Finite Group Databasebeta

← #13079292

Subgroups — #13079292

Order 1408.

374 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#10623174C211yesmaximal, characteristic, complemented
2#10623150C211yesmaximal, characteristic, complemented
3C11×#468C211yesmaximal, characteristic, complemented
4#10622789C211yesmaximal, characteristic, complemented
5SD16×Dic11C211yesmaximal, characteristic, complemented
6#10622748C211yesmaximal, characteristic, complemented
7#10622735C211yesmaximal, characteristic, complemented
8#10622661C211yesmaximal, characteristic, complemented
9#10622651C211yesmaximal, characteristic, complemented
10#10622489C211yesmaximal, characteristic, complemented
11#10622485C211yesmaximal, characteristic, complemented
12#10622430C211yesmaximal, characteristic, complemented
13#10622413C211yesmaximal, characteristic, complemented
14#10622398C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×M16C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20#67000C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66992—21no—
25#66991—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983C2211yescharacteristic
29#66983C2211yescharacteristic
30#66979C2211yescharacteristic
31C22×C11⋊C8C2211yescharacteristic
32C2×D88C2211yescharacteristic
33#66951—21no—
34#66950—21no—
35#66946C2211yescharacteristic
36#66946C2211yescharacteristic
37#66943C2211yescharacteristic
38#66941C2211yescharacteristic
39#66939—21no—
40#66938—21no—
41#66936—21no—
42#66936—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66881C2211yescharacteristic
51#66879C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C2×D44C2311yescharacteristic
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×Dic22—21no—
73C11×SD16—22no—
74C11×M16—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84C22⋊Dic11D411yescharacteristic
85#4325—22no—
86#4323—22no—
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—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11D411yescharacteristic
96C4⋊Dic11D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8—22no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107D88—22no—
108#3179—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112C22×D11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—81no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—81no—
126C22⋊D11—81no—
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136D44—21no—
137D44—21no—
138D44—21no—
139D44—21no—
140C4×D11—81no—
141C4×D11—81no—
142Dic22—81no—
143C8×C11—21no—
144C8×C11#4112yes—
145C11⋊C8—21no—
146C11⋊C8#4112yes—
147#542—111no—
148#540—111no—
149#501—111no—
150#496—111no—
151#488—111no—
152#486—111no—
153#469—111no—
154#468D1111yescharacteristic, complemented
155#466—111no—
156#465—111no—
157#442—111no—
158#440—111no—
159C4×SD16—111no—
160C4×D8—111no—
161#405—111no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11C2×#4111yescharacteristic
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187C2×SD16—111no—
188C2×SD16C2×D1111yescharacteristic
189C2×D8—111no—
190C2×D8—111no—
191C2×M16C2×D1111yescharacteristic
192C22×C8—111no—
193C4⋊Q8—111no—
194#127—111no—
195#126—221no—
196#125—111no—
197#124—111no—
198#124—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—221no—
203C22⋊Q8C2×D1111yescharacteristic
204#121—111no—
205#121—111no—
206#121—221no—
207#121—221no—
208#121C2×D1111yescharacteristic
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213#117—111no—
214#107—111no—
215#107C2×D1111yescharacteristic
216#106—111no—
217#106—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225#102C2×D1111yescharacteristic
226#97—111no—
227#97—111no—
228C4×C8—111no—
229C4×C8—111no—
230C2×C11—41no—
231C2×C11—81no—
232C2×C11#53211yescharacteristic
233C2×C11#57611yescharacteristic
234C2×C11#57711yescharacteristic
235D11—81no—
236D11—81no—
237C2×Q8—221no—
238C2×Q8C22×D1111yescharacteristic
239C2×D4—21no—
240C2×D4—111no—
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251SD16—22no—
252SD16—222no—
253D8—222no—
254D8—222no—
255M16—22no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—222no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4C22×D1111yescharacteristic
271C4⋊C4C22×D1111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—111no—
275C22⋊C4—111no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C42—111no—
284C42—111no—
285C42—221no—
286C11#317911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—221no—
289C23—221no—
290C23D4×D1111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—881no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—221no—
298D4—221no—
299D4—221no—
300D4—221no—
301D4—881no—
302D4—881no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4D4×D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—21no—
322C8—112no—
323C8—221no—
324C8#434112yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—221no—
343C4—221no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4C2×#434111yescharacteristic
349C4#41×D1111yescharacteristic
350C2—41no—
351C2—81no—
352C2—881no—
353C2—881no—
354C2#1062312711yescharacteristic
355C2#1062330511yescharacteristic
356C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
hypercenter#468D11
hypocenterC11#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623174C2semidirect
2. #10623150C2semidirect
3. C11×#468C2semidirect
4. #10622789C2semidirect
5. SD16×Dic11C2semidirect
6. #10622748C2semidirect
7. #10622735C2semidirect
8. #10622661C2semidirect
9. #10622651C2semidirect
10. #10622489C2semidirect
11. #10622485C2semidirect
12. #10622430C2semidirect
13. #10622413C2semidirect
14. #10622398C2semidirect
15. #10622373C2semidirect
154. #468D11semidirect
286. C11#3179semidirect

Maximal subgroups

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

subgroupindex
#106231742
#106231502
C11×#4682
#106227892
SD16×Dic112
#106227482
#106227352
#106226612
#106226512
#106224892
#106224852
#106224302
#106224132
#106223982
#106223732
#317911