Finite Group Databasebeta

← #37545791

Subgroups — #37545791

Order 23168.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042000C211yesmaximal, characteristic, complemented
2#26041936C211yesmaximal, characteristic
3#26041637C211yesmaximal, characteristic, complemented
4#26041621C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041572C211yesmaximal, characteristic, complemented
7#26041522C211yesmaximal, characteristic, complemented
8#26041518C211yesmaximal, characteristic, complemented
9#26041499C211yesmaximal, characteristic, complemented
10#26041433C211yesmaximal, characteristic, complemented
11#26041386C211yesmaximal, characteristic, complemented
12#26041347C211yesmaximal, characteristic, complemented
13#26041286C211yesmaximal, characteristic, complemented
14#26041275C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×Q8×D181C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C22×#13089678C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153811—21no—
22#19153809—21no—
23#19153803—21no—
24#19153803C2211yescharacteristic
25#19153802—21no—
26#19153795—21no—
27#19153795C2211yescharacteristic
28#19153792C2211yescharacteristic
29#19153787—21no—
30#19153787C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32Q8×Dic181C2211yescharacteristic
33#19153781—21no—
34C4×C22⋊D181—21no—
35C4×C22⋊D181C2211yescharacteristic
36#19153775C2211yescharacteristic
37#19153774C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62Q8×D181—22no—
63Q8×D181—41no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181D411yescharacteristic
66C2×C4×D181—21no—
67C2×C4×D181C2311yescharacteristic
68#15668439—41no—
69#15668432—41no—
70C2×#13089678—41no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426D411yescharacteristic
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96#41×C181—22no—
97#41×C181—41no—
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104Q16×C181—22no—
105SD16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—42no—
115Dic362—42no—
116C22⋊D181—41no—
117C22⋊D181—42no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—21no—
126C4×D181—21no—
127C4×D181—42no—
128#13089678—21no—
129#13089678—21no—
130C23×C181—21no—
131C23×C181C2×D411yescharacteristic
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181—21no—
135Q8×C181#4112yes—
136D4×C181—21no—
137D4×C181—21no—
138D4×C181—42no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—42no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—22no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181C2×#4111yescharacteristic
164C4×C181H(5,𝔽2)11yescharacteristic
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—41no—
173C2×C181—81no—
174C2×C181#54611yescharacteristic
175C2×C181#57511yescharacteristic
176C2×C181#57811yescharacteristic
177D181—41no—
178C181#331311yescharacteristic, complemented, Sylow
179#3313—1811nomaximal, Sylow
180#556—1811no—
181#548—1811no—
182#489—1811no—
183#485—1811no—
184#482—1811no—
185#477—1811no—
186#468—1811no—
187#467—1811no—
188#464—1811no—
189#452D18111yescharacteristic, complemented
190#451—1811no—
191#441—1811no—
192#435—1811no—
193#419—1811no—
194#416—1811no—
195C2×#41C2×D18111yescharacteristic
196C22×Q8—1811no—
197C2×Q16—1811no—
198C2×Q16C2×D18111yescharacteristic
199C2×SD16C2×D18111yescharacteristic
200C2×M16—1811no—
201C22×C8—1811no—
202C4⋊Q8—1811no—
203#126—3621no—
204#126—3621no—
205#124—3621no—
206#124—3621no—
207#124—1811no—
208C22⋊Q8—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8C2×D18111yescharacteristic
212#121—3621no—
213#121—1811no—
214C4×Q8—3621no—
215C4×Q8—1811no—
216C4×Q8—1811no—
217C4×D4—3621no—
218C4×D4—1811no—
219#117—1811no—
220#117—1811no—
221#107—1811no—
222#107—1811no—
223#106—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102—1811no—
234#102C2×D18111yescharacteristic
235C22⋊C8—1811no—
236C22⋊C8C2×D18111yescharacteristic
237#97—1811no—
238#41—22no—
239#41—41no—
240C2×Q8—3621no—
241C2×Q8—3621no—
242C2×Q8—3622no—
243C2×Q8—1811no—
244C2×Q8—7241no—
245C2×Q8C22×D18111yescharacteristic
246C2×Q8C22×D18111yescharacteristic
247C2×D4—21no—
248C2×D4—3621no—
249C2×D4—1811no—
250C2×D4C22×D18111yescharacteristic
251C22×C4—21no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4C22×D18111yescharacteristic
255Q16—22no—
256Q16—7241no—
257SD16—41no—
258M16—7241no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—1811no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4C22×D18111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3621no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—1811no—
284C22⋊C4—1811no—
285C42—3621no—
286C42—3621no—
287C42—3621no—
288C42—3621no—
289C42—1811no—
290C23—21no—
291C23—1811no—
292C23D4×D18111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—3621no—
297Q8—3621no—
298Q8—7242no—
299Q8—7242no—
300Q8#1566844812yes—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—7241no—
305D4—7242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—7242no—
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—3621no—
343C4—3621no—
344C4—3621no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4C2×#1566844811yescharacteristic
350C4#1915386111yescharacteristic
351C2—41no—
352C2—81no—
353C2—7241no—
354C2#2604191611yescharacteristic
355C2#2604207611yescharacteristic
356C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radical#26041936C2
hypercenter#452D181
hypocenterC181#3313
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26042000C2semidirect
3. #26041637C2semidirect
4. #26041621C2semidirect
5. #26041602C2semidirect
6. #26041572C2semidirect
7. #26041522C2semidirect
8. #26041518C2semidirect
9. #26041499C2semidirect
10. #26041433C2semidirect
11. #26041386C2semidirect
12. #26041347C2semidirect
13. #26041286C2semidirect
14. #26041275C2semidirect
15. #452×C181C2semidirect
178. C181#3313semidirect
189. #452D181semidirect

Maximal subgroups

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

subgroupindex
#260420002
#260419362
#260416372
#260416212
#260416022
#260415722
#260415222
#260415182
#260414992
#260414332
#260413862
#260413472
#260412862
#260412752
#452×C1812
#3313181