Finite Group Databasebeta

← #13125970

Subgroups — #13125970

Order 1664.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719301C211yesmaximal, characteristic
2#11719222C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718696C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718552C211yesmaximal, characteristic, complemented
7#11718535C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718516C211yesmaximal, characteristic, complemented
10#11718427C211yesmaximal, characteristic, complemented
11#11718424C211yesmaximal, characteristic, complemented
12#11718421C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718379C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C13×#121C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88194C2211yescharacteristic
20#88193—21no—
21D4×Dic13C2211yescharacteristic
22#88184C2211yescharacteristic
23#88180C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25#88147C2211yescharacteristic
26#88144C2211yescharacteristic
27#88144C2211yescharacteristic
28#88142C2211yescharacteristic
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88139—21no—
32#88135—21no—
33#88132—21no—
34#88132—21no—
35C4×Dic26—21no—
36C4×Dic26—21no—
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88058C2211yescharacteristic
48#88057C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13D411yescharacteristic
67C22×Dic13D411yescharacteristic
68#6129—44no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13D411yescharacteristic
98C4×Dic13D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#3228—131nomaximal, Sylow
104C23×C13—21no—
105C23×C13C2×D411yescharacteristic
106C22×D13—21no—
107D4×C13—21no—
108D4×C13—21no—
109D4×C13—42no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C22⋊D13—42no—
118C22⋊D13—42no—
119C22⋊D13—42no—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—42no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132C4×D13—42no—
133Dic26—42no—
134Dic26—42no—
135Dic26—42no—
136C8×C13—21no—
137C8×C13—21no—
138#1055—21no—
139#1055—21no—
140#533—131no—
141#532—131no—
142#500—131no—
143#498—131no—
144#486—131no—
145#486—131no—
146#482—131no—
147#482—131no—
148#482—131no—
149#482D1311yescharacteristic, complemented
150#478—131no—
151#478—131no—
152#478—131no—
153#478—131no—
154#431—131no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C132−1+411yescharacteristic
170C4×C132−1+411yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13#13512yes—
177Dic13AGL(1,ℤ/8)12yes—
178C2×#41—261no—
179C4⋊Q8—131no—
180C4⋊Q8—131no—
181C4⋊Q8—131no—
182#127—131no—
183#125—131no—
184#125—131no—
185#124—261no—
186C22⋊Q8—261no—
187C22⋊Q8—261no—
188#121—131no—
189#121—261no—
190#121C2×D1311yescharacteristic
191C4×Q8—261no—
192C4×Q8—261no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—261no—
196#117—131no—
197#117C2×D1311yescharacteristic
198C2×C42—131no—
199#107—131no—
200#107—131no—
201#107—131no—
202#107C2×D1311yescharacteristic
203#106—131no—
204#106—131no—
205#106—131no—
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208C4⋊C8—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#102C2×D1311yescharacteristic
216#102C2×D1311yescharacteristic
217C22⋊C8—131no—
218C22⋊C8C2×D1311yescharacteristic
219C4×C8—131no—
220C4×C8—131no—
221C2×C13—41no—
222C2×C13—81no—
223C2×C13#53611yescharacteristic
224C2×C13C2×#13511yescharacteristic
225C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
226D13—81no—
227#41—524no—
228C2×Q8—261no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×D4—21no—
232C2×D4—131no—
233C2×D4—261no—
234C2×D4—261no—
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242C2×C8—131no—
243C2×C8—131no—
244C2×C8C22×D1311yescharacteristic
245C2×C8C22×D1311yescharacteristic
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C42—21no—
266C42—131no—
267C42—131no—
268C42—131no—
269C42—131no—
270C42—261no—
271C13#322811yescharacteristic, complemented, Sylow
272C23—21no—
273C23—261no—
274C23D4×D1311yescharacteristic
275Q8—522no—
276Q8—522no—
277Q8—522no—
278D4—21no—
279D4—21no—
280D4—42no—
281D4—261no—
282D4—261no—
283D4—522no—
284D4—522no—
285D4—522no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—262no—
296C2×C4—262no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4D4×D1311yescharacteristic
303C2×C4C23×D1311yescharacteristic
304C8—21no—
305C8—21no—
306C8—261no—
307C8—261no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—132no—
323C4—132no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4#8825711yescharacteristic
330C4#8825711yescharacteristic
331C2—41no—
332C2—81no—
333C2—1041no—
334C2#1171935311yescharacteristic
335C2D13×#13511yescharacteristic
336C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#482D13
hypocenterC13#3228
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719222C2semidirect
3. C13×#482C2semidirect
4. #11718696C2semidirect
5. #11718664C2semidirect
6. #11718552C2semidirect
7. #11718535C2semidirect
8. #11718532C2semidirect
9. #11718516C2semidirect
10. #11718427C2semidirect
11. #11718424C2semidirect
12. #11718421C2semidirect
13. #11718421C2semidirect
14. #11718398C2semidirect
15. #11718379C2semidirect
149. #482D13semidirect
271. C13#3228semidirect

Maximal subgroups

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

subgroupindex
#117193012
#117192222
C13×#4822
#117186962
#117186642
#117185522
#117185352
#117185322
#117185162
#117184272
#117184242
#117184212
#117183982
#117183792
#322813