Finite Group Databasebeta

← #37545126

Subgroups — #37545126

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#26041900C211yesmaximal, characteristic, complemented
2#26041583C211yesmaximal, characteristic, complemented
3#26041576C211yesmaximal, characteristic, complemented
4#26041569C211yesmaximal, characteristic, complemented
5#26041559C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041523C211yesmaximal, characteristic, complemented
8#26041513C211yesmaximal, characteristic, complemented
9#26041506C211yesmaximal, characteristic, complemented
10#26041494C211yesmaximal, characteristic, complemented
11#26041494C211yesmaximal, characteristic, complemented
12#26041476C211yesmaximal, characteristic, complemented
13#26041471C211yesmaximal, characteristic, complemented
14#26041306C211yesmaximal, characteristic, complemented
15#540×C181C211yesmaximal, characteristic, complemented
16C2×#15668437C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668433C2211yescharacteristic
21C22×#13089678C2211yescharacteristic
22#19153816C2211yescharacteristic
23#19153811—21no—
24#19153804C2211yescharacteristic
25#19153802—21no—
26#19153798—21no—
27#19153795C2211yescharacteristic
28#19153794—21no—
29#19153790C2211yescharacteristic
30C4×Dic362C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153749C2211yescharacteristic
33#19153749C2211yescharacteristic
34#19153747C2211yescharacteristic
35#19153747C2211yescharacteristic
36C4⋊#13089678C2211yescharacteristic
37C4⋊#13089678C2211yescharacteristic
38C4⋊#13089678C2211yescharacteristic
39C4⋊#13089678C2211yescharacteristic
40#19153739C2211yescharacteristic
41#19153739C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44#19153737C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#127×C181C2211yescharacteristic
49#125×C181C2211yescharacteristic
50#123×C181—21no—
51#123×C181—21no—
52#121×C181—21no—
53#121×C181—21no—
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56C4×D4×C181C2211yescharacteristic
57C4×D4×C181C2211yescharacteristic
58#117×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C4×D181—21no—
64#15668437—41no—
65#15668437—41no—
66#15668434—41no—
67#15668434—41no—
68#15668433—41no—
69C2×#13089678—41no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C4⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79C22⋊Dic181—21no—
80#15668426—21no—
81#15668426—21no—
82#15668426—21no—
83#15668426—21no—
84C4×Dic181—21no—
85C2×D4×C181—21no—
86C2×D4×C181—21no—
87C2×D4×C181—21no—
88C2×D4×C181—21no—
89C2×D4×C181C2311yescharacteristic
90C2×D4×C181C2311yescharacteristic
91C22×C4×C181—21no—
92C22×C4×C181—21no—
93C22×C4×C181C2311yescharacteristic
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181D411yescharacteristic
97C4⋊C4×C181D411yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C22⋊C4×C181—21no—
103C22⋊C4×C181—21no—
104C22⋊C4×C181D411yescharacteristic
105C22⋊C4×C181D411yescharacteristic
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109Dic362—21no—
110Dic362—21no—
111Dic362—81no—
112D724—21no—
113D724—21no—
114C22⋊D181—81no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C4×D181—81no—
119#13089678—21no—
120#13089678—21no—
121#13089678—21no—
122#13089678—21no—
123C23×C181—21no—
124C23×C181—21no—
125C23×C181C2×D411yescharacteristic
126D4×C181—21no—
127D4×C181—21no—
128D4×C181—21no—
129D4×C181—21no—
130D4×C181—81no—
131D4×C181—81no—
132D4×C181—81no—
133D4×C181—81no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—81no—
139C2×C4×C181—81no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C22×C181—21no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—21no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181H(5,𝔽2)11yescharacteristic
167C4×C1812−1+411yescharacteristic
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171C2×C181—41no—
172C2×C181—81no—
173C2×C181—81no—
174C2×C181#53711yescharacteristic
175C2×C181#57611yescharacteristic
176C2×C181#57711yescharacteristic
177D181—81no—
178C181#325711yescharacteristic, complemented, Sylow
179#3257—1811nomaximal, Sylow
180#542—1811no—
181#540D18111yescharacteristic, complemented
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#459—1811no—
194#424—1811no—
195C2×SD16—1811no—
196C2×SD16—1811no—
197C2×D8—1811no—
198C2×D8—1811no—
199C2×M16—1811no—
200C22×C8—1811no—
201C4⋊Q8—1811no—
202#127C2×D18111yescharacteristic
203#126—3621no—
204#125C2×D18111yescharacteristic
205#124—3621no—
206#124—1811no—
207#123—21no—
208#123—21no—
209#123—3621no—
210C22⋊Q8—3621no—
211C22⋊Q8—1811no—
212#121—21no—
213#121—21no—
214#121—1811no—
215#121C2×D18111yescharacteristic
216#121C2×D18111yescharacteristic
217C4×Q8—1811no—
218C4×D4—1811no—
219C4×D4C2×D18111yescharacteristic
220C4×D4C2×D18111yescharacteristic
221#117C2×D18111yescharacteristic
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229C4⋊C8—1811no—
230#103—1811no—
231#103—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102—1811no—
238C2×Q8—3621no—
239C2×Q8—1811no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—3621no—
245C2×D4—1811no—
246C2×D4C22×D18111yescharacteristic
247C2×D4C22×D18111yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3621no—
251C22×C4C22×D18111yescharacteristic
252SD16—7241no—
253SD16—7241no—
254D8—7241no—
255D8—7241no—
256M16—7241no—
257C2×C8—1811no—
258C2×C8—1811no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3621no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—1811no—
268C4⋊C4—1811no—
269C4⋊C4C22⋊D18111yescharacteristic
270C4⋊C4C22⋊D18111yescharacteristic
271C4⋊C4C22×D18111yescharacteristic
272C4⋊C4C22×D18111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4C22⋊D18111yescharacteristic
283C22⋊C4C22⋊D18111yescharacteristic
284C42—3621no—
285C42C22×D18111yescharacteristic
286C42C22×D18111yescharacteristic
287C23—21no—
288C23—21no—
289C23—3621no—
290C23C2×C22⋊D18111yescharacteristic
291Q8—3621no—
292Q8—3621no—
293Q8—14481no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—3621no—
303D4—3621no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—14481no—
315C2×C4C2×C22⋊D18111yescharacteristic
316C2×C4C2×C22⋊D18111yescharacteristic
317C2×C4C2×C22⋊D18111yescharacteristic
318C2×C4C2×C22⋊D18111yescharacteristic
319C2×C4C2×C22⋊D18111yescharacteristic
320C2×C4C23×D18111yescharacteristic
321C8—3621no—
322C8—3621no—
323C8—3621no—
324C8—3621no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22C22×C22⋊D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4#1915386211yescharacteristic
349C4#1915386311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—14481no—
354C2#2604185711yescharacteristic
355C2#2604208211yescharacteristic
356C2#2604209011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#540×C181C2
socleC22×C181C22×D4
hypercenter#540D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #26041900C2semidirect
2. #26041583C2semidirect
3. #26041576C2semidirect
4. #26041569C2semidirect
5. #26041559C2semidirect
6. #26041530C2semidirect
7. #26041523C2semidirect
8. #26041513C2semidirect
9. #26041506C2semidirect
10. #26041494C2semidirect
11. #26041494C2semidirect
12. #26041476C2semidirect
13. #26041471C2semidirect
14. #26041306C2semidirect
15. #540×C181C2semidirect
178. C181#3257semidirect
181. #540D181semidirect

Maximal subgroups

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

subgroupindex
#260419002
#260415832
#260415762
#260415692
#260415592
#260415302
#260415232
#260415132
#260415062
#260414942
#260414762
#260414712
#260413062
#540×C1812
#3257181