Finite Group Databasebeta

← #37543982

Subgroups — #37543982

Order 23168.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041898C211yesmaximal, characteristic, complemented
2#26041761C211yesmaximal, characteristic, complemented
3#26041613C211yesmaximal, characteristic, complemented
4#26041591C211yesmaximal, characteristic, complemented
5#26041574C211yesmaximal, characteristic, complemented
6#26041560C211yesmaximal, characteristic, complemented
7#26041491C211yesmaximal, characteristic, complemented
8#26041440C211yesmaximal, characteristic, complemented
9#26041423C211yesmaximal, characteristic
10#26041382C211yesmaximal, characteristic, complemented
11#26041380C211yesmaximal, characteristic, complemented
12Q16×Dic181C211yesmaximal, characteristic, complemented
13#26041359C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#464×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19#19153816C2211yescharacteristic
20#19153809—21no—
21#19153802—21no—
22#19153800—21no—
23#19153793—21no—
24#19153792C2211yescharacteristic
25#19153787C2211yescharacteristic
26Q8×Dic181C2211yescharacteristic
27Q8×Dic181C2211yescharacteristic
28C4×D724—21no—
29C4×D724C2211yescharacteristic
30D4×Dic181C2211yescharacteristic
31#19153778—21no—
32#19153778C2211yescharacteristic
33#19153773—21no—
34#19153773C2211yescharacteristic
35C4⋊C4×D181—21no—
36C4⋊C4×D181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61C2×Dic362—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C22×Dic181—21no—
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71#15668436—22no—
72#15668434—22no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181—21no—
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426D411yescharacteristic
91#15668426D411yescharacteristic
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98Q16×C181—22no—
99SD16×C181—22no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110Dic362—81no—
111D724—24no—
112D724—21no—
113D724#4112yes—
114C22⋊D181—81no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—81no—
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C4×D181—24no—
123C4×D181—21no—
124C4×D181—21no—
125C4×D181—81no—
126C4×D181—81no—
127C4×D181—81no—
128#13089678—21no—
129#13089678—21no—
130C23×C181—21no—
131Q8×C181—21no—
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181#4112yes—
135D4×C181—21no—
136D4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C22×C181—41no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181C22×D411yescharacteristic
149C2×D181—21no—
150C2×D181—22no—
151C2×D181—21no—
152C2×D181—21no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—22no—
156C4×C181—21no—
157C4×C181—21no—
158C4×C181—41no—
159C4×C181—41no—
160C4×C181C2×#4111yescharacteristic
161C4×C181C2×#4111yescharacteristic
162Dic181—21no—
163Dic181—21no—
164Dic181—21no—
165Dic181—41no—
166Dic181—41no—
167Dic181—41no—
168C2×C181—81no—
169C2×C181#52511yescharacteristic
170C2×C181#57611yescharacteristic
171C2×C181#57811yescharacteristic
172D181—41no—
173D181—42no—
174C181#312411yescharacteristic, complemented, Sylow
175#3124—1811nomaximal, Sylow
176#542—1811no—
177#520—1811no—
178#484—1811no—
179#480—1811no—
180#477—1811no—
181#474—1811no—
182#464D18111yescharacteristic, complemented
183#463—1811no—
184#452—1811no—
185#449—1811no—
186#440—1811no—
187#440—1811no—
188C4×Q16—1811no—
189C4×D8—1811no—
190#433—1811no—
191C2×#41—1811no—
192C2×Q16C2×D18111yescharacteristic
193C2×SD16—1811no—
194C2×SD16C2×D18111yescharacteristic
195C2×D8—1811no—
196C4⋊Q8—1811no—
197#126—3621no—
198#124—3621no—
199#124C2×D18111yescharacteristic
200#123—3621no—
201C22⋊Q8—3621no—
202C22⋊Q8—1811no—
203#121—1811no—
204C4×Q8—1811no—
205C4×Q8—1811no—
206C4×Q8C2×D18111yescharacteristic
207C4×D4—3621no—
208C4×D4—3621no—
209C4×D4—1811no—
210C4×D4—1811no—
211C4×D4—1811no—
212#117—3621no—
213#117—1811no—
214C2×C4⋊C4—3621no—
215C2×C4⋊C4—1811no—
216#107—1811no—
217#107—1811no—
218#107—1811no—
219#107—1811no—
220C4⋊C8—1811no—
221C4⋊C8C2×D18111yescharacteristic
222#103—1811no—
223#103—1811no—
224#103—1811no—
225#103C2×D18111yescharacteristic
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102C2×D18111yescharacteristic
230C22⋊C8—1811no—
231C22⋊C8—1811no—
232#97—1811no—
233C4×C8—1811no—
234#41—3622no—
235#41—3622no—
236C2×Q8—3621no—
237C2×Q8C22×D18111yescharacteristic
238C2×Q8C22×D18111yescharacteristic
239C2×D4—3621no—
240C2×D4—3621no—
241C2×D4—1811no—
242C2×D4C22×D18111yescharacteristic
243C22×C4—3621no—
244C22×C4—3621no—
245C22×C4—3621no—
246C22×C4—3621no—
247C22×C4—3621no—
248C22×C4—1811no—
249Q16—22no—
250SD16—22no—
251SD16—3622no—
252D8—3622no—
253C2×C8—1811no—
254C2×C8—1811no—
255C2×C8C22×D18111yescharacteristic
256C2×C8C22×D18111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4—1811no—
268C4⋊C4C22×D18111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4—1811no—
277C22⋊C4—1811no—
278C42—21no—
279C42—3621no—
280C42—3621no—
281C42—1811no—
282C42C22×D18111yescharacteristic
283C23—21no—
284C23—3621no—
285C23—1811no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—14481no—
290Q8#1566844812yes—
291D4—21no—
292D4—21no—
293D4—3624no—
294D4—3621no—
295D4—14481no—
296D4—1812no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—3624no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—3621no—
306C2×C4—14481no—
307C2×C4—14481no—
308C2×C4—14481no—
309C2×C4—14481no—
310C2×C4—1811no—
311C2×C4—1811no—
312C2×C4—1811no—
313C2×C4D4×D18111yescharacteristic
314C2×C4D4×D18111yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3621no—
319C8—3621no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—3621no—
324C22—3622no—
325C22—3621no—
326C22—3621no—
327C22—7241no—
328C22—7241no—
329C22C2×D4×D18111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—3621no—
336C4—3621no—
337C4—3621no—
338C4—7241no—
339C4—7241no—
340C4—7241no—
341C4#41×D18111yescharacteristic
342C4C2×#1566844811yescharacteristic
343C2—81no—
344C2—7241no—
345C2—7242no—
346C2#2604178911yescharacteristic
347C2#2604208111yescharacteristic
348C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#464×C181C2
socleC22×C181C22×D4
prime radical#26041423C2
hypercenter#464D181
hypocenterC181#3124
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #26041898C2semidirect
2. #26041761C2semidirect
3. #26041613C2semidirect
4. #26041591C2semidirect
5. #26041574C2semidirect
6. #26041560C2semidirect
7. #26041491C2semidirect
8. #26041440C2semidirect
10. #26041382C2semidirect
11. #26041380C2semidirect
12. Q16×Dic181C2semidirect
13. #26041359C2semidirect
14. #26041339C2semidirect
15. #464×C181C2semidirect
174. C181#3124semidirect
182. #464D181semidirect

Maximal subgroups

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

subgroupindex
#260418982
#260417612
#260416132
#260415912
#260415742
#260415602
#260414912
#260414402
#260414232
#260413822
#260413802
Q16×Dic1812
#260413592
#260413392
#464×C1812
#3124181