Finite Group Databasebeta

← #37545726

Subgroups — #37545726

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#26041982C211yesmaximal, characteristic, complemented
2#26041949C211yesmaximal, characteristic, complemented
3#26041601C211yesmaximal, characteristic, complemented
4#26041591C211yesmaximal, characteristic, complemented
5#26041583C211yesmaximal, characteristic, complemented
6#26041531C211yesmaximal, characteristic, complemented
7#26041514C211yesmaximal, characteristic, complemented
8#26041471C211yesmaximal, characteristic, complemented
9#26041425C211yesmaximal, characteristic, complemented
10#26041425C211yesmaximal, characteristic, complemented
11#26041381C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041277C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#490×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic
23#19153812—21no—
24#19153811—21no—
25#19153801—21no—
26#19153791—21no—
27#19153791C2211yescharacteristic
28#19153791C2211yescharacteristic
29#19153788—21no—
30#19153788—21no—
31#19153787C2211yescharacteristic
32#19153787C2211yescharacteristic
33C4×Dic362C2211yescharacteristic
34C4×D724C2211yescharacteristic
35C4×D724C2211yescharacteristic
36D4×Dic181—21no—
37#19153778—21no—
38#19153774C2211yescharacteristic
39C4⋊C4×D181C2211yescharacteristic
40#19153750C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52#127×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#102×C181C2211yescharacteristic
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—22no—
61#15668448—41no—
62#15668448—41no—
63C2×Dic362C2311yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724D411yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C22×Dic181—21no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77C2×C4×D181C2311yescharacteristic
78#15668438—22no—
79#15668434—41no—
80#15668434—41no—
81#15668432—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C8×D181—41no—
85C4⋊Dic181D411yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181C2×D411yescharacteristic
113C22×D181C2×D411yescharacteristic
114Dic362—21no—
115Dic362#4112yes—
116D724—21no—
117D724—21no—
118D724—41no—
119D724—42no—
120D724—81no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—42no—
129C2×Dic181—42no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—81no—
137C4×D181—81no—
138#13089678—21no—
139#13089678—21no—
140C23×C181—21no—
141C23×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—42no—
147D4×C181—81no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181C2×#4111yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—22no—
180Dic181—41no—
181Dic181—41no—
182C2×C181—81no—
183C2×C181—81no—
184C2×C181#54611yescharacteristic
185C2×C181#57511yescharacteristic
186C2×C181#57611yescharacteristic
187D181—41no—
188D181—41no—
189D181—81no—
190C181#330911yescharacteristic, complemented, Sylow
191#3309—1811nomaximal, Sylow
192#553—1811no—
193#550—1811no—
194#490D18111yescharacteristic, complemented
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×#41—1811no—
208C2×#41—1811no—
209C2×SD16—1811no—
210C2×D8—1811no—
211C2×D8—1811no—
212C2×M16—1811no—
213C22×C8—1811no—
214#127—3621no—
215#127C2×D18111yescharacteristic
216#126—3621no—
217#125C2×D18111yescharacteristic
218#123—3621no—
219#121—3621no—
220#121—3621no—
221#121—3621no—
222#121—1811no—
223#121—1811no—
224#121—1811no—
225#121—1811no—
226C4×Q8—1811no—
227C4×D4—3621no—
228C4×D4—3621no—
229C4×D4—1811no—
230C4×D4—1811no—
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#102C2×D18111yescharacteristic
244#102C2×D18111yescharacteristic
245#102C2×D18111yescharacteristic
246#102C2×D18111yescharacteristic
247C22⋊C8—1811no—
248C22⋊C8—1811no—
249#97C2×D18111yescharacteristic
250#41—3622no—
251#41—3622no—
252#41—7241no—
253#41—7241no—
254C2×Q8—1811no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4C22×D18111yescharacteristic
266C2×D4C22×D18111yescharacteristic
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—1811no—
272C22×C4—1811no—
273SD16—3622no—
274D8—7241no—
275D8—7241no—
276M16—7241no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8—7241no—
280C2×C8C22×D18111yescharacteristic
281C2×C8C22×D18111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—1811no—
287C4⋊C4—1811no—
288C4⋊C4—1811no—
289C4⋊C4C22×D18111yescharacteristic
290C4⋊C4C22×D18111yescharacteristic
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—1811no—
298C22⋊C4—1811no—
299C42—3621no—
300C42—3621no—
301C42C22×D18111yescharacteristic
302C23—21no—
303C23—21no—
304C23—3621no—
305C23—1811no—
306C23—1811no—
307Q8—3621no—
308Q8—1812no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—3621no—
316D4—3621no—
317D4—14481no—
318D4—14481no—
319D4—14481no—
320D4—7241no—
321D4—7242no—
322D4—7242no—
323D4—7242no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—14481no—
334C2×C4—14481no—
335C2×C4—1811no—
336C2×C4—1811no—
337C2×C4—7242no—
338C2×C4—7242no—
339C2×C4D4×D18111yescharacteristic
340C2×C4D4×D18111yescharacteristic
341C2×C4C23×D18111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3621no—
345C8—3621no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3621no—
353C22—3621no—
354C22—3621no—
355C22—3621no—
356C22—3621no—
357C22—3621no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C2×D4×D18111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—3621no—
367C4—3621no—
368C4—3622no—
369C4—7241no—
370C4—7241no—
371C4#41×D18111yescharacteristic
372C4#1915386211yescharacteristic
373C2—81no—
374C2—81no—
375C2—14481no—
376C2—7241no—
377C2—7241no—
378C2#2604192211yescharacteristic
379C2#2604207511yescharacteristic
380C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
hypercenter#490D181
hypocenterC181#3309
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #26041982C2semidirect
2. #26041949C2semidirect
3. #26041601C2semidirect
4. #26041591C2semidirect
5. #26041583C2semidirect
6. #26041531C2semidirect
7. #26041514C2semidirect
8. #26041471C2semidirect
9. #26041425C2semidirect
10. #26041425C2semidirect
11. #26041381C2semidirect
12. #26041352C2semidirect
13. #26041277C2semidirect
14. #26041272C2semidirect
15. #490×C181C2semidirect
190. C181#3309semidirect
194. #490D181semidirect

Maximal subgroups

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

subgroupindex
#260419822
#260419492
#260416012
#260415912
#260415832
#260415312
#260415142
#260414712
#260414252
#260413812
#260413522
#260412772
#260412722
#490×C1812
#3309181