Finite Group Databasebeta

← #37545078

Subgroups — #37545078

Order 23168.

392 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041824C211yesmaximal, characteristic, complemented
2#26041815C211yesmaximal, characteristic, complemented
3#26041582C211yesmaximal, characteristic, complemented
4#26041581C211yesmaximal, characteristic, complemented
5#26041562C211yesmaximal, characteristic, complemented
6#26041558C211yesmaximal, characteristic, complemented
7#26041532C211yesmaximal, characteristic, complemented
8#26041530C211yesmaximal, characteristic, complemented
9#26041527C211yesmaximal, characteristic, complemented
10#26041497C211yesmaximal, characteristic, complemented
11#26041496C211yesmaximal, characteristic, complemented
12#26041477C211yesmaximal, characteristic, complemented
13#26041473C211yesmaximal, characteristic, complemented
14#26041302C211yesmaximal, characteristic, complemented
15#468×C181C211yesmaximal, characteristic, complemented
16C2×#15668448—21no—
17C2×#15668436C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668433C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153812C2211yescharacteristic
23#19153811—21no—
24#19153807C2211yescharacteristic
25#19153805C2211yescharacteristic
26#19153802—21no—
27#19153800—21no—
28#19153790C2211yescharacteristic
29#19153790C2211yescharacteristic
30#19153788—21no—
31Q8×Dic181C2211yescharacteristic
32D4×Dic181C2211yescharacteristic
33#19153778C2211yescharacteristic
34#19153778C2211yescharacteristic
35#19153776—21no—
36#19153776—21no—
37#19153774—21no—
38C2×C4×Dic181C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153736C2211yescharacteristic
51#19153736C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668448—44no—
60C2×Dic362—21no—
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C22×Dic181D411yescharacteristic
69C22×Dic181D411yescharacteristic
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72#15668436—41no—
73D1448—41no—
74#15668434—41no—
75#15668433—41no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C4⋊Dic181—21no—
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428—21no—
84C22⋊Dic181—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91C4×Dic181—21no—
92C4×Dic181D411yescharacteristic
93C4×Dic181D411yescharacteristic
94C4×Dic181C2311yescharacteristic
95C4×Dic181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181C2311yescharacteristic
100SD16×C181—41no—
101M16×C181—41no—
102C2×C8×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C4⋊C4×C181—21no—
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22×D181—21no—
110C22×D181—21no—
111Dic362—42no—
112D724—21no—
113D724—21no—
114D724—21no—
115D724—21no—
116C22⋊D181—42no—
117C22⋊D181—42no—
118C22⋊D181—42no—
119C22⋊D181—42no—
120C2×Dic181—22no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—41no—
124C2×Dic181—42no—
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—42no—
130C4×D181—42no—
131#13089678—21no—
132#13089678—21no—
133C23×C181—21no—
134C23×C181C2×D411yescharacteristic
135Q8×C181—21no—
136Q8×C181—21no—
137D4×C181—21no—
138D4×C181—21no—
139D4×C181—42no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
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—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C4×C181—21no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181H(5,𝔽2)11yescharacteristic
167C4×C1812−1+411yescharacteristic
168Dic181—21no—
169Dic181—21no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173Dic181AGL(1,ℤ/8)12yes—
174C2×C181—41no—
175C2×C181—81no—
176C2×C181#53711yescharacteristic
177C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C181#57511yescharacteristic
179D181—81no—
180D181—81no—
181C181#325111yescharacteristic, complemented, Sylow
182#3251—1811nomaximal, Sylow
183#532—1811no—
184#529—1811no—
185#478—1811no—
186#478—1811no—
187#475—1811no—
188#474—1811no—
189#469—1811no—
190#469—1811no—
191#468—1811no—
192#468D18111yescharacteristic, complemented
193#463—1811no—
194#463—1811no—
195#460—1811no—
196#459—1811no—
197#423—1811no—
198C2×#41—3621no—
199C2×SD16—1811no—
200C2×SD16C2×D18111yescharacteristic
201C2×D8—1811no—
202C2×D8—1811no—
203C2×M16—1811no—
204C2×M16C2×D18111yescharacteristic
205C4⋊Q8—1811no—
206#127—1811no—
207#126—3621no—
208#125—1811no—
209#124—3621no—
210#124—1811no—
211#123—3621no—
212C22⋊Q8C2×D18111yescharacteristic
213#121—3621no—
214#121—1811no—
215#121—1811no—
216#121C2×D18111yescharacteristic
217C4×Q8—1811no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—1811no—
221C4×D4—1811no—
222C4×D4—1811no—
223#117—3621no—
224C2×C42—1811no—
225#107—1811no—
226#107C2×D18111yescharacteristic
227#106—1811no—
228#106—1811no—
229C4⋊C8—1811no—
230C4⋊C8—1811no—
231C4⋊C8—1811no—
232C4⋊C8—1811no—
233#103—1811no—
234#103C2×D18111yescharacteristic
235#102—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241#41—7244no—
242C2×Q8—3621no—
243C2×Q8C22×D18111yescharacteristic
244C2×D4—21no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—1811no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—1811no—
256C22×C4—1811no—
257C22×C4C22×D18111yescharacteristic
258SD16—41no—
259SD16—7241no—
260D8—7241no—
261D8—7241no—
262M16—41no—
263M16—7241no—
264C2×C8—1811no—
265C2×C8—1811no—
266C2×C8C22×D18111yescharacteristic
267C2×C8C22×D18111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—1811no—
274C4⋊C4—1811no—
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C42—3621no—
287C42—1811no—
288C42—1811no—
289C42—1811no—
290C42—1811no—
291C23—21no—
292C23—3621no—
293C23—3621no—
294C23D4×D18111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—7242no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—3621no—
302D4—3621no—
303D4—3621no—
304D4—3621no—
305D4—7242no—
306D4—7242no—
307D4—7242no—
308D4—7242no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3622no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—1811no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—7242no—
322C2×C4—7242no—
323C2×C4—7241no—
324C2×C4—7242no—
325C2×C4D4×D18111yescharacteristic
326C2×C4C23×D18111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3621no—
330C8—3621no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3621no—
349C4—3621no—
350C4—3621no—
351C4—1812no—
352C4—7241no—
353C4—7241no—
354C4#1915386111yescharacteristic
355C4#1915386311yescharacteristic
356C2—41no—
357C2—81no—
358C2—14481no—
359C2—14481no—
360C2#2604185611yescharacteristic
361C2AGL(1,ℤ/8)×D18111yescharacteristic
362C2#2604207811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#468×C181C2
socleC22×C181C22×D4
hypercenter#468D181
hypocenterC181#3251
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #26041824C2semidirect
2. #26041815C2semidirect
3. #26041582C2semidirect
4. #26041581C2semidirect
5. #26041562C2semidirect
6. #26041558C2semidirect
7. #26041532C2semidirect
8. #26041530C2semidirect
9. #26041527C2semidirect
10. #26041497C2semidirect
11. #26041496C2semidirect
12. #26041477C2semidirect
13. #26041473C2semidirect
14. #26041302C2semidirect
15. #468×C181C2semidirect
181. C181#3251semidirect
192. #468D181semidirect

Maximal subgroups

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

subgroupindex
#260418242
#260418152
#260415822
#260415812
#260415622
#260415582
#260415322
#260415302
#260415272
#260414972
#260414962
#260414772
#260414732
#260413022
#468×C1812
#3251181