Finite Group Databasebeta

← #36327231

Subgroups — #36327231

Order 21376.

464 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128822C211yesmaximal, characteristic
2#24923168C211yesmaximal, characteristic
3#24923166C211yesmaximal, characteristic
4#24923166C211yesmaximal, characteristic
5#24923166C211yesmaximal, characteristic
6#24923156C211yesmaximal, characteristic
7#24923154C211yesmaximal, characteristic
8#24923150C211yesmaximal, characteristic
9C4⋊C4×Dic167C211yesmaximal, characteristic
10C4×Dic167⋊C4C211yesmaximal, characteristic
11C4×C4⋊Dic167C211yesmaximal, characteristic
12#24923120C211yesmaximal, characteristic
13#24923120C211yesmaximal, characteristic
14#24923120C211yesmaximal, characteristic
15#387×C167C211yesmaximal, characteristic
16#19128822C418yescomplemented
17C2×C4⋊Dic167C2211yescharacteristic
18C2×C4⋊Dic167C2211yescharacteristic
19C2×C4⋊Dic167C2211yescharacteristic
20C2×C4⋊Dic167C2211yescharacteristic
21C2×Dic167⋊C4C2211yescharacteristic
22C2×Dic167⋊C4C2211yescharacteristic
23C2×Dic167⋊C4C2211yescharacteristic
24C2×Dic167⋊C4C2211yescharacteristic
25C2×Dic167⋊C4C2211yescharacteristic
26C2×Dic167⋊C4C2211yescharacteristic
27C2×Dic167⋊C4C2211yescharacteristic
28C2×Dic167⋊C4C2211yescharacteristic
29C2×C4×Dic167C2211yescharacteristic
30C2×C4×Dic167C2211yescharacteristic
31C2×C4×Dic167C2211yescharacteristic
32C2×C4×Dic167C2211yescharacteristic
33C2×C4×Dic167C2211yescharacteristic
34C2×C4×Dic167C2211yescharacteristic
35C2×C4×Dic167C2211yescharacteristic
36C2×C4×Dic167C2211yescharacteristic
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
52C22×Dic167C2311yescharacteristic
53C22×Dic167C2311yescharacteristic
54C22×Dic167C2311yescharacteristic
55C22×Dic167C2311yescharacteristic
56C22×Dic167C2311yescharacteristic
57C22×Dic167C2311yescharacteristic
58C22×Dic167C2311yescharacteristic
59C22×Dic167C2311yescharacteristic
60C4⋊Dic167—22no—
61C4⋊Dic167—22no—
62C4⋊Dic167—41no—
63C4⋊Dic167C2×C414yes—
64Dic167⋊C4—22no—
65Dic167⋊C4—22no—
66Dic167⋊C4—41no—
67Dic167⋊C4C2×C414yes—
68Dic167⋊C4C2×C414yes—
69Dic167⋊C4C2×C414yes—
70Dic167⋊C4C2×C414yes—
71Dic167⋊C4Q814yes—
72C4×Dic167—22no—
73C4×Dic167—22no—
74C4×Dic167—22no—
75C4×Dic167—41no—
76C4×Dic167—41no—
77C4×Dic167—41no—
78C4×Dic167—41no—
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—22no—
88C4⋊C4×C167C2×C414yes—
89C42×C167—22no—
90C2×Dic167—21no—
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—
114C23×C167C2411yescharacteristic
115C2×C4×C167—21no—
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×C167C22×C412yes—
132C2×C4×C167C22×C412yes—
133C2×C4×C167C22×C412yes—
134C2×C4×C167C2×Q812yes—
135C2×C4×C167#4112yes—
136C22×C167C23×C411yescharacteristic
137C22×C167C22×Q811yescharacteristic
138C22×C167C2×#4111yescharacteristic
139C22×C167C2×#4111yescharacteristic
140C22×C167C2×#4111yescharacteristic
141C22×C167H(5,𝔽2)11yescharacteristic
142C22×C1672−1+411yescharacteristic
143C4×C167—22no—
144C4×C167—22no—
145C4×C167—22no—
146C4×C167—22no—
147C4×C167—22no—
148C4×C167—41no—
149C4×C167—41no—
150Dic167—22no—
151Dic167—22no—
152Dic167—22no—
153Dic167—22no—
154Dic167—22no—
155Dic167—41no—
156Dic167—41no—
157Dic167C4×Q814yes—
158C2×C167C2×C4×Q811yescharacteristic
159C2×C167C4×#4111yescharacteristic
160C2×C167#52011yescharacteristic
161C2×C167#55211yescharacteristic
162C2×C167#55311yescharacteristic
163C2×C167#55411yescharacteristic
164C2×C167#55711yescharacteristic
165C167#237011yescharacteristic, complemented, Sylow
166#2370—1671nomaximal, Sylow
167C2×#125—1671no—
168#389—1671no—
169#389—1671no—
170#389—1671no—
171#389—1671no—
172#387—1671no—
173#387—1671no—
174#387—1671no—
175#387D16711yescharacteristic
176C4×C4⋊C4—1671no—
177C4×C4⋊C4—1671no—
178C4×C4⋊C4—1671no—
179C4×C4⋊C4—1671no—
180C4×C4⋊C4—1671no—
181C4×C4⋊C4—1671no—
182#125—1678no—
183C2×C4⋊C4—1671no—
184C2×C4⋊C4—1671no—
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⋊C4—1671no—
195C2×C4⋊C4C2×D16711yescharacteristic
196C2×C4⋊C4C2×D16711yescharacteristic
197C2×C42—1671no—
198C2×C42—1671no—
199C2×C42—1671no—
200C2×C42—1671no—
201C2×C42—1671no—
202C2×C42—1671no—
203C2×C42—1671no—
204C2×C42—1671no—
205C2×C42C2×D16711yescharacteristic
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#95C2×D16711yescharacteristic
215#95C2×D16711yescharacteristic
216#95C2×D16711yescharacteristic
217#95C2×D16711yescharacteristic
218C22×C4—1671no—
219C22×C4—1671no—
220C22×C4—1671no—
221C22×C4—1671no—
222C22×C4—1671no—
223C22×C4—1671no—
224C22×C4—1671no—
225C22×C4—1671no—
226C22×C4C22×D16711yescharacteristic
227C22×C4C22×D16711yescharacteristic
228C22×C4C22×D16711yescharacteristic
229C22×C4C22×D16711yescharacteristic
230C22×C4C22×D16711yescharacteristic
231C22×C4C22×D16711yescharacteristic
232C22×C4C22×D16711yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—3342no—
235C4⋊C4—3342no—
236C4⋊C4—3342no—
237C4⋊C4—3342no—
238C4⋊C4—6681no—
239C4⋊C4—6681no—
240C4⋊C4—1674no—
241C4⋊C4—1674no—
242C4⋊C4—1674no—
243C4⋊C4—1674no—
244C4⋊C4—1674no—
245C4⋊C4—1674no—
246C4⋊C4C4×D16714yes—
247C42—22no—
248C42—3342no—
249C42—3342no—
250C42—3342no—
251C42—6681no—
252C42—6681no—
253C42—6681no—
254C42—6681no—
255C42—1674no—
256C23C23×D16711yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
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—3341no—
274C2×C4—3341no—
275C2×C4—3341no—
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—1672no—
290C2×C4—1672no—
291C2×C4—1672no—
292C2×C4—1672no—
293C2×C4—1672no—
294C2×C4—1672no—
295C2×C4—1672no—
296C2×C4—1672no—
297C2×C4C2×C4×D16712yes—
298C2×C4C2×C4×D16712yes—
299C2×C4C2×C4×D16712yes—
300C2×C4Q8×D16712yes—
301C2×C4#1458194912yes—
302C22C22×C4×D16711yescharacteristic
303C22C2×Q8×D16711yescharacteristic
304C22#41×D16711yescharacteristic
305C22#41×D16711yescharacteristic
306C22C2×#1458194911yescharacteristic
307C22#1912887811yescharacteristic
308C22#1912887911yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—3342no—
317C4—3342no—
318C4—3342no—
319C4—3342no—
320C4—3342no—
321C4—6681no—
322C4—6681no—
323C4—1674no—
324C2C4×Q8×D16711yescharacteristic
325C2C4×#1458194911yescharacteristic
326C2#2492374911yescharacteristic
327C2#2492395611yescharacteristic
328C2#2492397011yescharacteristic
329C2#2492397711yescharacteristic
330C2#2492399611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D167
commutatorC22×C167C23×C4
Fitting#387×C167C2
socle, prime radical, cosocleC23×C167C24
hypercenter#387D167
hypocenterC167#2370
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #19128822C4semidirect
165. C167#2370semidirect

Maximal subgroups

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

subgroupindex
C2×#191288222
#249231682
#249231662
#249231562
#249231542
#249231502
C4⋊C4×Dic1672
C4×Dic167⋊C42
C4×C4⋊Dic1672
#249231202
#387×C1672
#2370167