Finite Group Databasebeta

← #13119349

Subgroups — #13119349

Order 1664.

436 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88143C211yesmaximal, characteristic
2C2×#88124C211yesmaximal, characteristic
3C13×#387C211yesmaximal, characteristic
4#11718641C211yesmaximal, characteristic
5#11718637C211yesmaximal, characteristic
6#11718633C211yesmaximal, characteristic
7C4×#6101C211yesmaximal, characteristic
8#11718322C211yesmaximal, characteristic
9#11718321C211yesmaximal, characteristic
10#11718319C211yesmaximal, characteristic
11#11718314C211yesmaximal, characteristic
12#11718310C211yesmaximal, characteristic
13#11718308C211yesmaximal, characteristic
14#11718308C211yesmaximal, characteristic
15#11718308C211yesmaximal, characteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39#88143—24no—
40#88124—24no—
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C42×C13—22no—
71C4⋊Dic13—22no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—22no—
75#6101—22no—
76#6101—22no—
77#6101—22no—
78#6101—22no—
79#6101—22no—
80#6101—22no—
81#6101—22no—
82#6101—22no—
83#6101—22no—
84#6101—22no—
85#6101D414yes—
86#6101Q814yes—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91#2506—131nomaximal, Sylow
92C23×C13C2411yescharacteristic
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13C2×D412yes—
112C2×C4×C13C2×Q812yes—
113C2×C4×C13#4112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13C2×D412yes—
133C2×Dic13C2×D412yes—
134C2×Dic13C2×Q812yes—
135C2×Dic13C2×Q812yes—
136C2×Dic13#4112yes—
137C2×Dic13#4112yes—
138C2×#125—131no—
139C2×#125—131no—
140#400—131no—
141#400—131no—
142#398—131no—
143#398—131no—
144#389—131no—
145#389—131no—
146#389—131no—
147#389—131no—
148#387—131no—
149#387D1311yescharacteristic
150#384—131no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—131no—
153C22×C13C22×D411yescharacteristic
154C22×C13C22×Q811yescharacteristic
155C22×C13C2×#4111yescharacteristic
156C22×C13C2×#4111yescharacteristic
157C22×C13C2×#4111yescharacteristic
158C22×C132−1+411yescharacteristic
159C22×C132−1+411yescharacteristic
160C4×C13—22no—
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167Dic13—22no—
168Dic13—22no—
169Dic13—22no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13#12514yescomplemented
175#125—264no—
176#125—264no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4C2×D1311yescharacteristic
194C2×C4⋊C4C2×D1311yescharacteristic
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42C2×D1311yescharacteristic
200#95—131no—
201#95—131no—
202#95—131no—
203#95—131no—
204#95—131no—
205#95—131no—
206#95—131no—
207#95—131no—
208#95C2×D1311yescharacteristic
209#95C2×D1311yescharacteristic
210#95C2×D1311yescharacteristic
211#95C2×D1311yescharacteristic
212C2×C13C2×#12511yescharacteristic
213C2×C13#53211yescharacteristic
214C2×C13#54111yescharacteristic
215C2×C13#54711yescharacteristic
216C2×C13D4×Q811yescharacteristic
217C2×C13#55211yescharacteristic
218C2×C13#55711yescharacteristic
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4C22×D1311yescharacteristic
228C22×C4C22×D1311yescharacteristic
229C22×C4C22×D1311yescharacteristic
230C22×C4C22×D1311yescharacteristic
231C22×C4C22×D1311yescharacteristic
232C22×C4C22×D1311yescharacteristic
233C22×C4C22×D1311yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—134no—
237C4⋊C4—134no—
238C4⋊C4—262no—
239C4⋊C4—262no—
240C4⋊C4—262no—
241C4⋊C4—262no—
242C4⋊C4—262no—
243C4⋊C4—262no—
244C4⋊C4—262no—
245C4⋊C4—262no—
246C4⋊C4—262no—
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—262no—
250C4⋊C4—262no—
251C4⋊C4—262no—
252C42—22no—
253C42—262no—
254C42—262no—
255C42—262no—
256C42—262no—
257C13#250611yescharacteristic, complemented, Sylow
258C23C23×D1311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—132no—
278C2×C4—132no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4#612712yes—
302C2×C4D4×D1312yes—
303C2×C4Q8×D1312yes—
304C22C2×#612711yescharacteristic
305C22C2×D4×D1311yescharacteristic
306C22C2×Q8×D1311yescharacteristic
307C22#41×D1311yescharacteristic
308C22#41×D1311yescharacteristic
309C22#8825711yescharacteristic
310C22#8825711yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—134no—
319C4—262no—
320C4—262no—
321C4—262no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C2#1171923611yescharacteristic
327C2#1171925311yescharacteristic
328C2#1171927211yescharacteristic
329C2#1171933711yescharacteristic
330C2#1171936011yescharacteristic
331C2D13×#12511yescharacteristic
332C2#1171940611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#387C2
hypercenter#387D13
hypocenterC13#2506
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
174. Dic13#125semidirect
257. C13#2506semidirect

Maximal subgroups

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

subgroupindex
C2×#881432
C2×#881242
C13×#3872
#117186412
#117186372
#117186332
C4×#61012
#117183222
#117183212
#117183192
#117183142
#117183102
#117183082
#250613