Finite Group Databasebeta

← #37543672

Subgroups — #37543672

Order 23168.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041845C211yesmaximal, characteristic
2#26041760C211yesmaximal, characteristic, complemented
3#26041606C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041601C211yesmaximal, characteristic, complemented
6#26041600C211yesmaximal, characteristic, complemented
7#26041597C211yesmaximal, characteristic, complemented
8#26041596C211yesmaximal, characteristic, complemented
9#26041594C211yesmaximal, characteristic, complemented
10#26041320C211yesmaximal, characteristic, complemented
11#26041316C211yesmaximal, characteristic, complemented
12#26041282C211yesmaximal, characteristic, complemented
13#102×D181C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153812—21no—
21#19153802—21no—
22#19153791C2211yescharacteristic
23#19153790C2211yescharacteristic
24#19153787C2211yescharacteristic
25#19153786—21no—
26#19153784—21no—
27#19153781—21no—
28#19153778—21no—
29C4×C22⋊D181—21no—
30C4×C22⋊D181—21no—
31#19153775C2211yescharacteristic, complemented
32#19153774C2211yescharacteristic
33#19153774C2211yescharacteristic
34#19153774C2211yescharacteristic, complemented
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic, complemented
37#19153750C2211yescharacteristic, complemented
38#19153749C2211yescharacteristic, complemented
39#19153748C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153747C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#107×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—22no—
61#15668449—22no—
62C2×Dic362D411yescharacteristic
63C2×D724—21no—
64C2×D724D411yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C2×C22⋊D181D411yescharacteristic
71D4×D181—22no—
72D4×D181—22no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76C2×C4×D181C2311yescharacteristic
77#15668432—22no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—22no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181—21no—
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181—21no—
100C22×C4×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181—21no—
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22×D181—21no—
109C22×D181—42no—
110C22×D181—81no—
111C22×D181—81no—
112C22×D181C2×D411yescharacteristic
113C22×D181C2×D411yescharacteristic
114Dic362—22no—
115D724—22no—
116D724—21no—
117D724—21no—
118D724—81no—
119C22⋊D181—22no—
120C22⋊D181—22no—
121C22⋊D181—42no—
122C22⋊D181—81no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—81no—
132C4×D181—81no—
133C4×D181#4112yes—
134C4×D181#4112yes—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138C23×C181C2×D411yescharacteristic
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—81no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—81no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—84no—
168C2×D181#12312yes—
169C4×C181—21no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181C2×#4111yescharacteristic
174C4×C181C2×#4111yescharacteristic
175Dic181—21no—
176Dic181—41no—
177Dic181—41no—
178Dic181—41no—
179Dic181#12312yes—
180C2×C181—41no—
181C2×C181—81no—
182C2×C181C2×#12311yescharacteristic
183C2×C181#57611yescharacteristic
184C2×C181#57711yescharacteristic
185D181—22no—
186D181—41no—
187D181—81no—
188C181#309611yescharacteristic, complemented, Sylow
189#3096—1811nomaximal, Sylow
190#535—1811no—
191#520—1811no—
192#482—1811no—
193#482—1811no—
194#482—1811no—
195#482—1811no—
196#481—1811no—
197#481—1811no—
198#480—1811no—
199#480D18111yescharacteristic, complemented
200#428—1811no—
201#427—1811no—
202#418—1811no—
203C2×#102—1811no—
204#408—1811no—
205C2×#41—1811no—
206C22×D4—1811no—
207C2×M16—1811no—
208C22×C8—1811no—
209#127—3621no—
210#124—3621no—
211#121—1811no—
212#121—1811no—
213#121—1811no—
214#121C2×D18111yescharacteristic
215#120—3621no—
216#120—3621no—
217C4×Q8—3621no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—3621no—
221#117—1811no—
222#117—1811no—
223#117—1811no—
224#117—1811no—
225C2×C4⋊C4—1811no—
226C2×C4⋊C4—1811no—
227C2×C4⋊C4C2×D18111yescharacteristic, complemented
228#107—1811no—
229#107—1811no—
230#107C2×D18111yescharacteristic, complemented
231#107C2×D18111yescharacteristic, complemented
232#106—1811no—
233#106—1811no—
234#106—1811no—
235#106—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102C2×D18111yescharacteristic
243#102C2×D18111yescharacteristic
244C22⋊C8—1811no—
245C22⋊C8—1811no—
246C22⋊C8—1811no—
247C22⋊C8C2×D18111yescharacteristic, complemented
248C24—3621no—
249#41—3622no—
250#41—3622no—
251C2×Q8—1811no—
252C2×D4—21no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—3622no—
257C2×D4—3622no—
258C2×D4—3621no—
259C2×D4—1811no—
260C2×D4—1811no—
261C2×D4—1811no—
262C2×D4—1811no—
263C2×D4C22×D18111yescharacteristic
264C22×C4—21no—
265C22×C4—3621no—
266C22×C4—3621no—
267C22×C4—1811no—
268C22×C4—1811no—
269C22×C4C22×D18111yescharacteristic
270M16—3622no—
271C2×C8—3622no—
272C2×C8—1811no—
273C2×C8—1811no—
274C2×C8C22×D18111yescharacteristic
275C2×C8C22×D18111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22×D18111yescharacteristic
283C4⋊C4C22×D18111yescharacteristic
284C4⋊C4C22×D18111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C42—3621no—
294C42—3621no—
295C42—3621no—
296C42—3621no—
297C23—21no—
298C23—3621no—
299C23—14481no—
300C23—14481no—
301C23—1811no—
302C23—1811no—
303C23—7242no—
304C23D4×D18111yescharacteristic
305Q8—3622no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—3622no—
310D4—3622no—
311D4—3622no—
312D4—3621no—
313D4—3621no—
314D4—14481no—
315D4—14481no—
316D4—14481no—
317D4—7242no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—14481no—
330C2×C4—14481no—
331C2×C4—1811no—
332C2×C4—1811no—
333C2×C4—1812no—
334C2×C4—1812no—
335C2×C4D4×D18111yescharacteristic
336C2×C4C23×D18111yescharacteristic
337C8—21no—
338C8—21no—
339C8—3621no—
340C8—3621no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—3621no—
348C22—3621no—
349C22—3621no—
350C22—3621no—
351C22—3621no—
352C22—14484no—
353C22—1812no—
354C22—7241no—
355C22—7241no—
356C22—7241no—
357C22C2×D4×D18111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3621no—
363C4—1812no—
364C4—7241no—
365C4—7241no—
366C4—7241no—
367C4#41×D18111yescharacteristic
368C4#41×D18111yescharacteristic
369C2—41no—
370C2—81no—
371C2—3622no—
372C2—14481no—
373C2—7241no—
374C2#123×D18111yescharacteristic
375C2#2604208011yescharacteristic
376C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
prime radical#26041845C2
hypercenter#480D181
hypocenterC181#3096
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #26041760C2semidirect
3. #26041606C2semidirect
4. #26041604C2semidirect
5. #26041601C2semidirect
6. #26041600C2semidirect
7. #26041597C2semidirect
8. #26041596C2semidirect
9. #26041594C2semidirect
10. #26041320C2semidirect
11. #26041316C2semidirect
12. #26041282C2semidirect
13. #102×D181C2semidirect
14. #26041244C2semidirect
15. #480×C181C2semidirect
31. #19153775C22semidirect
34. #19153774C22semidirect
36. C4⋊C4×D181C22semidirect
37. #19153750C22semidirect
38. #19153749C22semidirect
39. #19153748C22semidirect
40. #19153747C22semidirect
41. #19153747C22semidirect
42. #19153747C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. #19153728C22semidirect
53. C2×C4⋊C4×C181C22semidirect
54. #107×C181C22semidirect
55. #107×C181C22semidirect
58. C22⋊C8×C181C22semidirect
188. C181#3096semidirect
199. #480D181semidirect
227. C2×C4⋊C4C2×D181semidirect
230. #107C2×D181semidirect
231. #107C2×D181semidirect
247. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418452
#260417602
#260416062
#260416042
#260416012
#260416002
#260415972
#260415962
#260415942
#260413202
#260413162
#260412822
#102×D1812
#260412442
#480×C1812
#3096181