Finite Group Databasebeta

← #13080586

Subgroups — #13080586

Order 1408.

394 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
1C11×#553C211yesmaximal, characteristic, complemented
2#10623082C211yesmaximal, characteristic, complemented
3#10622682C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622655C211yesmaximal, characteristic, complemented
6#10622654C211yesmaximal, characteristic, complemented
7#10622650C211yesmaximal, characteristic, complemented
8#10622650C211yesmaximal, characteristic, complemented
9#10622632C211yesmaximal, characteristic, complemented
10#10622627C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622615C211yesmaximal, characteristic, complemented
13#10622609C211yesmaximal, characteristic, complemented
14#10622584C211yesmaximal, characteristic, complemented
15#10622579C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×#126—21no—
19C11×#125C2211yescharacteristic
20C11×#123—21no—
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C4×D4×C11—21no—
25C4×D4×C11C2211yescharacteristic
26C4×D4×C11C2211yescharacteristic
27C11×#117C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29#66991—21no—
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32C2×#4323C2211yescharacteristic
33#66977C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37C4⋊C4×D11—21no—
38#66936—21no—
39#66936—21no—
40C4×D44C2211yescharacteristic
41#66922C2211yescharacteristic
42#66896C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66874C2211yescharacteristic
50#66874C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11D411yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69#4339—22no—
70#4339—22no—
71#4339—41no—
72#4339—41no—
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4D411yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4D411yescharacteristic
91C11×C22⋊C4D411yescharacteristic
92C42×C11—21no—
93C42×C11C2311yescharacteristic
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96#4324—41no—
97#4324—41no—
98#4323—22no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3307—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—41no—
119D4×C11—42no—
120D4×C11—81no—
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—21no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—42no—
136C22⋊D11—42no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140D44—21no—
141D44#4112yes—
142C4×D11—42no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#553D1111yescharacteristic, complemented
154#547—111no—
155#491—111no—
156#485—111no—
157#483—111no—
158#478—111no—
159#468—111no—
160#465—111no—
161#461—111no—
162#449—111no—
163#449—111no—
164#442—111no—
165#435—111no—
166#417—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—22no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41—111no—
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×M16—111no—
199C22×C8—111no—
200C4⋊Q8—111no—
201#126—21no—
202#125C2×D1111yescharacteristic
203#123—21no—
204#123—221no—
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208#121—21no—
209#121—221no—
210#121C2×D1111yescharacteristic
211#121C2×D1111yescharacteristic
212C4×D4—21no—
213C4×D4—111no—
214C4×D4C2×D1111yescharacteristic
215C4×D4C2×D1111yescharacteristic
216#117C2×D1111yescharacteristic
217C2×C4⋊C4—221no—
218C2×C4⋊C4C2×D1111yescharacteristic
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233C22⋊C8—111no—
234C22⋊C8—111no—
235#97—111no—
236C2×C11—41no—
237C2×C11—41no—
238C2×C11—81no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—42no—
243#41—222no—
244#41—222no—
245#41—441no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4C22⋊D1111yescharacteristic
255C2×D4C22×D1111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263SD16—441no—
264SD16—441no—
265D8—222no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—441no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22⋊D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C4⋊C4C22×D1111yescharacteristic
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4C22⋊D1111yescharacteristic
292C22⋊C4C22⋊D1111yescharacteristic
293C42—21no—
294C42C22×D1111yescharacteristic
295C11#330711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—221no—
298C23C2×C22⋊D1111yescharacteristic
299C23C2×C22⋊D1111yescharacteristic
300Q8—221no—
301Q8—221no—
302Q8—221no—
303Q8—221no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—112no—
310D4—221no—
311D4—442no—
312D4—442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4C2×C22⋊D1111yescharacteristic
329C2×C4C2×C22⋊D1111yescharacteristic
330C2×C4C2×C22⋊D1111yescharacteristic
331C2×C4C2×C22⋊D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—221no—
334C8—221no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—222no—
347C22—441no—
348C22—441no—
349C22C22×C22⋊D1111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4#41×D1111yescharacteristic
361C4#6704211yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—442no—
366C2#1062335311yescharacteristic
367C2#1062336011yescharacteristic
368C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#553C2
socleC22×C11C22×D4
hypercenter#553D11
hypocenterC11#3307
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C11×#553C2semidirect
2. #10623082C2semidirect
3. #10622682C2semidirect
4. #10622679C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622650C2semidirect
8. #10622650C2semidirect
9. #10622632C2semidirect
10. #10622627C2semidirect
11. #10622624C2semidirect
12. #10622615C2semidirect
13. #10622609C2semidirect
14. #10622584C2semidirect
15. #10622579C2semidirect
153. #553D11semidirect
295. C11#3307semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
#106230822
#106226822
#106226792
#106226552
#106226542
#106226502
#106226322
#106226272
#106226242
#106226152
#106226092
#106225842
#106225792
#330711