Finite Group Databasebeta

← #13081101

Subgroups — #13081101

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#553C211yesmaximal, characteristic
2#10623074C211yesmaximal, characteristic, complemented
3#10622678C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622655C211yesmaximal, characteristic, complemented
6#10622654C211yesmaximal, characteristic, complemented
7#10622647C211yesmaximal, characteristic, complemented
8#10622646C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622624C211yesmaximal, characteristic, complemented
11#10622620C211yesmaximal, characteristic, complemented
12#10622609C211yesmaximal, characteristic, complemented
13#10622608C211yesmaximal, characteristic, complemented
14#10622583C211yesmaximal, characteristic, complemented
15C2×#66871C211yesmaximal, characteristic, complemented
16C11×#126—21no—
17C11×#125C2211yescharacteristic
18C11×#123—21no—
19C11×#121—21no—
20C11×#121C2211yescharacteristic
21C11×#121C2211yescharacteristic
22C4×D4×C11—21no—
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27D4×Dic11—21no—
28C2×#4324C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31#66977C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66943—21no—
36#66931—21no—
37#66931—21no—
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66896C2211yescharacteristic
41#66896C2211yescharacteristic
42#66896C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66874C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11D411yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4D411yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4D411yescharacteristic
83C11×C22⋊C4D411yescharacteristic
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4324—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3346—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109D4×C11—22no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—42no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8#4112yes—
141#554—111no—
142#553D1111yescharacteristic
143#501—111no—
144#485—111no—
145#484—111no—
146#481—111no—
147#480—111no—
148#479—111no—
149#474—111no—
150#468—111no—
151#465—111no—
152#440—111no—
153#435—111no—
154#428—111no—
155C2×#107—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11#13712yes—
165C22×C11C22×D411yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C112−1+411yescharacteristic
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×SD16—111no—
180C2×M16—111no—
181C22×C8—111no—
182C4⋊Q8—111no—
183#126—21no—
184#125—221no—
185#125C2×D1111yescharacteristic
186#123—21no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191#121—21no—
192#121C2×D1111yescharacteristic
193#121C2×D1111yescharacteristic
194C4×Q8—111no—
195C4×D4—21no—
196C4×D4—221no—
197C4×D4C2×D1111yescharacteristic
198C4×D4C2×D1111yescharacteristic
199#117C2×D1111yescharacteristic
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4C2×D1111yescharacteristic
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#106—111no—
210#106—111no—
211#106—111no—
212C4⋊C8—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219C22⋊C8—111no—
220C22⋊C8—111no—
221#97—111no—
222C2×C11—22no—
223C2×C11—41no—
224C2×C11—81no—
225C2×C11#54711yescharacteristic
226C2×C11C2×#13711yescharacteristic
227C2×C11#57611yescharacteristic
228C2×Q8—111no—
229C2×Q8—221no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4C22⋊D1111yescharacteristic
233C2×D4C22×D1111yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4C22×D1111yescharacteristic
239C22×C4C22×D1111yescharacteristic
240SD16—222no—
241M16—222no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22⋊D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4C22⋊D1111yescharacteristic
270C22⋊C4C22⋊D1111yescharacteristic
271C42—21no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#334611yescharacteristic, complemented, Sylow
275C23—21no—
276C23C2×C22⋊D1111yescharacteristic
277C23C2×C22⋊D1111yescharacteristic
278Q8—221no—
279Q8—221no—
280Q8—881no—
281D4—22no—
282D4—21no—
283D4—21no—
284D4—42no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×C22⋊D1111yescharacteristic
302C2×C4C2×C22⋊D1111yescharacteristic
303C2×C4C2×C22⋊D1111yescharacteristic
304C2×C4C2×C22⋊D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—112no—
307C8—221no—
308C8—221no—
309C8—221no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#6700412yes—
319C22C22×C22⋊D1111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4#41×D1111yescharacteristic
332C4#6704311yescharacteristic
333C2—22no—
334C2—41no—
335C2—81no—
336C2C2×#6700411yescharacteristic
337C2#1062335511yescharacteristic
338C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#553C2
socleC22×C11C22×D4
hypercenter#553D11
hypocenterC11#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
2. #10623074C2semidirect
3. #10622678C2semidirect
4. #10622676C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622647C2semidirect
8. #10622646C2semidirect
9. #10622631C2semidirect
10. #10622624C2semidirect
11. #10622620C2semidirect
12. #10622609C2semidirect
13. #10622608C2semidirect
14. #10622583C2semidirect
15. C2×#66871C2semidirect
274. C11#3346semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
#106230742
#106226782
#106226762
#106226552
#106226542
#106226472
#106226462
#106226312
#106226242
#106226202
#106226092
#106226082
#106225832
C2×#668712
#334611