Finite Group Databasebeta

← #37545135

Subgroups — #37545135

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#26041902C211yesmaximal, characteristic, complemented
2#26041882C211yesmaximal, characteristic, complemented
3#26041588C211yesmaximal, characteristic, complemented
4#26041578C211yesmaximal, characteristic, complemented
5#26041568C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041530C211yesmaximal, characteristic, complemented
8#26041527C211yesmaximal, characteristic, complemented
9#26041515C211yesmaximal, characteristic, complemented
10#26041497C211yesmaximal, characteristic, complemented
11#26041496C211yesmaximal, characteristic, complemented
12#26041477C211yesmaximal, characteristic, complemented
13#26041473C211yesmaximal, characteristic, complemented
14#26041305C211yesmaximal, characteristic, complemented
15#465×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×D1448C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668433C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153812C2211yescharacteristic
22#19153811—21no—
23#19153807C2211yescharacteristic
24#19153805C2211yescharacteristic
25#19153802—21no—
26#19153800—21no—
27#19153798—21no—
28#19153798—21no—
29#19153796—21no—
30#19153790C2211yescharacteristic
31#19153790C2211yescharacteristic
32#19153788—21no—
33#19153787—21no—
34Q8×Dic181C2211yescharacteristic
35D4×Dic181C2211yescharacteristic
36#19153778C2211yescharacteristic
37#19153778C2211yescharacteristic
38#19153775C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
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
53C22×C8×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×D724C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C22×Dic181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69#15668436—41no—
70D1448—41no—
71#15668434—41no—
72#15668433—41no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181D411yescharacteristic
78C4⋊Dic181D411yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181D411yescharacteristic
85C22⋊Dic181D411yescharacteristic
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181C2311yescharacteristic
99SD16×C181—41no—
100C2×C8×C181—41no—
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181—21no—
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22×D181—21no—
109C22×D181—21no—
110Dic362—81no—
111D724—21no—
112D724—21no—
113D724—21no—
114D724—21no—
115C22⋊D181—81no—
116C22⋊D181—81no—
117C22⋊D181—81no—
118C22⋊D181—81no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—81no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—81no—
127C4×D181—81no—
128#13089678—21no—
129#13089678—21no—
130C23×C181—21no—
131C23×C181C2×D411yescharacteristic
132Q8×C181—21no—
133Q8×C181—21no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—81no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2411yescharacteristic
144C8×C181—21no—
145C8×C181—21no—
146C22×C181—21no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181C22×D411yescharacteristic
153C2×D181—41no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181H(5,𝔽2)11yescharacteristic
164C4×C1812−1+411yescharacteristic
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—21no—
169Dic181—41no—
170Dic181—41no—
171C2×C181—41no—
172C2×C181—81no—
173C2×C181#53711yescharacteristic
174C2×C181#57611yescharacteristic
175C2×C181#57711yescharacteristic
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#474—1811no—
186#469—1811no—
187#468—1811no—
188#466—1811no—
189#465D18111yescharacteristic, complemented
190#463—1811no—
191#463—1811no—
192#460—1811no—
193#459—1811no—
194#424—1811no—
195C2×SD16—1811no—
196C2×SD16C2×D18111yescharacteristic
197C2×D8—1811no—
198C2×D8—1811no—
199C2×M16—1811no—
200C22×C8C2×D18111yescharacteristic
201C4⋊Q8—1811no—
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⋊Q8C2×D18111yescharacteristic
212#121—3621no—
213#121—3621no—
214#121—1811no—
215#121—1811no—
216#121C2×D18111yescharacteristic
217C4×Q8—1811no—
218C4×D4—1811no—
219C4×D4—1811no—
220C4×D4—1811no—
221#117—1811no—
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106C2×D18111yescharacteristic
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229C4⋊C8—1811no—
230#103—1811no—
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102C2×D18111yescharacteristic
238C2×Q8—3621no—
239C2×Q8C22×D18111yescharacteristic
240C2×D4—21no—
241C2×D4—3621no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—1811no—
246C2×D4—1811no—
247C2×D4C22×D18111yescharacteristic
248C22×C4—3621no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4C22×D18111yescharacteristic
252SD16—41no—
253SD16—7241no—
254D8—7241no—
255D8—7241no—
256M16—7241no—
257C2×C8—41no—
258C2×C8—1811no—
259C2×C8—1811no—
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⋊C4C22×D18111yescharacteristic
272C4⋊C4C22×D18111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
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—
286C42—1811no—
287C23—21no—
288C23—3621no—
289C23—3621no—
290C23D4×D18111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—14481no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—3621no—
298D4—3621no—
299D4—3621no—
300D4—3621no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
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×C4—1811no—
319C2×C4D4×D18111yescharacteristic
320C2×C4C23×D18111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3621no—
324C8—3621no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—7241no—
332C22—7241no—
333C22—7241no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3621no—
343C4—3621no—
344C4—3621no—
345C4—3621no—
346C4—7241no—
347C4—7241no—
348C4#1915386111yescharacteristic
349C4#1915386311yescharacteristic
350C2—41no—
351C2—81no—
352C2—14481no—
353C2—14481no—
354C2#2604185611yescharacteristic
355C2#2604208111yescharacteristic
356C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#465×C181C2
socleC22×C181C22×D4
hypercenter#465D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #26041902C2semidirect
2. #26041882C2semidirect
3. #26041588C2semidirect
4. #26041578C2semidirect
5. #26041568C2semidirect
6. #26041557C2semidirect
7. #26041530C2semidirect
8. #26041527C2semidirect
9. #26041515C2semidirect
10. #26041497C2semidirect
11. #26041496C2semidirect
12. #26041477C2semidirect
13. #26041473C2semidirect
14. #26041305C2semidirect
15. #465×C181C2semidirect
178. C181#3257semidirect
189. #465D181semidirect

Maximal subgroups

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

subgroupindex
#260419022
#260418822
#260415882
#260415782
#260415682
#260415572
#260415302
#260415272
#260415152
#260414972
#260414962
#260414772
#260414732
#260413052
#465×C1812
#3257181