Finite Group Databasebeta

← #37536587

Subgroups — #37536587

Order 23168.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153774C211yesmaximal, characteristic
2C2×#19153773C211yesmaximal, characteristic
3C2×C4⋊C4×D181C211yesmaximal, characteristic
4#26041176C211yesmaximal, characteristic, complemented
5#26041174C211yesmaximal, characteristic, complemented
6#26041165C211yesmaximal, characteristic, complemented
7#26041164C211yesmaximal, characteristic, complemented
8#26041162C211yesmaximal, characteristic, complemented
9#26041141C211yesmaximal, characteristic
10#26041141C211yesmaximal, characteristic
11#26041138C211yesmaximal, characteristic
12C4×#15668428C211yesmaximal, characteristic, complemented
13#26041130C211yesmaximal, characteristic, complemented
14#26041126C211yesmaximal, characteristic
15#387×C181C211yesmaximal, characteristic, complemented
16C22×C4×D181C2211yescharacteristic
17C22×C4×D181C2211yescharacteristic
18C22×C4×D181C2211yescharacteristic
19#19153774—24no—
20#19153773—24no—
21C2×C4⋊Dic181C2211yescharacteristic
22C2×C4⋊Dic181C2211yescharacteristic
23C2×#15668428C2211yescharacteristic
24C2×#15668428C2211yescharacteristic
25C2×#15668428C2211yescharacteristic
26C2×#15668428C2211yescharacteristic
27C2×#15668428C2211yescharacteristic
28C2×#15668428C2211yescharacteristic
29C4⋊C4×D181C418yescomplemented
30C2×#15668426C2211yescharacteristic
31C2×#15668426C2211yescharacteristic
32C2×#15668426C2211yescharacteristic
33C2×#15668426C2211yescharacteristic
34C2×C4×Dic181C2211yescharacteristic
35C2×C4×Dic181C2211yescharacteristic
36C2×C4×Dic181C2211yescharacteristic
37C2×C4×Dic181C2211yescharacteristic
38C2×C4×Dic181C2211yescharacteristic
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
54C23×D181C2311yescharacteristic
55C22×Dic181C2311yescharacteristic
56C22×Dic181C2311yescharacteristic
57C22×Dic181C2311yescharacteristic
58C22×Dic181C2311yescharacteristic
59C22×Dic181C2311yescharacteristic
60C22×Dic181C2311yescharacteristic
61C22×Dic181C2311yescharacteristic
62C2×C4×D181—22no—
63C2×C4×D181—22no—
64C2×C4×D181—22no—
65C2×C4×D181—22no—
66C2×C4×D181—22no—
67C2×C4×D181—22no—
68C2×C4×D181C2×C414yes—
69C2×C4×D181C2×C414yes—
70C2×C4×D181C2×C414yes—
71C4⋊Dic181—22no—
72C4⋊Dic181C2×C414yes—
73#15668428—22no—
74#15668428—22no—
75#15668428—22no—
76#15668428—22no—
77#15668428C2×C414yes—
78#15668428C2×C414yes—
79#15668426—22no—
80#15668426—22no—
81#15668426—22no—
82#15668426D414yes—
83C4×Dic181—22no—
84C4×Dic181—22no—
85C4×Dic181—22no—
86C4×Dic181—22no—
87C4×Dic181—22no—
88C22×C4×C181C2311yescharacteristic
89C22×C4×C181C2311yescharacteristic
90C22×C4×C181C2311yescharacteristic
91C22×C4×C181C2311yescharacteristic
92C22×C4×C181C2311yescharacteristic
93C22×C4×C181C2311yescharacteristic
94C22×C4×C181C2311yescharacteristic
95C4⋊C4×C181—22no—
96C4⋊C4×C181C2×C414yes—
97C42×C181—22no—
98C22×D181—21no—
99C22×D181—21no—
100C22×D181—21no—
101C22×D181—21no—
102C22×D181C22×C412yes—
103C22×D181C2×D412yes—
104C22×D181#4112yes—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181C22×C412yes—
121C2×Dic181C22×C412yes—
122C2×Dic181C22×C412yes—
123C2×Dic181C2×D412yes—
124C2×Dic181#4112yes—
125C2×Dic181#4112yes—
126C4×D181—28no—
127C4×D181—28no—
128C4×D181—28no—
129C23×C181C2411yescharacteristic
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×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181C22×C412yes—
148C2×C4×C181C22×C412yes—
149C2×C4×C181C22×C412yes—
150C2×C4×C181C2×D412yes—
151C22×C181C23×C411yescharacteristic
152C22×C181C22×D411yescharacteristic
153C22×C181C2×#4111yescharacteristic
154C22×C181C2×#4111yescharacteristic
155C22×C181C2×#4111yescharacteristic
156C22×C1812−1+411yescharacteristic
157C22×C1812−1+411yescharacteristic
158C2×D181—22no—
159C2×D181—22no—
160C2×D181—22no—
161C2×D181—22no—
162C2×D181—22no—
163C2×D181—22no—
164C2×D181C4×D414yes—
165C4×C181—22no—
166C4×C181—22no—
167C4×C181—22no—
168C4×C181—22no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181—41no—
172Dic181—22no—
173Dic181—22no—
174Dic181—22no—
175Dic181—41no—
176Dic181—41no—
177Dic181—41no—
178Dic181#11714yescomplemented
179C2×C181C2×#11711yescharacteristic
180C2×C181C2×C4×D411yescharacteristic
181C2×C181#51911yescharacteristic
182C2×C181#54711yescharacteristic
183C2×C181#54711yescharacteristic
184C2×C181#55211yescharacteristic
185C2×C181#55211yescharacteristic
186D181—24no—
187C181#234411yescharacteristic, complemented, Sylow
188#2344—1811nomaximal, Sylow
189C2×#117—1811no—
190C2×#117—1811no—
191C22×C4⋊C4—1811no—
192#389—1811no—
193#389—1811no—
194#387—1811no—
195#387—1811no—
196#387—1811no—
197#387D18111yescharacteristic, complemented
198#381—1811no—
199#381—1811no—
200#380—1811no—
201C4×C4⋊C4—1811no—
202C4×C4⋊C4—1811no—
203C4×C22⋊C4—1811no—
204C23×C4—1811no—
205C23×C4—1811no—
206C23×C4—1811no—
207#117—3624no—
208#117—3624no—
209C2×C4⋊C4—1811no—
210C2×C4⋊C4—1811no—
211C2×C4⋊C4—1811no—
212C2×C4⋊C4—1811no—
213C2×C4⋊C4—1811no—
214C2×C4⋊C4—1811no—
215C2×C4⋊C4—1811no—
216C2×C4⋊C4—1811no—
217C2×C4⋊C4—1818no—
218C2×C4⋊C4C2×D18111yescharacteristic
219C2×C4⋊C4C2×D18111yescharacteristic
220C2×C22⋊C4—1811no—
221C2×C22⋊C4—1811no—
222C2×C22⋊C4—1811no—
223C2×C22⋊C4—1811no—
224C2×C42—1811no—
225C2×C42—1811no—
226C2×C42—1811no—
227C2×C42—1811no—
228C2×C42—1811no—
229C2×C42C2×D18111yescharacteristic
230#95—1811no—
231#95—1811no—
232#95—1811no—
233#95—1811no—
234#95—1811no—
235#95—1811no—
236#95—1811no—
237#95—1811no—
238#95C2×D18111yescharacteristic
239#95C2×D18111yescharacteristic
240#95C2×D18111yescharacteristic
241#95C2×D18111yescharacteristic
242C24—1811no—
243C22×C4—3622no—
244C22×C4—3622no—
245C22×C4—3622no—
246C22×C4—3622no—
247C22×C4—3622no—
248C22×C4—3622no—
249C22×C4—1811no—
250C22×C4—1811no—
251C22×C4—1811no—
252C22×C4—1811no—
253C22×C4—1811no—
254C22×C4—1811no—
255C22×C4—1814no—
256C22×C4—1814no—
257C22×C4—1814no—
258C22×C4—1811no—
259C22×C4C22×D18111yescharacteristic
260C22×C4C22×D18111yescharacteristic
261C22×C4C22×D18111yescharacteristic
262C22×C4C22×D18111yescharacteristic
263C22×C4C22×D18111yescharacteristic
264C22×C4C22×D18111yescharacteristic
265C22×C4C22×D18111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—3622no—
268C4⋊C4—3622no—
269C4⋊C4—3622no—
270C4⋊C4—3622no—
271C4⋊C4—3622no—
272C4⋊C4—1814no—
273C4⋊C4—1814no—
274C4⋊C4—1814no—
275C4⋊C4C4×D18114yes—
276C22⋊C4—3622no—
277C22⋊C4—3622no—
278C22⋊C4—3622no—
279C22⋊C4—1814no—
280C42—22no—
281C42—3622no—
282C42—3622no—
283C42—3622no—
284C42—3622no—
285C42—3622no—
286C23—3621no—
287C23—3621no—
288C23—3621no—
289C23—3621no—
290C23—1812no—
291C23—1812no—
292C23—1812no—
293C23C23×D18111yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3628no—
312C2×C4—3628no—
313C2×C4—3628no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—3621no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—1812no—
330C2×C4—1812no—
331C2×C4—1812no—
332C2×C4—1812no—
333C2×C4—1812no—
334C2×C4—1812no—
335C2×C4C2×C4×D18112yes—
336C2×C4C2×C4×D18112yes—
337C2×C4C2×C4×D18112yes—
338C2×C4D4×D18112yes—
339C22—3622no—
340C22—3622no—
341C22—3622no—
342C22—3622no—
343C22—3622no—
344C22—3622no—
345C22—1814no—
346C22C22×C4×D18111yescharacteristic
347C22C2×D4×D18111yescharacteristic
348C22#41×D18111yescharacteristic
349C22#41×D18111yescharacteristic
350C22#41×D18111yescharacteristic
351C22#1915386311yescharacteristic
352C22#1915386411yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3622no—
361C4—3622no—
362C4—3622no—
363C4—1814no—
364C4—7241no—
365C4—7241no—
366C4—7241no—
367C2—3624no—
368C2#117×D18111yescharacteristic
369C2C4×D4×D18111yescharacteristic
370C2#2604175511yescharacteristic
371C2#2604192711yescharacteristic
372C2#2604193111yescharacteristic
373C2#2604196111yescharacteristic
374C2#2604196511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#387×C181C2
socle, cosocleC23×C181C24
prime radicalC23×D181C23
hypercenter#387D181
hypocenterC181#2344
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #26041176C2semidirect
5. #26041174C2semidirect
6. #26041165C2semidirect
7. #26041164C2semidirect
8. #26041162C2semidirect
12. C4×#15668428C2semidirect
13. #26041130C2semidirect
15. #387×C181C2semidirect
29. C4⋊C4×D181C4semidirect
178. Dic181#117semidirect
187. C181#2344semidirect
197. #387D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191537742
C2×#191537732
C2×C4⋊C4×D1812
#260411762
#260411742
#260411652
#260411642
#260411622
#260411412
#260411382
C4×#156684282
#260411302
#260411262
#387×C1812
#2344181