Finite Group Databasebeta

← #13081100

Subgroups — #13081100

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
1#10623261C211yesmaximal, characteristic, complemented
2#10623226C211yesmaximal, characteristic
3C11×#501C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622676C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622495C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622480C211yesmaximal, characteristic, complemented
11#10622477C211yesmaximal, characteristic, complemented
12#10622476C211yesmaximal, characteristic, complemented
13#10622474C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66999—21no—
19#66999—21no—
20C2×#4314C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66951—21no—
24#66950C2211yescharacteristic
25#66950C2211yescharacteristic
26#66948—21no—
27#66948C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946—21no—
31#66946—21no—
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66943—21no—
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D44—21no—
61C2×D44—21no—
62C2×D44D411yescharacteristic
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×C4×D11C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C42×C11C2311yescharacteristic
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11D411yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#4314—22no—
103#4313—22no—
104C8×D11—22no—
105#3346—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122D44—22no—
123D44—21no—
124D44—21no—
125D44—42no—
126D44—81no—
127C4×D11—21no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—81no—
132C4×D11—81no—
133C4×D11—81no—
134C4×D11—81no—
135Dic22—21no—
136Dic22—21no—
137C8×C11—21no—
138C8×C11#4112yes—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#554—111no—
142#553—111no—
143#501D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11#13712yes—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C112−1+411yescharacteristic
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×SD16—111no—
180C2×M16—111no—
181C22×C8—111no—
182C4⋊Q8C2×D1111yescharacteristic
183#126—221no—
184#125—221no—
185#125C2×D1111yescharacteristic
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191#121—111no—
192#121—111no—
193#121—221no—
194C4×Q8—111no—
195C4×D4—111no—
196C4×D4—111no—
197C4×D4—221no—
198C4×D4—221no—
199#117—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#107C2×D1111yescharacteristic
209#106—111no—
210#106C2×D1111yescharacteristic
211#106C2×D1111yescharacteristic
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#97C2×D1111yescharacteristic
222C2×C11#54711yescharacteristic
223C2×C11C2×#13711yescharacteristic
224C2×C11#57611yescharacteristic
225D11—22no—
226D11—41no—
227D11—81no—
228C2×Q8—21no—
229C2×Q8—111no—
230C2×D4—111no—
231C2×D4—111no—
232C2×D4—221no—
233C2×D4—221no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240SD16—222no—
241M16—222no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—222no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
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—111no—
264C22⋊C4—111no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—221no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#334611yescharacteristic, complemented, Sylow
275C23—111no—
276C23—111no—
277C23—221no—
278Q8—81no—
279Q8—221no—
280Q8—221no—
281D4—222no—
282D4—221no—
283D4—221no—
284D4—442no—
285D4—881no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4D4×D1111yescharacteristic
304C2×C4D4×D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—21no—
307C8—221no—
308C8—221no—
309C8#434312yes—
310C22—112no—
311C22—221no—
312C22—221no—
313C22—221no—
314C22—221no—
315C22—221no—
316C22—441no—
317C22—441no—
318C22—441no—
319C22C2×D4×D1111yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—221no—
327C4—221no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4C2×#434311yescharacteristic
332C4#6704011yescharacteristic
333C2—222no—
334C2—441no—
335C2—881no—
336C2#1062325711yescharacteristic
337C2#1062330511yescharacteristic
338C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radical#10623226C2
hypercenter#501D11
hypocenterC11#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #10623261C2semidirect
3. C11×#501C2semidirect
4. #10622700C2semidirect
5. #10622676C2semidirect
6. #10622499C2semidirect
7. #10622497C2semidirect
8. #10622495C2semidirect
9. D11×#107C2semidirect
10. #10622480C2semidirect
11. #10622477C2semidirect
12. #10622476C2semidirect
13. #10622474C2semidirect
14. #10622323C2semidirect
15. #10622319C2semidirect
143. #501D11semidirect
274. C11#3346semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106232262
C11×#5012
#106227002
#106226762
#106224992
#106224972
#106224952
D11×#1072
#106224802
#106224772
#106224762
#106224742
#106223232
#106223192
#334611