Finite Group Databasebeta

← #13078826

Subgroups — #13078826

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623114C211yesmaximal, characteristic, complemented
2#10623077C211yesmaximal, characteristic
3C4×C11×SD16C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic
5#10622775C211yesmaximal, characteristic, complemented
6#10622643C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622422C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic
13#10622379C211yesmaximal, characteristic, complemented
14C4×Dic44C211yesmaximal, characteristic, complemented
15#10622303C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25C4×C22⋊D11—21no—
26C2×Dic11⋊C4—21no—
27C2×Dic44C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943C2211yescharacteristic
32#66942—21no—
33#66940C2211yescharacteristic
34(C22⋊D11)⋊C4—21no—
35#66930—21no—
36#66929—21no—
37#66925C2211yescharacteristic
38#66923—21no—
39C4×Dic22C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C4×C8×C11C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65#4341—22no—
66#4341—22no—
67C2×C4×D11—21no—
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C11×SD16—22no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81#4326—22no—
82#4324—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4D411yescharacteristic
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108#3120—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11#4112yes—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—81no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—24no—
123C2×Dic11—24no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—81no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22#4112yes—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#541—111no—
144#520—111no—
145#484—111no—
146#483—111no—
147#479—111no—
148#478—111no—
149#462—111no—
150#461—111no—
151#452—111no—
152#452—111no—
153#441—111no—
154#440—111no—
155C4×Q16—111no—
156C4×SD16D1111yescharacteristic, complemented
157#433—111no—
158C22×C11—22no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C2×D11—21no—
163C2×D11—21no—
164C2×D11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C11C2×#4111yescharacteristic
172Dic11—22no—
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×#41—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×SD16—111no—
183C2×SD16C2×D1111yescharacteristic
184C4⋊Q8—111no—
185#126—221no—
186#126—221no—
187#125—111no—
188#125—221no—
189#125—221no—
190C22⋊Q8—111no—
191C22⋊Q8—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8C2×D1111yescharacteristic
196C4×D4—111no—
197C4×D4—221no—
198C4×D4—221no—
199C4×D4C2×D1111yescharacteristic
200#117—111no—
201#117—221no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204#107—111no—
205#107—111no—
206#106—111no—
207#106C2×D1111yescharacteristic
208C4⋊C8—111no—
209C4⋊C8—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103C2×D1111yescharacteristic
216#102—111no—
217#102C2×D1111yescharacteristic
218C22⋊C8—111no—
219C22⋊C8—111no—
220#97—111no—
221C4×C8C2×D1111yescharacteristic
222C2×C11—42no—
223C2×C11#52511yescharacteristic
224C2×C11#57711yescharacteristic
225C2×C11#57811yescharacteristic
226D11—41no—
227#41—222no—
228#41—222no—
229C2×Q8—111no—
230C2×Q8—111no—
231C2×Q8C22×D1111yescharacteristic
232C2×D4—221no—
233C2×D4C22×D1111yescharacteristic
234C22×C4—21no—
235C22×C4—111no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239Q16—222no—
240Q16—222no—
241SD16—22no—
242SD16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—111no—
266C22⋊C4—111no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C42—21no—
271C42—111no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#312011yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279Q8—21no—
280Q8—21no—
281Q8—112no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285D4—21no—
286D4—224no—
287D4#433912yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—224no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—221no—
315C22—221no—
316C22—221no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—222no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4C2×#433911yescharacteristic
331C4#41×D1111yescharacteristic
332C2—42no—
333C2—441no—
334C2#1062307811yescharacteristic
335C2#1062329311yescharacteristic
336C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenterC4×SD16D11
hypocenterC11#3120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10623114C2semidirect
3. C4×C11×SD16C2semidirect
5. #10622775C2semidirect
6. #10622643C2semidirect
7. #10622631C2semidirect
8. #10622475C2semidirect
9. #10622470C2semidirect
10. #10622422C2semidirect
11. #10622406C2semidirect
13. #10622379C2semidirect
14. C4×Dic44C2semidirect
15. #10622303C2semidirect
156. C4×SD16D11semidirect
276. C11#3120semidirect

Maximal subgroups

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

subgroupindex
#106231142
#106230772
C4×C11×SD162
#106227862
#106227752
#106226432
#106226312
#106224752
#106224702
#106224222
#106224062
#106223962
#106223792
C4×Dic442
#106223032
#312011