Finite Group Databasebeta

← #37546431

Subgroups — #37546431

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041985C211yesmaximal, characteristic, complemented
2#26041950C211yesmaximal, characteristic, complemented
3#26041645C211yesmaximal, characteristic, complemented
4#26041642C211yesmaximal, characteristic, complemented
5#26041624C211yesmaximal, characteristic, complemented
6#26041582C211yesmaximal, characteristic, complemented
7#26041568C211yesmaximal, characteristic, complemented
8#26041475C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041473C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041390C211yesmaximal, characteristic, complemented
13#26041389C211yesmaximal, characteristic, complemented
14#26041361C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×D1448C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153813C2211yescharacteristic
22#19153812C2211yescharacteristic
23#19153812C2211yescharacteristic
24#19153807C2211yescharacteristic
25#19153796—21no—
26#19153794—21no—
27#19153794—21no—
28#19153790—21no—
29#19153789—21no—
30#19153789—21no—
31C4×Dic362C2211yescharacteristic
32C4×D724C2211yescharacteristic
33#19153778C2211yescharacteristic
34#19153778C2211yescharacteristic
35#19153778C2211yescharacteristic
36#19153778C2211yescharacteristic
37C4⋊C4×D181—21no—
38#19153747C2211yescharacteristic
39#19153745C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153738C2211yescharacteristic
42#19153738C2211yescharacteristic
43#19153737C2211yescharacteristic
44#19153736C2211yescharacteristic
45#19153736C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362—21no—
61C2×Dic362D411yescharacteristic
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76D1448—22no—
77D1448—22no—
78#15668434—22no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181D411yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428D411yescharacteristic
87#15668428D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93C4×Dic181C2311yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181—21no—
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C42×C181C2311yescharacteristic
106C22×D181—21no—
107C22×D181—21no—
108C22×D181—21no—
109Dic362—22no—
110Dic362—81no—
111D724—21no—
112D724—21no—
113D724—21no—
114D724—21no—
115D724—21no—
116D724—42no—
117D724—81no—
118D724#4112yescomplemented
119C22⋊D181—42no—
120C22⋊D181—42no—
121C22⋊D181—81no—
122C22⋊D181—81no—
123C2×Dic181—21no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—42no—
129C4×D181—42no—
130C4×D181—42no—
131C4×D181—81no—
132C4×D181—81no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136D4×C181—21no—
137D4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—42no—
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2411yescharacteristic
145C8×C181—21no—
146C8×C181—21no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181C22×D411yescharacteristic
151C2×D181—22no—
152C2×D181—41no—
153C2×D181—41no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C4×C181—21no—
161C4×C181—21no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181C2×#4111yescharacteristic
166C4×C1812−1+411yescharacteristic
167Dic181—21no—
168Dic181—21no—
169Dic181—21no—
170Dic181—41no—
171Dic181AGL(1,ℤ/8)12yes—
172C2×C181—81no—
173C2×C181#54811yescharacteristic
174C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C181#57611yescharacteristic
176D181—42no—
177D181—81no—
178D181—81no—
179C181#336611yescharacteristic, complemented, Sylow
180#3366—1811nomaximal, Sylow
181#554—1811no—
182#550—1811no—
183#490—1811no—
184#490—1811no—
185#486—1811no—
186#478—1811no—
187#478D18111yescharacteristic, complemented
188#476—1811no—
189#459—1811no—
190#459—1811no—
191#459—1811no—
192#446—1811no—
193#442—1811no—
194#442—1811no—
195C4×D8—1811no—
196C2×#41—3621no—
197C2×D8—1811no—
198C2×D8—1811no—
199C2×D8—1811no—
200C4⋊Q8—1811no—
201#127—1811no—
202#127—1811no—
203#127—1811no—
204#125—1811no—
205#125C2×D18111yescharacteristic
206C22⋊Q8—3621no—
207C22⋊Q8—3621no—
208C22⋊Q8—3621no—
209#121—3621no—
210#121—3621no—
211#121—3621no—
212C4×Q8—1811no—
213C4×D4—1811no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4—1811no—
218C4×D4C2×D18111yescharacteristic
219C2×C4⋊C4—3621no—
220#107C2×D18111yescharacteristic
221#106—1811no—
222#106C2×D18111yescharacteristic
223C4⋊C8—1811no—
224C4⋊C8—1811no—
225C4⋊C8C2×D18111yescharacteristic
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102C2×D18111yescharacteristic
235#102C2×D18111yescharacteristic
236#97—1811no—
237#97—1811no—
238C4×C8—1811no—
239#41—7244no—
240C2×Q8—3621no—
241C2×Q8—1811no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4—1811no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—3621no—
258D8—3622no—
259D8—3622no—
260D8—3622no—
261C2×C8—1811no—
262C2×C8—1811no—
263C2×C8C22×D18111yescharacteristic
264C2×C8C22×D18111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—1811no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4C22×D18111yescharacteristic
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C42—1811no—
284C42—1811no—
285C42C22×D18111yescharacteristic
286C23—21no—
287C23—3621no—
288C23—3621no—
289C23—3621no—
290Q8—3622no—
291Q8—14481no—
292D4—21no—
293D4—21no—
294D4—3621no—
295D4—3621no—
296D4—3621no—
297D4—3621no—
298D4—3621no—
299D4—14481no—
300D4—14481no—
301D4—14481no—
302D4—1812no—
303D4—7242no—
304D4—7242no—
305D4—7242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3621no—
311C2×C4—14481no—
312C2×C4—14481no—
313C2×C4—1811no—
314C2×C4—1811no—
315C2×C4—1811no—
316C2×C4—1811no—
317C2×C4—7242no—
318C2×C4—7242no—
319C2×C4—7242no—
320C2×C4D4×D18111yescharacteristic
321C2×C4D4×D18111yescharacteristic
322C2×C4C23×D18111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3621no—
326C8—3621no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—3622no—
331C22—7241no—
332C22—7241no—
333C22—7241no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22—7241no—
338C22—7241no—
339C22C2×D4×D18111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—3621no—
346C4—3621no—
347C4—3621no—
348C4—1812no—
349C4—7241no—
350C4#41×D18111yescharacteristic
351C4#1915386411yescharacteristic
352C2—81no—
353C2—14481no—
354C2—14481no—
355C2—7242no—
356C2#2604193911yescharacteristic
357C2AGL(1,ℤ/8)×D18111yescharacteristic
358C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
hypercenter#478D181
hypocenterC181#3366
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041985C2semidirect
2. #26041950C2semidirect
3. #26041645C2semidirect
4. #26041642C2semidirect
5. #26041624C2semidirect
6. #26041582C2semidirect
7. #26041568C2semidirect
8. #26041475C2semidirect
9. #26041473C2semidirect
10. #26041473C2semidirect
11. #26041408C2semidirect
12. #26041390C2semidirect
13. #26041389C2semidirect
14. #26041361C2semidirect
15. #478×C181C2semidirect
118. D724#41semidirect
179. C181#3366semidirect
187. #478D181semidirect

Maximal subgroups

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

subgroupindex
#260419852
#260419502
#260416452
#260416422
#260416242
#260415822
#260415682
#260414752
#260414732
#260414082
#260413902
#260413892
#260413612
#478×C1812
#3366181