Finite Group Databasebeta

← #37545827

Subgroups — #37545827

Order 23168.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041987C211yesmaximal, characteristic, complemented
2#26041939C211yesmaximal, characteristic
3#26041640C211yesmaximal, characteristic, complemented
4#26041607C211yesmaximal, characteristic, complemented
5#26041599C211yesmaximal, characteristic, complemented
6#26041563C211yesmaximal, characteristic, complemented
7#26041511C211yesmaximal, characteristic, complemented
8#26041503C211yesmaximal, characteristic, complemented
9#26041439C211yesmaximal, characteristic, complemented
10#26041433C211yesmaximal, characteristic, complemented
11#26041383C211yesmaximal, characteristic, complemented
12#26041348C211yesmaximal, characteristic, complemented
13#26041281C211yesmaximal, characteristic, complemented
14#103×D181C211yesmaximal, characteristic, complemented
15#470×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153806—21no—
23#19153805C2211yescharacteristic
24#19153802—21no—
25#19153796—21no—
26#19153794—21no—
27#19153793—21no—
28#19153792C2211yescharacteristic
29#19153791C2211yescharacteristic
30#19153789—21no—
31Q8×Dic181C2211yescharacteristic
32#19153781C2211yescharacteristic
33#19153778—21no—
34C4×C22⋊D181C2211yescharacteristic
35#19153776—21no—
36C2×C4⋊Dic181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153747C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153741C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—41no—
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×Dic362C2311yescharacteristic
64Q8×D181—22no—
65Q8×D181—41no—
66C2×D724—21no—
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C22×Dic181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668439—22no—
76#15668436—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C8×D181—41no—
80C4⋊Dic181—21no—
81C4⋊Dic181—21no—
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89C22⋊Dic181D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C22×C4×C181C2311yescharacteristic
101Q16×C181—41no—
102M16×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C22⋊C4×C181—21no—
111C22×D181—21no—
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—42no—
115Dic362—81no—
116Dic362#4112yes—
117D724—21no—
118D724—21no—
119D724—42no—
120C22⋊D181—22no—
121C22⋊D181—42no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—81no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—42no—
132C4×D181—42no—
133C4×D181—81no—
134#13089678—21no—
135#13089678—21no—
136C23×C181C2×D411yescharacteristic
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181C22×D411yescharacteristic
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181#13712yes—
161C4×C181—21no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181C2×#4111yescharacteristic
167C4×C181H(5,𝔽2)11yescharacteristic
168Dic181—21no—
169Dic181—22no—
170Dic181—21no—
171Dic181—21no—
172Dic181—41no—
173Dic181—41no—
174C2×C181—41no—
175C2×C181#54611yescharacteristic
176C2×C181C2×#13711yescharacteristic
177C2×C181#57711yescharacteristic
178D181—22no—
179D181—81no—
180C181#331611yescharacteristic, complemented, Sylow
181#3316—1811nomaximal, Sylow
182#554—1811no—
183#548—1811no—
184#489—1811no—
185#483—1811no—
186#481—1811no—
187#475—1811no—
188#470D18111yescharacteristic, complemented
189#465—1811no—
190#464—1811no—
191#452—1811no—
192#451—1811no—
193#441—1811no—
194#435—1811no—
195#417—1811no—
196C2×#103—1811no—
197C2×#41—1811no—
198C22×Q8—1811no—
199C2×Q16—1811no—
200C2×Q16C2×D18111yescharacteristic
201C2×SD16—1811no—
202C2×M16C2×D18111yescharacteristic
203C22×C8—1811no—
204C4⋊Q8—1811no—
205#125—3621no—
206#124—3621no—
207#124—1811no—
208C22⋊Q8—3621no—
209C22⋊Q8—3621no—
210C22⋊Q8—3621no—
211C22⋊Q8—1811no—
212C22⋊Q8C2×D18111yescharacteristic
213C22⋊Q8C2×D18111yescharacteristic
214#121—3621no—
215#121—1811no—
216C4×Q8—1811no—
217C4×Q8—1811no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—1811no—
221C2×C4⋊C4—1811no—
222C2×C4⋊C4—1811no—
223#106—1811no—
224#106—1811no—
225#106C2×D18111yescharacteristic
226C4⋊C8—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103—1811no—
232#103C2×D18111yescharacteristic
233#103C2×D18111yescharacteristic
234#102—1811no—
235#102—1811no—
236#102—1811no—
237C22⋊C8—1811no—
238C22⋊C8—1811no—
239#97—1811no—
240#41—3622no—
241#41—7241no—
242C2×Q8—3621no—
243C2×Q8—3621no—
244C2×Q8—3622no—
245C2×Q8—1811no—
246C2×Q8—7241no—
247C2×Q8C22×D18111yescharacteristic
248C2×Q8C22×D18111yescharacteristic
249C2×D4—3621no—
250C2×D4—3621no—
251C2×D4—1811no—
252C2×D4—1811no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—1811no—
258C22×C4C22×D18111yescharacteristic
259Q16—41no—
260Q16—3622no—
261SD16—7241no—
262M16—41no—
263C2×C8—1811no—
264C2×C8—1811no—
265C2×C8—7241no—
266C2×C8C22×D18111yescharacteristic
267C2×C8C22×D18111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4C22×D18111yescharacteristic
280C4⋊C4C22×D18111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—1811no—
288C22⋊C4—1811no—
289C42—3621no—
290C42—3621no—
291C42—1811no—
292C23—3621no—
293C23—1811no—
294C23D4×D18111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—3621no—
300Q8—14481no—
301Q8—1812no—
302Q8—7242no—
303D4—3622no—
304D4—3621no—
305D4—3621no—
306D4—7242no—
307D4—7242no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—14481no—
320C2×C4—14481no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4—1811no—
324C2×C4—7242no—
325C2×C4—7242no—
326C2×C4D4×D18111yescharacteristic
327C2×C4C23×D18111yescharacteristic
328C8—21no—
329C8—21no—
330C8—3621no—
331C8—3621no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—3621no—
336C22—3621no—
337C22—1812no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22C2×D4×D18111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3621no—
348C4—3622no—
349C4—3621no—
350C4—3621no—
351C4—7241no—
352C4—7241no—
353C4#41×D18111yescharacteristic
354C4#1915386111yescharacteristic
355C2—41no—
356C2—3622no—
357C2—14481no—
358C2#2604191811yescharacteristic
359C2#137×D18111yescharacteristic
360C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#470×C181C2
socleC22×C181C22×D4
prime radical#26041939C2
hypercenter#470D181
hypocenterC181#3316
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #26041987C2semidirect
3. #26041640C2semidirect
4. #26041607C2semidirect
5. #26041599C2semidirect
6. #26041563C2semidirect
7. #26041511C2semidirect
8. #26041503C2semidirect
9. #26041439C2semidirect
10. #26041433C2semidirect
11. #26041383C2semidirect
12. #26041348C2semidirect
13. #26041281C2semidirect
14. #103×D181C2semidirect
15. #470×C181C2semidirect
180. C181#3316semidirect
188. #470D181semidirect

Maximal subgroups

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

subgroupindex
#260419872
#260419392
#260416402
#260416072
#260415992
#260415632
#260415112
#260415032
#260414392
#260414332
#260413832
#260413482
#260412812
#103×D1812
#470×C1812
#3316181