Finite Group Databasebeta

← #13080865

Subgroups — #13080865

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#10623348C211yesmaximal, characteristic, complemented
2#10623061C211yesmaximal, characteristic, complemented
3C11×#419C211yesmaximal, characteristic, complemented
4#10622840C211yesmaximal, characteristic, complemented
5#10622748C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622616C211yesmaximal, characteristic, complemented
8#10622432C211yesmaximal, characteristic, complemented
9#10622425C211yesmaximal, characteristic, complemented
10#10622424C211yesmaximal, characteristic, complemented
11#10622418C211yesmaximal, characteristic, complemented
12#10622416C211yesmaximal, characteristic, complemented
13#10622413C211yesmaximal, characteristic, complemented
14#10622412C211yesmaximal, characteristic, complemented
15#10622401C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#67000—21no—
21#67000C2211yescharacteristic
22#66999—21no—
23#66999C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27#66983—21no—
28#66983C2211yescharacteristic
29#66983C2211yescharacteristic
30C4×C22⋊D11—21no—
31C4×C22⋊D11C2211yescharacteristic
32C2×D88C2211yescharacteristic
33C2×#4313C2211yescharacteristic
34#66948C2211yescharacteristic
35#66946C2211yescharacteristic
36C4⋊C4×D11C2211yescharacteristic
37#66943C2211yescharacteristic
38#66937—21no—
39#66936—21no—
40#66929—21no—
41C4×D44—21no—
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66881C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69#4343—22no—
70#4343—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C11×M16—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C22⋊Dic11D411yescharacteristic
87#4325—22no—
88#4325—41no—
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)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109D88—41no—
110#4313—41no—
111#3326—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—42no—
120Q8×C11#4112yes—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—42no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—41no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140D44—21no—
141D44—21no—
142D44—42no—
143D44—42no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147C4×D11—81no—
148C4×D11—81no—
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#479—111no—
159#469—111no—
160#468—111no—
161#463—111no—
162#449—111no—
163#448—111no—
164C4×SD16—111no—
165#436—111no—
166#419D1111yescharacteristic, complemented
167#417—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C22×D411yescharacteristic
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—21no—
182C4×C11—22no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11C2×#4111yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8C2×D1111yescharacteristic
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×M16—111no—
199C2×M16C2×D1111yescharacteristic
200#126—221no—
201#125—111no—
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×Q8—111no—
213C4×D4—111no—
214C4×D4—111no—
215C4×D4—221no—
216C4×D4—221no—
217#117C2×D1111yescharacteristic
218C2×C4⋊C4—111no—
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#103C2×D1111yescharacteristic
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—41no—
237C2×C11#54611yescharacteristic
238C2×C11#57511yescharacteristic
239C2×C11#57711yescharacteristic
240D11—41no—
241D11—81no—
242D11—81no—
243#41—222no—
244#41—441no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8C22×D1111yescharacteristic
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—21no—
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263SD16—222no—
264SD16—441no—
265D8—441no—
266M16—41no—
267M16—441no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22×D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—21no—
293C42—111no—
294C42—221no—
295C11#332611yescharacteristic, complemented, Sylow
296C23—111no—
297C23—221no—
298C23—221no—
299C23D4×D1111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#433912yes—
305D4—221no—
306D4—221no—
307D4—221no—
308D4—221no—
309D4—442no—
310D4—442no—
311D4—441no—
312D4—442no—
313D4—881no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—442no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—221no—
341C22—221no—
342C22—221no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—221no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—441no—
360C4C2×#433911yescharacteristic
361C4#6703711yescharacteristic
362C2—41no—
363C2—441no—
364C2—881no—
365C2—881no—
366C2#1062302111yescharacteristic
367C2#1062330811yescharacteristic
368C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
hypercenter#419D11
hypocenterC11#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #10623348C2semidirect
2. #10623061C2semidirect
3. C11×#419C2semidirect
4. #10622840C2semidirect
5. #10622748C2semidirect
6. #10622741C2semidirect
7. #10622616C2semidirect
8. #10622432C2semidirect
9. #10622425C2semidirect
10. #10622424C2semidirect
11. #10622418C2semidirect
12. #10622416C2semidirect
13. #10622413C2semidirect
14. #10622412C2semidirect
15. #10622401C2semidirect
166. #419D11semidirect
295. C11#3326semidirect

Maximal subgroups

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

subgroupindex
#106233482
#106230612
C11×#4192
#106228402
#106227482
#106227412
#106226162
#106224322
#106224252
#106224242
#106224182
#106224162
#106224132
#106224122
#106224012
#332611