Finite Group Databasebeta

← #37545130

Subgroups — #37545130

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#26041901C211yesmaximal, characteristic, complemented
2#26041883C211yesmaximal, characteristic, complemented
3#26041586C211yesmaximal, characteristic, complemented
4#26041580C211yesmaximal, characteristic, complemented
5#26041567C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041522C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041505C211yesmaximal, characteristic, complemented
11#26041496C211yesmaximal, characteristic, complemented
12#26041496C211yesmaximal, characteristic, complemented
13#26041471C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#460×C181C211yesmaximal, characteristic, complemented
16C2×#15668434C2211yescharacteristic
17C2×#15668434C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153810—21no—
22#19153808C2211yescharacteristic
23#19153805C2211yescharacteristic
24#19153804—21no—
25#19153801—21no—
26#19153797—21no—
27#19153797—21no—
28#19153794—21no—
29#19153792C2211yescharacteristic
30#19153791C2211yescharacteristic
31#19153788—21no—
32#19153788—21no—
33#19153787C2211yescharacteristic
34#19153787C2211yescharacteristic
35C4×D724C2211yescharacteristic
36D4×Dic181C2211yescharacteristic
37D4×Dic181C2211yescharacteristic
38#19153773C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153737C2211yescharacteristic
51#19153737C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#127×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×D724—21no—
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C22×Dic181—21no—
65C22×Dic181—21no—
66C2×C4×D181—21no—
67C2×C4×D181C2311yescharacteristic
68#15668434—41no—
69#15668434—41no—
70#15668432—41no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C8×D181—41no—
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—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93#15668426D411yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×D4×C181—21no—
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100SD16×C181—41no—
101SD16×C181—41no—
102C2×C8×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C4⋊C4×C181—21no—
105C4⋊C4×C181C2311yescharacteristic
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110Dic362—81no—
111D724—21no—
112D724—21no—
113D724—81no—
114C22⋊D181—81no—
115C22⋊D181—81no—
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—
126C4×D181—81no—
127#13089678—21no—
128#13089678—21no—
129C23×C181—21no—
130C23×C181—21no—
131Q8×C181—21no—
132Q8×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—21no—
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×C181C22×D411yescharacteristic
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181H(5,𝔽2)11yescharacteristic
164C4×C1812−1+411yescharacteristic
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171C2×C181—81no—
172C2×C181—81no—
173C2×C181#53711yescharacteristic
174C2×C181#57611yescharacteristic
175C2×C181#57711yescharacteristic
176D181—41no—
177D181—81no—
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#460D18111yescharacteristic, complemented
193#459—1811no—
194#424—1811no—
195C2×SD16C2×D18111yescharacteristic
196C2×SD16C2×D18111yescharacteristic
197C2×D8—1811no—
198C2×D8—1811no—
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×Q8C2×D18111yescharacteristic
218C4×D4—1811no—
219C4×D4—1811no—
220C4×D4—1811no—
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×Q8C22×D18111yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—1811no—
246C2×D4C22×D18111yescharacteristic
247C2×D4C22×D18111yescharacteristic
248C22×C4—3621no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4—1811no—
252SD16—41no—
253SD16—41no—
254D8—7241no—
255D8—7241no—
256M16—7241no—
257C2×C8—1811no—
258C2×C8—1811no—
259C2×C8—7241no—
260C2×C8C22×D18111yescharacteristic
261C2×C8C22×D18111yescharacteristic
262C4⋊C4—21no—
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—3621no—
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—21no—
285C42—1811no—
286C42C22×D18111yescharacteristic
287C23—21no—
288C23—21no—
289C23—3621no—
290C23—1811no—
291Q8—21no—
292Q8—21no—
293Q8—14481no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—3621no—
301D4—3621no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—3621no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—14481no—
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—3621no—
332C22—3621no—
333C22—3621no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—3621no—
343C4—3621no—
344C4—3621no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4#1915386111yescharacteristic
349C4#1915386311yescharacteristic
350C2—81no—
351C2—81no—
352C2—14481no—
353C2—7241no—
354C2#2604185811yescharacteristic
355C2#2604208311yescharacteristic
356C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#460×C181C2
socleC22×C181C22×D4
hypercenter#460D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #26041901C2semidirect
2. #26041883C2semidirect
3. #26041586C2semidirect
4. #26041580C2semidirect
5. #26041567C2semidirect
6. #26041557C2semidirect
7. #26041531C2semidirect
8. #26041522C2semidirect
9. #26041514C2semidirect
10. #26041505C2semidirect
11. #26041496C2semidirect
12. #26041496C2semidirect
13. #26041471C2semidirect
14. #26041304C2semidirect
15. #460×C181C2semidirect
178. C181#3257semidirect
192. #460D181semidirect

Maximal subgroups

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

subgroupindex
#260419012
#260418832
#260415862
#260415802
#260415672
#260415572
#260415312
#260415222
#260415142
#260415052
#260414962
#260414712
#260413042
#460×C1812
#3257181