Finite Group Databasebeta

← #13080033

Subgroups — #13080033

Order 1408.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623229C211yesmaximal, characteristic, complemented
2#10623113C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622640C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622496C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622478C211yesmaximal, characteristic, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622432C211yesmaximal, characteristic, complemented
14#10622425C211yesmaximal, characteristic, complemented
15#10622420C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#67000C2211yescharacteristic
19#66999C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22C2×D88C2211yescharacteristic
23C2×D88C2211yescharacteristic
24C2×#4313C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66949—21no—
27#66948—21no—
28#66948—21no—
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic
32#66947—21no—
33#66947—21no—
34#66947—21no—
35#66946C2211yescharacteristic
36#66946C2211yescharacteristic
37#66941C2211yescharacteristic
38#66929—21no—
39#66928—21no—
40#66927C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66925C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44—21no—
61C2×D44—21no—
62C2×D44—21no—
63C2×D44—21no—
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×D44C2311yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C42×C11—21no—
82C42×C11C2311yescharacteristic
83#4325—41no—
84#4325—41no—
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)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4D411yescharacteristic
95(C2×D11)⋊C4D411yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104D88—41no—
105D88—41no—
106#4313—41no—
107C8×D11—41no—
108#3257—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11C2×D411yescharacteristic
113Q8×C11—21no—
114Q8×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126D44—21no—
127D44—21no—
128D44—21no—
129D44—21no—
130D44—21no—
131D44—21no—
132D44—81no—
133D44—81no—
134D44—81no—
135D44—81no—
136D44—81no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—81no—
140C4×D11—81no—
141C4×D11—81no—
142Dic22—81no—
143C8×C11—21no—
144C8×C11—21no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147#542—111no—
148#540—111no—
149#479D1111yescharacteristic, complemented
150#478—111no—
151#476—111no—
152#474—111no—
153#469—111no—
154#468—111no—
155#466—111no—
156#465—111no—
157#463—111no—
158#463—111no—
159#460—111no—
160#459—111no—
161#424—111no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11H(5,𝔽2)11yescharacteristic
182C4×C112−1+411yescharacteristic
183Dic11—21no—
184Dic11—21no—
185Dic11—21no—
186Dic11—41no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×D8—111no—
190C2×D8—111no—
191C2×M16—111no—
192C22×C8—111no—
193C4⋊Q8—111no—
194#127—111no—
195#126—221no—
196#125C2×D1111yescharacteristic
197#124—111no—
198#124—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204#121—111no—
205#121—111no—
206#121—111no—
207#121—221no—
208#121—221no—
209C4×Q8C2×D1111yescharacteristic
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213#117—111no—
214#107—111no—
215#107C2×D1111yescharacteristic
216#106—111no—
217#106C2×D1111yescharacteristic
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221C4⋊C8C2×D1111yescharacteristic
222#103C2×D1111yescharacteristic
223#103C2×D1111yescharacteristic
224#102—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230C2×C11#53711yescharacteristic
231C2×C11#57611yescharacteristic
232C2×C11#57711yescharacteristic
233D11—41no—
234D11—81no—
235D11—81no—
236D11—81no—
237C2×Q8—221no—
238C2×Q8C22×D1111yescharacteristic
239C2×D4—111no—
240C2×D4—111no—
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C22×C4—111no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251SD16—441no—
252SD16—441no—
253D8—441no—
254D8—441no—
255M16—441no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—441no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C4⋊C4C22×D1111yescharacteristic
272C22⋊C4—111no—
273C22⋊C4—111no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C42—21no—
284C42—111no—
285C42C22×D1111yescharacteristic
286C11#325711yescharacteristic, complemented, Sylow
287C23—111no—
288C23—221no—
289C23—221no—
290C23—221no—
291Q8—21no—
292Q8—21no—
293Q8—881no—
294D4—221no—
295D4—221no—
296D4—221no—
297D4—221no—
298D4—221no—
299D4—221no—
300D4—881no—
301D4—881no—
302D4—881no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—881no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4D4×D1111yescharacteristic
319C2×C4D4×D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—21no—
322C8—21no—
323C8—221no—
324C8—221no—
325C22—221no—
326C22—221no—
327C22—221no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—221no—
345C4—221no—
346C4—221no—
347C4—441no—
348C4#6704011yescharacteristic
349C4#6704211yescharacteristic
350C2—441no—
351C2—881no—
352C2—881no—
353C2—881no—
354C2#1062316011yescharacteristic
355C2#1062330011yescharacteristic
356C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
hypercenter#479D11
hypocenterC11#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #10623229C2semidirect
2. #10623113C2semidirect
3. C11×#479C2semidirect
4. #10622679C2semidirect
5. #10622640C2semidirect
6. #10622503C2semidirect
7. #10622496C2semidirect
8. #10622483C2semidirect
9. #10622478C2semidirect
10. #10622456C2semidirect
11. #10622452C2semidirect
12. #10622432C2semidirect
13. #10622432C2semidirect
14. #10622425C2semidirect
15. #10622420C2semidirect
149. #479D11semidirect
286. C11#3257semidirect

Maximal subgroups

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

subgroupindex
#106232292
#106231132
C11×#4792
#106226792
#106226402
#106225032
#106224962
#106224832
#106224782
#106224562
#106224522
#106224322
#106224252
#106224202
#325711