Finite Group Databasebeta

← #37545128

Subgroups — #37545128

Order 23168.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041894C211yesmaximal, characteristic, complemented
2#26041883C211yesmaximal, characteristic, complemented
3#26041587C211yesmaximal, characteristic, complemented
4#26041579C211yesmaximal, characteristic, complemented
5#26041567C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041529C211yesmaximal, characteristic, complemented
8#26041524C211yesmaximal, characteristic, complemented
9#26041512C211yesmaximal, characteristic, complemented
10#26041507C211yesmaximal, characteristic, complemented
11#26041492C211yesmaximal, characteristic, complemented
12#26041492C211yesmaximal, characteristic, complemented
13#26041476C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#459×C181C211yesmaximal, characteristic, complemented
16C2×#15668437C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153809—21no—
22#19153808C2211yescharacteristic
23#19153803C2211yescharacteristic
24#19153802—21no—
25#19153799—21no—
26#19153797—21no—
27#19153797—21no—
28#19153796C2211yescharacteristic
29#19153795—21no—
30#19153788—21no—
31#19153788—21no—
32#19153787C2211yescharacteristic
33#19153787C2211yescharacteristic
34#19153787C2211yescharacteristic
35C4×Dic362C2211yescharacteristic
36D4×Dic181C2211yescharacteristic
37D4×Dic181C2211yescharacteristic
38#19153773C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153737C2211yescharacteristic
51#19153737C2211yescharacteristic
52C2×D8×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54#127×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×C22⋊D181—21no—
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C22×Dic181—21no—
65C22×Dic181—21no—
66C2×C4×D181C2311yescharacteristic
67#15668437—41no—
68#15668437—41no—
69#15668432—41no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C8×D181—41no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181C2311yescharacteristic
95C2×D4×C181—21no—
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C22×C4×C181—21no—
101D8×C181—41no—
102D8×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181C2×D411yescharacteristic
109Dic362—21no—
110Dic362—21no—
111Dic362—81no—
112C22⋊D181—81no—
113C22⋊D181—81no—
114C22⋊D181—81no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—81no—
120C2×Dic181—81no—
121C2×Dic181C2×D411yescharacteristic
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C4×D181—21no—
125C4×D181—21no—
126#13089678—21no—
127#13089678—21no—
128C23×C181—21no—
129C23×C181—21no—
130C23×C181—21no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—81no—
138D4×C181—81no—
139C2×C4×C181—21no—
140C2×C4×C181—81no—
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2411yescharacteristic
144C8×C181—21no—
145C8×C181—21no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181H(5,𝔽2)11yescharacteristic
163C4×C1812−1+411yescharacteristic
164Dic181—21no—
165Dic181—21no—
166Dic181—21no—
167Dic181—41no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171C2×C181—81no—
172C2×C181—81no—
173C2×C181—81no—
174C2×C181#53711yescharacteristic
175C2×C181#57611yescharacteristic
176C2×C181#57711yescharacteristic
177D181—41no—
178C181#325711yescharacteristic, complemented, Sylow
179#3257—1811nomaximal, Sylow
180#542—1811no—
181#540—1811no—
182#479—1811no—
183#478—1811no—
184#476—1811no—
185#474—1811no—
186#469—1811no—
187#468—1811no—
188#466—1811no—
189#465—1811no—
190#463—1811no—
191#463—1811no—
192#460—1811no—
193#459D18111yescharacteristic, complemented
194#424—1811no—
195C2×SD16—1811no—
196C2×SD16—1811no—
197C2×D8C2×D18111yescharacteristic
198C2×D8C2×D18111yescharacteristic
199C2×M16—1811no—
200C22×C8—1811no—
201C4⋊Q8—1811no—
202#127C2×D18111yescharacteristic
203#126—3621no—
204#125—1811no—
205#124—3621no—
206#124—1811no—
207#123—3621no—
208#123—3621no—
209#123—3621no—
210C22⋊Q8—3621no—
211C22⋊Q8—1811no—
212#121—3621no—
213#121—3621no—
214#121—1811no—
215#121—1811no—
216#121—1811no—
217C4×Q8—1811no—
218C4×D4—1811no—
219C4×D4—1811no—
220C4×D4C2×D18111yescharacteristic
221#117—1811no—
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229C4⋊C8C2×D18111yescharacteristic
230#103—1811no—
231#103—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102C2×D18111yescharacteristic
237#102C2×D18111yescharacteristic
238C2×Q8—3621no—
239C2×Q8—1811no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4C22×D18111yescharacteristic
246C2×D4C22×D18111yescharacteristic
247C2×D4C22×D18111yescharacteristic
248C22×C4—21no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4—1811no—
252SD16—7241no—
253SD16—7241no—
254D8—41no—
255D8—41no—
256M16—7241no—
257C2×C8—1811no—
258C2×C8—1811no—
259C2×C8—7241no—
260C2×C8C22×D18111yescharacteristic
261C2×C8C22×D18111yescharacteristic
262C4⋊C4—3621no—
263C4⋊C4—3621no—
264C4⋊C4—3621no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—1811no—
268C4⋊C4—1811no—
269C4⋊C4—1811no—
270C4⋊C4—1811no—
271C4⋊C4—1811no—
272C4⋊C4C22×D18111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4—3621no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—1811no—
283C22⋊C4—1811no—
284C42—3621no—
285C42—1811no—
286C42C22×D18111yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—1811no—
291Q8—3621no—
292Q8—3621no—
293Q8—14481no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—3621no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—14481no—
314C2×C4—14481no—
315C2×C4—1811no—
316C2×C4—1811no—
317C2×C4—1811no—
318C2×C4D4×D18111yescharacteristic
319C2×C4D4×D18111yescharacteristic
320C2×C4C23×D18111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3621no—
324C8—3621no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—3621no—
342C4—3621no—
343C4—3621no—
344C4—7241no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4#1915386111yescharacteristic
349C4#1915386311yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—7241no—
354C2#2604185811yescharacteristic
355C2#2604208011yescharacteristic
356C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#459×C181C2
socleC22×C181C22×D4
hypercenter#459D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26041894C2semidirect
2. #26041883C2semidirect
3. #26041587C2semidirect
4. #26041579C2semidirect
5. #26041567C2semidirect
6. #26041557C2semidirect
7. #26041529C2semidirect
8. #26041524C2semidirect
9. #26041512C2semidirect
10. #26041507C2semidirect
11. #26041492C2semidirect
12. #26041492C2semidirect
13. #26041476C2semidirect
14. #26041304C2semidirect
15. #459×C181C2semidirect
178. C181#3257semidirect
193. #459D181semidirect

Maximal subgroups

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

subgroupindex
#260418942
#260418832
#260415872
#260415792
#260415672
#260415572
#260415292
#260415242
#260415122
#260415072
#260414922
#260414762
#260413042
#459×C1812
#3257181