Finite Group Databasebeta

← #37545567

Subgroups — #37545567

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041977C211yesmaximal, characteristic, complemented
2#26041923C211yesmaximal, characteristic, complemented
3#26041632C211yesmaximal, characteristic, complemented
4#26041614C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041581C211yesmaximal, characteristic, complemented
7#26041514C211yesmaximal, characteristic, complemented
8#26041508C211yesmaximal, characteristic, complemented
9#26041493C211yesmaximal, characteristic, complemented
10#26041425C211yesmaximal, characteristic, complemented
11#26041413C211yesmaximal, characteristic, complemented
12#26041359C211yesmaximal, characteristic, complemented
13C8×C22⋊D181C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15C2×#102×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668438C2211yescharacteristic, complemented
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic, complemented
21#19153811—21no—
22#19153807C2211yescharacteristic, complemented
23#19153803C2211yescharacteristic
24#19153801—21no—
25#19153797—21no—
26#19153795C2211yescharacteristic
27#19153791C2211yescharacteristic, complemented
28#19153790—21no—
29#19153790C2211yescharacteristic
30#19153788—21no—
31#19153787C2211yescharacteristic
32#19153785—21no—
33D4×Dic181C2211yescharacteristic
34#19153778C2211yescharacteristic, complemented
35C4×C22⋊D181—21no—
36C4×C22⋊D181C2211yescharacteristic
37#19153774C2211yescharacteristic, complemented
38C2×C22⋊Dic181—21no—
39#19153749C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153741C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153739C2211yescharacteristic, complemented
46#19153738C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181D411yescharacteristic
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72#15668438—41no—
73#15668434—22no—
74#15668434—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—41no—
78C4⋊Dic181—21no—
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C24×C181—21no—
98C2×D4×C181—22no—
99C2×D4×C181—21no—
100C2×D4×C181—41no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105C2×C8×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—21no—
115D724—21no—
116D724—21no—
117D724—81no—
118C22⋊D181—22no—
119C22⋊D181—42no—
120C22⋊D181—42no—
121C22⋊D181—81no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—42no—
126C2×Dic181—81no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—81no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136C23×C181—21no—
137C23×C181—42no—
138C23×C181—42no—
139C23×C181—81no—
140C23×C181C2×D411yescharacteristic
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—42no—
145D4×C181#4112yes—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—81no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—22no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—84no—
164C22×C181#13512yes—
165C22×C181C22×D411yescharacteristic
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181C2×#4111yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—22no—
184C2×C181—42no—
185C2×C181—81no—
186C2×C181#54611yescharacteristic
187C2×C181C2×#13511yescharacteristic
188C2×C181#57611yescharacteristic
189D181—41no—
190D181—81no—
191C181#329711yescharacteristic, complemented, Sylow
192#3297—1811nomaximal, Sylow
193#553—1811no—
194#546—1811no—
195#488—1811no—
196#484—1811no—
197#482—1811no—
198#478—1811no—
199#466—1811no—
200#465—1811no—
201#463—1811no—
202#449—1811no—
203#447—1811no—
204C4×D8—1811no—
205C8×D4—1811no—
206#416—1811no—
207C2×#102D18111yescharacteristic, complemented
208C2×#41—1811no—
209C22×D4C2×D18111yescharacteristic
210C2×SD16—1811no—
211C2×D8—1811no—
212C2×D8—1811no—
213C22×C8—1811no—
214C22×C8C2×D18111yescharacteristic
215#126—3621no—
216#125—1811no—
217#124—1811no—
218#123—3621no—
219#123—3621no—
220C22⋊Q8—1811no—
221#121—3621no—
222#121—3621no—
223#121—1811no—
224#121—1811no—
225#121—1811no—
226#120—3621no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4—1811no—
231#117—1811no—
232C2×C4⋊C4C2×D18111yescharacteristic
233C2×C22⋊C4—3621no—
234#107—1811no—
235#107—1811no—
236#106—1811no—
237C4⋊C8—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102C2×D18111yescharacteristic
245#102C2×D18111yescharacteristic
246#102C2×D18111yescharacteristic
247#102C2×D18111yescharacteristic
248C22⋊C8—1811no—
249C22⋊C8—1811no—
250C4×C8—1811no—
251C24—21no—
252#41—3622no—
253#41—7241no—
254C2×Q8—1811no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—1811no—
263C2×D4—1811no—
264C2×D4C22×D18111yescharacteristic
265C2×D4C22×D18111yescharacteristic
266C22×C4—21no—
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4C22×D18111yescharacteristic
272SD16—7241no—
273D8—3622no—
274D8—7241no—
275C2×C8—41no—
276C2×C8—1811no—
277C2×C8—1811no—
278C2×C8—7241no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4—1811no—
288C4⋊C4C22×D18111yescharacteristic
289C4⋊C4C22×D18111yescharacteristic
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—1811no—
300C22⋊C4—1811no—
301C42—3621no—
302C42—1811no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—3621no—
309C23—1811no—
310C23D4×D18111yescharacteristic
311Q8—3621no—
312Q8—3621no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—3622no—
318D4—3621no—
319D4—3621no—
320D4—14481no—
321D4—14481no—
322D4—7242no—
323D4—7242no—
324D4#1566844912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—7242no—
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—84no—
356C22—3621no—
357C22—3621no—
358C22—3621no—
359C22—7241no—
360C22—7241no—
361C22—7241no—
362C22#1915383712yes—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3621no—
368C4—3621no—
369C4—3621no—
370C4—7241no—
371C4—7241no—
372C4—7241no—
373C4C2×#1566844911yescharacteristic
374C4#1915386111yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—14481no—
379C2—7241no—
380C2#2604191911yescharacteristic
381C2C2×#1915383711yescharacteristic
382C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#102×C181C2
socleC22×C181C22×D4
hypercenterC2×#102D181
hypocenterC181#3297
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #26041977C2semidirect
2. #26041923C2semidirect
3. #26041632C2semidirect
4. #26041614C2semidirect
5. #26041602C2semidirect
6. #26041581C2semidirect
7. #26041514C2semidirect
8. #26041508C2semidirect
9. #26041493C2semidirect
10. #26041425C2semidirect
11. #26041413C2semidirect
12. #26041359C2semidirect
13. C8×C22⋊D181C2semidirect
14. #26041272C2semidirect
15. C2×#102×C181C2semidirect
17. C2×#15668438C22semidirect
20. C2×C8×D181C22semidirect
22. #19153807C22semidirect
27. #19153791C22semidirect
34. #19153778C22semidirect
37. #19153774C22semidirect
39. #19153749C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153745C22semidirect
43. #19153741C22semidirect
44. #19153739C22semidirect
45. #19153739C22semidirect
46. #19153738C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
191. C181#3297semidirect
207. C2×#102D181semidirect

Maximal subgroups

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

subgroupindex
#260419772
#260419232
#260416322
#260416142
#260416022
#260415812
#260415142
#260415082
#260414932
#260414252
#260414132
#260413592
C8×C22⋊D1812
#260412722
C2×#102×C1812
#3297181