Finite Group Databasebeta

← #36327092

Subgroups — #36327092

Order 21376.

480 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×#19128797C211yesmaximal, characteristic
2#24923173C211yesmaximal, characteristic
3#24923173C211yesmaximal, characteristic
4#24923156C211yesmaximal, characteristic
5#24923155C211yesmaximal, characteristic
6#24923150C211yesmaximal, characteristic
7#24923138C211yesmaximal, characteristic
8#24923133C211yesmaximal, characteristic
9#24923133C211yesmaximal, characteristic
10C4×Dic167⋊C4C211yesmaximal, characteristic
11C4×Dic167⋊C4C211yesmaximal, characteristic
12#24923120C211yesmaximal, characteristic
13#24923120C211yesmaximal, characteristic
14#24923120C211yesmaximal, characteristic
15#387×C167C211yesmaximal, characteristic
16C22×Dic334C2211yescharacteristic
17#19128797C418yescomplemented
18C2×C4⋊Dic167C2211yescharacteristic
19C2×Dic167⋊C4C2211yescharacteristic
20C2×Dic167⋊C4C2211yescharacteristic
21C2×Dic167⋊C4C2211yescharacteristic
22C2×Dic167⋊C4C2211yescharacteristic
23C2×Dic167⋊C4C2211yescharacteristic
24C2×Dic167⋊C4C2211yescharacteristic
25C2×Dic167⋊C4C2211yescharacteristic
26C2×Dic167⋊C4C2211yescharacteristic
27C2×C4×Dic167C2211yescharacteristic
28C2×C4×Dic167C2211yescharacteristic
29C2×C4×Dic167C2211yescharacteristic
30C2×C4×Dic167C2211yescharacteristic
31C2×C4×Dic167C2211yescharacteristic
32C2×C4×Dic167C2211yescharacteristic
33C2×C4×Dic167C2211yescharacteristic
34C2×C4×Dic167C2211yescharacteristic
35C167⋊#95C2211yescharacteristic
36C167⋊#95C2211yescharacteristic
37C167⋊#95C2211yescharacteristic
38C167⋊#95C2211yescharacteristic
39C167⋊#95C2211yescharacteristic
40C167⋊#95C2211yescharacteristic
41C167⋊#95C2211yescharacteristic
42C167⋊#95C2211yescharacteristic
43C167⋊#95C2211yescharacteristic
44C167⋊#95C2211yescharacteristic
45C2×C4⋊C4×C167C2211yescharacteristic
46C2×C4⋊C4×C167C2211yescharacteristic
47C2×C42×C167C2211yescharacteristic
48#95×C167C2211yescharacteristic
49#95×C167C2211yescharacteristic
50#95×C167C2211yescharacteristic
51#95×C167C2211yescharacteristic
52C2×Dic334—22no—
53C2×Dic334—22no—
54C2×Dic334C2×C414yes—
55C22×Dic167C2311yescharacteristic
56C22×Dic167C2311yescharacteristic
57C22×Dic167C2311yescharacteristic
58C22×Dic167C2311yescharacteristic
59C22×Dic167C2311yescharacteristic
60C22×Dic167C2311yescharacteristic
61C22×Dic167C2311yescharacteristic
62C22×Dic167C2311yescharacteristic
63C4⋊Dic167—41no—
64Dic167⋊C4—22no—
65Dic167⋊C4—22no—
66Dic167⋊C4—22no—
67Dic167⋊C4—22no—
68Dic167⋊C4—22no—
69Dic167⋊C4C2×C414yes—
70Dic167⋊C4C2×C414yes—
71Dic167⋊C4Q814yescomplemented
72C4×Dic167—22no—
73C4×Dic167—22no—
74C4×Dic167—41no—
75C4×Dic167—41no—
76C4×Dic167—41no—
77C4×Dic167C2×C414yes—
78C4×Dic167C2×C414yes—
79C4×Dic167C2×C414yes—
80C22×C4×C167C2311yescharacteristic
81C22×C4×C167C2311yescharacteristic
82C22×C4×C167C2311yescharacteristic
83C22×C4×C167C2311yescharacteristic
84C22×C4×C167C2311yescharacteristic
85C22×C4×C167C2311yescharacteristic
86C22×C4×C167C2311yescharacteristic
87C4⋊C4×C167—41no—
88C4⋊C4×C167C2×C414yes—
89C42×C167—41no—
90Dic334—28no—
91C2×Dic167—21no—
92C2×Dic167—21no—
93C2×Dic167—21no—
94C2×Dic167—21no—
95C2×Dic167—21no—
96C2×Dic167—21no—
97C2×Dic167—21no—
98C2×Dic167—21no—
99C2×Dic167—21no—
100C2×Dic167—21no—
101C2×Dic167—21no—
102C2×Dic167—21no—
103C2×Dic167—21no—
104C2×Dic167—21no—
105C2×Dic167—21no—
106C2×Dic167C22×C412yes—
107C2×Dic167C22×C412yes—
108C2×Dic167C22×C412yes—
109C2×Dic167C22×C412yes—
110C2×Dic167C2×Q812yes—
111C2×Dic167C2×Q812yes—
112C2×Dic167#4112yes—
113C2×Dic167#4112yes—
114C2×Dic167#4112yes—
115C23×C167C2411yescharacteristic
116C2×C4×C167—21no—
117C2×C4×C167—21no—
118C2×C4×C167—21no—
119C2×C4×C167—21no—
120C2×C4×C167—21no—
121C2×C4×C167—21no—
122C2×C4×C167—21no—
123C2×C4×C167—21no—
124C2×C4×C167—21no—
125C2×C4×C167—21no—
126C2×C4×C167—21no—
127C2×C4×C167—21no—
128C2×C4×C167—21no—
129C2×C4×C167—21no—
130C2×C4×C167—21no—
131C2×C4×C167—21no—
132C2×C4×C167—21no—
133C2×C4×C167C22×C412yes—
134C2×C4×C167C22×C412yes—
135C2×C4×C167C22×C412yes—
136C2×C4×C167C2×Q812yes—
137C22×C167C23×C411yescharacteristic
138C22×C167C22×Q811yescharacteristic
139C22×C167C2×#4111yescharacteristic
140C22×C167C2×#4111yescharacteristic
141C22×C167C2×#4111yescharacteristic
142C22×C167H(5,𝔽2)11yescharacteristic
143C22×C1672−1+411yescharacteristic
144C4×C167—22no—
145C4×C167—22no—
146C4×C167—22no—
147C4×C167—22no—
148C4×C167—41no—
149C4×C167—41no—
150C4×C167—41no—
151Dic167—22no—
152Dic167—22no—
153Dic167—22no—
154Dic167—41no—
155Dic167—41no—
156Dic167—41no—
157Dic167#11714yes—
158Dic167C4×Q814yes—
159C2×C167C2×#11711yescharacteristic
160C2×C167C2×C4×Q811yescharacteristic
161C2×C167#52011yescharacteristic
162C2×C167#55411yescharacteristic
163C2×C167#55611yescharacteristic
164C2×C167#55711yescharacteristic
165C2×C167#55911yescharacteristic
166C167#235511yescharacteristic, complemented, Sylow
167#2355—1671nomaximal, Sylow
168C2×C4×Q8—1671no—
169#391—1671no—
170#391—1671no—
171#387—1671no—
172#387—1671no—
173#387—1671no—
174#387D16711yescharacteristic
175#384—1671no—
176#382—1671no—
177#382—1671no—
178C4×C4⋊C4—1671no—
179C4×C4⋊C4—1671no—
180C4×C4⋊C4—1671no—
181C4×C4⋊C4—1671no—
182C4×C4⋊C4—1671no—
183C22×Q8—1671no—
184C4×Q8—1678no—
185C2×C4⋊C4—1671no—
186C2×C4⋊C4—1671no—
187C2×C4⋊C4—1671no—
188C2×C4⋊C4—1671no—
189C2×C4⋊C4—1671no—
190C2×C4⋊C4—1671no—
191C2×C4⋊C4—1671no—
192C2×C4⋊C4—1671no—
193C2×C4⋊C4—1671no—
194C2×C4⋊C4C2×D16711yescharacteristic
195C2×C4⋊C4C2×D16711yescharacteristic
196C2×C42—1671no—
197C2×C42—1671no—
198C2×C42—1671no—
199C2×C42—1671no—
200C2×C42—1671no—
201C2×C42—1671no—
202C2×C42—1671no—
203C2×C42—1671no—
204C2×C42C2×D16711yescharacteristic
205#95—1671no—
206#95—1671no—
207#95—1671no—
208#95—1671no—
209#95—1671no—
210#95—1671no—
211#95—1671no—
212#95—1671no—
213#95—1671no—
214#95—1671no—
215#95C2×D16711yescharacteristic
216#95C2×D16711yescharacteristic
217#95C2×D16711yescharacteristic
218#95C2×D16711yescharacteristic
219C2×Q8—3342no—
220C2×Q8—3342no—
221C2×Q8—1674no—
222C22×C4—1671no—
223C22×C4—1671no—
224C22×C4—1671no—
225C22×C4—1671no—
226C22×C4—1671no—
227C22×C4—1671no—
228C22×C4—1671no—
229C22×C4—1671no—
230C22×C4C22×D16711yescharacteristic
231C22×C4C22×D16711yescharacteristic
232C22×C4C22×D16711yescharacteristic
233C22×C4C22×D16711yescharacteristic
234C22×C4C22×D16711yescharacteristic
235C22×C4C22×D16711yescharacteristic
236C22×C4C22×D16711yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—3342no—
239C4⋊C4—3342no—
240C4⋊C4—3342no—
241C4⋊C4—3342no—
242C4⋊C4—3342no—
243C4⋊C4—6681no—
244C4⋊C4—1674no—
245C4⋊C4—1674no—
246C4⋊C4—1674no—
247C4⋊C4C4×D16714yes—
248C42—41no—
249C42—3342no—
250C42—3342no—
251C42—6681no—
252C42—6681no—
253C42—6681no—
254C42—1674no—
255C42—1674no—
256C42—1674no—
257C23C23×D16711yescharacteristic
258Q8—3348no—
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—3341no—
277C2×C4—3341no—
278C2×C4—3341no—
279C2×C4—3341no—
280C2×C4—3341no—
281C2×C4—3341no—
282C2×C4—3341no—
283C2×C4—3341no—
284C2×C4—3341no—
285C2×C4—3341no—
286C2×C4—3341no—
287C2×C4—3341no—
288C2×C4—3341no—
289C2×C4—3341no—
290C2×C4—3341no—
291C2×C4—1672no—
292C2×C4—1672no—
293C2×C4—1672no—
294C2×C4—1672no—
295C2×C4—1672no—
296C2×C4—1672no—
297C2×C4—1672no—
298C2×C4—1672no—
299C2×C4—1672no—
300C2×C4C2×C4×D16712yes—
301C2×C4C2×C4×D16712yes—
302C2×C4C2×C4×D16712yes—
303C2×C4Q8×D16712yes—
304C22C22×C4×D16711yescharacteristic
305C22C2×Q8×D16711yescharacteristic
306C22#41×D16711yescharacteristic
307C22#41×D16711yescharacteristic
308C22#41×D16711yescharacteristic
309C22#1912887711yescharacteristic
310C22#1912887911yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3342no—
319C4—3342no—
320C4—3342no—
321C4—6681no—
322C4—6681no—
323C4—6681no—
324C4—1674no—
325C4—1674no—
326C2#117×D16711yescharacteristic
327C2C4×Q8×D16711yescharacteristic
328C2#2492374811yescharacteristic
329C2#2492397311yescharacteristic
330C2#2492398611yescharacteristic
331C2#2492399611yescharacteristic
332C2#2492400311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D167
commutatorC22×C167C23×C4
Fitting#387×C167C2
socle, prime radical, cosocleC23×C167C24
hypercenter#387D167
hypocenterC167#2355
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #19128797C4semidirect
71. Dic167⋊C4Q8semidirect
166. C167#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#191287972
#249231732
#249231562
#249231552
#249231502
#249231382
#249231332
C4×Dic167⋊C42
#249231202
#387×C1672
#2355167