Finite Group Databasebeta

← #13078883

Subgroups — #13078883

Order 1408.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623264C211yesmaximal, characteristic, complemented
2#10623077C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622629C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622495C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic, complemented
13#10622394C211yesmaximal, characteristic
14#10622370C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C11×C4⋊Q8C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#67000—21no—
20#66999—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24C4×C22⋊D11—21no—
25C2×Dic11⋊C4—21no—
26C2×Dic44C2211yescharacteristic
27C2×#4314C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30#66948C2211yescharacteristic
31#66947—21no—
32#66946C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66940C2211yescharacteristic
35#66940C2211yescharacteristic
36(C22⋊D11)⋊C4—21no—
37#66930—21no—
38#66928C2211yescharacteristic
39#66925C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66885C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65#4341—22no—
66#4341—22no—
67C2×D44—21no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22C2311yescharacteristic
73C2×Dic22C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83#4324—22no—
84#4323—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4D411yescharacteristic
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107#4314—22no—
108#3124—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—81no—
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—81no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—21no—
133D44—81no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—81no—
137C4×D11—81no—
138Dic22—21no—
139Dic22—21no—
140Dic22—21no—
141Dic22#4112yes—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#542—111no—
147#520—111no—
148#484—111no—
149#480—111no—
150#477—111no—
151#474D1111yescharacteristic, complemented
152#464—111no—
153#463—111no—
154#452—111no—
155#449—111no—
156#440—111no—
157#440—111no—
158C4×Q16—111no—
159C4×D8—111no—
160#433—111no—
161C22×C11—22no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11C22×D411yescharacteristic
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C11C2×#4111yescharacteristic
178Dic11—22no—
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184C2×#41—111no—
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×D8—111no—
189C4⋊Q8C2×D1111yescharacteristic
190#126—221no—
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×D4—111no—
201C4×D4—111no—
202C4×D4—221no—
203C4×D4—221no—
204C4×D4C2×D1111yescharacteristic
205#117—111no—
206#117—221no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209#107—111no—
210#107—111no—
211#107C2×D1111yescharacteristic
212#107C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8C2×D1111yescharacteristic
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102C2×D1111yescharacteristic
222#102C2×D1111yescharacteristic
223C22⋊C8—111no—
224C22⋊C8—111no—
225#97—111no—
226C4×C8—111no—
227C2×C11—42no—
228C2×C11#52511yescharacteristic
229C2×C11#57611yescharacteristic
230C2×C11#57811yescharacteristic
231D11—41no—
232D11—81no—
233#41—222no—
234#41—222no—
235C2×Q8—21no—
236C2×Q8—111no—
237C2×Q8—111no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4C22×D1111yescharacteristic
242C22×C4—21no—
243C22×C4—111no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248Q16—222no—
249SD16—222no—
250SD16—222no—
251D8—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4C22×D1111yescharacteristic
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—111no—
270C22⋊C4—111no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C42—111no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#312411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—111no—
285C23—221no—
286Q8—81no—
287Q8—112no—
288Q8—221no—
289Q8—221no—
290Q8—221no—
291D4—21no—
292D4—224no—
293D4—221no—
294D4—221no—
295D4—881no—
296D4#434312yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—224no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4D4×D1111yescharacteristic
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—221no—
324C22—221no—
325C22—221no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4C2×#434311yescharacteristic
342C4#41×D1111yescharacteristic
343C2—42no—
344C2—441no—
345C2—881no—
346C2#1062315811yescharacteristic
347C2#1062328811yescharacteristic
348C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
prime radical#10622394C2
hypercenter#474D11
hypocenterC11#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623264C2semidirect
2. #10623077C2semidirect
3. C11×#474C2semidirect
4. #10622704C2semidirect
5. #10622629C2semidirect
6. #10622502C2semidirect
7. #10622497C2semidirect
8. #10622495C2semidirect
9. #10622486C2semidirect
10. #10622458C2semidirect
11. #10622453C2semidirect
12. #10622396C2semidirect
14. #10622370C2semidirect
15. #10622369C2semidirect
151. #474D11semidirect
282. C11#3124semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106230772
C11×#4742
#106227042
#106226292
#106225022
#106224972
#106224952
#106224862
#106224582
#106224532
#106223962
#106223942
#106223702
#106223692
#312411