Finite Group Databasebeta

← #37541890

Subgroups — #37541890

Order 23168.

416 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041221C211yesmaximal, characteristic, complemented
2#26041206C211yesmaximal, characteristic, complemented
3#26041205C211yesmaximal, characteristic, complemented
4#26041199C211yesmaximal, characteristic, complemented
5#26041197C211yesmaximal, characteristic
6#26041197C211yesmaximal, characteristic
7#26041196C211yesmaximal, characteristic
8#26041192C211yesmaximal, characteristic, complemented
9#26041192C211yesmaximal, characteristic, complemented
10#26041192C211yesmaximal, characteristic, complemented
11#26041192C211yesmaximal, characteristic, complemented
12#26041183C211yesmaximal, characteristic, complemented
13#26041171C211yesmaximal, characteristic, complemented
14#26041169C211yesmaximal, characteristic, complemented
15#400×C181C211yesmaximal, characteristic, complemented
16C22×Dic362C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C22×D724C2211yescharacteristic
19C2×C4⋊Dic181C2211yescharacteristic
20C2×#15668428C2211yescharacteristic
21C2×#15668428C2211yescharacteristic
22C2×#15668426C2211yescharacteristic
23C2×#15668426C2211yescharacteristic
24C2×#15668426C2211yescharacteristic
25C2×#15668426C2211yescharacteristic
26C2×#15668426C2211yescharacteristic
27C2×#15668426C2211yescharacteristic
28C2×#15668426C2211yescharacteristic
29C2×#15668426C2211yescharacteristic
30C2×#15668426C2211yescharacteristic
31C2×#15668426C2211yescharacteristic
32C2×#15668426C2211yescharacteristic
33C2×#15668426C2211yescharacteristic
34C2×C4×Dic181C2211yescharacteristic
35#19153723C2211yescharacteristic
36#19153723C2211yescharacteristic
37#19153723C2211yescharacteristic
38#19153723C2211yescharacteristic
39#19153723C2211yescharacteristic
40#19153723C2211yescharacteristic
41#19153723C2211yescharacteristic
42#19153723C2211yescharacteristic
43#19153723C2211yescharacteristic
44C2×C4⋊C4×C181C2211yescharacteristic
45C2×C4⋊C4×C181C2211yescharacteristic
46#95×C181C2211yescharacteristic
47#95×C181C2211yescharacteristic
48#95×C181C2211yescharacteristic
49#95×C181C2211yescharacteristic
50#95×C181C2211yescharacteristic
51C23×D181C2311yescharacteristic
52C23×D181C2311yescharacteristic
53C2×Dic362—22no—
54C2×Dic362—41no—
55C2×Dic362—41no—
56C2×Dic362—41no—
57C2×Dic362—41no—
58C2×Dic362—41no—
59C2×D724—41no—
60C2×D724—41no—
61C2×D724—41no—
62C22×Dic181C2311yescharacteristic
63C22×Dic181C2311yescharacteristic
64C22×Dic181C2311yescharacteristic
65C22×Dic181C2311yescharacteristic
66C22×Dic181C2311yescharacteristic
67C22×Dic181C2311yescharacteristic
68C4⋊Dic181—41no—
69#15668428—41no—
70#15668428—41no—
71#15668426—22no—
72#15668426—22no—
73#15668426—41no—
74#15668426—41no—
75#15668426—41no—
76#15668426—41no—
77#15668426—41no—
78#15668426—41no—
79#15668426—41no—
80#15668426—41no—
81#15668426—41no—
82#15668426—41no—
83C4×Dic181—41no—
84C22×C4×C181C2311yescharacteristic
85C22×C4×C181C2311yescharacteristic
86C22×C4×C181C2311yescharacteristic
87C22×C4×C181C2311yescharacteristic
88C22×C4×C181C2311yescharacteristic
89C22×C4×C181C2311yescharacteristic
90C22×C4×C181C2311yescharacteristic
91C4⋊C4×C181—41no—
92C4⋊C4×C181—41no—
93C22×D181—21no—
94C22×D181—21no—
95C22×D181—21no—
96C22×D181—21no—
97C22×D181—21no—
98C22×D181—21no—
99C22×D181—21no—
100C22×D181—21no—
101C22×D181—21no—
102C22×D181—21no—
103C22×D181—21no—
104C22×D181—21no—
105C22×D181—21no—
106C22×D181—21no—
107Dic362—44no—
108Dic362—44no—
109D724—44no—
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×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181#4112yes—
128C23×C181C2411yescharacteristic
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×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×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C22×C181C2×#4111yescharacteristic
151C22×C181H(5,𝔽2)11yescharacteristic
152C22×C181H(5,𝔽2)11yescharacteristic
153C22×C181H(5,𝔽2)11yescharacteristic
154C22×C181H(5,𝔽2)11yescharacteristic
155C22×C1812−1+411yescharacteristic
156C22×C1812−1+411yescharacteristic
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181—41no—
178Dic181—22no—
179Dic181—41no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183Dic181—41no—
184C2×C181#53811yescharacteristic
185C2×C181#54211yescharacteristic
186C2×C181#54211yescharacteristic
187C2×C181H(3,𝔽4)11yescharacteristic
188C2×C181#56211yescharacteristic
189C2×C181#56211yescharacteristic
190C2×C181#56311yescharacteristic
191D181—81no—
192D181—81no—
193C181#283211yescharacteristic, complemented, Sylow
194#2832—1811nomaximal, Sylow
195#400—1811no—
196#400D18111yescharacteristic, complemented
197#397—1811no—
198#397—1811no—
199#395—1811no—
200#394—1811no—
201#394—1811no—
202#394—1811no—
203#393—1811no—
204#393—1811no—
205#393—1811no—
206#393—1811no—
207#391—1811no—
208#388—1811no—
209#388—1811no—
210C22×Q8—1811no—
211C22×Q8—1811no—
212C22×D4—1811no—
213C2×C4⋊C4—1811no—
214C2×C4⋊C4—1811no—
215C2×C4⋊C4—1811no—
216C2×C4⋊C4C2×D18111yescharacteristic
217C2×C4⋊C4C2×D18111yescharacteristic
218C2×C22⋊C4—1811no—
219C2×C22⋊C4—1811no—
220C2×C22⋊C4—1811no—
221C2×C22⋊C4—1811no—
222C2×C22⋊C4—1811no—
223C2×C22⋊C4—1811no—
224C2×C22⋊C4—1811no—
225C2×C22⋊C4—1811no—
226C2×C22⋊C4—1811no—
227C2×C22⋊C4—1811no—
228C2×C22⋊C4—1811no—
229C2×C22⋊C4—1811no—
230C2×C42—1811no—
231#95—1811no—
232#95—1811no—
233#95—1811no—
234#95—1811no—
235#95—1811no—
236#95—1811no—
237#95—1811no—
238#95—1811no—
239#95—1811no—
240#95C2×D18111yescharacteristic
241#95C2×D18111yescharacteristic
242#95C2×D18111yescharacteristic
243#95C2×D18111yescharacteristic
244#95C2×D18111yescharacteristic
245C24—1811no—
246C24—1811no—
247C2×Q8—3622no—
248C2×Q8—7241no—
249C2×Q8—7241no—
250C2×Q8—7241no—
251C2×Q8—7241no—
252C2×Q8—7241no—
253C2×D4—7241no—
254C2×D4—7241no—
255C2×D4—7241no—
256C22×C4—1811no—
257C22×C4—1811no—
258C22×C4—1811no—
259C22×C4—1811no—
260C22×C4—1811no—
261C22×C4—1811no—
262C22×C4C22×D18111yescharacteristic
263C22×C4C22×D18111yescharacteristic
264C22×C4C22×D18111yescharacteristic
265C22×C4C22×D18111yescharacteristic
266C22×C4C22×D18111yescharacteristic
267C22×C4C22×D18111yescharacteristic
268C22×C4C22×D18111yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—7241no—
272C4⋊C4—7241no—
273C4⋊C4—7241no—
274C22⋊C4—3622no—
275C22⋊C4—3622no—
276C22⋊C4—7241no—
277C22⋊C4—7241no—
278C22⋊C4—7241no—
279C22⋊C4—7241no—
280C22⋊C4—7241no—
281C22⋊C4—7241no—
282C22⋊C4—7241no—
283C22⋊C4—7241no—
284C22⋊C4—7241no—
285C22⋊C4—7241no—
286C42—7241no—
287C23—3621no—
288C23—3621no—
289C23—3621no—
290C23—3621no—
291C23—3621no—
292C23—3621no—
293C23—3621no—
294C23—3621no—
295C23—3621no—
296C23—3621no—
297C23—3621no—
298C23—3621no—
299C23—3621no—
300C23—3621no—
301C23C23×D18111yescharacteristic
302Q8—7244no—
303Q8—7244no—
304D4—7244no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—3621no—
339C2×C4—3621no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—1812no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22—7241no—
352C22—7241no—
353C22—7241no—
354C22—7241no—
355C22—7241no—
356C22—7241no—
357C22—7241no—
358C22#41×D18111yescharacteristic
359C22#1915386111yescharacteristic
360C22#1915386211yescharacteristic
361C22#1915386211yescharacteristic
362C22#1915386211yescharacteristic
363C22#1915386311yescharacteristic
364C22#1915386411yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3622no—
373C4—7241no—
374C4—7241no—
375C4—7241no—
376C4—7241no—
377C4—7241no—
378C2—14481no—
379C2—14481no—
380C2#2604186811yescharacteristic
381C2#2604189511yescharacteristic
382C2#2604189911yescharacteristic
383C2#2604202111yescharacteristic
384C2#2604202611yescharacteristic
385C2#2604202711yescharacteristic
386C2#2604203311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#400×C181C2
prime radicalC22×D724C22
hypercenter#400D181
hypocenterC181#2832
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #26041221C2semidirect
2. #26041206C2semidirect
3. #26041205C2semidirect
4. #26041199C2semidirect
8. #26041192C2semidirect
9. #26041192C2semidirect
10. #26041192C2semidirect
11. #26041192C2semidirect
12. #26041183C2semidirect
13. #26041171C2semidirect
14. #26041169C2semidirect
15. #400×C181C2semidirect
193. C181#2832semidirect
196. #400D181semidirect

Maximal subgroups

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

subgroupindex
#260412212
#260412062
#260412052
#260411992
#260411972
#260411962
#260411922
#260411832
#260411712
#260411692
#400×C1812
#2832181