Finite Group Databasebeta

← #37546223

Subgroups — #37546223

Order 23168.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041994C211yesmaximal, characteristic, complemented
2#26041975C211yesmaximal, characteristic, complemented
3#26041688C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041604C211yesmaximal, characteristic, complemented
6#26041604C211yesmaximal, characteristic, complemented
7#26041593C211yesmaximal, characteristic, complemented
8#26041580C211yesmaximal, characteristic, complemented
9#26041560C211yesmaximal, characteristic, complemented
10#26041532C211yesmaximal, characteristic, complemented
11#26041515C211yesmaximal, characteristic, complemented
12#26041392C211yesmaximal, characteristic, complemented
13#26041321C211yesmaximal, characteristic, complemented
14#26041317C211yesmaximal, characteristic, complemented
15#435×C181C211yesmaximal, characteristic, complemented
16C2×D1448C2211yescharacteristic
17#19153816C2211yescharacteristic
18#19153811—21no—
19#19153808C2211yescharacteristic
20#19153802—21no—
21#19153802—21no—
22#19153798—21no—
23#19153790C2211yescharacteristic
24#19153790C2211yescharacteristic
25#19153790C2211yescharacteristic
26#19153790C2211yescharacteristic
27#19153788—21no—
28#19153787—21no—
29C4×D724C2211yescharacteristic
30C4×D724C2211yescharacteristic
31#19153776—21no—
32#19153775C2211yescharacteristic
33#19153775C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153774—21no—
36C2×C4⋊Dic181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153750C2211yescharacteristic
41#19153750C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153748C2211yescharacteristic
44#19153748C2211yescharacteristic
45#19153748C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153738C2211yescharacteristic
52C2×M16×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55C4⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57C22⋊C8×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×D724C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C22×Dic181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69D1448—22no—
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80C22⋊Dic181—21no—
81C22⋊Dic181—21no—
82C22⋊Dic181—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C2×D4×C181D411yescharacteristic
93C22×C4×C181C2311yescharacteristic
94C22×C4×C181C2311yescharacteristic
95M16×C181—22no—
96C2×C8×C181—22no—
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181D411yescharacteristic
102C22⋊C4×C181D411yescharacteristic
103C22⋊C4×C181D411yescharacteristic
104C42×C181C2311yescharacteristic
105C22×D181—21no—
106C22×D181—21no—
107Dic362—81no—
108D724—21no—
109D724—21no—
110D724—21no—
111D724—21no—
112C22⋊D181—42no—
113C22⋊D181—81no—
114C22⋊D181—81no—
115C22⋊D181—81no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—81no—
123C4×D181—42no—
124C4×D181—81no—
125C23×C181C2×D411yescharacteristic
126C23×C181C2×D411yescharacteristic
127D4×C181—41no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181C2×D411yescharacteristic
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2×D411yescharacteristic
136C2×C4×C181C2411yescharacteristic
137C8×C181—21no—
138C8×C181—21no—
139C8×C181—21no—
140C8×C181#4112yes—
141C22×C181—21no—
142C22×C181—21no—
143C22×C181—21no—
144C22×C181—21no—
145C22×C181—21no—
146C22×C181—21no—
147C22×C181C22×D411yescharacteristic
148C2×D181—41no—
149C2×D181—41no—
150C2×D181—41no—
151C2×D181—41no—
152C2×D181—41no—
153C2×D181—41no—
154C4×C181—21no—
155C4×C181—21no—
156C4×C181—21no—
157C4×C181—21no—
158C4×C181C2×#4111yescharacteristic
159C4×C1812−1+411yescharacteristic
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—41no—
167C2×C181—41no—
168C2×C181#54711yescharacteristic
169C2×C181#57511yescharacteristic
170C2×C181#57611yescharacteristic
171D181—81no—
172D181—81no—
173C181#334711yescharacteristic, complemented, Sylow
174#3347—1811nomaximal, Sylow
175#555—1811no—
176#553—1811no—
177#501—1811no—
178#482—1811no—
179#482—1811no—
180#482—1811no—
181#480—1811no—
182#478—1811no—
183#474—1811no—
184#469—1811no—
185#466—1811no—
186#442—1811no—
187#435D18111yescharacteristic, complemented
188#428—1811no—
189#427—1811no—
190C2×D8—1811no—
191C2×M16C2×D18111yescharacteristic
192C22×C8C2×D18111yescharacteristic
193C4⋊Q8—1811no—
194#126—3621no—
195#125—1811no—
196#124—3621no—
197#124—3621no—
198#123—3621no—
199#121—3621no—
200#121—3621no—
201#121—1811no—
202#121—1811no—
203#121—1811no—
204#121—1811no—
205C4×D4—3621no—
206C4×D4—1811no—
207C4×D4—1811no—
208C4×D4C2×D18111yescharacteristic
209#117—3621no—
210#117—1811no—
211#117—1811no—
212#117—1811no—
213C2×C4⋊C4—1811no—
214#107—1811no—
215#107—1811no—
216#107—1811no—
217#107—1811no—
218#107—1811no—
219#106—1811no—
220#106—1811no—
221#106—1811no—
222#106—1811no—
223C4⋊C8C2×D18111yescharacteristic
224#102—1811no—
225#102—1811no—
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230C22⋊C8C2×D18111yescharacteristic
231C22⋊C8C2×D18111yescharacteristic
232#97C2×D18111yescharacteristic
233C2×Q8—3621no—
234C2×D4—3621no—
235C2×D4—3621no—
236C2×D4—3621no—
237C2×D4—3621no—
238C2×D4—1811no—
239C2×D4—1811no—
240C2×D4D72411yescharacteristic
241C22×C4—3621no—
242C22×C4—3621no—
243C22×C4—3621no—
244C22×C4C22×D18111yescharacteristic
245C22×C4C22×D18111yescharacteristic
246D8—3622no—
247M16—22no—
248C2×C8—22no—
249C2×C8C22×D18111yescharacteristic
250C2×C8C22×D18111yescharacteristic
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—1811no—
258C4⋊C4—1811no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4—1811no—
262C4⋊C4—1811no—
263C4⋊C4D72411yescharacteristic
264C22⋊C4—3621no—
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4D72411yescharacteristic
274C22⋊C4D72411yescharacteristic
275C42—3621no—
276C42—3621no—
277C42—3621no—
278C42C22×D18111yescharacteristic
279C23—3621no—
280C23—3621no—
281C23C2×D72411yescharacteristic
282C23C2×D72411yescharacteristic
283Q8—14481no—
284D4—41no—
285D4—3621no—
286D4—3621no—
287D4—3621no—
288D4—3621no—
289D4—14481no—
290D4—14481no—
291D4—14481no—
292D4—7242no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—14481no—
304C2×C4—14481no—
305C2×C4—7242no—
306C2×C4C2×D72411yescharacteristic
307C2×C4C2×D72411yescharacteristic
308C2×C4C2×D72411yescharacteristic
309C2×C4C2×D72411yescharacteristic
310C2×C4C23×D18111yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#1566844812yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—7241no—
322C22—7241no—
323C22—7241no—
324C22—7241no—
325C22—7241no—
326C22—7241no—
327C22C22×D72411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—7241no—
333C4—7241no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4—7241no—
338C4C2×#1566844811yescharacteristic
339C4#1915386311yescharacteristic
340C2—41no—
341C2—41no—
342C2—14481no—
343C2—14481no—
344C2#2604193311yescharacteristic
345C2#2604207911yescharacteristic
346C2#2604208411yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#435×C181C2
socleC22×C181C22×D4
hypercenter#435D181
hypocenterC181#3347
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #26041994C2semidirect
2. #26041975C2semidirect
3. #26041688C2semidirect
4. #26041604C2semidirect
5. #26041604C2semidirect
6. #26041604C2semidirect
7. #26041593C2semidirect
8. #26041580C2semidirect
9. #26041560C2semidirect
10. #26041532C2semidirect
11. #26041515C2semidirect
12. #26041392C2semidirect
13. #26041321C2semidirect
14. #26041317C2semidirect
15. #435×C181C2semidirect
173. C181#3347semidirect
187. #435D181semidirect

Maximal subgroups

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

subgroupindex
#260419942
#260419752
#260416882
#260416042
#260415932
#260415802
#260415602
#260415322
#260415152
#260413922
#260413212
#260413172
#435×C1812
#3347181