Finite Group Databasebeta

← #13079697

Subgroups — #13079697

Order 1408.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623356C211yesmaximal, characteristic
2#10623156C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic
4#10622852C211yesmaximal, characteristic
5#10622795C211yesmaximal, characteristic, complemented
6#10622794C211yesmaximal, characteristic, complemented
7#10622780C211yesmaximal, characteristic, complemented
8#10622779C211yesmaximal, characteristic, complemented
9#10622663C211yesmaximal, characteristic, complemented
10#10622410C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic, complemented
13#10622380C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66997C2211yescharacteristic
23#66997C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28#66989C2211yescharacteristic
29#66989C2211yescharacteristic
30#66988—21no—
31#66988—21no—
32C2×#4324C2211yescharacteristic
33#66979C2211yescharacteristic
34#66977—21no—
35#66977—21no—
36#66977C2211yescharacteristic
37C2×Dic44C2211yescharacteristic
38C2×Dic44C2211yescharacteristic
39#66943—21no—
40#66943C2211yescharacteristic
41#66942—21no—
42#66940C2211yescharacteristic
43#66932—21no—
44#66932—21no—
45C11×#103C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66874C2211yescharacteristic
58#66874C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—21no—
68C2×Dic22—21no—
69C2×Dic22—41no—
70C2×Dic22—41no—
71C2×Dic22C2311yescharacteristic
72C2×Dic22C2311yescharacteristic
73C2×Dic22C2311yescharacteristic
74C11×Q16—41no—
75C11×SD16—41no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11D411yescharacteristic
87C22⋊Dic11D411yescharacteristic
88#4326—41no—
89#4326—41no—
90#4326—41no—
91#4324—41no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11D411yescharacteristic
95C4⋊Dic11D411yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11C2311yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113Dic44—41no—
114#3223—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—42no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—42no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#541—111no—
153#536—111no—
154#497—111no—
155#494—111no—
156#491—111no—
157#488—111no—
158#464—111no—
159#464—111no—
160#462—111no—
161#462—111no—
162#452—111no—
163#452D1111yescharacteristic
164#451—111no—
165#451—111no—
166#433—111no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C4×C11—21no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11H(5,𝔽2)11yescharacteristic
179C4×C11H(5,𝔽2)11yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41C2×D1111yescharacteristic
189C22×Q8—111no—
190C2×Q16—111no—
191C2×Q16—111no—
192C2×Q16—111no—
193C2×Q16—111no—
194C2×Q16—111no—
195C2×Q16C2×D1111yescharacteristic
196C2×SD16—111no—
197C2×SD16C2×D1111yescharacteristic
198C4⋊Q8—111no—
199C4⋊Q8—111no—
200C4⋊Q8—111no—
201#126—221no—
202#126—221no—
203#125—111no—
204#125—221no—
205#125—221no—
206#124—111no—
207#124—111no—
208#123—221no—
209#123—221no—
210C22⋊Q8—111no—
211C22⋊Q8—221no—
212C22⋊Q8—221no—
213C22⋊Q8C2×D1111yescharacteristic
214C4×Q8—111no—
215C4×Q8—111no—
216#117—111no—
217C4⋊C8—111no—
218C4⋊C8—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103C2×D1111yescharacteristic
225#102—111no—
226#102C2×D1111yescharacteristic
227C22⋊C8—111no—
228C22⋊C8C2×D1111yescharacteristic
229#97—111no—
230C4×C8—111no—
231C2×C11—41no—
232C2×C11—81no—
233C2×C11#53511yescharacteristic
234C2×C11#57811yescharacteristic
235C2×C11#57811yescharacteristic
236#41—41no—
237#41—41no—
238C2×Q8—111no—
239C2×Q8—111no—
240C2×Q8—111no—
241C2×Q8—221no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8C22×D1111yescharacteristic
245C2×Q8C22×D1111yescharacteristic
246C2×D4—21no—
247C2×D4C22×D1111yescharacteristic
248C22×C4—21no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251Q16—41no—
252Q16—441no—
253Q16—441no—
254Q16—441no—
255Q16—441no—
256Q16—441no—
257SD16—41no—
258SD16—441no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4C22×D1111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—111no—
281C22⋊C4—111no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C42—111no—
288C42—111no—
289C42—221no—
290C42—221no—
291C11#322311yescharacteristic, complemented, Sylow
292C23—21no—
293C23D4×D1111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—221no—
299Q8—221no—
300Q8—221no—
301Q8—221no—
302Q8—221no—
303Q8—221no—
304Q8—442no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—111no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—442no—
323C2×C4D4×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C8—21no—
326C8—21no—
327C8—221no—
328C8—221no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—221no—
341C4—221no—
342C4—221no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4#6703711yescharacteristic
349C4#6703711yescharacteristic
350C2—41no—
351C2—81no—
352C2#1062312311yescharacteristic
353C2#1062330211yescharacteristic
354C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#452D11
hypocenterC11#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10623156C2semidirect
5. #10622795C2semidirect
6. #10622794C2semidirect
7. #10622780C2semidirect
8. #10622779C2semidirect
9. #10622663C2semidirect
10. #10622410C2semidirect
11. #10622406C2semidirect
12. #10622381C2semidirect
13. #10622380C2semidirect
14. #10622352C2semidirect
15. #10622333C2semidirect
291. C11#3223semidirect

Maximal subgroups

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

subgroupindex
#106233562
#106231562
C11×#4522
#106228522
#106227952
#106227942
#106227802
#106227792
#106226632
#106224102
#106224062
#106223812
#106223802
#106223522
#106223332
#322311