14#10623072C213yesmaximal, complemented
15#10623069C213yesmaximal
16C22×Q8×C11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C11×C4⋊Q8C2213yes—
20C11×C22⋊Q8C2213yes—
21C11×C22⋊Q8C2213yes—
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2213yes—
24#66999C2213yes—
25#66999C2213yes—
26Q8×Dic11C2213yes—
27Q8×Dic11C2213yes—
28Q8×Dic11C2213yes—
29Q8×Dic11C2213yes—
30Q8×Dic11C2211yescharacteristic
31Q8×Dic11C2211yescharacteristic
32Q8×Dic11C2211yescharacteristic
33#66997C2213yes—
34#66997C2213yes—
35#66992C2211yescharacteristic
36#66988C2213yes—
37C4×C22⋊D11C2213yes—
38C4×C22⋊D11C2213yes—
39#66979C2213yes—
40#66979C2213yes—
41C2×C4⋊Dic11C2213yes—
42#66977C2213yes—
43#66977C2213yes—
44C2×C4×Dic11C2213yes—
45#66951C2213yes—
46#66951C2216yes—
47#66945C2213yes—
48#66943C2216yes—
49#66943C2213yes—
50#66942C2213yes—
51#66942C2216yes—
52#66942C2216yes—
53#66941C2213yes—
54#66940C2216yes—
55#66940C2213yes—
56#66939C2213yes—
57#66938C2213yes—
58#66932C2213yes—
59#66932C2216yes—
60#66931C2213yes—
61#66930C2216yes—
62#66925C2213yes—
63#66923C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C2×Q8×C11—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11C2313yes—
69C2×Q8×C11C2313yes—
70C2×Q8×C11C2311yescharacteristic
71C2×D4×C11C2311yescharacteristic
72C22×C4×C11C2313yes—
73C22×C4×C11C2313yes—
74C2×C22⋊D11C2311yescharacteristic
75C2×C22⋊D11C2311yescharacteristic
76C22×Dic11C2313yes—
77C22×Dic11C2311yescharacteristic
78Q8×D11—24no—
79C2×C4×D11C2313yes—
80C2×Dic22C2313yes—
81C2×Dic22C2313yes—
82C11×C4⋊C4C2313yes—
83C11×C4⋊C4C2316yes—
84C11×C4⋊C4C2313yes—
85C11×C22⋊C4C2313yes—
86C11×C22⋊C4C2313yes—
87C42×C11C2313yes—
88C22⋊Dic11C2313yes—
89C22⋊Dic11C2313yes—
90C22⋊Dic11C2311yescharacteristic
91C22⋊Dic11C2313yes—
92(C2×D11)⋊C4C2311yescharacteristic
93(C2×D11)⋊C4C2313yes—
94(C2×D11)⋊C4C2313yes—
95(C2×D11)⋊C4C2313yes—
96C4⋊Dic11C2313yes—
97C4⋊Dic11C2313yes—
98C4⋊Dic11C2313yes—
99C4⋊Dic11C2313yes—
100C4⋊Dic11C2313yes—
101C4⋊Dic11C2316yes—
102C4⋊Dic11C2313yes—
103Dic11⋊C4C2311yescharacteristic
104Dic11⋊C4C2313yes—
105Dic11⋊C4C2313yes—
106Dic11⋊C4C2316yes—
107Dic11⋊C4C2313yes—
108Dic11⋊C4C2316yes—
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2316yes—
111Dic11⋊C4C2313yes—
112C4×Dic11C2316yes—
113C4×Dic11C2313yes—
114C4×Dic11C2313yes—
115C4×Dic11C2313yes—
116C4×Dic11C2316yes—
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119#3523—111nomaximal, Sylow
120C23×C11C2411yescharacteristic
121C23×C11C2411yescharacteristic
122C22×D11C2411yescharacteristic
123Q8×C11—26no—
124Q8×C11—26no—
125Q8×C11#4114yes—
126D4×C11—22no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11C2413yes—
130C2×C4×C11C2413yes—
131C2×C4×C11C2413yes—
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2413yes—
134C22⋊D11—22no—
135C22⋊D11—22no—
136C2×Dic11—26no—
137C2×Dic11—22no—
138C2×Dic11C2411yescharacteristic
139C2×Dic11C2413yes—
140C2×Dic11C2413yes—
141C2×Dic11C2411yescharacteristic
142C2×Dic11C2413yes—
143C2×Dic11C2413yes—
144C2×Dic11C2411yescharacteristic
145C4×D11—26no—
146Dic22—26no—
147Dic22—26no—
148#557—113no—
149#557—111no—
150#556—113no—
151#552—113no—
152#552—113no—
153D4×Q8—111no—
154D4×Q8—111no—
155D4×Q8D1111yescharacteristic, complemented
156#541—113no—
157#541—113no—
158#533—113no—
159#529—113no—
160#519—111no—
161#519—111no—
162C2×C4×Q8—111no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C112−1+412yes—
169C22×C11C2511yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C4×C11—23no—
174C4×C11—23no—
175C4×C11—21no—
176C4×C11—23no—
177C4×C11C2×#4116yes—
178Dic11—23no—
179Dic11—23no—
180Dic11—23no—
181Dic11—23no—
182Dic11—21no—
183Dic11—21no—
184Dic112−1+412yes—
185C22×Q8—111no—
186C22×Q8C2×D1111yescharacteristic
187C22×Q8C2×D1111yescharacteristic
188C4⋊Q8—113no—
189C4⋊Q8—113no—
190C4⋊Q8—113no—
191C4⋊Q8C2×D1113yes—
192#126—113no—
193#126—116no—
194#126—113no—
195#126—116no—
196#125—113no—
197#125—116no—
198#125—116no—
199#125—116no—
200#125—113no—
201#125—113no—
202#124—113no—
203#123—113no—
204#123—113no—
205C22⋊Q8—113no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8—113no—
209C22⋊Q8—113no—
210C22⋊Q8C2×D1113yes—
211C22⋊Q8C2×D1113yes—
212#121—111no—
213C4×Q8—111no—
214C4×Q8—113no—
215C4×Q8—111no—
216C4×Q8—113no—
217C4×Q8—113no—
218C4×Q8—111no—
219C4×Q8—113no—
220C4×Q8—113no—
221C4×Q8—116no—
222C4×Q8—113no—
223C4×Q8—113no—
224C4×Q8C2×D1111yescharacteristic
225C4×D4—113no—
226C4×D4—113no—
227C4×D4C2×D1113yes—
228#117—113no—
229#117—113no—
230#117—113no—
231#117—116no—
232#117—113no—
233C2×C4⋊C4—113no—
234C2×C42—113no—
235C2×C11—22no—
236C2×C11—41no—
237C2×C11C22×#4111yescharacteristic
238C2×C11C2×2−1+411yescharacteristic
239C2×C11C2×2−1+411yescharacteristic
240D11—41no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—113no—
244C2×Q8—113no—
245C2×Q8—224no—
246C2×Q8C22×D1113yes—
247C2×Q8C22×D1113yes—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—111no—
251C2×D4C22×D1111yescharacteristic
252C22×C4—111no—
253C22×C4—113no—
254C22×C4—113no—
255C22×C4C22×D1113yes—
256C22×C4C22×D1113yes—
257C4⋊C4—113no—
258C4⋊C4—113no—
259C4⋊C4—116no—
260C4⋊C4—113no—
261C4⋊C4—113no—
262C4⋊C4—113no—
263C4⋊C4—113no—
264C4⋊C4—113no—
265C4⋊C4—116no—
266C4⋊C4—116no—
267C4⋊C4—113no—
268C4⋊C4—113no—
269C4⋊C4—111no—
270C4⋊C4—116no—
271C4⋊C4—113no—
272C4⋊C4—113no—
273C4⋊C4C22×D1113yes—
274C4⋊C4C22×D1113yes—
275C4⋊C4C22×D1116yes—
276C22⋊C4—111no—
277C22⋊C4—113no—
278C22⋊C4—113no—
279C22⋊C4—113no—
280C22⋊C4—111no—
281C22⋊C4—113no—
282C22⋊C4—113no—
283C22⋊C4—113no—
284C22⋊C4C22×D1113yes—
285C22⋊C4C22×D1113yes—
286C42—113no—
287C42—113no—
288C42—113no—
289C42—113no—
290C42—116no—
291C42—116no—
292C42—113no—
293C42C22×D1113yes—
294C11#352311yescharacteristic, complemented, Sylow
295C23—111no—
296C23C23×D1111yescharacteristic
297C23C23×D1111yescharacteristic
298Q8—26no—
299Q8—26no—
300Q8—226no—
301Q8—226no—
302Q8#434114yes—
303D4—22no—
304D4—222no—
305D4—222no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—111no—
309C2×C4—113no—
310C2×C4—111no—
311C2×C4—113no—
312C2×C4—111no—
313C2×C4—113no—
314C2×C4—113no—
315C2×C4—222no—
316C2×C4—226no—
317C2×C4—226no—
318C2×C4C23×D1113yes—
319C2×C4C23×D1113yes—
320C2×C4C23×D1113yes—
321C2×C4C23×D1111yescharacteristic
322C2×C4C23×D1113yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22#6704012yes—
332C22C24×D1111yescharacteristic
333C4—23no—
334C4—23no—
335C4—21no—
336C4—23no—
337C4—112no—
338C4—223no—
339C4—223no—
340C4—223no—
341C4—221no—
342C4—221no—
343C4—223no—
344C4C2×#434116yes—
345C2—22no—
346C2—41no—
347C2—441no—
348C2C22×#434111yescharacteristic
349C2C2×#6704011yescharacteristic
350C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingD4×Q8×C11C2
prime radical#66992C22
hypercenterD4×Q8D11
hypocenterC11#3523
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C11C2semidirect
2. Q8×C22⋊D11C2semidirect
3. Q8×C22⋊D11C2semidirect
4. #10623343C2semidirect
5. C2×Q8×Dic11C2semidirect
6. #10623262C2semidirect
7. #10623252C2semidirect
8. #10623173C2semidirect
9. #10623172C2semidirect
10. #10623156C2semidirect
11. #10623153C2semidirect
12. #10623103C2semidirect
13. #10623100C2semidirect
14. #10623072C2semidirect
155. D4×Q8D11semidirect
294. C11#3523semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C112
Q8×C22⋊D112
#106233432
C2×Q8×Dic112
#106232622
#106232522
#106231732
#106231722
#106231562
#106231532
#106231032
#106231002
#106230722
#106230692
#352311