Finite Group Databasebeta

← #13081324

Subgroups — #13081324

Order 1408.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623084C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#442C211yesmaximal, characteristic, complemented
4#10622763C211yesmaximal, characteristic, complemented
5#10622763C211yesmaximal, characteristic, complemented
6#10622628C211yesmaximal, characteristic, complemented
7#10622622C211yesmaximal, characteristic, complemented
8#10622484C211yesmaximal, characteristic, complemented
9#10622483C211yesmaximal, characteristic, complemented
10#10622398C211yesmaximal, characteristic, complemented
11#10622377C211yesmaximal, characteristic, complemented
12#10622373C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic, complemented
14#10622326C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×D8C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66993C2211yescharacteristic
21#66993C2211yescharacteristic
22D4×Dic11C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26#66983—21no—
27#66977—21no—
28C2×Dic11⋊C4—21no—
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66943C2211yescharacteristic
32#66941C2211yescharacteristic
33#66937—21no—
34#66937—21no—
35#66931—21no—
36#66931—21no—
37#66927C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69#4339—44no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×Dic22—21no—
77C2×Dic22D411yescharacteristic
78C11×D8—22no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4323—22no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11D411yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#3366—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11—21no—
109C22×D11—21no—
110C22×D11—21no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11#4112yescomplemented
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—81no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—42no—
123C22⋊D11—42no—
124C22⋊D11—81no—
125C22⋊D11—81no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11—81no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—42no—
139D44—81no—
140C4×D11—42no—
141C4×D11—42no—
142Dic22—22no—
143Dic22—81no—
144C8×C11—21no—
145C8×C11—21no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148#554—111no—
149#550—111no—
150#490—111no—
151#490—111no—
152#486—111no—
153#478—111no—
154#478—111no—
155#476—111no—
156#459—111no—
157#459—111no—
158#459—111no—
159#446—111no—
160#442—111no—
161#442D1111yescharacteristic, complemented
162C4×D8—111no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11C22×D411yescharacteristic
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C112−1+411yescharacteristic
182Dic11—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11AGL(1,ℤ/8)12yes—
188C2×#41—221no—
189C2×D8—111no—
190C2×D8—111no—
191C2×D8C2×D1111yescharacteristic
192C4⋊Q8—111no—
193#127—111no—
194#127—111no—
195#127—111no—
196#125—111no—
197#125—111no—
198C22⋊Q8—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201#121—221no—
202#121—221no—
203#121—221no—
204C4×Q8—111no—
205C4×D4—111no—
206C4×D4—111no—
207C4×D4—111no—
208C4×D4—111no—
209C4×D4C2×D1111yescharacteristic
210C4×D4C2×D1111yescharacteristic
211C2×C4⋊C4—221no—
212#107—111no—
213#106—111no—
214#106C2×D1111yescharacteristic
215C4⋊C8—111no—
216C4⋊C8—111no—
217C4⋊C8—111no—
218#102—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225#102—111no—
226#102C2×D1111yescharacteristic
227#102C2×D1111yescharacteristic
228#97—111no—
229#97C2×D1111yescharacteristic
230C4×C8—111no—
231C2×C11—42no—
232C2×C11—81no—
233C2×C11#54811yescharacteristic
234C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C11#57611yescharacteristic
236D11—81no—
237D11—81no—
238#41—444no—
239C2×Q8—111no—
240C2×Q8—221no—
241C2×D4—111no—
242C2×D4—111no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4C22×D1111yescharacteristic
250C2×D4C22×D1111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257D8—22no—
258D8—222no—
259D8—222no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8C22×D1111yescharacteristic
263C2×C8C22×D1111yescharacteristic
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—111no—
268C4⋊C4—111no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C42—111no—
283C42—111no—
284C42C22×D1111yescharacteristic
285C11#336611yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—221no—
289C23—221no—
290Q8—222no—
291Q8—881no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—221no—
296D4—221no—
297D4—221no—
298D4—221no—
299D4—442no—
300D4—442no—
301D4—442no—
302D4—881no—
303D4—881no—
304D4—881no—
305D4#433912yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—881no—
320C2×C4D4×D1111yescharacteristic
321C2×C4D4×D1111yescharacteristic
322C2×C4C23×D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—221no—
326C8—221no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22—441no—
338C22—441no—
339C22C2×D4×D1111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—112no—
345C4—221no—
346C4—221no—
347C4—221no—
348C4—441no—
349C4—441no—
350C4C2×#433911yescharacteristic
351C4#6704311yescharacteristic
352C2—42no—
353C2—81no—
354C2—881no—
355C2—881no—
356C2#1062308311yescharacteristic
357C2D11×AGL(1,ℤ/8)11yescharacteristic
358C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
hypercenter#442D11
hypocenterC11#3366
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10623084C2semidirect
2. #10623070C2semidirect
3. C11×#442C2semidirect
4. #10622763C2semidirect
5. #10622763C2semidirect
6. #10622628C2semidirect
7. #10622622C2semidirect
8. #10622484C2semidirect
9. #10622483C2semidirect
10. #10622398C2semidirect
11. #10622377C2semidirect
12. #10622373C2semidirect
13. #10622369C2semidirect
14. #10622326C2semidirect
15. #10622314C2semidirect
114. D4×C11#41semidirect
161. #442D11semidirect
285. C11#3366semidirect
305. D4#4339semidirect

Maximal subgroups

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

subgroupindex
#106230842
#106230702
C11×#4422
#106227632
#106226282
#106226222
#106224842
#106224832
#106223982
#106223772
#106223732
#106223692
#106223262
#106223142
#336611