Finite Group Databasebeta

← #37536436

Subgroups — #37536436

Order 23168.

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×#19153815C211yesmaximal, characteristic
2C2×C4×Dic362C211yesmaximal, characteristic
3C2×#19153781C211yesmaximal, characteristic
4#26041183C211yesmaximal, characteristic
5#26041183C211yesmaximal, characteristic
6#26041166C211yesmaximal, characteristic
7#26041165C211yesmaximal, characteristic
8#26041164C211yesmaximal, characteristic
9#26041163C211yesmaximal, characteristic
10#26041162C211yesmaximal, characteristic
11#26041161C211yesmaximal, characteristic
12#26041160C211yesmaximal, characteristic
13#26041143C211yesmaximal, characteristic
14#26041124C211yesmaximal, characteristic
15#387×C181C211yesmaximal, characteristic
16C22×Dic362C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18#19153815C418yescomplemented
19C4×Dic362—24no—
20#19153781—24no—
21C2×C4⋊Dic181C2211yescharacteristic
22C2×C4⋊Dic181C2211yescharacteristic
23C2×#15668428C2211yescharacteristic
24C2×#15668428C2211yescharacteristic
25C2×#15668428C2211yescharacteristic
26C2×#15668428C2211yescharacteristic
27C2×#15668428C2211yescharacteristic
28C2×#15668428C2211yescharacteristic
29C2×C4×Dic181C2211yescharacteristic
30C2×C4×Dic181C2211yescharacteristic
31C2×C4×Dic181C2211yescharacteristic
32C2×C4×Dic181C2211yescharacteristic
33C2×C4×Dic181C2211yescharacteristic
34C2×C4×Dic181C2211yescharacteristic
35#19153723C2211yescharacteristic
36#19153723C2211yescharacteristic
37#19153723C2211yescharacteristic
38#19153723C2211yescharacteristic
39#19153723C2211yescharacteristic
40#19153723C2211yescharacteristic
41#19153723C2211yescharacteristic
42#19153723C2211yescharacteristic
43#19153723C2211yescharacteristic
44#19153723C2211yescharacteristic
45#19153723C2211yescharacteristic
46#19153723C2211yescharacteristic
47C2×C4⋊C4×C181C2211yescharacteristic
48C2×C4⋊C4×C181C2211yescharacteristic
49C2×C42×C181C2211yescharacteristic
50#95×C181C2211yescharacteristic
51#95×C181C2211yescharacteristic
52#95×C181C2211yescharacteristic
53#95×C181C2211yescharacteristic
54C2×Dic362—22no—
55C2×Dic362—22no—
56C2×Dic362—22no—
57C2×Dic362—22no—
58C2×Dic362C2×C414yes—
59C2×Dic362C2×C414yes—
60C22×Dic181C2311yescharacteristic
61C22×Dic181C2311yescharacteristic
62C22×Dic181C2311yescharacteristic
63C22×Dic181C2311yescharacteristic
64C22×Dic181C2311yescharacteristic
65C22×Dic181C2311yescharacteristic
66C22×Dic181C2311yescharacteristic
67C22×Dic181C2311yescharacteristic
68C4⋊Dic181—22no—
69C4⋊Dic181C2×C414yes—
70#15668428—22no—
71#15668428—22no—
72#15668428—22no—
73#15668428—22no—
74#15668428C2×C414yes—
75#15668428C2×C414yes—
76C4×Dic181—22no—
77C4×Dic181—22no—
78C4×Dic181—22no—
79C4×Dic181—22no—
80C4×Dic181C2×C414yes—
81C4×Dic181D414yes—
82C22×C4×C181C2311yescharacteristic
83C22×C4×C181C2311yescharacteristic
84C22×C4×C181C2311yescharacteristic
85C22×C4×C181C2311yescharacteristic
86C22×C4×C181C2311yescharacteristic
87C22×C4×C181C2311yescharacteristic
88C22×C4×C181C2311yescharacteristic
89C4⋊C4×C181—22no—
90C4⋊C4×C181C2×C414yes—
91C42×C181—22no—
92Dic362—28no—
93Dic362—28no—
94C2×Dic181—21no—
95C2×Dic181—21no—
96C2×Dic181—21no—
97C2×Dic181—21no—
98C2×Dic181—21no—
99C2×Dic181—21no—
100C2×Dic181—21no—
101C2×Dic181—21no—
102C2×Dic181—21no—
103C2×Dic181—21no—
104C2×Dic181—21no—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181C22×C412yes—
112C2×Dic181C22×C412yes—
113C2×Dic181C22×C412yes—
114C2×Dic181C22×C412yes—
115C2×Dic181C2×D412yes—
116C2×Dic181C2×D412yes—
117C2×Dic181#4112yes—
118C23×C181C2411yescharacteristic
119C2×C4×C181—21no—
120C2×C4×C181—21no—
121C2×C4×C181—21no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181C22×C412yes—
137C2×C4×C181C22×C412yes—
138C2×C4×C181C22×C412yes—
139C2×C4×C181C2×D412yes—
140C22×C181C23×C411yescharacteristic
141C22×C181C22×D411yescharacteristic
142C22×C181C2×#4111yescharacteristic
143C22×C1812−1+411yescharacteristic
144C22×C1812−1+411yescharacteristic
145C22×C1812−1+411yescharacteristic
146C22×C1812−1+411yescharacteristic
147C4×C181—22no—
148C4×C181—22no—
149C4×C181—22no—
150C4×C181—22no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181—41no—
154Dic181—22no—
155Dic181—22no—
156Dic181—22no—
157Dic181—22no—
158Dic181—41no—
159Dic181—41no—
160Dic181—41no—
161Dic181C4×D414yes—
162C2×C181C2×C4×D411yescharacteristic
163C2×C181#51911yescharacteristic
164C2×C181#51911yescharacteristic
165C2×C181#53611yescharacteristic
166C2×C181#53611yescharacteristic
167C2×C181#54111yescharacteristic
168C2×C181#54111yescharacteristic
169C181#232711yescharacteristic, complemented, Sylow
170#2327—1811nomaximal, Sylow
171C2×C4⋊Q8—1811no—
172C2×C4×Q8—1811no—
173C2×C4×Q8—1811no—
174#391—1811no—
175#391—1811no—
176#387—1811no—
177#387—1811no—
178#387—1811no—
179#387—1811no—
180#387—1811no—
181#387—1811no—
182#387—1811no—
183#387D18111yescharacteristic
184#382—1811no—
185#376—1811no—
186C22×Q8—1811no—
187C22×Q8—1811no—
188C4⋊Q8—1818no—
189C4×Q8—3624no—
190C4×Q8—3624no—
191C2×C4⋊C4—1811no—
192C2×C4⋊C4—1811no—
193C2×C4⋊C4—1811no—
194C2×C4⋊C4—1811no—
195C2×C4⋊C4—1811no—
196C2×C4⋊C4—1811no—
197C2×C4⋊C4—1811no—
198C2×C4⋊C4—1811no—
199C2×C4⋊C4C2×D18111yescharacteristic
200C2×C4⋊C4C2×D18111yescharacteristic
201C2×C42—1811no—
202C2×C42—1811no—
203C2×C42—1811no—
204C2×C42—1811no—
205C2×C42—1811no—
206C2×C42—1811no—
207C2×C42C2×D18111yescharacteristic
208#95—1811no—
209#95—1811no—
210#95—1811no—
211#95—1811no—
212#95—1811no—
213#95—1811no—
214#95—1811no—
215#95—1811no—
216#95—1811no—
217#95—1811no—
218#95—1811no—
219#95—1811no—
220#95C2×D18111yescharacteristic
221#95C2×D18111yescharacteristic
222#95C2×D18111yescharacteristic
223#95C2×D18111yescharacteristic
224C2×Q8—3622no—
225C2×Q8—3622no—
226C2×Q8—3622no—
227C2×Q8—3622no—
228C2×Q8—1814no—
229C2×Q8—1814no—
230C22×C4—1811no—
231C22×C4—1811no—
232C22×C4—1811no—
233C22×C4—1811no—
234C22×C4—1811no—
235C22×C4—1811no—
236C22×C4—1811no—
237C22×C4—1811no—
238C22×C4C22×D18111yescharacteristic
239C22×C4C22×D18111yescharacteristic
240C22×C4C22×D18111yescharacteristic
241C22×C4C22×D18111yescharacteristic
242C22×C4C22×D18111yescharacteristic
243C22×C4C22×D18111yescharacteristic
244C22×C4C22×D18111yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—3622no—
247C4⋊C4—3622no—
248C4⋊C4—3622no—
249C4⋊C4—3622no—
250C4⋊C4—3622no—
251C4⋊C4—1814no—
252C4⋊C4—1814no—
253C4⋊C4—1814no—
254C4⋊C4C4×D18114yes—
255C42—22no—
256C42—3622no—
257C42—3622no—
258C42—3622no—
259C42—3622no—
260C42—1814no—
261C42—1814no—
262C23C23×D18111yescharacteristic
263Q8—3628no—
264Q8—3628no—
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—3621no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—3621no—
291C2×C4—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—1812no—
300C2×C4—1812no—
301C2×C4—1812no—
302C2×C4—1812no—
303C2×C4—1812no—
304C2×C4—1812no—
305C2×C4—1812no—
306C2×C4C2×C4×D18112yes—
307C2×C4C2×C4×D18112yes—
308C2×C4C2×C4×D18112yes—
309C2×C4D4×D18112yes—
310C22C22×C4×D18111yescharacteristic
311C22C2×D4×D18111yescharacteristic
312C22#41×D18111yescharacteristic
313C22#1915386311yescharacteristic
314C22#1915386311yescharacteristic
315C22#1915386311yescharacteristic
316C22#1915386411yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3622no—
325C4—3622no—
326C4—3622no—
327C4—3622no—
328C4—1814no—
329C4—7241no—
330C4—7241no—
331C4—7241no—
332C2C4×D4×D18111yescharacteristic
333C2#2604175511yescharacteristic
334C2#2604175611yescharacteristic
335C2#2604185111yescharacteristic
336C2#2604185211yescharacteristic
337C2#2604188611yescharacteristic
338C2#2604188811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#387×C181C2
socle, prime radical, cosocleC23×C181C24
hypercenter#387D181
hypocenterC181#2327
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #19153815C4semidirect
169. C181#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#191538152
C2×C4×Dic3622
C2×#191537812
#260411832
#260411662
#260411652
#260411642
#260411632
#260411622
#260411612
#260411602
#260411432
#260411242
#387×C1812
#2327181