Finite Group Databasebeta

← #37546267

Subgroups — #37546267

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#26041997C211yesmaximal, characteristic, complemented
2#26041977C211yesmaximal, characteristic
3#26041686C211yesmaximal, characteristic, complemented
4#26041623C211yesmaximal, characteristic, complemented
5#26041609C211yesmaximal, characteristic, complemented
6#26041606C211yesmaximal, characteristic, complemented
7#26041603C211yesmaximal, characteristic, complemented
8#26041585C211yesmaximal, characteristic, complemented
9#26041568C211yesmaximal, characteristic, complemented
10#26041525C211yesmaximal, characteristic, complemented
11#26041509C211yesmaximal, characteristic, complemented
12#26041378C211yesmaximal, characteristic, complemented
13#26041348C211yesmaximal, characteristic, complemented
14#26041316C211yesmaximal, characteristic, complemented
15#428×C181C211yesmaximal, characteristic, complemented
16C2×#15668438C2211yescharacteristic
17C2×C8×D181C2211yescharacteristic
18#19153815C2211yescharacteristic
19#19153811—21no—
20#19153810—21no—
21#19153809—21no—
22#19153807C2211yescharacteristic
23#19153802—21no—
24#19153801—21no—
25#19153796C2211yescharacteristic
26#19153795C2211yescharacteristic
27#19153791C2211yescharacteristic
28#19153790—21no—
29#19153790C2211yescharacteristic
30C4×Dic362—21no—
31#19153781C2211yescharacteristic
32#19153778C2211yescharacteristic
33C4×C22⋊D181—21no—
34C4×C22⋊D181C2211yescharacteristic
35#19153774C2211yescharacteristic
36#19153774C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×M16×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#106×C181C2211yescharacteristic
58#106×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×D724—21no—
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181D411yescharacteristic
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67#15668438—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C8×D181—22no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428D411yescharacteristic
80C22⋊Dic181—21no—
81C22⋊Dic181D411yescharacteristic
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426D411yescharacteristic
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181C2311yescharacteristic
93C22×C4×C181—21no—
94C22×C4×C181C2311yescharacteristic
95M16×C181—22no—
96C2×C8×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C4⋊C4×C181—21no—
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C42×C181—21no—
105C22×D181—21no—
106C22×D181C2×D411yescharacteristic
107Dic362—21no—
108Dic362—21no—
109Dic362—42no—
110D724—21no—
111D724—21no—
112D724—81no—
113C22⋊D181—41no—
114C22⋊D181—42no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—21no—
122C4×D181—21no—
123C4×D181—81no—
124#13089678—21no—
125#13089678—21no—
126C23×C181C2×D411yescharacteristic
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#4112yes—
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#335011yescharacteristic, complemented, Sylow
168#3350—1811nomaximal, Sylow
169#556—1811no—
170#553—1811no—
171#501—1811no—
172#485—1811no—
173#483—1811no—
174#482—1811no—
175#482—1811no—
176#479—1811no—
177#476—1811no—
178#468—1811no—
179#465—1811no—
180#440—1811no—
181#435—1811no—
182#428D18111yescharacteristic, complemented
183#427—1811no—
184C2×SD16—1811no—
185C2×M16C2×D18111yescharacteristic
186C22×C8—1811no—
187C4⋊Q8—1811no—
188#126—3621no—
189#126—3621no—
190#126—3621no—
191#125—1811no—
192#124—3621no—
193#123—3621no—
194C22⋊Q8—1811no—
195C22⋊Q8—1811no—
196#121—3621no—
197#121—1811no—
198#121—1811no—
199C4×Q8—3621no—
200C4×Q8—1811no—
201C4×D4—3621no—
202C4×D4—1811no—
203C4×D4—1811no—
204#117—1811no—
205#117—1811no—
206#117C2×D18111yescharacteristic
207C2×C4⋊C4C2×D18111yescharacteristic
208#107—1811no—
209#107—1811no—
210#107C2×D18111yescharacteristic
211#107C2×D18111yescharacteristic
212#106—1811no—
213#106—1811no—
214#106—1811no—
215#106C2×D18111yescharacteristic
216#106C2×D18111yescharacteristic
217C4⋊C8—1811no—
218#103—1811no—
219#103—1811no—
220#103—1811no—
221#102—1811no—
222#102—1811no—
223#102—1811no—
224C22⋊C8—1811no—
225C22⋊C8—1811no—
226#97—1811no—
227C2×Q8—3621no—
228C2×Q8—1811no—
229C2×D4—3621no—
230C2×D4—3621no—
231C2×D4—1811no—
232C2×D4—1811no—
233C22×C4—21no—
234C22×C4—3621no—
235C22×C4—1811no—
236C22×C4C22×D18111yescharacteristic
237SD16—3622no—
238M16—22no—
239C2×C8—3622no—
240C2×C8—1811no—
241C2×C8—1811no—
242C2×C8C22×D18111yescharacteristic
243C2×C8C22×D18111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4C22×D18111yescharacteristic
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C22⋊C4—3621no—
266C22⋊C4—1811no—
267C22⋊C4—1811no—
268C42—21no—
269C42—3621no—
270C42—3621no—
271C42—3621no—
272C42—1811no—
273C23—3621no—
274C23—1811no—
275C23D4×D18111yescharacteristic
276Q8—3621no—
277Q8—3621no—
278Q8—7242no—
279D4—3621no—
280D4—3621no—
281D4—14481no—
282D4—7241no—
283D4—7242no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—14481no—
297C2×C4—1811no—
298C2×C4—1811no—
299C2×C4—1811no—
300C2×C4D4×D18111yescharacteristic
301C2×C4C23×D18111yescharacteristic
302C8—21no—
303C8—3621no—
304C8—3621no—
305C8#1566844912yes—
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—
327C4C2×#1566844911yescharacteristic
328C4#1915386411yescharacteristic
329C2—41no—
330C2—14481no—
331C2—7241no—
332C2#2604193011yescharacteristic
333C2#2604207811yescharacteristic
334C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#428×C181C2
socleC22×C181C22×D4
prime radical#26041977C2
hypercenter#428D181
hypocenterC181#3350
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #26041997C2semidirect
3. #26041686C2semidirect
4. #26041623C2semidirect
5. #26041609C2semidirect
6. #26041606C2semidirect
7. #26041603C2semidirect
8. #26041585C2semidirect
9. #26041568C2semidirect
10. #26041525C2semidirect
11. #26041509C2semidirect
12. #26041378C2semidirect
13. #26041348C2semidirect
14. #26041316C2semidirect
15. #428×C181C2semidirect
167. C181#3350semidirect
182. #428D181semidirect

Maximal subgroups

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

subgroupindex
#260419972
#260419772
#260416862
#260416232
#260416092
#260416062
#260416032
#260415852
#260415682
#260415252
#260415092
#260413782
#260413482
#260413162
#428×C1812
#3350181