Finite Group Databasebeta

← #13127606

Subgroups — #13127606

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719290C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic, complemented
3C13×#446C211yesmaximal, characteristic, complemented
4#11718509C211yesmaximal, characteristic
5#11718508C211yesmaximal, characteristic, complemented
6#11718506C211yesmaximal, characteristic, complemented
7#11718506C211yesmaximal, characteristic, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718490C211yesmaximal, characteristic, complemented
10#11718377C211yesmaximal, characteristic, complemented
11#11718375C211yesmaximal, characteristic, complemented
12#11718374C211yesmaximal, characteristic
13#11718371C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15C4×#6095C211yesmaximal, characteristic, complemented
16C4×Q8×C13C2211yescharacteristic
17#88201—21no—
18#88198—21no—
19C2×Dic52C2211yescharacteristic
20C2×#6095C2211yescharacteristic
21C2×#6095C2211yescharacteristic
22#88148—21no—
23#88148—21no—
24#88147—21no—
25#88143—21no—
26#88143—21no—
27#88141—21no—
28#88129C2211yescharacteristic
29#88129C2211yescharacteristic
30#88128C2211yescharacteristic
31C4×D52C2211yescharacteristic
32C4×D52C2211yescharacteristic
33#88124C2211yescharacteristic
34#88124C2211yescharacteristic
35#88123C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#97C2211yescharacteristic
44C13×#97C2211yescharacteristic
45C4×C8×C13C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88058C2211yescharacteristic
53#88057C2211yescharacteristic
54#88057C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×Q8×C13D411yescharacteristic
60C2×D52—21no—
61C2×D52—21no—
62C2×D52C2311yescharacteristic
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×Dic26C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C42×C13C2311yescharacteristic
77C42×C13C2311yescharacteristic
78C42×C13C2311yescharacteristic
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102Dic52—22no—
103#6095—22no—
104#6095—22no—
105#3371—131nomaximal, Sylow
106C22×D13—21no—
107C22×D13—21no—
108Q8×C13—41no—
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122D52—21no—
123D52—21no—
124D52—21no—
125D52—21no—
126D52—42no—
127D52—81no—
128C4×D13—81no—
129C4×D13—81no—
130Dic26—21no—
131Dic26—21no—
132Dic26—21no—
133Dic26—42no—
134Dic26#4112yes—
135C8×C13—21no—
136C8×C13—21no—
137C8×C13—21no—
138C8×C13—21no—
139#559—131no—
140#557—131no—
141#490—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#476—131no—
147#464—131no—
148#464—131no—
149#460—131no—
150#446D1311yescharacteristic, complemented
151#441—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13C22×D411yescharacteristic
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13C2×#4111yescharacteristic
168C4×C132−1+411yescharacteristic
169Dic13—22no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C2×Q16—131no—
176C2×SD16—131no—
177C2×SD16—131no—
178C4⋊Q8—131no—
179C4⋊Q8—261no—
180#127—131no—
181#125—131no—
182#125—131no—
183#125—261no—
184#125—261no—
185#124—131no—
186#124—131no—
187#124—261no—
188#123—261no—
189#123—261no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—261no—
195C4×Q8C2×D1311yescharacteristic
196C4×D4—131no—
197C4×D4—131no—
198C4×D4—261no—
199#107—131no—
200#106—131no—
201#106—131no—
202C4⋊C8C2×D1311yescharacteristic
203C4⋊C8C2×D1311yescharacteristic
204C4⋊C8C2×D1311yescharacteristic
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#97C2×D1311yescharacteristic
216#97C2×D1311yescharacteristic
217C4×C8C2×D1311yescharacteristic
218C2×C13#54811yescharacteristic
219C2×C13#57511yescharacteristic
220C2×C13#57711yescharacteristic
221D13—81no—
222D13—81no—
223C2×Q8—131no—
224C2×Q8—131no—
225C2×Q8—261no—
226C2×Q8D5211yescharacteristic
227C2×D4—131no—
228C2×D4—131no—
229C2×D4—261no—
230C2×D4—261no—
231C22×C4—261no—
232C22×C4—261no—
233Q16—262no—
234SD16—262no—
235SD16—262no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4D5211yescharacteristic
254C4⋊C4D5211yescharacteristic
255C4⋊C4D5211yescharacteristic
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42—261no—
266C42C22×D1311yescharacteristic
267C42C22×D1311yescharacteristic
268C42C22×D1311yescharacteristic
269C13#337111yescharacteristic, complemented, Sylow
270C23—261no—
271C23—261no—
272Q8—41no—
273Q8—132no—
274Q8—261no—
275Q8—261no—
276Q8—261no—
277Q8—522no—
278D4—261no—
279D4—261no—
280D4—261no—
281D4—261no—
282D4—522no—
283D4—1041no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4C2×D5211yescharacteristic
293C2×C4C2×D5211yescharacteristic
294C2×C4C2×D5211yescharacteristic
295C2×C4C2×D5211yescharacteristic
296C2×C4C2×D5211yescharacteristic
297C2×C4C2×D5211yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—521no—
304C22—521no—
305C22—521no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22C22×D5211yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—262no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4#8825411yescharacteristic
323C4#41×D1311yescharacteristic
324C2—1041no—
325C2—1041no—
326C2#1171928111yescharacteristic
327C2#1171945311yescharacteristic
328C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#446C2
socleC22×C13C22×D4
prime radical#88128C22
hypercenter#446D13
hypocenterC13#3371
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #11719272C2semidirect
3. C13×#446C2semidirect
5. #11718508C2semidirect
6. #11718506C2semidirect
7. #11718506C2semidirect
8. #11718503C2semidirect
9. #11718490C2semidirect
10. #11718377C2semidirect
11. #11718375C2semidirect
13. #11718371C2semidirect
14. #11718358C2semidirect
15. C4×#6095C2semidirect
150. #446D13semidirect
269. C13#3371semidirect

Maximal subgroups

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

subgroupindex
#117192902
#117192722
C13×#4462
#117185092
#117185082
#117185062
#117185032
#117184902
#117183772
#117183752
#117183742
#117183712
#117183582
C4×#60952
#337113