Finite Group Databasebeta

← #37546284

Subgroups — #37546284

Order 23168.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041977C211yesmaximal, characteristic
2#26041963C211yesmaximal, characteristic, complemented
3#26041679C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041604C211yesmaximal, characteristic, complemented
6#26041599C211yesmaximal, characteristic, complemented
7#26041588C211yesmaximal, characteristic, complemented
8#26041578C211yesmaximal, characteristic, complemented
9#26041528C211yesmaximal, characteristic, complemented
10#26041527C211yesmaximal, characteristic, complemented
11#26041364C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041319C211yesmaximal, characteristic, complemented
14#26041318C211yesmaximal, characteristic, complemented
15#483×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668433C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19#19153811—21no—
20#19153809—21no—
21#19153807C2211yescharacteristic
22#19153807C2211yescharacteristic
23#19153806—21no—
24#19153801—21no—
25#19153798—21no—
26#19153792C2211yescharacteristic
27#19153791C2211yescharacteristic
28#19153790—21no—
29#19153790C2211yescharacteristic
30Q8×Dic181C2211yescharacteristic
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33C4×C22⋊D181C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153774—21no—
36#19153774C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C22⋊Q8×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#106×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×D724—21no—
60C2×D724C2311yescharacteristic
61C2×C22⋊D181—21no—
62C2×C22⋊D181D411yescharacteristic
63C2×C4×D181—21no—
64C2×C4×D181—21no—
65C2×C4×D181C2311yescharacteristic
66#15668436—22no—
67#15668433—22no—
68#15668432—22no—
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82C22⋊Dic181—21no—
83C22⋊Dic181D411yescharacteristic
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C22×C4×C181—21no—
96C22×C4×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22×D181—21no—
106C22×D181C2×D411yescharacteristic
107D724—21no—
108D724—21no—
109D724—81no—
110C22⋊D181—41no—
111C22⋊D181—42no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—42no—
121C4×D181—81no—
122#13089678—21no—
123#13089678#4112yes—
124C23×C181C2×D411yescharacteristic
125Q8×C181—21no—
126Q8×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—81no—
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2411yescharacteristic
136C8×C181—21no—
137C8×C181—21no—
138C22×C181—21no—
139C22×C181—21no—
140C22×C181—21no—
141C22×C181C22×D411yescharacteristic
142C2×D181—21no—
143C2×D181—21no—
144C2×D181—21no—
145C2×D181—41no—
146C2×D181—41no—
147C2×D181—41no—
148C4×C181—21no—
149C4×C181—41no—
150C4×C181—41no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181C2×#4111yescharacteristic
154C4×C1812−1+411yescharacteristic
155Dic181—21no—
156Dic181—21no—
157Dic181—21no—
158Dic181—41no—
159Dic181—41no—
160Dic181—41no—
161C2×C181—41no—
162C2×C181#54711yescharacteristic
163C2×C181#57511yescharacteristic
164C2×C181#57711yescharacteristic
165D181—41no—
166D181—81no—
167C181#335111yescharacteristic, complemented, Sylow
168#3351—1811nomaximal, Sylow
169#553—1811no—
170#552—1811no—
171#499—1811no—
172#485—1811no—
173#483D18111yescharacteristic, complemented
174#482—1811no—
175#481—1811no—
176#479—1811no—
177#478—1811no—
178#468—1811no—
179#468—1811no—
180C4×SD16—1811no—
181#436—1811no—
182#428—1811no—
183#428—1811no—
184C2×SD16—1811no—
185C2×M16—1811no—
186C2×M16—1811no—
187#126—3621no—
188#126—3621no—
189#125—3621no—
190#125—1811no—
191#125—1811no—
192#123—3621no—
193#123—3621no—
194C22⋊Q8—1811no—
195C22⋊Q8C2×D18111yescharacteristic
196#121—3621no—
197#121—1811no—
198#121—1811no—
199C4×Q8—1811no—
200C4×D4—3621no—
201C4×D4—1811no—
202C4×D4—1811no—
203#117—3621no—
204#117—1811no—
205#117—1811no—
206C2×C4⋊C4—1811no—
207C2×C4⋊C4C2×D18111yescharacteristic
208#107—1811no—
209#107—1811no—
210#107—1811no—
211#107—1811no—
212#106—1811no—
213#106—1811no—
214#106—1811no—
215#106C2×D18111yescharacteristic
216#106C2×D18111yescharacteristic
217C4⋊C8—1811no—
218#103—1811no—
219#103C2×D18111yescharacteristic
220#103C2×D18111yescharacteristic
221#102—1811no—
222#102—1811no—
223#102—1811no—
224C22⋊C8—1811no—
225C22⋊C8C2×D18111yescharacteristic
226C4×C8—1811no—
227C2×Q8C22×D18111yescharacteristic
228C2×D4—3621no—
229C2×D4—3621no—
230C2×D4—1811no—
231C2×D4—1811no—
232C22×C4—21no—
233C22×C4—3621no—
234C22×C4—3621no—
235C22×C4—1811no—
236C22×C4C22×D18111yescharacteristic
237SD16—3622no—
238M16—3622no—
239M16—3622no—
240C2×C8—1811no—
241C2×C8—1811no—
242C2×C8C22×D18111yescharacteristic
243C2×C8C22×D18111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4—1811no—
256C4⋊C4—1811no—
257C4⋊C4C22×D18111yescharacteristic
258C4⋊C4C22×D18111yescharacteristic
259C4⋊C4C22×D18111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—1811no—
268C22⋊C4—1811no—
269C42—3621no—
270C42—3621no—
271C42—3621no—
272C42—1811no—
273C23—3621no—
274C23—1811no—
275C23D4×D18111yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—3621no—
279D4—3621no—
280D4—14481no—
281D4—7241no—
282D4—7242no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—3621no—
291C2×C4—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—14481no—
296C2×C4—1811no—
297C2×C4—1811no—
298C2×C4—1811no—
299C2×C4—7242no—
300C2×C4D4×D18111yescharacteristic
301C2×C4C23×D18111yescharacteristic
302C8—21no—
303C8—21no—
304C8—3621no—
305C8—1812no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—3621no—
310C22—3621no—
311C22—3621no—
312C22—7241no—
313C22—7241no—
314C22—7241no—
315C22C2×D4×D18111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—3621no—
322C4—3621no—
323C4—3621no—
324C4—7241no—
325C4—7241no—
326C4—7241no—
327C4#41×D18111yescharacteristic
328C4#1915386311yescharacteristic
329C2—41no—
330C2—14481no—
331C2—7241no—
332C2#2604192711yescharacteristic
333C2#2604207811yescharacteristic
334C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#483×C181C2
socleC22×C181C22×D4
prime radical#26041977C2
hypercenter#483D181
hypocenterC181#3351
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #26041963C2semidirect
3. #26041679C2semidirect
4. #26041618C2semidirect
5. #26041604C2semidirect
6. #26041599C2semidirect
7. #26041588C2semidirect
8. #26041578C2semidirect
9. #26041528C2semidirect
10. #26041527C2semidirect
11. #26041364C2semidirect
12. #26041354C2semidirect
13. #26041319C2semidirect
14. #26041318C2semidirect
15. #483×C181C2semidirect
167. C181#3351semidirect
173. #483D181semidirect

Maximal subgroups

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

subgroupindex
#260419772
#260419632
#260416792
#260416182
#260416042
#260415992
#260415882
#260415782
#260415282
#260415272
#260413642
#260413542
#260413192
#260413182
#483×C1812
#3351181