Finite Group Databasebeta

← #37543920

Subgroups — #37543920

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041884C211yesmaximal, characteristic, complemented
2#26041597C211yesmaximal, characteristic, complemented
3#26041592C211yesmaximal, characteristic, complemented
4#26041586C211yesmaximal, characteristic, complemented
5#26041579C211yesmaximal, characteristic, complemented
6#26041479C211yesmaximal, characteristic, complemented
7#26041474C211yesmaximal, characteristic, complemented
8#26041424C211yesmaximal, characteristic, complemented
9#26041424C211yesmaximal, characteristic, complemented
10#26041389C211yesmaximal, characteristic, complemented
11#26041377C211yesmaximal, characteristic, complemented
12C4×#15668436C211yesmaximal, characteristic, complemented
13C4×#15668434C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#520×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153813C2211yescharacteristic
21#19153808C2211yescharacteristic
22#19153801—21no—
23#19153801—21no—
24#19153790C2211yescharacteristic
25#19153790C2211yescharacteristic
26#19153789—21no—
27#19153789—21no—
28C4×D724C2211yescharacteristic
29C4×D724C2211yescharacteristic
30#19153749C2211yescharacteristic
31#19153749C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153737C2211yescharacteristic
39#19153737C2211yescharacteristic
40#19153736C2211yescharacteristic
41#19153736C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48C2×#41×C181C2211yescharacteristic
49C4×Q8×C181C2211yescharacteristic
50C4×Q8×C181C2211yescharacteristic
51C4×D4×C181—21no—
52C4×D4×C181—21no—
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#117×C181—21no—
56#117×C181C2211yescharacteristic
57C2×C4⋊C4×C181—21no—
58C2×C4⋊C4×C181C2211yescharacteristic
59C2×D724—21no—
60C2×D724—21no—
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67#15668436—22no—
68#15668436—22no—
69#15668434—22no—
70#15668434—22no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668426—21no—
80#15668426—21no—
81#15668426—21no—
82#15668426—21no—
83#41×C181—22no—
84#41×C181—22no—
85C2×Q8×C181C2311yescharacteristic
86C2×D4×C181—21no—
87C2×D4×C181C2311yescharacteristic
88C22×C4×C181—21no—
89C22×C4×C181—21no—
90C22×C4×C181—21no—
91C22×C4×C181—21no—
92C22×C4×C181C2311yescharacteristic
93C4⋊C4×C181—21no—
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×C181D411yescharacteristic
103C22⋊C4×C181D411yescharacteristic
104C42×C181—21no—
105C42×C181—21no—
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110D724—21no—
111D724—21no—
112D724—21no—
113D724—21no—
114D724—81no—
115D724—81no—
116C22⋊D181—81no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C4×D181—81no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124#13089678—21no—
125#13089678—21no—
126C23×C181—21no—
127C23×C181C2×D411yescharacteristic
128Q8×C181—21no—
129Q8×C181#4112yes—
130D4×C181—24no—
131D4×C181—21no—
132D4×C181#4112yes—
133C2×C4×C181—24no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—81no—
140C2×C4×C181—81no—
141C2×C4×C181—81no—
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2411yescharacteristic
148C22×C181—21no—
149C22×C181—22no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181C22×D411yescharacteristic
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C4×C181—21no—
162C4×C181—22no—
163C4×C181—21no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181C2×#4111yescharacteristic
170C4×C181C2×#4111yescharacteristic
171Dic181—41no—
172Dic181—41no—
173C2×C181—41no—
174C2×C181—42no—
175C2×C181#52511yescharacteristic
176C2×C181#57611yescharacteristic
177C2×C181#57711yescharacteristic
178D181—81no—
179D181—81no—
180C181#311911yescharacteristic, complemented, Sylow
181#3119—1811nomaximal, Sylow
182#540—1811no—
183#520D18111yescharacteristic, complemented
184#481—1811no—
185#480—1811no—
186#479—1811no—
187#478—1811no—
188#460—1811no—
189#459—1811no—
190#449—1811no—
191#449—1811no—
192#442—1811no—
193#440—1811no—
194C4×SD16—1811no—
195C4×D8—1811no—
196#433—1811no—
197C2×#41C2×D18111yescharacteristic
198C2×SD16—1811no—
199C2×SD16—1811no—
200C2×D8—1811no—
201C2×D8—1811no—
202#127—1811no—
203#125—1811no—
204#123—3621no—
205#123—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121—1811no—
210C4×Q8C2×D18111yescharacteristic
211C4×Q8C2×D18111yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4C2×D18111yescharacteristic
217C4×D4C2×D18111yescharacteristic
218#117—21no—
219#117C2×D18111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D18111yescharacteristic
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228#103—1811no—
229#103—1811no—
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236C22⋊C8—1811no—
237C22⋊C8—1811no—
238#97—1811no—
239C4×C8—1811no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D18111yescharacteristic
243C2×D4—21no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4—1811no—
250C2×D4C22×D18111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4C22×D18111yescharacteristic
258SD16—3622no—
259SD16—3622no—
260D8—3622no—
261D8—3622no—
262C2×C8—1811no—
263C2×C8—1811no—
264C2×C8—1811no—
265C2×C8—1811no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4C22⋊D18111yescharacteristic
274C4⋊C4C22⋊D18111yescharacteristic
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4C22⋊D18111yescharacteristic
284C22⋊C4C22⋊D18111yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D18111yescharacteristic
288C42C22×D18111yescharacteristic
289C23—21no—
290C23—3621no—
291C23—3621no—
292C23C2×C22⋊D18111yescharacteristic
293Q8—21no—
294Q8#1566844912yes—
295D4—24no—
296D4—21no—
297D4—3621no—
298D4—3621no—
299D4—3621no—
300D4—3621no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305D4#1566844912yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4C2×C22⋊D18111yescharacteristic
320C2×C4C2×C22⋊D18111yescharacteristic
321C2×C4C2×C22⋊D18111yescharacteristic
322C2×C4C2×C22⋊D18111yescharacteristic
323C2×C4C2×C22⋊D18111yescharacteristic
324C2×C4C23×D18111yescharacteristic
325C8—3621no—
326C8—3621no—
327C8—3621no—
328C8—3621no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—7241no—
336C22—7241no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22C22×C22⋊D18111yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—7241no—
351C4—7241no—
352C4C2×#1566844911yescharacteristic
353C4C2×#1566844911yescharacteristic
354C2—41no—
355C2—42no—
356C2—14481no—
357C2—14481no—
358C2#2604179011yescharacteristic
359C2#2604208211yescharacteristic
360C2#2604208711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#520×C181C2
socleC22×C181C22×D4
hypercenter#520D181
hypocenterC181#3119
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #26041884C2semidirect
2. #26041597C2semidirect
3. #26041592C2semidirect
4. #26041586C2semidirect
5. #26041579C2semidirect
6. #26041479C2semidirect
7. #26041474C2semidirect
8. #26041424C2semidirect
9. #26041424C2semidirect
10. #26041389C2semidirect
11. #26041377C2semidirect
12. C4×#15668436C2semidirect
13. C4×#15668434C2semidirect
14. #26041340C2semidirect
15. #520×C181C2semidirect
180. C181#3119semidirect
183. #520D181semidirect

Maximal subgroups

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

subgroupindex
#260418842
#260415972
#260415922
#260415862
#260415792
#260414792
#260414742
#260414242
#260413892
#260413772
C4×#156684362
C4×#156684342
#260413402
#520×C1812
#3119181