Finite Group Databasebeta

← #37545727

Subgroups — #37545727

Order 23168.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041975C211yesmaximal, characteristic, complemented
2#26041643C211yesmaximal, characteristic, complemented
3#26041600C211yesmaximal, characteristic, complemented
4#26041590C211yesmaximal, characteristic, complemented
5#26041586C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041513C211yesmaximal, characteristic, complemented
8#26041471C211yesmaximal, characteristic, complemented
9#26041424C211yesmaximal, characteristic, complemented
10#26041424C211yesmaximal, characteristic, complemented
11#26041377C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041280C211yesmaximal, characteristic, complemented
14#26041275C211yesmaximal, characteristic, complemented
15#550×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668434C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668433C2211yescharacteristic
20C22×#13089678C2211yescharacteristic
21#19153811—21no—
22#19153808C2211yescharacteristic
23#19153798—21no—
24#19153790C2211yescharacteristic
25#19153790C2211yescharacteristic
26#19153788—21no—
27C4×D724C2211yescharacteristic
28#19153776—21no—
29#19153775C2211yescharacteristic
30C2×C4⋊Dic181C2211yescharacteristic
31#19153749C2211yescharacteristic
32#19153749C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35#19153740C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153737C2211yescharacteristic
39#19153737C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44#19153736C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic
47#19153727C2211yescharacteristic
48C2×#41×C181C2211yescharacteristic
49C2×#41×C181C2211yescharacteristic
50#127×C181—21no—
51#127×C181C2211yescharacteristic
52#121×C181—21no—
53#121×C181—21no—
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56C4×Q8×C181C2211yescharacteristic
57C4×D4×C181—21no—
58C4×D4×C181C2211yescharacteristic
59C2×D724C2311yescharacteristic
60C2×C22⋊D181—21no—
61C2×C22⋊D181—21no—
62C22×Dic181—21no—
63C2×C4×D181—21no—
64#15668436—22no—
65#15668434—41no—
66#15668434—41no—
67#15668433—41no—
68C2×#13089678—41no—
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79C22⋊Dic181—21no—
80#15668426—21no—
81#15668426—21no—
82#15668426—21no—
83C4×Dic181—21no—
84#41×C181—22no—
85#41×C181—22no—
86#41×C181—41no—
87#41×C181—41no—
88C2×Q8×C181C2311yescharacteristic
89C2×D4×C181—21no—
90C2×D4×C181—21no—
91C2×D4×C181—21no—
92C2×D4×C181—21no—
93C2×D4×C181—21no—
94C2×D4×C181—21no—
95C2×D4×C181D411yescharacteristic
96C2×D4×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C22×C4×C181—21no—
100C22×C4×C181C2311yescharacteristic
101C22×C4×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181D411yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C22⋊C4×C181D411yescharacteristic
108C22⋊C4×C181D411yescharacteristic
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112D724—21no—
113D724—21no—
114C22⋊D181—42no—
115C22⋊D181—81no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—81no—
120C4×D181—81no—
121#13089678—21no—
122#13089678—21no—
123#13089678—21no—
124#13089678—21no—
125C23×C181—21no—
126C23×C181—21no—
127C23×C181C2×D411yescharacteristic
128C23×C181C2×D411yescharacteristic
129Q8×C181—21no—
130Q8×C181#4112yes—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134D4×C181—21no—
135D4×C181—41no—
136D4×C181—42no—
137D4×C181—42no—
138D4×C181—42no—
139D4×C181—81no—
140D4×C181—81no—
141D4×C181—81no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—42no—
149C2×C4×C181—42no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181C22×D411yescharacteristic
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—21no—
173C4×C181—22no—
174C4×C181—21no—
175C4×C181—21no—
176C4×C181—41no—
177C4×C181C2×#4111yescharacteristic
178C4×C181H(5,𝔽2)11yescharacteristic
179Dic181—41no—
180Dic181—41no—
181Dic181—41no—
182C2×C181—41no—
183C2×C181—41no—
184C2×C181—81no—
185C2×C181—81no—
186C2×C181#54611yescharacteristic
187C2×C181#57511yescharacteristic
188C2×C181#57611yescharacteristic
189D181—81no—
190C181#330911yescharacteristic, complemented, Sylow
191#3309—1811nomaximal, Sylow
192#553—1811no—
193#550D18111yescharacteristic, complemented
194#490—1811no—
195#482—1811no—
196#480—1811no—
197#479—1811no—
198#469—1811no—
199#466—1811no—
200#459—1811no—
201#449—1811no—
202#449—1811no—
203#440—1811no—
204#435—1811no—
205#417—1811no—
206#416—1811no—
207C2×#41C2×D18111yescharacteristic
208C2×#41C2×D18111yescharacteristic
209C2×SD16—1811no—
210C2×D8—1811no—
211C2×D8—1811no—
212C2×M16—1811no—
213C22×C8—1811no—
214#127—21no—
215#127C2×D18111yescharacteristic
216#126—3621no—
217#125—1811no—
218#123—3621no—
219#121—21no—
220#121—21no—
221#121—3621no—
222#121—1811no—
223#121—1811no—
224#121C2×D18111yescharacteristic
225#121C2×D18111yescharacteristic
226C4×Q8C2×D18111yescharacteristic
227C4×D4—21no—
228C4×D4—3621no—
229C4×D4—1811no—
230C4×D4C2×D18111yescharacteristic
231#117—1811no—
232C2×C4⋊C4—1811no—
233#107—1811no—
234#107—1811no—
235#106—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103—1811no—
239#103—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247C22⋊C8—1811no—
248C22⋊C8—1811no—
249#97—1811no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D18111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—1811no—
264C2×D4C22⋊D18111yescharacteristic
265C2×D4C22×D18111yescharacteristic
266C2×D4C22×D18111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4C22×D18111yescharacteristic
272C22×C4C22×D18111yescharacteristic
273SD16—3622no—
274D8—7241no—
275D8—7241no—
276M16—7241no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8—1811no—
280C2×C8—1811no—
281C2×C8—7241no—
282C4⋊C4—21no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—1811no—
287C4⋊C4—1811no—
288C4⋊C4—1811no—
289C4⋊C4C22⋊D18111yescharacteristic
290C4⋊C4C22×D18111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4C22⋊D18111yescharacteristic
298C22⋊C4C22⋊D18111yescharacteristic
299C42—21no—
300C42—3621no—
301C42C22×D18111yescharacteristic
302C23—21no—
303C23—21no—
304C23—3621no—
305C23C2×C22⋊D18111yescharacteristic
306C23C2×C22⋊D18111yescharacteristic
307Q8—21no—
308Q8#1566844812yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—3621no—
321D4—3621no—
322D4—14481no—
323D4—7242no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4C2×C22⋊D18111yescharacteristic
338C2×C4C2×C22⋊D18111yescharacteristic
339C2×C4C2×C22⋊D18111yescharacteristic
340C2×C4C2×C22⋊D18111yescharacteristic
341C2×C4C23×D18111yescharacteristic
342C8—3621no—
343C8—3621no—
344C8—3621no—
345C8—3621no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C22×C22⋊D18111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—7241no—
369C4—7241no—
370C4—7241no—
371C4C2×#1566844811yescharacteristic
372C4#1915386111yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—14481no—
378C2#2604192311yescharacteristic
379C2#2604207711yescharacteristic
380C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#550×C181C2
socleC22×C181C22×D4
hypercenter#550D181
hypocenterC181#3309
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #26041975C2semidirect
2. #26041643C2semidirect
3. #26041600C2semidirect
4. #26041590C2semidirect
5. #26041586C2semidirect
6. #26041530C2semidirect
7. #26041513C2semidirect
8. #26041471C2semidirect
9. #26041424C2semidirect
10. #26041424C2semidirect
11. #26041377C2semidirect
12. #26041351C2semidirect
13. #26041280C2semidirect
14. #26041275C2semidirect
15. #550×C181C2semidirect
190. C181#3309semidirect
193. #550D181semidirect

Maximal subgroups

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

subgroupindex
#260419752
#260416432
#260416002
#260415902
#260415862
#260415302
#260415132
#260414712
#260414242
#260413772
#260413512
#260412802
#260412752
#550×C1812
#3309181