Finite Group Databasebeta

← #37546041

Subgroups — #37546041

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#26041948C211yesmaximal, characteristic, complemented
2#26041929C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041598C211yesmaximal, characteristic, complemented
5#26041596C211yesmaximal, characteristic, complemented
6#26041562C211yesmaximal, characteristic, complemented
7#26041530C211yesmaximal, characteristic, complemented
8#26041529C211yesmaximal, characteristic, complemented
9#26041472C211yesmaximal, characteristic, complemented
10#26041423C211yesmaximal, characteristic, complemented
11SD16×Dic181C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041280C211yesmaximal, characteristic, complemented
14#26041279C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668448—21no—
18C2×#15668434C2211yescharacteristic
19C2×#15668433C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153812—21no—
23#19153812C2211yescharacteristic
24#19153798—21no—
25#19153797—21no—
26#19153793—21no—
27#19153790—21no—
28#19153790C2211yescharacteristic
29#19153787—21no—
30#19153787C2211yescharacteristic
31#19153787C2211yescharacteristic
32Q8×Dic181C2211yescharacteristic
33D4×Dic181C2211yescharacteristic
34C4×C22⋊D181—21no—
35C4×C22⋊D181C2211yescharacteristic
36C2×C4⋊Dic181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—41no—
61#15668448—44no—
62C2×Dic362—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181D411yescharacteristic
71C22×Dic181—21no—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668434—41no—
77#15668433—41no—
78#15668432—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181D411yescharacteristic
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97#41×C181—22no—
98#41×C181—41no—
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C22×C4×C181—21no—
105C22×C4×C181C2311yescharacteristic
106SD16×C181—22no—
107D8×C181—41no—
108C2×C8×C181C2311yescharacteristic
109C2×C8×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181C2×D411yescharacteristic
114Dic362—42no—
115D724—21no—
116D724—21no—
117D724—42no—
118C22⋊D181—22no—
119C22⋊D181—42no—
120C22⋊D181—42no—
121C22⋊D181—81no—
122C22⋊D181—81no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—42no—
128C2×Dic181—42no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135C4×D181—42no—
136#13089678—21no—
137#13089678—21no—
138C23×C181—21no—
139C23×C181—21no—
140C23×C181C2×D411yescharacteristic
141Q8×C181—21no—
142Q8×C181#4112yescomplemented
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—42no—
148D4×C181—42no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—42no—
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—22no—
176C4×C181—41no—
177C4×C181C2×#4111yescharacteristic
178C4×C181H(5,𝔽2)11yescharacteristic
179Dic181—21no—
180Dic181—21no—
181Dic181—41no—
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#469—1811no—
203#459—1811no—
204#449—1811no—
205#449D18111yescharacteristic, complemented
206C4×SD16—1811no—
207#436—1811no—
208#417—1811no—
209#417—1811no—
210C2×#41—3621no—
211C2×#41—1811no—
212C2×#41C2×D18111yescharacteristic
213C2×SD16C2×D18111yescharacteristic
214C2×D8—1811no—
215C2×D8C2×D18111yescharacteristic
216C2×M16—1811no—
217C2×M16—1811no—
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#121—1811no—
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#106—1811no—
239C4⋊C8—1811no—
240#103—1811no—
241#103—1811no—
242#103C2×D18111yescharacteristic
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102C2×D18111yescharacteristic
250C22⋊C8—1811no—
251C22⋊C8C2×D18111yescharacteristic
252C4×C8—1811no—
253#41—22no—
254#41—41no—
255#41—3622no—
256#41—7241no—
257#41—7244no—
258C2×Q8—3621no—
259C2×Q8C22×D18111yescharacteristic
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—21no—
273C22×C4—3621no—
274C22×C4—3621no—
275C22×C4—3621no—
276C22×C4—3621no—
277C22×C4—1811no—
278C22×C4C22×D18111yescharacteristic
279SD16—22no—
280D8—41no—
281D8—7241no—
282M16—7241no—
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⋊C4—1811no—
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—3621no—
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—21no—
312Q8—7242no—
313Q8#1566844812yescomplemented
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—3622no—
321D4—3621no—
322D4—3621no—
323D4—14481no—
324D4—14481no—
325D4—14481no—
326D4—7242no—
327D4—7242no—
328D4—7242no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—3621no—
339C2×C4—1811no—
340C2×C4—1811no—
341C2×C4—1811no—
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—22no—
370C4—41no—
371C4—3621no—
372C4—3621no—
373C4—1812no—
374C4—7241no—
375C4—7241no—
376C4—7241no—
377C4C2×#1566844811yescharacteristic
378C4#1915386111yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—14481no—
383C2—7241no—
384C2#2604191611yescharacteristic
385C2AGL(1,ℤ/8)×D18111yescharacteristic
386C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3332
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041948C2semidirect
2. #26041929C2semidirect
3. #26041624C2semidirect
4. #26041598C2semidirect
5. #26041596C2semidirect
6. #26041562C2semidirect
7. #26041530C2semidirect
8. #26041529C2semidirect
9. #26041472C2semidirect
10. #26041423C2semidirect
11. SD16×Dic181C2semidirect
12. #26041354C2semidirect
13. #26041280C2semidirect
14. #26041279C2semidirect
15. #449×C181C2semidirect
142. Q8×C181#41semidirect
193. C181#3332semidirect
205. #449D181semidirect
313. Q8#15668448semidirect

Maximal subgroups

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

subgroupindex
#260419482
#260419292
#260416242
#260415982
#260415962
#260415622
#260415302
#260415292
#260414722
#260414232
SD16×Dic1812
#260413542
#260412802
#260412792
#449×C1812
#3332181