Finite Group Databasebeta

← #37545139

Subgroups — #37545139

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#26041903C211yesmaximal, characteristic, complemented
2#26041880C211yesmaximal, characteristic, complemented
3#26041585C211yesmaximal, characteristic, complemented
4#26041582C211yesmaximal, characteristic, complemented
5#26041566C211yesmaximal, characteristic, complemented
6#26041531C211yesmaximal, characteristic, complemented
7#26041526C211yesmaximal, characteristic, complemented
8#26041516C211yesmaximal, characteristic, complemented
9#26041507C211yesmaximal, characteristic, complemented
10#26041495C211yesmaximal, characteristic, complemented
11#26041494C211yesmaximal, characteristic, complemented
12#26041478C211yesmaximal, characteristic, complemented
13#26041473C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#474×C181C211yesmaximal, characteristic, complemented
16C2×#15668438C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153812C2211yescharacteristic
23#19153811—21no—
24#19153807C2211yescharacteristic
25#19153805—21no—
26#19153804C2211yescharacteristic
27#19153801—21no—
28#19153799—21no—
29#19153798—21no—
30#19153796C2211yescharacteristic
31#19153792—21no—
32#19153791C2211yescharacteristic
33#19153791C2211yescharacteristic
34#19153790—21no—
35#19153789—21no—
36#19153787C2211yescharacteristic
37#19153781C2211yescharacteristic
38C4×D724C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153773C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153736C2211yescharacteristic
51#19153736C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×D724—21no—
61C2×D724—21no—
62C2×D724C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181C2311yescharacteristic
70#15668438—41no—
71#15668437—41no—
72D1448—41no—
73#15668434—41no—
74#15668432—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—41no—
78C4⋊Dic181—21no—
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181—21no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181C2×D411yescharacteristic
111Dic362—21no—
112Dic362—21no—
113D724—21no—
114D724—21no—
115D724—21no—
116D724—21no—
117D724—81no—
118D724—81no—
119C22⋊D181—81no—
120C22⋊D181—81no—
121C22⋊D181—81no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C4×D181—21no—
128C4×D181—21no—
129C4×D181—81no—
130C4×D181—81no—
131#13089678—21no—
132#13089678—21no—
133C23×C181—21no—
134Q8×C181—81no—
135D4×C181—21no—
136D4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
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×C181C22×D411yescharacteristic
150C2×D181—21no—
151C2×D181—21no—
152C2×D181—21no—
153C2×D181—41no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181H(5,𝔽2)11yescharacteristic
165C4×C1812−1+411yescharacteristic
166Dic181—21no—
167Dic181—21no—
168Dic181—21no—
169Dic181—41no—
170Dic181—41no—
171C2×C181—81no—
172C2×C181#53711yescharacteristic
173C2×C181#57611yescharacteristic
174C2×C181#57711yescharacteristic
175D181—41no—
176D181—81no—
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#474D18111yescharacteristic, complemented
186#469—1811no—
187#468—1811no—
188#466—1811no—
189#465—1811no—
190#463—1811no—
191#463—1811no—
192#460—1811no—
193#459—1811no—
194#424—1811no—
195C2×SD16—1811no—
196C2×SD16—1811no—
197C2×D8—1811no—
198C2×D8—1811no—
199C2×M16—1811no—
200C22×C8—1811no—
201C4⋊Q8C2×D18111yescharacteristic
202#127—1811no—
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#107C2×D18111yescharacteristic
223#107C2×D18111yescharacteristic
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—21no—
239C2×Q8—1811no—
240C2×D4—3621no—
241C2×D4—3621no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—1811no—
246C2×D4—1811no—
247C2×D4C22×D18111yescharacteristic
248C22×C4—21no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4—1811no—
252SD16—7241no—
253SD16—7241no—
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⋊C4C22×D18111yescharacteristic
271C4⋊C4C22×D18111yescharacteristic
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—3621no—
289C23—3621no—
290C23—1811no—
291Q8—81no—
292Q8—3621no—
293Q8—3621no—
294D4—21no—
295D4—21no—
296D4—3621no—
297D4—3621no—
298D4—3621no—
299D4—3621no—
300D4—14481no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
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—3621no—
329C22—3621no—
330C22—3621no—
331C22—7241no—
332C22—7241no—
333C22—7241no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3621no—
344C4—3621no—
345C4—3621no—
346C4—7241no—
347C4—7241no—
348C4#1915386211yescharacteristic
349C4#1915386411yescharacteristic
350C2—81no—
351C2—14481no—
352C2—14481no—
353C2—7241no—
354C2#2604185911yescharacteristic
355C2#2604208011yescharacteristic
356C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#474×C181C2
socleC22×C181C22×D4
hypercenter#474D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #26041903C2semidirect
2. #26041880C2semidirect
3. #26041585C2semidirect
4. #26041582C2semidirect
5. #26041566C2semidirect
6. #26041531C2semidirect
7. #26041526C2semidirect
8. #26041516C2semidirect
9. #26041507C2semidirect
10. #26041495C2semidirect
11. #26041494C2semidirect
12. #26041478C2semidirect
13. #26041473C2semidirect
14. #26041304C2semidirect
15. #474×C181C2semidirect
178. C181#3257semidirect
185. #474D181semidirect

Maximal subgroups

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

subgroupindex
#260419032
#260418802
#260415852
#260415822
#260415662
#260415312
#260415262
#260415162
#260415072
#260414952
#260414942
#260414782
#260414732
#260413042
#474×C1812
#3257181