Finite Group Databasebeta

← #30670474

Subgroups — #30670474

Order 16768.

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×#16862238C211yesmaximal, characteristic
2C2×#16862236C211yesmaximal, characteristic
3#22553254C211yesmaximal, characteristic
4#22553253C211yesmaximal, characteristic
5#22553244C211yesmaximal, characteristic
6#22553243C211yesmaximal, characteristic
7#22553209C211yesmaximal, characteristic
8#22553209C211yesmaximal, characteristic
9#22553209C211yesmaximal, characteristic
10#22553207C211yesmaximal, characteristic
11#22553197C211yesmaximal, characteristic
12#22553181C211yesmaximal, characteristic
13C4×Dic131⋊C4C211yesmaximal, characteristic
14#22553163C211yesmaximal, characteristic
15#387×C131C211yesmaximal, characteristic
16#16862238—24no—
17#16862236—24no—
18C2×C4⋊Dic131C2211yescharacteristic
19C2×C4⋊Dic131C2211yescharacteristic
20C2×C4⋊Dic131C2211yescharacteristic
21C2×C4⋊Dic131C2211yescharacteristic
22C2×Dic131⋊C4C2211yescharacteristic
23C2×Dic131⋊C4C2211yescharacteristic
24C2×Dic131⋊C4C2211yescharacteristic
25C2×Dic131⋊C4C2211yescharacteristic
26C2×Dic131⋊C4C2211yescharacteristic
27C2×Dic131⋊C4C2211yescharacteristic
28C2×Dic131⋊C4C2211yescharacteristic
29C2×Dic131⋊C4C2211yescharacteristic
30C2×Dic131⋊C4C2211yescharacteristic
31C2×Dic131⋊C4C2211yescharacteristic
32C2×Dic131⋊C4C2211yescharacteristic
33C2×Dic131⋊C4C2211yescharacteristic
34C2×C4×Dic131C2211yescharacteristic
35C2×C4×Dic131C2211yescharacteristic
36C2×C4×Dic131C2211yescharacteristic
37C2×C4×Dic131C2211yescharacteristic
38C131⋊#95C2211yescharacteristic
39C131⋊#95C2211yescharacteristic
40C131⋊#95C2211yescharacteristic
41C131⋊#95C2211yescharacteristic
42C131⋊#95C2211yescharacteristic
43C131⋊#95C2211yescharacteristic
44C131⋊#95C2211yescharacteristic
45C131⋊#95C2211yescharacteristic
46C2×C4⋊C4×C131C2211yescharacteristic
47C2×C4⋊C4×C131C2211yescharacteristic
48C2×C42×C131C2211yescharacteristic
49#95×C131C2211yescharacteristic
50#95×C131C2211yescharacteristic
51#95×C131C2211yescharacteristic
52#95×C131C2211yescharacteristic
53C22×Dic131C2311yescharacteristic
54C22×Dic131C2311yescharacteristic
55C22×Dic131C2311yescharacteristic
56C22×Dic131C2311yescharacteristic
57C22×Dic131C2311yescharacteristic
58C22×Dic131C2311yescharacteristic
59C22×Dic131C2311yescharacteristic
60C22×Dic131C2311yescharacteristic
61C4⋊Dic131—22no—
62C4⋊Dic131—22no—
63C4⋊Dic131—22no—
64C4⋊Dic131—22no—
65Dic131⋊C4—22no—
66Dic131⋊C4—22no—
67Dic131⋊C4—22no—
68Dic131⋊C4—22no—
69Dic131⋊C4—22no—
70Dic131⋊C4—22no—
71Dic131⋊C4—22no—
72Dic131⋊C4—22no—
73Dic131⋊C4—22no—
74Dic131⋊C4—22no—
75Dic131⋊C4D414yes—
76Dic131⋊C4Q814yes—
77C4×Dic131—22no—
78C4×Dic131—22no—
79C4×Dic131—22no—
80C4×Dic131—22no—
81C22×C4×C131C2311yescharacteristic
82C22×C4×C131C2311yescharacteristic
83C22×C4×C131C2311yescharacteristic
84C22×C4×C131C2311yescharacteristic
85C22×C4×C131C2311yescharacteristic
86C22×C4×C131C2311yescharacteristic
87C22×C4×C131C2311yescharacteristic
88C4⋊C4×C131—22no—
89C4⋊C4×C131—22no—
90C42×C131—22no—
91C2×Dic131—21no—
92C2×Dic131—21no—
93C2×Dic131—21no—
94C2×Dic131—21no—
95C2×Dic131—21no—
96C2×Dic131—21no—
97C2×Dic131—21no—
98C2×Dic131—21no—
99C2×Dic131—21no—
100C2×Dic131—21no—
101C2×Dic131—21no—
102C2×Dic131—21no—
103C2×Dic131—21no—
104C2×Dic131—21no—
105C2×Dic131—21no—
106C2×Dic131—21no—
107C2×Dic131—21no—
108C2×Dic131—21no—
109C2×Dic131C2×D412yes—
110C2×Dic131C2×D412yes—
111C2×Dic131C2×Q812yes—
112C2×Dic131C2×Q812yes—
113C2×Dic131#4112yes—
114C2×Dic131#4112yes—
115C23×C131C2411yescharacteristic
116C2×C4×C131—21no—
117C2×C4×C131—21no—
118C2×C4×C131—21no—
119C2×C4×C131—21no—
120C2×C4×C131—21no—
121C2×C4×C131—21no—
122C2×C4×C131—21no—
123C2×C4×C131—21no—
124C2×C4×C131—21no—
125C2×C4×C131—21no—
126C2×C4×C131—21no—
127C2×C4×C131—21no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131C2×D412yes—
135C2×C4×C131C2×Q812yes—
136C2×C4×C131#4112yes—
137C22×C131C22×D411yescharacteristic
138C22×C131C22×Q811yescharacteristic
139C22×C131C2×#4111yescharacteristic
140C22×C131C2×#4111yescharacteristic
141C22×C131C2×#4111yescharacteristic
142C22×C1312−1+411yescharacteristic
143C22×C1312−1+411yescharacteristic
144C4×C131—22no—
145C4×C131—22no—
146C4×C131—22no—
147C4×C131—41no—
148C4×C131—41no—
149C4×C131—41no—
150C4×C131—41no—
151Dic131—22no—
152Dic131—22no—
153Dic131—22no—
154Dic131—41no—
155Dic131—41no—
156Dic131—41no—
157Dic131—41no—
158Dic131#12514yescomplemented
159C2×C131C2×#12511yescharacteristic
160C2×C131#53211yescharacteristic
161C2×C131#54111yescharacteristic
162C2×C131#54711yescharacteristic
163C2×C131D4×Q811yescharacteristic
164C2×C131#55211yescharacteristic
165C2×C131#55711yescharacteristic
166C131#250611yescharacteristic, complemented, Sylow
167#2506—1311nomaximal, Sylow
168C2×#125—1311no—
169C2×#125—1311no—
170#400—1311no—
171#400—1311no—
172#398—1311no—
173#398—1311no—
174#389—1311no—
175#389—1311no—
176#389—1311no—
177#389—1311no—
178#387—1311no—
179#387D13111yescharacteristic
180#384—1311no—
181C4×C4⋊C4—1311no—
182C4×C4⋊C4—1311no—
183#125—2624no—
184#125—2624no—
185C2×C4⋊C4—1311no—
186C2×C4⋊C4—1311no—
187C2×C4⋊C4—1311no—
188C2×C4⋊C4—1311no—
189C2×C4⋊C4—1311no—
190C2×C4⋊C4—1311no—
191C2×C4⋊C4—1311no—
192C2×C4⋊C4—1311no—
193C2×C4⋊C4—1311no—
194C2×C4⋊C4—1311no—
195C2×C4⋊C4—1311no—
196C2×C4⋊C4—1311no—
197C2×C4⋊C4—1311no—
198C2×C4⋊C4—1311no—
199C2×C4⋊C4—1311no—
200C2×C4⋊C4—1311no—
201C2×C4⋊C4C2×D13111yescharacteristic
202C2×C4⋊C4C2×D13111yescharacteristic
203C2×C42—1311no—
204C2×C42—1311no—
205C2×C42—1311no—
206C2×C42—1311no—
207C2×C42C2×D13111yescharacteristic
208#95—1311no—
209#95—1311no—
210#95—1311no—
211#95—1311no—
212#95—1311no—
213#95—1311no—
214#95—1311no—
215#95—1311no—
216#95C2×D13111yescharacteristic
217#95C2×D13111yescharacteristic
218#95C2×D13111yescharacteristic
219#95C2×D13111yescharacteristic
220C22×C4—1311no—
221C22×C4—1311no—
222C22×C4—1311no—
223C22×C4—1311no—
224C22×C4—1311no—
225C22×C4—1311no—
226C22×C4—1311no—
227C22×C4—1311no—
228C22×C4C22×D13111yescharacteristic
229C22×C4C22×D13111yescharacteristic
230C22×C4C22×D13111yescharacteristic
231C22×C4C22×D13111yescharacteristic
232C22×C4C22×D13111yescharacteristic
233C22×C4C22×D13111yescharacteristic
234C22×C4C22×D13111yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—2622no—
238C4⋊C4—2622no—
239C4⋊C4—2622no—
240C4⋊C4—2622no—
241C4⋊C4—2622no—
242C4⋊C4—2622no—
243C4⋊C4—2622no—
244C4⋊C4—2622no—
245C4⋊C4—2622no—
246C4⋊C4—2622no—
247C4⋊C4—2622no—
248C4⋊C4—2622no—
249C4⋊C4—2622no—
250C4⋊C4—2622no—
251C4⋊C4—1314no—
252C4⋊C4—1314no—
253C42—22no—
254C42—2622no—
255C42—2622no—
256C42—2622no—
257C42—2622no—
258C23C23×D13111yescharacteristic
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—2621no—
278C2×C4—2621no—
279C2×C4—2621no—
280C2×C4—2621no—
281C2×C4—2621no—
282C2×C4—2621no—
283C2×C4—2621no—
284C2×C4—2621no—
285C2×C4—2621no—
286C2×C4—2621no—
287C2×C4—2621no—
288C2×C4—2621no—
289C2×C4—2621no—
290C2×C4—2621no—
291C2×C4—2621no—
292C2×C4—2621no—
293C2×C4—2621no—
294C2×C4—2621no—
295C2×C4—1312no—
296C2×C4—1312no—
297C2×C4—1312no—
298C2×C4—1312no—
299C2×C4—1312no—
300C2×C4—1312no—
301C2×C4D4×D13112yes—
302C2×C4Q8×D13112yes—
303C2×C4#1452351312yes—
304C22C2×D4×D13111yescharacteristic
305C22C2×Q8×D13111yescharacteristic
306C22#41×D13111yescharacteristic
307C22#41×D13111yescharacteristic
308C22C2×#1452351311yescharacteristic
309C22#1686229311yescharacteristic
310C22#1686229311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2622no—
319C4—2622no—
320C4—2622no—
321C4—5241no—
322C4—5241no—
323C4—5241no—
324C4—5241no—
325C4—1314no—
326C2#125×D13111yescharacteristic
327C2#2255385911yescharacteristic
328C2#2255391911yescharacteristic
329C2#2255396011yescharacteristic
330C2#2255397511yescharacteristic
331C2#2255399511yescharacteristic
332C2#2255404011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D131
commutator, socle, prime radical, cosocleC23×C131C24
Fitting#387×C131C2
hypercenter#387D131
hypocenterC131#2506
LCSG ▷ C23×C131 ▷ C131
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
158. Dic131#125semidirect
166. C131#2506semidirect

Maximal subgroups

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

subgroupindex
C2×#168622382
C2×#168622362
#225532542
#225532532
#225532442
#225532432
#225532092
#225532072
#225531972
#225531812
C4×Dic131⋊C42
#225531632
#387×C1312
#2506131