Finite Group Databasebeta

← #13079696

Subgroups — #13079696

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#10623206C211yesmaximal, characteristic
2#10623114C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622799C211yesmaximal, characteristic, complemented
5#10622794C211yesmaximal, characteristic, complemented
6#10622786C211yesmaximal, characteristic
7#10622780C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622644C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622410C211yesmaximal, characteristic, complemented
14#10622396C211yesmaximal, characteristic
15#10622381C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22#66999C2211yescharacteristic
23#66997C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28#66989C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×Dic44C2211yescharacteristic
31C2×Dic44C2211yescharacteristic
32#66951—21no—
33#66950C2211yescharacteristic
34#66943C2211yescharacteristic
35#66942—21no—
36#66936—21no—
37#66936—21no—
38#66931—21no—
39#66931—21no—
40#66929—21no—
41#66925C2211yescharacteristic
42#66923—21no—
43#66922C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66874C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64Q8×D11—41no—
65Q8×D11—41no—
66#4341—41no—
67#4341—41no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
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—
81C11×C22⋊C4—21no—
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86#4326—41no—
87#4326—41no—
88#4326—41no—
89#4324—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107Dic11⋊C4D411yescharacteristic
108C4×Dic11—21no—
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113Dic44—41no—
114#3223—111nomaximal, Sylow
115C23×C11—21no—
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C22⋊D11—42no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—42no—
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#464D1111yescharacteristic, complemented
160#462—111no—
161#462—111no—
162#452—111no—
163#452—111no—
164#451—111no—
165#451—111no—
166#433—111no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11H(5,𝔽2)11yescharacteristic
180C4×C11H(5,𝔽2)11yescharacteristic
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
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#124C2×D1111yescharacteristic
208#123—221no—
209#123—221no—
210C22⋊Q8—111no—
211C22⋊Q8—111no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C4×Q8—111no—
215C4×Q8C2×D1111yescharacteristic
216#117—111no—
217C4⋊C8—111no—
218C4⋊C8C2×D1111yescharacteristic
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⋊C8—111no—
229#97—111no—
230C4×C8—111no—
231C2×C11—81no—
232C2×C11#53511yescharacteristic
233C2×C11#57811yescharacteristic
234C2×C11#57811yescharacteristic
235D11—41no—
236#41—441no—
237#41—441no—
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—221no—
247C2×D4C22×D1111yescharacteristic
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
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—21no—
281C22⋊C4—111no—
282C22⋊C4—111no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C42—21no—
288C42—111no—
289C42—221no—
290C42C22×D1111yescharacteristic
291C11#322311yescharacteristic, complemented, Sylow
292C23—21no—
293C23—111no—
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—442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4D4×D1111yescharacteristic
323C2×C4D4×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C8—21no—
326C8—21no—
327C8—221no—
328C8—221no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—221no—
333C22—221no—
334C22—221no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—221no—
342C4—221no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4#6703711yescharacteristic
349C4#6704211yescharacteristic
350C2—81no—
351C2—441no—
352C2#1062313811yescharacteristic
353C2#1062330211yescharacteristic
354C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#464D11
hypocenterC11#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10623114C2semidirect
3. C11×#464C2semidirect
4. #10622799C2semidirect
5. #10622794C2semidirect
7. #10622780C2semidirect
8. #10622667C2semidirect
9. #10622644C2semidirect
10. #10622462C2semidirect
11. #10622453C2semidirect
12. #10622421C2semidirect
13. #10622410C2semidirect
15. #10622381C2semidirect
159. #464D11semidirect
291. C11#3223semidirect

Maximal subgroups

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

subgroupindex
#106232062
#106231142
C11×#4642
#106227992
#106227942
#106227862
#106227802
#106226672
#106226442
#106224622
#106224532
#106224212
#106224102
#106223962
#106223812
#322311