Finite Group Databasebeta

← #37545708

Subgroups — #37545708

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041940C211yesmaximal, characteristic, complemented
2#26041930C211yesmaximal, characteristic, complemented
3#26041640C211yesmaximal, characteristic, complemented
4#26041613C211yesmaximal, characteristic, complemented
5#26041592C211yesmaximal, characteristic, complemented
6#26041572C211yesmaximal, characteristic, complemented
7#26041528C211yesmaximal, characteristic, complemented
8#26041515C211yesmaximal, characteristic, complemented
9#26041497C211yesmaximal, characteristic, complemented
10#26041427C211yesmaximal, characteristic, complemented
11#26041418C211yesmaximal, characteristic, complemented
12#26041382C211yesmaximal, characteristic, complemented
13#26041350C211yesmaximal, characteristic, complemented
14#26041279C211yesmaximal, characteristic, complemented
15C2×#103×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449—21no—
18C2×#15668436C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22#19153815C2211yescharacteristic
23#19153805—21no—
24#19153805C2211yescharacteristic
25#19153801—21no—
26#19153799—21no—
27#19153794—21no—
28#19153792—21no—
29#19153792C2211yescharacteristic
30#19153791C2211yescharacteristic
31#19153790—21no—
32#19153790C2211yescharacteristic
33#19153790C2211yescharacteristic
34Q8×Dic181C2211yescharacteristic
35#19153778C2211yescharacteristic
36C4×C22⋊D181—21no—
37C4×C22⋊D181C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C22×Q8×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—41no—
61#15668449—44no—
62C2×Dic362—21no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74#15668436—22no—
75#15668436—41no—
76D1448—41no—
77#15668432—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C4⋊Dic181—21no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428D411yescharacteristic
87C22⋊Dic181D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C2×Q8×C181—21no—
99C2×Q8×C181—22no—
100C2×Q8×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181—21no—
105C22×C4×C181C2311yescharacteristic
106C2×C8×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181—21no—
110C4⋊C4×C181C2311yescharacteristic
111C4⋊C4×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181C2×D411yescharacteristic
115Dic362—42no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—42no—
121D724—42no—
122C22⋊D181—22no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—42no—
133C4×D181—42no—
134C4×D181—42no—
135#13089678—21no—
136#13089678—21no—
137C23×C181C2×D411yescharacteristic
138Q8×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
141Q8×C181—42no—
142Q8×C181#4112yescomplemented
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—42no—
150C2×C4×C181—42no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181AGL(1,ℤ/8)12yes—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C4×C181—21no—
169C4×C181—22no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181C2×#4111yescharacteristic
174C4×C181H(5,𝔽2)11yescharacteristic
175Dic181—21no—
176Dic181—21no—
177Dic181—21no—
178Dic181—41no—
179Dic181—41no—
180C2×C181—22no—
181C2×C181#54611yescharacteristic
182C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C181#57811yescharacteristic
184D181—41no—
185D181—81no—
186D181—81no—
187C181#330811yescharacteristic, complemented, Sylow
188#3308—1811nomaximal, Sylow
189#548—1811no—
190#547—1811no—
191#489—1811no—
192#484—1811no—
193#480—1811no—
194#477—1811no—
195#468—1811no—
196#466—1811no—
197#463—1811no—
198#449—1811no—
199#448—1811no—
200#440—1811no—
201#435—1811no—
202#417—1811no—
203C2×#103D18111yescharacteristic, complemented
204C2×#41—3621no—
205C2×#41—1811no—
206C22×Q8C2×D18111yescharacteristic
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×D8—1811no—
210C2×M16—1811no—
211C22×C8C2×D18111yescharacteristic
212C4⋊Q8—1811no—
213#124—3621no—
214#124—1811no—
215#123—3621no—
216#123—3621no—
217C22⋊Q8—3621no—
218C22⋊Q8—3621no—
219C22⋊Q8—1811no—
220#121—3621no—
221#121—1811no—
222#121—1811no—
223#121—1811no—
224C4×Q8—1811no—
225C4×D4—3621no—
226C4×D4—1811no—
227C4×D4—1811no—
228C2×C4⋊C4—1811no—
229C2×C4⋊C4C2×D18111yescharacteristic
230#107—1811no—
231#107—1811no—
232#107—1811no—
233C4⋊C8—1811no—
234#103—1811no—
235#103—1811no—
236#103C2×D18111yescharacteristic
237#103C2×D18111yescharacteristic
238#103C2×D18111yescharacteristic
239#103C2×D18111yescharacteristic
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244C22⋊C8—1811no—
245C22⋊C8—1811no—
246#97—1811no—
247#41—3622no—
248#41—7244no—
249#41—7241no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—3621no—
254C2×Q8C22×D18111yescharacteristic
255C2×Q8C22×D18111yescharacteristic
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—1811no—
261C2×D4—1811no—
262C2×D4—1811no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3621no—
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—1811no—
269C22×C4C22×D18111yescharacteristic
270SD16—3622no—
271SD16—7241no—
272D8—7241no—
273M16—7241no—
274C2×C8—41no—
275C2×C8—1811no—
276C2×C8—1811no—
277C2×C8C22×D18111yescharacteristic
278C2×C8C22×D18111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4C22×D18111yescharacteristic
288C4⋊C4C22×D18111yescharacteristic
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—1811no—
297C22⋊C4—1811no—
298C42—3621no—
299C42—1811no—
300C23—3621no—
301C23—3621no—
302C23—1811no—
303C23D4×D18111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—7242no—
309Q8#1566844912yescomplemented
310D4—3622no—
311D4—3621no—
312D4—3621no—
313D4—3621no—
314D4—3621no—
315D4—7242no—
316D4—7242no—
317D4—7242no—
318D4—7242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—1811no—
332C2×C4—1811no—
333C2×C4—1811no—
334C2×C4—7242no—
335C2×C4—7242no—
336C2×C4—7242no—
337C2×C4D4×D18111yescharacteristic
338C2×C4C23×D18111yescharacteristic
339C8—21no—
340C8—21no—
341C8—3621no—
342C8—3621no—
343C22—21no—
344C22—21no—
345C22—3621no—
346C22—3621no—
347C22—3621no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22—7241no—
352C22—7241no—
353C22—7241no—
354C22#1915384312yes—
355C22C2×D4×D18111yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3621no—
362C4—3621no—
363C4—3621no—
364C4—7241no—
365C4—7241no—
366C4C2×#1566844911yescharacteristic
367C4#1915386111yescharacteristic
368C2—22no—
369C2—14481no—
370C2—14481no—
371C2—7241no—
372C2#2604191911yescharacteristic
373C2C2×#1915384311yescharacteristic
374C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#103×C181C2
socleC22×C181C22×D4
hypercenterC2×#103D181
hypocenterC181#3308
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #26041940C2semidirect
2. #26041930C2semidirect
3. #26041640C2semidirect
4. #26041613C2semidirect
5. #26041592C2semidirect
6. #26041572C2semidirect
7. #26041528C2semidirect
8. #26041515C2semidirect
9. #26041497C2semidirect
10. #26041427C2semidirect
11. #26041418C2semidirect
12. #26041382C2semidirect
13. #26041350C2semidirect
14. #26041279C2semidirect
15. C2×#103×C181C2semidirect
142. Q8×C181#41semidirect
187. C181#3308semidirect
203. C2×#103D181semidirect
309. Q8#15668449semidirect

Maximal subgroups

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

subgroupindex
#260419402
#260419302
#260416402
#260416132
#260415922
#260415722
#260415282
#260415152
#260414972
#260414272
#260414182
#260413822
#260413502
#260412792
C2×#103×C1812
#3308181