Finite Group Databasebeta

← #37546805

Subgroups — #37546805

Order 23168.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042014C211yesmaximal, characteristic, complemented
2#26041669C211yesmaximal, characteristic, complemented
3#26041666C211yesmaximal, characteristic, complemented
4#26041661C211yesmaximal, characteristic, complemented
5#26041501C211yesmaximal, characteristic, complemented
6#26041498C211yesmaximal, characteristic, complemented
7#26041494C211yesmaximal, characteristic, complemented
8#26041491C211yesmaximal, characteristic, complemented
9#26041474C211yesmaximal, characteristic, complemented
10#26041471C211yesmaximal, characteristic, complemented
11#26041410C211yesmaximal, characteristic, complemented
12#26041379C211yesmaximal, characteristic, complemented
13#26041377C211yesmaximal, characteristic, complemented
14C4×#15668434C211yesmaximal, characteristic, complemented
15#559×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24C2×#15668434C2211yescharacteristic
25#19153813C2211yescharacteristic
26#19153805—21no—
27#19153804C2211yescharacteristic
28#19153804C2211yescharacteristic
29#19153801—21no—
30#19153801—21no—
31C4×Dic362C2211yescharacteristic
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34#19153778—21no—
35#19153749C2211yescharacteristic
36C4⋊#13089678C2211yescharacteristic
37C4⋊#13089678C2211yescharacteristic
38C4⋊#13089678C2211yescharacteristic
39#19153740C2211yescharacteristic
40#19153739C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153736C2211yescharacteristic
44#19153736C2211yescharacteristic
45#19153727C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48#127×C181C2211yescharacteristic
49#124×C181—21no—
50#124×C181C2211yescharacteristic
51#124×C181C2211yescharacteristic
52#123×C181—21no—
53#123×C181—21no—
54C4×Q8×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4×D4×C181—21no—
57C4×D4×C181C2211yescharacteristic
58C4×D4×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×D724—21no—
61C2×D724—21no—
62C2×D724C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66#15668439—41no—
67#15668437—22no—
68#15668437—41no—
69#15668436—22no—
70#15668436—41no—
71#15668434—22no—
72#15668434—41no—
73#15668434—41no—
74#15668434—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668426—21no—
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87C4×Dic181—21no—
88C2×Q8×C181D411yescharacteristic
89C2×Q8×C181C2311yescharacteristic
90C2×D4×C181—21no—
91C2×D4×C181—21no—
92C2×D4×C181C2311yescharacteristic
93C2×D4×C181C2311yescharacteristic
94C22×C4×C181—21no—
95C22×C4×C181—21no—
96C4⋊C4×C181—21no—
97C4⋊C4×C181D411yescharacteristic
98C4⋊C4×C181D411yescharacteristic
99C4⋊C4×C181D411yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C22⋊C4×C181—21no—
102C22⋊C4×C181—21no—
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181—21no—
108C42×C181C2311yescharacteristic
109C42×C181C2311yescharacteristic
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—21no—
113Dic362—21no—
114Dic362—21no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—42no—
120D724—81no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C4×D181—81no—
124C4×D181—81no—
125#13089678—21no—
126#13089678—21no—
127#13089678—21no—
128#13089678#4112yes—
129C23×C181—21no—
130C23×C181—21no—
131Q8×C181—21no—
132Q8×C181—21no—
133Q8×C181—41no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—21no—
138D4×C181—42no—
139D4×C181—81no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—81no—
143C2×C4×C181—81no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2411yescharacteristic
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181C22×D411yescharacteristic
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181—21no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181C2×#4111yescharacteristic
173C4×C181H(5,𝔽2)11yescharacteristic
174Dic181—41no—
175Dic181—41no—
176C2×C181—81no—
177C2×C181—81no—
178C2×C181#55011yescharacteristic
179C2×C181#57511yescharacteristic
180C2×C181#57611yescharacteristic
181D181—81no—
182D181—81no—
183C181#340311yescharacteristic, complemented, Sylow
184#3403—1811nomaximal, Sylow
185#559—1811no—
186#559D18111yescharacteristic, complemented
187#496—1811no—
188#496—1811no—
189#495—1811no—
190#464—1811no—
191#464—1811no—
192#463—1811no—
193#463—1811no—
194#459—1811no—
195#459—1811no—
196#446—1811no—
197#440—1811no—
198#440—1811no—
199C4×D8—1811no—
200C2×Q16—1811no—
201C2×SD16—1811no—
202C2×SD16—1811no—
203C2×SD16—1811no—
204C2×SD16—1811no—
205C2×D8—1811no—
206C2×D8—1811no—
207C2×D8—1811no—
208C2×D8—1811no—
209#127—1811no—
210#127C2×D18111yescharacteristic
211#124—21no—
212#124—3621no—
213#124—1811no—
214#124—1811no—
215#124C2×D18111yescharacteristic
216#124C2×D18111yescharacteristic
217#123—21no—
218#123—21no—
219#123—3621no—
220#123—3621no—
221C4×Q8—1811no—
222C4×Q8C2×D18111yescharacteristic
223C4×Q8C2×D18111yescharacteristic
224C4×D4—21no—
225C4×D4—3621no—
226C4×D4—1811no—
227C4×D4—1811no—
228C4×D4C2×D18111yescharacteristic
229C4×D4C2×D18111yescharacteristic
230#107—1811no—
231C4⋊C8—1811no—
232C4⋊C8—1811no—
233C4⋊C8—1811no—
234#103—1811no—
235#103—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#97—1811no—
241#97—1811no—
242C4×C8—1811no—
243C2×Q8—1811no—
244C2×Q8C22⋊D18111yescharacteristic
245C2×Q8C22×D18111yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4—1811no—
252C2×D4C22×D18111yescharacteristic
253C2×D4C22×D18111yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—3621no—
257C22×C4—3621no—
258Q16—7241no—
259SD16—3622no—
260SD16—3622no—
261SD16—7241no—
262SD16—7241no—
263D8—3622no—
264D8—7241no—
265D8—7241no—
266D8—7241no—
267C2×C8—1811no—
268C2×C8—1811no—
269C2×C8—1811no—
270C2×C8—1811no—
271C4⋊C4—21no—
272C4⋊C4—3621no—
273C4⋊C4—1811no—
274C4⋊C4C22⋊D18111yescharacteristic
275C4⋊C4C22⋊D18111yescharacteristic
276C4⋊C4C22⋊D18111yescharacteristic
277C4⋊C4C22×D18111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C42—21no—
291C42—3621no—
292C42C22×D18111yescharacteristic
293C42C22×D18111yescharacteristic
294C42C22×D18111yescharacteristic
295C23—21no—
296C23—21no—
297C23—3621no—
298C23—3621no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—3621no—
303Q8—3621no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3621no—
311D4—3621no—
312D4—3621no—
313D4—3621no—
314D4—14481no—
315D4—7242no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—14481no—
323C2×C4—14481no—
324C2×C4C2×C22⋊D18111yescharacteristic
325C2×C4C2×C22⋊D18111yescharacteristic
326C2×C4C2×C22⋊D18111yescharacteristic
327C2×C4C2×C22⋊D18111yescharacteristic
328C2×C4C2×C22⋊D18111yescharacteristic
329C2×C4C2×C22⋊D18111yescharacteristic
330C2×C4C23×D18111yescharacteristic
331C8—3621no—
332C8—3621no—
333C8—3621no—
334C8—1812no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—7241no—
342C22—7241no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C22×C22⋊D18111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—7241no—
357C4—7241no—
358C4#41×D18111yescharacteristic
359C4#1915386211yescharacteristic
360C2—81no—
361C2—81no—
362C2—14481no—
363C2—14481no—
364C2#2604194811yescharacteristic
365C2#2604207711yescharacteristic
366C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#559×C181C2
socleC22×C181C22×D4
hypercenter#559D181
hypocenterC181#3403
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #26042014C2semidirect
2. #26041669C2semidirect
3. #26041666C2semidirect
4. #26041661C2semidirect
5. #26041501C2semidirect
6. #26041498C2semidirect
7. #26041494C2semidirect
8. #26041491C2semidirect
9. #26041474C2semidirect
10. #26041471C2semidirect
11. #26041410C2semidirect
12. #26041379C2semidirect
13. #26041377C2semidirect
14. C4×#15668434C2semidirect
15. #559×C181C2semidirect
183. C181#3403semidirect
186. #559D181semidirect

Maximal subgroups

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

subgroupindex
#260420142
#260416692
#260416662
#260416612
#260415012
#260414982
#260414942
#260414912
#260414742
#260414712
#260414102
#260413792
#260413772
C4×#156684342
#559×C1812
#3403181