Finite Group Databasebeta

← #37545967

Subgroups — #37545967

Order 23168.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041981C211yesmaximal, characteristic, complemented
2#26041936C211yesmaximal, characteristic, complemented
3#26041632C211yesmaximal, characteristic, complemented
4#26041610C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041584C211yesmaximal, characteristic, complemented
7#26041529C211yesmaximal, characteristic, complemented
8#26041523C211yesmaximal, characteristic, complemented
9#26041492C211yesmaximal, characteristic, complemented
10#26041416C211yesmaximal, characteristic, complemented
11SD16×Dic181C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041286C211yesmaximal, characteristic, complemented
14#26041280C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×Q8×D181C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668433C2211yescharacteristic
19C2×#15668432C2211yescharacteristic
20#19153809—21no—
21#19153807C2211yescharacteristic
22#19153803—21no—
23#19153803C2211yescharacteristic
24#19153800—21no—
25#19153795—21no—
26#19153795C2211yescharacteristic
27#19153788—21no—
28#19153787—21no—
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32D4×Dic181—21no—
33D4×Dic181C2211yescharacteristic
34C4×C22⋊D181—21no—
35C4×C22⋊D181C2211yescharacteristic
36#19153774C2211yescharacteristic
37C2×C4⋊Dic181C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61Q8×D181—22no—
62Q8×D181—41no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181D411yescharacteristic
66C22×Dic181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181C2311yescharacteristic
70#15668437—41no—
71#15668433—41no—
72#15668432—41no—
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
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181D411yescharacteristic
91#15668426—21no—
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96#41×C181—22no—
97#41×C181—41no—
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105SD16×C181—22no—
106D8×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—42no—
115C22⋊D181—41no—
116C22⋊D181—42no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—81no—
123C2×Dic181—81no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C4×D181—21no—
128C4×D181—21no—
129C4×D181—42no—
130#13089678—21no—
131#13089678—21no—
132C23×C181—21no—
133C23×C181—21no—
134C23×C181C2×D411yescharacteristic
135Q8×C181—21no—
136Q8×C181#4112yes—
137D4×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—42no—
142D4×C181—42no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—42no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C4×C181—21no—
166C4×C181—22no—
167C4×C181—41no—
168C4×C181C2×#4111yescharacteristic
169C4×C181H(5,𝔽2)11yescharacteristic
170Dic181—21no—
171Dic181—21no—
172Dic181—21no—
173Dic181—41no—
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181—81no—
179C2×C181—81no—
180C2×C181#54611yescharacteristic
181C2×C181#57511yescharacteristic
182C2×C181#57711yescharacteristic
183D181—41no—
184C181#332611yescharacteristic, complemented, Sylow
185#3326—1811nomaximal, Sylow
186#553—1811no—
187#548—1811no—
188#488—1811no—
189#483—1811no—
190#482—1811no—
191#479—1811no—
192#469—1811no—
193#468—1811no—
194#463—1811no—
195#449D18111yescharacteristic, complemented
196#448—1811no—
197C4×SD16—1811no—
198#436—1811no—
199#419—1811no—
200#417—1811no—
201C2×#41C2×D18111yescharacteristic
202C22×Q8—1811no—
203C2×SD16—1811no—
204C2×SD16C2×D18111yescharacteristic
205C2×D8C2×D18111yescharacteristic
206C2×M16—1811no—
207C2×M16—1811no—
208#126—3621no—
209#125—1811no—
210#124—3621no—
211#124—1811no—
212#123—3621no—
213C22⋊Q8—3621no—
214C22⋊Q8—1811no—
215#121—3621no—
216#121—3621no—
217#121—1811no—
218#121—1811no—
219#121C2×D18111yescharacteristic
220C4×Q8—1811no—
221C4×D4—3621no—
222C4×D4—3621no—
223C4×D4—1811no—
224C4×D4—1811no—
225#117—1811no—
226C2×C4⋊C4—1811no—
227#107—1811no—
228#106—1811no—
229#106—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241C22⋊C8—1811no—
242C22⋊C8C2×D18111yescharacteristic
243C4×C8—1811no—
244#41—22no—
245#41—41no—
246C2×Q8—3621no—
247C2×Q8—3622no—
248C2×Q8—1811no—
249C2×Q8—7241no—
250C2×Q8C22×D18111yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4C22×D18111yescharacteristic
257C2×D4C22×D18111yescharacteristic
258C22×C4—21no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4C22×D18111yescharacteristic
264SD16—22no—
265SD16—7241no—
266D8—41no—
267M16—7241no—
268M16—7241no—
269C2×C8—1811no—
270C2×C8—1811no—
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22×D18111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—1811no—
292C22⋊C4—1811no—
293C42—3621no—
294C42—3621no—
295C42—1811no—
296C23—21no—
297C23—21no—
298C23—1811no—
299C23D4×D18111yescharacteristic
300Q8—21no—
301Q8—3621no—
302Q8—3621no—
303Q8—7242no—
304Q8#1566844812yes—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—42no—
311D4—14481no—
312D4—7241no—
313D4—7242no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—3621no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—14481no—
326C2×C4—14481no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4D4×D18111yescharacteristic
332C2×C4C23×D18111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3621no—
336C8—3621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3621no—
347C22—3621no—
348C22—3621no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—3621no—
354C4—3621no—
355C4—3621no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4—7241no—
360C4C2×#1566844811yescharacteristic
361C4#1915386111yescharacteristic
362C2—41no—
363C2—81no—
364C2—81no—
365C2—7241no—
366C2#2604191611yescharacteristic
367C2#2604207511yescharacteristic
368C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3326
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041981C2semidirect
2. #26041936C2semidirect
3. #26041632C2semidirect
4. #26041610C2semidirect
5. #26041602C2semidirect
6. #26041584C2semidirect
7. #26041529C2semidirect
8. #26041523C2semidirect
9. #26041492C2semidirect
10. #26041416C2semidirect
11. SD16×Dic181C2semidirect
12. #26041354C2semidirect
13. #26041286C2semidirect
14. #26041280C2semidirect
15. #449×C181C2semidirect
184. C181#3326semidirect
195. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260419812
#260419362
#260416322
#260416102
#260416022
#260415842
#260415292
#260415232
#260414922
#260414162
SD16×Dic1812
#260413542
#260412862
#260412802
#449×C1812
#3326181