Finite Group Databasebeta

← #36356278

Subgroups — #36356278

Order 22144.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19149678C211yesmaximal, characteristic
2C2×C4×Dic346C211yesmaximal, characteristic
3C2×#19149644C211yesmaximal, characteristic
4#26011395C211yesmaximal, characteristic
5#26011395C211yesmaximal, characteristic
6#26011378C211yesmaximal, characteristic
7#26011377C211yesmaximal, characteristic
8#26011376C211yesmaximal, characteristic
9#26011375C211yesmaximal, characteristic
10#26011374C211yesmaximal, characteristic
11#26011373C211yesmaximal, characteristic
12#26011372C211yesmaximal, characteristic
13#26011355C211yesmaximal, characteristic
14#26011336C211yesmaximal, characteristic
15#387×C173C211yesmaximal, characteristic
16C22×Dic346C2211yescharacteristic
17C22×Dic346C2211yescharacteristic
18#19149678C418yescomplemented
19C4×Dic346—24no—
20#19149644—24no—
21C2×C4⋊Dic173C2211yescharacteristic
22C2×C4⋊Dic173C2211yescharacteristic
23C2×#14583805C2211yescharacteristic
24C2×#14583805C2211yescharacteristic
25C2×#14583805C2211yescharacteristic
26C2×#14583805C2211yescharacteristic
27C2×#14583805C2211yescharacteristic
28C2×#14583805C2211yescharacteristic
29C2×C4×Dic173C2211yescharacteristic
30C2×C4×Dic173C2211yescharacteristic
31C2×C4×Dic173C2211yescharacteristic
32C2×C4×Dic173C2211yescharacteristic
33C2×C4×Dic173C2211yescharacteristic
34C2×C4×Dic173C2211yescharacteristic
35#19149586C2211yescharacteristic
36#19149586C2211yescharacteristic
37#19149586C2211yescharacteristic
38#19149586C2211yescharacteristic
39#19149586C2211yescharacteristic
40#19149586C2211yescharacteristic
41#19149586C2211yescharacteristic
42#19149586C2211yescharacteristic
43#19149586C2211yescharacteristic
44#19149586C2211yescharacteristic
45#19149586C2211yescharacteristic
46#19149586C2211yescharacteristic
47C2×C4⋊C4×C173C2211yescharacteristic
48C2×C4⋊C4×C173C2211yescharacteristic
49C2×C42×C173C2211yescharacteristic
50#95×C173C2211yescharacteristic
51#95×C173C2211yescharacteristic
52#95×C173C2211yescharacteristic
53#95×C173C2211yescharacteristic
54C2×Dic346—22no—
55C2×Dic346—22no—
56C2×Dic346—22no—
57C2×Dic346—22no—
58C2×Dic346C2×C414yes—
59C2×Dic346C2×C414yes—
60C22×Dic173C2311yescharacteristic
61C22×Dic173C2311yescharacteristic
62C22×Dic173C2311yescharacteristic
63C22×Dic173C2311yescharacteristic
64C22×Dic173C2311yescharacteristic
65C22×Dic173C2311yescharacteristic
66C22×Dic173C2311yescharacteristic
67C22×Dic173C2311yescharacteristic
68C4⋊Dic173—22no—
69C4⋊Dic173C2×C414yes—
70#14583805—22no—
71#14583805—22no—
72#14583805—22no—
73#14583805—22no—
74#14583805C2×C414yes—
75#14583805C2×C414yes—
76C4×Dic173—22no—
77C4×Dic173—22no—
78C4×Dic173—22no—
79C4×Dic173—22no—
80C4×Dic173C2×C414yes—
81C4×Dic173D414yes—
82C22×C4×C173C2311yescharacteristic
83C22×C4×C173C2311yescharacteristic
84C22×C4×C173C2311yescharacteristic
85C22×C4×C173C2311yescharacteristic
86C22×C4×C173C2311yescharacteristic
87C22×C4×C173C2311yescharacteristic
88C22×C4×C173C2311yescharacteristic
89C4⋊C4×C173—22no—
90C4⋊C4×C173C2×C414yes—
91C42×C173—22no—
92Dic346—28no—
93Dic346—28no—
94C2×Dic173—21no—
95C2×Dic173—21no—
96C2×Dic173—21no—
97C2×Dic173—21no—
98C2×Dic173—21no—
99C2×Dic173—21no—
100C2×Dic173—21no—
101C2×Dic173—21no—
102C2×Dic173—21no—
103C2×Dic173—21no—
104C2×Dic173—21no—
105C2×Dic173—21no—
106C2×Dic173—21no—
107C2×Dic173—21no—
108C2×Dic173—21no—
109C2×Dic173—21no—
110C2×Dic173—21no—
111C2×Dic173C22×C412yes—
112C2×Dic173C22×C412yes—
113C2×Dic173C22×C412yes—
114C2×Dic173C22×C412yes—
115C2×Dic173C2×D412yes—
116C2×Dic173C2×D412yes—
117C2×Dic173#4112yes—
118C23×C173C2411yescharacteristic
119C2×C4×C173—21no—
120C2×C4×C173—21no—
121C2×C4×C173—21no—
122C2×C4×C173—21no—
123C2×C4×C173—21no—
124C2×C4×C173—21no—
125C2×C4×C173—21no—
126C2×C4×C173—21no—
127C2×C4×C173—21no—
128C2×C4×C173—21no—
129C2×C4×C173—21no—
130C2×C4×C173—21no—
131C2×C4×C173—21no—
132C2×C4×C173—21no—
133C2×C4×C173—21no—
134C2×C4×C173—21no—
135C2×C4×C173—21no—
136C2×C4×C173C22×C412yes—
137C2×C4×C173C22×C412yes—
138C2×C4×C173C22×C412yes—
139C2×C4×C173C2×D412yes—
140C22×C173C23×C411yescharacteristic
141C22×C173C22×D411yescharacteristic
142C22×C173C2×#4111yescharacteristic
143C22×C1732−1+411yescharacteristic
144C22×C1732−1+411yescharacteristic
145C22×C1732−1+411yescharacteristic
146C22×C1732−1+411yescharacteristic
147C4×C173—22no—
148C4×C173—22no—
149C4×C173—22no—
150C4×C173—22no—
151C4×C173—41no—
152C4×C173—41no—
153C4×C173—41no—
154Dic173—22no—
155Dic173—22no—
156Dic173—22no—
157Dic173—22no—
158Dic173—41no—
159Dic173—41no—
160Dic173—41no—
161Dic173C4×D414yes—
162C2×C173C2×C4×D411yescharacteristic
163C2×C173#51911yescharacteristic
164C2×C173#51911yescharacteristic
165C2×C173#53611yescharacteristic
166C2×C173#53611yescharacteristic
167C2×C173#54111yescharacteristic
168C2×C173#54111yescharacteristic
169C173#232711yescharacteristic, complemented, Sylow
170#2327—1731nomaximal, Sylow
171C2×C4⋊Q8—1731no—
172C2×C4×Q8—1731no—
173C2×C4×Q8—1731no—
174#391—1731no—
175#391—1731no—
176#387—1731no—
177#387—1731no—
178#387—1731no—
179#387—1731no—
180#387—1731no—
181#387—1731no—
182#387—1731no—
183#387D17311yescharacteristic
184#382—1731no—
185#376—1731no—
186C22×Q8—1731no—
187C22×Q8—1731no—
188C4⋊Q8—1738no—
189C4×Q8—3464no—
190C4×Q8—3464no—
191C2×C4⋊C4—1731no—
192C2×C4⋊C4—1731no—
193C2×C4⋊C4—1731no—
194C2×C4⋊C4—1731no—
195C2×C4⋊C4—1731no—
196C2×C4⋊C4—1731no—
197C2×C4⋊C4—1731no—
198C2×C4⋊C4—1731no—
199C2×C4⋊C4C2×D17311yescharacteristic
200C2×C4⋊C4C2×D17311yescharacteristic
201C2×C42—1731no—
202C2×C42—1731no—
203C2×C42—1731no—
204C2×C42—1731no—
205C2×C42—1731no—
206C2×C42—1731no—
207C2×C42C2×D17311yescharacteristic
208#95—1731no—
209#95—1731no—
210#95—1731no—
211#95—1731no—
212#95—1731no—
213#95—1731no—
214#95—1731no—
215#95—1731no—
216#95—1731no—
217#95—1731no—
218#95—1731no—
219#95—1731no—
220#95C2×D17311yescharacteristic
221#95C2×D17311yescharacteristic
222#95C2×D17311yescharacteristic
223#95C2×D17311yescharacteristic
224C2×Q8—3462no—
225C2×Q8—3462no—
226C2×Q8—3462no—
227C2×Q8—3462no—
228C2×Q8—1734no—
229C2×Q8—1734no—
230C22×C4—1731no—
231C22×C4—1731no—
232C22×C4—1731no—
233C22×C4—1731no—
234C22×C4—1731no—
235C22×C4—1731no—
236C22×C4—1731no—
237C22×C4—1731no—
238C22×C4C22×D17311yescharacteristic
239C22×C4C22×D17311yescharacteristic
240C22×C4C22×D17311yescharacteristic
241C22×C4C22×D17311yescharacteristic
242C22×C4C22×D17311yescharacteristic
243C22×C4C22×D17311yescharacteristic
244C22×C4C22×D17311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—3462no—
247C4⋊C4—3462no—
248C4⋊C4—3462no—
249C4⋊C4—3462no—
250C4⋊C4—3462no—
251C4⋊C4—1734no—
252C4⋊C4—1734no—
253C4⋊C4—1734no—
254C4⋊C4C4×D17314yes—
255C42—22no—
256C42—3462no—
257C42—3462no—
258C42—3462no—
259C42—3462no—
260C42—1734no—
261C42—1734no—
262C23C23×D17311yescharacteristic
263Q8—3468no—
264Q8—3468no—
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—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—3461no—
283C2×C4—3461no—
284C2×C4—3461no—
285C2×C4—3461no—
286C2×C4—3461no—
287C2×C4—3461no—
288C2×C4—3461no—
289C2×C4—3461no—
290C2×C4—3461no—
291C2×C4—3461no—
292C2×C4—3461no—
293C2×C4—3461no—
294C2×C4—3461no—
295C2×C4—3461no—
296C2×C4—3461no—
297C2×C4—3461no—
298C2×C4—3461no—
299C2×C4—1732no—
300C2×C4—1732no—
301C2×C4—1732no—
302C2×C4—1732no—
303C2×C4—1732no—
304C2×C4—1732no—
305C2×C4—1732no—
306C2×C4C2×C4×D17312yes—
307C2×C4C2×C4×D17312yes—
308C2×C4C2×C4×D17312yes—
309C2×C4D4×D17312yes—
310C22C22×C4×D17311yescharacteristic
311C22C2×D4×D17311yescharacteristic
312C22#41×D17311yescharacteristic
313C22#1914972611yescharacteristic
314C22#1914972611yescharacteristic
315C22#1914972611yescharacteristic
316C22#1914972711yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3462no—
325C4—3462no—
326C4—3462no—
327C4—3462no—
328C4—1734no—
329C4—6921no—
330C4—6921no—
331C4—6921no—
332C2C4×D4×D17311yescharacteristic
333C2#2601196711yescharacteristic
334C2#2601196811yescharacteristic
335C2#2601206311yescharacteristic
336C2#2601206411yescharacteristic
337C2#2601209811yescharacteristic
338C2#2601210011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D173
commutatorC22×C173C23×C4
Fitting#387×C173C2
socle, prime radical, cosocleC23×C173C24
hypercenter#387D173
hypocenterC173#2327
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #19149678C4semidirect
169. C173#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#191496782
C2×C4×Dic3462
C2×#191496442
#260113952
#260113782
#260113772
#260113762
#260113752
#260113742
#260113732
#260113722
#260113552
#260113362
#387×C1732
#2327173