Finite Group Databasebeta

← #13080866

Subgroups — #13080866

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#10623226C211yesmaximal, characteristic, complemented
2#10623107C211yesmaximal, characteristic, complemented
3C11×#479C211yesmaximal, characteristic, complemented
4#10622681C211yesmaximal, characteristic, complemented
5C4×#4325C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622498C211yesmaximal, characteristic, complemented
8#10622478C211yesmaximal, characteristic, complemented
9#10622475C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622451C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622416C211yesmaximal, characteristic, complemented
15#10622415C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C11×#125C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21C2×D88C2211yescharacteristic
22C2×#4314C2211yescharacteristic
23C2×#4313C2211yescharacteristic
24C2×#4313C2211yescharacteristic
25#66951—21no—
26#66950—21no—
27#66950C2211yescharacteristic
28#66948—21no—
29#66948—21no—
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66946—21no—
35#66945C2211yescharacteristic
36C4⋊C4×D11C2211yescharacteristic
37#66928—21no—
38#66928C2211yescharacteristic
39C4×D44—21no—
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×C4⋊C8C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#103C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60#4343—22no—
61#4343—41no—
62Q8×D11—22no—
63Q8×D11—41no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44D411yescharacteristic
69C2×D44C2311yescharacteristic
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×C4×D11C2311yescharacteristic
77C2×Dic22—21no—
78C2×Dic22C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C42×C11—21no—
88C42×C11C2311yescharacteristic
89#4325—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4D411yescharacteristic
99(C2×D11)⋊C4D411yescharacteristic
100C4⋊Dic11—21no—
101C4⋊Dic11D411yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107D88—41no—
108#4314—41no—
109#4313—41no—
110#4313—41no—
111#3326—111nomaximal, Sylow
112C22×D11—21no—
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11#4112yes—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129D44—21no—
130D44—21no—
131D44—21no—
132D44—21no—
133D44—41no—
134D44—42no—
135D44—42no—
136D44—42no—
137D44—81no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—42no—
143C4×D11—42no—
144C4×D11—81no—
145C4×D11—81no—
146Dic22—21no—
147Dic22—21no—
148Dic22—42no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#553—111no—
154#548—111no—
155#488—111no—
156#483—111no—
157#482—111no—
158#479D1111yescharacteristic, complemented
159#469—111no—
160#468—111no—
161#463—111no—
162#449—111no—
163#448—111no—
164C4×SD16—111no—
165#436—111no—
166#419—111no—
167#417—111no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8—111no—
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×M16—111no—
199C2×M16—111no—
200#126—221no—
201#125C2×D1111yescharacteristic
202#124—111no—
203#124—221no—
204#123—221no—
205C22⋊Q8—111no—
206C22⋊Q8—221no—
207#121—111no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121—221no—
212C4×Q8C2×D1111yescharacteristic
213C4×D4—111no—
214C4×D4—111no—
215C4×D4—221no—
216C4×D4—221no—
217#117—111no—
218C2×C4⋊C4—111no—
219#107C2×D1111yescharacteristic
220#106—111no—
221#106C2×D1111yescharacteristic
222C4⋊C8C2×D1111yescharacteristic
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233C22⋊C8—111no—
234C22⋊C8—111no—
235C4×C8—111no—
236C2×C11#54611yescharacteristic
237C2×C11#57511yescharacteristic
238C2×C11#57711yescharacteristic
239D11—41no—
240D11—41no—
241D11—81no—
242D11—81no—
243#41—222no—
244#41—441no—
245C2×Q8—111no—
246C2×Q8—221no—
247C2×Q8—222no—
248C2×Q8—441no—
249C2×Q8C22×D1111yescharacteristic
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—111no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263SD16—222no—
264SD16—441no—
265D8—441no—
266M16—441no—
267M16—441no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—111no—
283C22⋊C4—111no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—21no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#332611yescharacteristic, complemented, Sylow
296C23—111no—
297C23—111no—
298C23—221no—
299C23—221no—
300Q8—21no—
301Q8—221no—
302Q8—221no—
303Q8—442no—
304Q8#434312yes—
305D4—221no—
306D4—221no—
307D4—221no—
308D4—221no—
309D4—441no—
310D4—442no—
311D4—442no—
312D4—442no—
313D4—881no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4D4×D1111yescharacteristic
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—221no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22—221no—
342C22—221no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—441no—
360C4C2×#434311yescharacteristic
361C4#6704211yescharacteristic
362C2—441no—
363C2—441no—
364C2—881no—
365C2—881no—
366C2#1062316111yescharacteristic
367C2#1062329911yescharacteristic
368C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
hypercenter#479D11
hypocenterC11#3326
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. #10623226C2semidirect
2. #10623107C2semidirect
3. C11×#479C2semidirect
4. #10622681C2semidirect
5. C4×#4325C2semidirect
6. #10622499C2semidirect
7. #10622498C2semidirect
8. #10622478C2semidirect
9. #10622475C2semidirect
10. #10622457C2semidirect
11. #10622451C2semidirect
12. #10622424C2semidirect
13. #10622419C2semidirect
14. #10622416C2semidirect
15. #10622415C2semidirect
158. #479D11semidirect
295. C11#3326semidirect

Maximal subgroups

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

subgroupindex
#106232262
#106231072
C11×#4792
#106226812
C4×#43252
#106224992
#106224982
#106224782
#106224752
#106224572
#106224512
#106224242
#106224192
#106224162
#106224152
#332611