Finite Group Databasebeta

← #37546043

Subgroups — #37546043

Order 23168.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041947C211yesmaximal, characteristic, complemented
2#26041929C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041595C211yesmaximal, characteristic, complemented
6#26041563C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041472C211yesmaximal, characteristic, complemented
9#26041422C211yesmaximal, characteristic, complemented
10#26041421C211yesmaximal, characteristic, complemented
11#26041370C211yesmaximal, characteristic, complemented
12#26041355C211yesmaximal, characteristic, complemented
13#26041281C211yesmaximal, characteristic, complemented
14#26041277C211yesmaximal, characteristic, complemented
15#469×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668448—21no—
18C2×#15668448C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22#19153815C2211yescharacteristic
23#19153812—21no—
24#19153812C2211yescharacteristic
25#19153798—21no—
26#19153797—21no—
27#19153793—21no—
28#19153791C2211yescharacteristic
29#19153789—21no—
30#19153788—21no—
31#19153787C2211yescharacteristic
32#19153781C2211yescharacteristic
33D4×Dic181C2211yescharacteristic
34C4×C22⋊D181C2211yescharacteristic
35#19153776—21no—
36C2×C4⋊Dic181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153747C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153741C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×D8×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—41no—
61#15668448—22no—
62#15668448—41no—
63#15668448—44no—
64C2×Dic362—21no—
65C2×Dic362C2311yescharacteristic
66C2×D724—21no—
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181D411yescharacteristic
74C22×Dic181—21no—
75C22×Dic181—21no—
76C22×Dic181—21no—
77C2×C4×D181—21no—
78C2×C4×D181—21no—
79C2×C4×D181C2311yescharacteristic
80#15668437—22no—
81#15668434—41no—
82#15668432—41no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C4⋊Dic181—21no—
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668428D411yescharacteristic
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94C22⋊Dic181D411yescharacteristic
95#15668426—21no—
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181C2311yescharacteristic
104D8×C181—41no—
105M16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181C2×D411yescharacteristic
114Dic362—21no—
115Dic362—42no—
116Dic362#4112yescomplemented
117D724—21no—
118D724—21no—
119D724—81no—
120C22⋊D181—22no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—42no—
130C2×Dic181—42no—
131C2×Dic181—42no—
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—42no—
138C4×D181—42no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181—21no—
143C23×C181C2×D411yescharacteristic
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—42no—
149D4×C181—81no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×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—21no—
169C2×D181—21no—
170C2×D181—21no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C4×C181—21no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181C2×#4111yescharacteristic
178C4×C181H(5,𝔽2)11yescharacteristic
179Dic181—21no—
180Dic181—22no—
181Dic181—21no—
182Dic181—41no—
183Dic181—41no—
184Dic181AGL(1,ℤ/8)12yes—
185C2×C181—41no—
186C2×C181—81no—
187C2×C181—81no—
188C2×C181#54611yescharacteristic
189C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C181#57711yescharacteristic
191D181—41no—
192D181—81no—
193C181#333211yescharacteristic, complemented, Sylow
194#3332—1811nomaximal, Sylow
195#550—1811no—
196#547—1811no—
197#486—1811no—
198#481—1811no—
199#481—1811no—
200#475—1811no—
201#469—1811no—
202#469D18111yescharacteristic, complemented
203#459—1811no—
204#449—1811no—
205#449—1811no—
206C4×SD16—1811no—
207#436—1811no—
208#417—1811no—
209#417—1811no—
210C2×#41—3621no—
211C2×#41—1811no—
212C2×#41—1811no—
213C2×SD16—1811no—
214C2×D8—1811no—
215C2×D8C2×D18111yescharacteristic
216C2×M16—1811no—
217C2×M16C2×D18111yescharacteristic
218C4⋊Q8—1811no—
219#127—3621no—
220#127—1811no—
221#123—3621no—
222#123—3621no—
223C22⋊Q8—3621no—
224#121—3621no—
225#121—3621no—
226#121—1811no—
227#121—1811no—
228#121C2×D18111yescharacteristic
229#121C2×D18111yescharacteristic
230C4×Q8—1811no—
231C4×D4—3621no—
232C4×D4—1811no—
233C4×D4—1811no—
234C2×C4⋊C4—1811no—
235C2×C4⋊C4—1811no—
236#106—1811no—
237#106—1811no—
238#106C2×D18111yescharacteristic
239C4⋊C8—1811no—
240#103—1811no—
241#103—1811no—
242#103—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102C2×D18111yescharacteristic
249#102C2×D18111yescharacteristic
250C22⋊C8—1811no—
251C22⋊C8—1811no—
252C4×C8—1811no—
253#41—3622no—
254#41—3622no—
255#41—7241no—
256#41—7241no—
257#41—7244no—
258C2×Q8—3621no—
259C2×Q8—1811no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—1811no—
269C2×D4—1811no—
270C2×D4C22×D18111yescharacteristic
271C2×D4C22×D18111yescharacteristic
272C22×C4—3621no—
273C22×C4—3621no—
274C22×C4—3621no—
275C22×C4—3621no—
276C22×C4—3621no—
277C22×C4—1811no—
278C22×C4C22×D18111yescharacteristic
279SD16—3622no—
280D8—41no—
281D8—7241no—
282M16—41no—
283M16—7241no—
284C2×C8—1811no—
285C2×C8—1811no—
286C2×C8C22×D18111yescharacteristic
287C2×C8C22×D18111yescharacteristic
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C4⋊C4C22×D18111yescharacteristic
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—1811no—
303C22⋊C4—1811no—
304C42—3621no—
305C42—1811no—
306C23—21no—
307C23—21no—
308C23—3621no—
309C23—1811no—
310C23D4×D18111yescharacteristic
311Q8—3621no—
312Q8—1812no—
313Q8—7242no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—81no—
320D4—3622no—
321D4—3621no—
322D4—3621no—
323D4—14481no—
324D4—14481no—
325D4—7242no—
326D4—7242no—
327D4—7242no—
328D4—7242no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—1811no—
341C2×C4—7242no—
342C2×C4—7242no—
343C2×C4—7242no—
344C2×C4—7242no—
345C2×C4—7242no—
346C2×C4D4×D18111yescharacteristic
347C2×C4C23×D18111yescharacteristic
348C8—21no—
349C8—21no—
350C8—3621no—
351C8—3621no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3621no—
362C22—3621no—
363C22—3621no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22C2×D4×D18111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—3621no—
372C4—3622no—
373C4—3621no—
374C4—1812no—
375C4—7241no—
376C4—7241no—
377C4#41×D18111yescharacteristic
378C4#1915386111yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—14481no—
383C2—7241no—
384C2#2604191811yescharacteristic
385C2AGL(1,ℤ/8)×D18111yescharacteristic
386C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#469×C181C2
socleC22×C181C22×D4
hypercenter#469D181
hypocenterC181#3332
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #26041947C2semidirect
2. #26041929C2semidirect
3. #26041624C2semidirect
4. #26041599C2semidirect
5. #26041595C2semidirect
6. #26041563C2semidirect
7. #26041531C2semidirect
8. #26041472C2semidirect
9. #26041422C2semidirect
10. #26041421C2semidirect
11. #26041370C2semidirect
12. #26041355C2semidirect
13. #26041281C2semidirect
14. #26041277C2semidirect
15. #469×C181C2semidirect
116. Dic362#41semidirect
193. C181#3332semidirect
202. #469D181semidirect

Maximal subgroups

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

subgroupindex
#260419472
#260419292
#260416242
#260415992
#260415952
#260415632
#260415312
#260414722
#260414222
#260414212
#260413702
#260413552
#260412812
#260412772
#469×C1812
#3332181