Finite Group Databasebeta

← #13080029

Subgroups — #13080029

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#10623066C211yesmaximal, characteristic, complemented
2#10623065C211yesmaximal, characteristic, complemented
3C11×#424C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622728C211yesmaximal, characteristic, complemented
7#10622727C211yesmaximal, characteristic, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622460C211yesmaximal, characteristic, complemented
10#10622459C211yesmaximal, characteristic, complemented
11#10622457C211yesmaximal, characteristic, complemented
12#10622457C211yesmaximal, characteristic, complemented
13#10622456C211yesmaximal, characteristic, complemented
14#10622455C211yesmaximal, characteristic, complemented
15#10622442C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#66983C2211yescharacteristic
20#66983C2211yescharacteristic
21#66983C2211yescharacteristic
22#66977C2211yescharacteristic
23C2×D88C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27#66951—21no—
28#66949—21no—
29#66947—21no—
30#66947—21no—
31#66938—21no—
32#66937—21no—
33#66937—21no—
34#66936—21no—
35#66928C2211yescharacteristic
36#66927C2211yescharacteristic
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66923C2211yescharacteristic
41#66922C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×C4⋊C8C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53#66882C2211yescharacteristic
54#66882C2211yescharacteristic
55#66881C2211yescharacteristic
56#66881C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—21no—
61C2×C22⋊D11—21no—
62C2×C22⋊D11—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×Dic22—21no—
72C2×Dic22C2311yescharacteristic
73C11×M16—41no—
74C2×C8×C11—41no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4D411yescharacteristic
80C11×C4⋊C4D411yescharacteristic
81C11×C22⋊C4D411yescharacteristic
82C11×C22⋊C4D411yescharacteristic
83C42×C11C2311yescharacteristic
84C42×C11C2311yescharacteristic
85C22⋊Dic11—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—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104D88—41no—
105D88—41no—
106#4314—41no—
107#4314—41no—
108#3257—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—81no—
122C22⋊D11—81no—
123C22⋊D11—81no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129D44—21no—
130D44—21no—
131D44—21no—
132D44—21no—
133D44—21no—
134D44—21no—
135D44—81no—
136D44—81no—
137C4×D11—81no—
138C4×D11—81no—
139C4×D11—81no—
140Dic22—21no—
141Dic22—21no—
142Dic22—81no—
143C8×C11—21no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11—21no—
147#542—111no—
148#540—111no—
149#479—111no—
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#424D1111yescharacteristic, complemented
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11C22×D411yescharacteristic
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—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11H(5,𝔽2)11yescharacteristic
181C4×C112−1+411yescharacteristic
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×D8—111no—
190C2×D8—111no—
191C2×M16C2×D1111yescharacteristic
192C22×C8C2×D1111yescharacteristic
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—111no—
203C22⋊Q8—221no—
204#121—111no—
205#121—111no—
206#121—111no—
207#121—221no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213#117C2×D1111yescharacteristic
214#107—111no—
215#107—111no—
216#106—111no—
217#106—111no—
218C4⋊C8C2×D1111yescharacteristic
219C4⋊C8C2×D1111yescharacteristic
220C4⋊C8C2×D1111yescharacteristic
221C4⋊C8C2×D1111yescharacteristic
222#103—111no—
223#103—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230C2×C11—41no—
231C2×C11#53711yescharacteristic
232C2×C11#57611yescharacteristic
233C2×C11#57711yescharacteristic
234D11—81no—
235D11—81no—
236D11—81no—
237C2×Q8—111no—
238C2×Q8—221no—
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—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251SD16—441no—
252SD16—441no—
253D8—441no—
254D8—441no—
255M16—41no—
256C2×C8—41no—
257C2×C8C22×D1111yescharacteristic
258C2×C8C22×D1111yescharacteristic
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4D4411yescharacteristic
271C4⋊C4D4411yescharacteristic
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4D4411yescharacteristic
282C22⋊C4D4411yescharacteristic
283C42—221no—
284C42C22×D1111yescharacteristic
285C42C22×D1111yescharacteristic
286C11#325711yescharacteristic, complemented, Sylow
287C23—221no—
288C23—221no—
289C23—221no—
290C23C2×D4411yescharacteristic
291Q8—221no—
292Q8—221no—
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—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4C2×D4411yescharacteristic
316C2×C4C2×D4411yescharacteristic
317C2×C4C2×D4411yescharacteristic
318C2×C4C2×D4411yescharacteristic
319C2×C4C2×D4411yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C22×D4411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—441no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4#6703711yescharacteristic
349C4#6704011yescharacteristic
350C2—41no—
351C2—881no—
352C2—881no—
353C2—881no—
354C2#1062304111yescharacteristic
355C2#1062328211yescharacteristic
356C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#424C2
socleC22×C11C22×D4
hypercenter#424D11
hypocenterC11#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #10623066C2semidirect
2. #10623065C2semidirect
3. C11×#424C2semidirect
4. #10622748C2semidirect
5. #10622747C2semidirect
6. #10622728C2semidirect
7. #10622727C2semidirect
8. #10622461C2semidirect
9. #10622460C2semidirect
10. #10622459C2semidirect
11. #10622457C2semidirect
12. #10622457C2semidirect
13. #10622456C2semidirect
14. #10622455C2semidirect
15. #10622442C2semidirect
161. #424D11semidirect
286. C11#3257semidirect

Maximal subgroups

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

subgroupindex
#106230662
#106230652
C11×#4242
#106227482
#106227472
#106227282
#106227272
#106224612
#106224602
#106224592
#106224572
#106224562
#106224552
#106224422
#325711