Finite Group Databasebeta

← #13080741

Subgroups — #13080741

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623249C211yesmaximal, characteristic
2#10623225C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic, complemented
4#10622688C211yesmaximal, characteristic, complemented
5#10622676C211yesmaximal, characteristic, complemented
6#10622396C211yesmaximal, characteristic, complemented
7#10622396C211yesmaximal, characteristic, complemented
8#10622393C211yesmaximal, characteristic, complemented
9#10622392C211yesmaximal, characteristic, complemented
10#10622391C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622385C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C11×#127C2211yescharacteristic
19C11×#125C2211yescharacteristic
20#66993—21no—
21#66992—21no—
22#66992—21no—
23#66991C2211yescharacteristic
24#66991C2211yescharacteristic
25D4×Dic11—21no—
26C2×#4324C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×Dic44C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30C2×C8×D11C2211yescharacteristic
31#66951—21no—
32#66950C2211yescharacteristic
33#66950C2211yescharacteristic
34#66947—21no—
35#66945—21no—
36#66945C2211yescharacteristic
37C4⋊C4×D11C2211yescharacteristic
38#66943—21no—
39C4×D44C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69#4341—22no—
70#4341—22no—
71#4341—41no—
72#4341—41no—
73C2×D44D411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×C4×D11C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4324—41no—
89#4324—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11D411yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108Dic44—22no—
109#4313—41no—
110C8×D11—41no—
111#3317—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C22×D11C2×D411yescharacteristic
115C22×D11C2×D411yescharacteristic
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—42no—
121D4×C11—81no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—42no—
128C22⋊D11—42no—
129C22⋊D11—81no—
130C22⋊D11—81no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—41no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22#4112yes—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#552—111no—
154#550—111no—
155#490D1111yescharacteristic, complemented
156#482—111no—
157#481—111no—
158#479—111no—
159#468—111no—
160#465—111no—
161#460—111no—
162#452—111no—
163#452—111no—
164#441—111no—
165#435—111no—
166#417—111no—
167#416—111no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—22no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41—111no—
195C2×Q16—111no—
196C2×SD16—111no—
197C2×SD16—111no—
198C2×M16—111no—
199C22×C8—111no—
200#127—221no—
201#127C2×D1111yescharacteristic
202#126—221no—
203#125—221no—
204#125C2×D1111yescharacteristic
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121—221no—
212C4×Q8—111no—
213C4×Q8—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—111no—
217#117—221no—
218C2×C4⋊C4—111no—
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#102—111no—
228#102—111no—
229#102C2×D1111yescharacteristic
230#102C2×D1111yescharacteristic
231#102C2×D1111yescharacteristic
232#102C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8—111no—
235#97C2×D1111yescharacteristic
236C2×C11—81no—
237C2×C11—81no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—41no—
242D11—41no—
243#41—222no—
244#41—222no—
245#41—441no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4C22×D1111yescharacteristic
257C2×D4C22×D1111yescharacteristic
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263Q16—222no—
264SD16—441no—
265SD16—441no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—441no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4C22×D1111yescharacteristic
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—111no—
285C22⋊C4—111no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C42—221no—
292C42—221no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#331711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—111no—
299C23—111no—
300Q8—112no—
301Q8—221no—
302Q8—221no—
303Q8—221no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—441no—
311D4—442no—
312D4—442no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4D4×D1111yescharacteristic
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—221no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—222no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4#41×D1111yescharacteristic
361C4#6704211yescharacteristic
362C2—81no—
363C2—81no—
364C2—441no—
365C2—441no—
366C2#1062320711yescharacteristic
367C2#1062330411yescharacteristic
368C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radical#10623249C2
hypercenter#490D11
hypocenterC11#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #10623225C2semidirect
3. C11×#490C2semidirect
4. #10622688C2semidirect
5. #10622676C2semidirect
6. #10622396C2semidirect
7. #10622396C2semidirect
8. #10622393C2semidirect
9. #10622392C2semidirect
10. #10622391C2semidirect
11. #10622390C2semidirect
12. #10622385C2semidirect
13. #10622384C2semidirect
14. #10622329C2semidirect
15. #10622319C2semidirect
155. #490D11semidirect
295. C11#3317semidirect

Maximal subgroups

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

subgroupindex
#106232492
#106232252
C11×#4902
#106226882
#106226762
#106223962
#106223932
#106223922
#106223912
#106223902
#106223852
#106223842
#106223292
#106223192
#331711