Finite Group Databasebeta

← #13126121

Subgroups — #13126121

Order 1664.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719239C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718511C211yesmaximal, characteristic, complemented
5#11718508C211yesmaximal, characteristic, complemented
6#11718507C211yesmaximal, characteristic, complemented
7#11718490C211yesmaximal, characteristic, complemented
8#11718398C211yesmaximal, characteristic
9#11718397C211yesmaximal, characteristic
10#11718384C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12#11718375C211yesmaximal, characteristic, complemented
13#11718363C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15#11718343C211yesmaximal, characteristic, complemented
16C13×#117C2211yescharacteristic
17#88184C2211yescharacteristic
18#88180C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20#88178C2211yescharacteristic
21#88152—21no—
22#88150—21no—
23#88144—21no—
24#88142—21no—
25#88139—21no—
26#88137—21no—
27#88132—21no—
28#88132—21no—
29#88129C2211yescharacteristic
30C4×D52C2211yescharacteristic
31#88124C2211yescharacteristic
32#88124C2211yescharacteristic
33#88123C2211yescharacteristic
34#88123C2211yescharacteristic
35#88123C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C13×C4⋊C8C2211yescharacteristic
38C13×C4⋊C8C2211yescharacteristic
39C13×C22⋊C8C2211yescharacteristic
40C13×C22⋊C8C2211yescharacteristic
41C13×#97C2211yescharacteristic
42C4×C8×C13C2211yescharacteristic
43#88061C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88057C2211yescharacteristic
54#88057C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C22×Dic13—21no—
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C22⋊C4D411yescharacteristic
75C13×C22⋊C4D411yescharacteristic
76C42×C13C2311yescharacteristic
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102#3243—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104C22×D13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2×D411yescharacteristic
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2411yescharacteristic
113C22⋊D13—81no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—81no—
122D52—21no—
123D52—21no—
124C4×D13—81no—
125Dic26—21no—
126Dic26—21no—
127Dic26—81no—
128Dic26—81no—
129Dic26—81no—
130C8×C13—21no—
131C8×C13—21no—
132C8×C13—21no—
133C8×C13—21no—
134#544—131no—
135#542—131no—
136#501—131no—
137#500—131no—
138#489—131no—
139#488—131no—
140#485—131no—
141#484—131no—
142#482—131no—
143#480—131no—
144#479—131no—
145#478—131no—
146#477—131no—
147#474—131no—
148#433D1311yescharacteristic, complemented
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13C22×D411yescharacteristic
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—41no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C132−1+411yescharacteristic
162C4×C132−1+411yescharacteristic
163Dic13—41no—
164Dic13—41no—
165Dic13—41no—
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172C4⋊Q8—131no—
173C4⋊Q8—261no—
174#126—261no—
175#125—131no—
176#125—131no—
177#125—261no—
178#124—131no—
179#124—261no—
180#123—261no—
181C22⋊Q8—131no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184C22⋊Q8—261no—
185#121—131no—
186C4×Q8—131no—
187C4×D4—131no—
188#117—131no—
189#117C2×D1311yescharacteristic
190C2×C4⋊C4—131no—
191#107—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#107—131no—
196#107—131no—
197#106—131no—
198#106—131no—
199C4⋊C8C2×D1311yescharacteristic
200C4⋊C8C2×D1311yescharacteristic
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#102—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209C22⋊C8C2×D1311yescharacteristic
210C22⋊C8C2×D1311yescharacteristic
211#97C2×D1311yescharacteristic
212C4×C8C2×D1311yescharacteristic
213C2×C13—41no—
214C2×C13#53611yescharacteristic
215C2×C13#57611yescharacteristic
216C2×C13#57811yescharacteristic
217D13—81no—
218C2×Q8—131no—
219C2×Q8—261no—
220C2×Q8—261no—
221C2×Q8—261no—
222C2×D4—131no—
223C2×D4—261no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4C22×D1311yescharacteristic
227C2×C8C22×D1311yescharacteristic
228C2×C8C22×D1311yescharacteristic
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—131no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4D5211yescharacteristic
248C4⋊C4D5211yescharacteristic
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4D5211yescharacteristic
256C22⋊C4D5211yescharacteristic
257C42—261no—
258C42—261no—
259C42C22×D1311yescharacteristic
260C42C22×D1311yescharacteristic
261C13#324311yescharacteristic, complemented, Sylow
262C23—261no—
263C23C2×D5211yescharacteristic
264Q8—261no—
265Q8—261no—
266Q8—1041no—
267Q8—1041no—
268Q8—1041no—
269D4—261no—
270D4—261no—
271D4—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—1041no—
282C2×C4—1041no—
283C2×C4C2×D5211yescharacteristic
284C2×C4C2×D5211yescharacteristic
285C2×C4C2×D5211yescharacteristic
286C2×C4C2×D5211yescharacteristic
287C2×C4C2×D5211yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22C22×D5211yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—521no—
306C4—521no—
307C4—521no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825711yescharacteristic
313C4#8825711yescharacteristic
314C2—41no—
315C2—1041no—
316C2#1171923111yescharacteristic
317C2#1171945711yescharacteristic
318C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#433D13
hypocenterC13#3243
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
3. C13×#433C2semidirect
4. #11718511C2semidirect
5. #11718508C2semidirect
6. #11718507C2semidirect
7. #11718490C2semidirect
10. #11718384C2semidirect
11. #11718383C2semidirect
12. #11718375C2semidirect
13. #11718363C2semidirect
14. #11718358C2semidirect
15. #11718343C2semidirect
148. #433D13semidirect
261. C13#3243semidirect

Maximal subgroups

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

subgroupindex
#117192392
#117192242
C13×#4332
#117185112
#117185082
#117185072
#117184902
#117183982
#117183972
#117183842
#117183832
#117183752
#117183632
#117183582
#117183432
#324313