Finite Group Databasebeta

← #14577460

Subgroups — #14577460

Order 2432.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927273C211yesmaximal, characteristic, complemented
2#11927270C211yesmaximal, characteristic, complemented
3#11927270C211yesmaximal, characteristic, complemented
4#11927255C213yesmaximal, complemented
5#11927254C213yesmaximal, complemented
6#11927250C213yesmaximal, complemented
7#11927250C213yesmaximal, complemented
8#11927174C213yesmaximal, complemented
9#11927171C213yesmaximal, complemented
10#11927098C213yesmaximal, complemented
11#125×D19C213yesmaximal, complemented
12#11927026C211yesmaximal, characteristic
13#11927026C211yesmaximal, characteristic
14C4×#64545C211yesmaximal, characteristic
15C19×#557C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C19×C4⋊Q8C2213yes—
18C19×#125C2213yes—
19C19×#125C2213yes—
20C4×Q8×C19C2213yes—
21C4×Q8×C19C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic
23C4×Q8×C19C2211yescharacteristic
24#10597392C2213yes—
25#10597392C2216yes—
26Q8×Dic19C2211yescharacteristic
27Q8×Dic19C2211yescharacteristic
28Q8×Dic19C2211yescharacteristic
29#10597390C2213yes—
30#10597343C2213yes—
31#10597343C2216yes—
32#10597342C2213yes—
33#10597342C2213yes—
34#10597342C2216yes—
35#10597342C2216yes—
36#10597339C2213yes—
37#10597339C2213yes—
38#10597339C2213yes—
39#10597338C2213yes—
40C4⋊C4×D19C2213yes—
41C4⋊C4×D19C2213yes—
42C4⋊C4×D19C2216yes—
43C4⋊C4×D19C2216yes—
44#10597336C2213yes—
45#10597336C2213yes—
46#10597336C2213yes—
47#10597336C2213yes—
48#10597335C2213yes—
49#10597335C2216yes—
50#10597335C2211yescharacteristic
51#10597334C2213yes—
52#10597334C2213yes—
53#10597334C2213yes—
54C4×D76C2213yes—
55C4×D76C2213yes—
56C4×D76C2213yes—
57#10597318C2213yes—
58#10597318C2213yes—
59C42×D19C2213yes—
60#10597316C2213yes—
61#10597316C2213yes—
62#10597315C2213yes—
63C4×Dic38C2213yes—
64C4×Dic38C2213yes—
65C4×Dic38C2213yes—
66C2×Q8×C19C2313yes—
67C2×Q8×C19C2311yescharacteristic
68#64545Q818yescomplemented
69C2×D76C2313yes—
70C2×C4×D19C2313yes—
71C2×C4×D19C2316yes—
72C2×C4×D19C2313yes—
73C2×C4×D19C2316yes—
74C2×C4×D19C2313yes—
75C2×Dic38C2313yes—
76C2×Dic38C2313yes—
77C2×Dic38C2313yes—
78C4⋊C4×C19C2311yescharacteristic
79C4⋊C4×C19C2313yes—
80C4⋊C4×C19C2313yes—
81C4⋊C4×C19C2313yes—
82C4⋊C4×C19C2313yes—
83C4⋊C4×C19C2313yes—
84C4⋊C4×C19C2316yes—
85C42×C19C2313yes—
86C42×C19C2313yes—
87C42×C19C2313yes—
88(C2×D19)⋊C4C2313yes—
89(C2×D19)⋊C4C2313yes—
90(C2×D19)⋊C4C2316yes—
91(C2×D19)⋊C4C2313yes—
92(C2×D19)⋊C4C2313yes—
93C4⋊Dic19C2313yes—
94C4⋊Dic19C2313yes—
95C4⋊Dic19C2313yes—
96C4⋊Dic19C2313yes—
97C4⋊Dic19C2316yes—
98C4⋊Dic19C2311yescharacteristic
99C4⋊Dic19C2313yes—
100Dic19⋊C4C2311yescharacteristic
101Dic19⋊C4C2313yes—
102Dic19⋊C4C2313yes—
103Dic19⋊C4C2313yes—
104Dic19⋊C4C2311yescharacteristic
105Dic19⋊C4C2313yes—
106Dic19⋊C4C2316yes—
107Dic19⋊C4C2311yescharacteristic
108Dic19⋊C4C2313yes—
109Dic19⋊C4C2316yes—
110Dic19⋊C4C2311yescharacteristic
111Dic19⋊C4C2313yes—
112C4×Dic19C2313yes—
113C4×Dic19C2313yes—
114C4×Dic19C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2311yescharacteristic
117C22×D19C2413yes—
118Q8×C19—43no—
119Q8×C19C2×Q814yes—
120C2×C4×C19C2411yescharacteristic
121C2×C4×C19C2413yes—
122C2×C4×C19C2411yescharacteristic
123C2×C4×C19C2413yes—
124C2×C4×C19C2413yes—
125C2×C4×C19C2411yescharacteristic
126C2×C4×C19C2413yes—
127C2×Dic19C2411yescharacteristic
128C2×Dic19C2411yescharacteristic
129C2×Dic19C2411yescharacteristic
130C2×Dic19C2413yes—
131C2×Dic19C2413yes—
132C2×Dic19C2413yes—
133C2×Dic19C2411yescharacteristic
134D76C2×Q8112yes—
135C4×D19—43no—
136C4×D19—46no—
137C4×D19—46no—
138C4×D19—43no—
139C4×D19C2×Q8112yes—
140Dic38—43no—
141Dic38—43no—
142Dic38—43no—
143#3504—191nomaximal, Sylow
144C22×C19C2511yescharacteristic
145C2×D19—23no—
146C2×D19—23no—
147C2×D19C22×Q816yes—
148C4×C19—21no—
149C4×C19—23no—
150C4×C19—23no—
151C4×C19—21no—
152C4×C19—23no—
153C4×C19—21no—
154C4×C19C22×Q816yes—
155Dic19—21no—
156Dic19—21no—
157Dic19—23no—
158Dic19—23no—
159Dic19—23no—
160Dic19—21no—
161Dic19C22×Q812yes—
162#557—191no—
163#557—191no—
164#557—191no—
165#557D1911yescharacteristic, complemented
166#554—193no—
167#554—193no—
168#554—193no—
169#554—193no—
170#544—193no—
171#544—193no—
172#533—193no—
173C2×#125—193no—
174#520—191no—
175#520—191no—
176C4×#41—191no—
177C2×C19C23×Q811yescharacteristic
178C2×C19#58511yescharacteristic
179C2×C19#58511yescharacteristic
180D19—26no—
181C2×#41—191no—
182C4⋊Q8—193no—
183C4⋊Q8—193no—
184C4⋊Q8—193no—
185C4⋊Q8—193no—
186C4⋊Q8—193no—
187C4⋊Q8C2×D1913yes—
188#125—193no—
189#125—196no—
190#125—193no—
191#125—193no—
192#125—191no—
193#125—193no—
194#125—193no—
195#125—193no—
196#125—193no—
197#125C2×D1913yes—
198#125C2×D1913yes—
199C22⋊Q8—193no—
200C22⋊Q8—196no—
201C22⋊Q8—193no—
202C22⋊Q8—193no—
203C22⋊Q8—193no—
204C22⋊Q8—196no—
205C22⋊Q8—196no—
206C22⋊Q8—196no—
207C4×Q8—191no—
208C4×Q8—191no—
209C4×Q8—191no—
210C4×Q8—193no—
211C4×Q8—193no—
212C4×Q8—193no—
213C4×Q8C2×D1911yescharacteristic
214C4×Q8C2×D1911yescharacteristic
215C4×Q8C2×D1911yescharacteristic
216C4×Q8C2×D1913yes—
217C4×D4—193no—
218C4×D4—193no—
219C4×D4—193no—
220C4×D4—193no—
221C4×D4—193no—
222C4×D4—193no—
223#117—193no—
224#117—193no—
225#117—193no—
226C2×C4⋊C4—193no—
227C2×C4⋊C4—193no—
228C2×C4⋊C4—196no—
229C2×C4⋊C4—196no—
230C2×C42—193no—
231C19#350411yescharacteristic, complemented, Sylow
232#41—198no—
233C2×Q8—193no—
234C2×Q8—193no—
235C2×Q8—193no—
236C2×Q8C22×D1913yes—
237C2×Q8C22×D1911yescharacteristic
238C2×D4—193no—
239C22×C4—193no—
240C22×C4—193no—
241C22×C4—193no—
242C22×C4—196no—
243C22×C4—196no—
244C4⋊C4—193no—
245C4⋊C4—193no—
246C4⋊C4—193no—
247C4⋊C4—193no—
248C4⋊C4—196no—
249C4⋊C4—196no—
250C4⋊C4—191no—
251C4⋊C4—191no—
252C4⋊C4—191no—
253C4⋊C4—191no—
254C4⋊C4—193no—
255C4⋊C4—193no—
256C4⋊C4—193no—
257C4⋊C4—193no—
258C4⋊C4—193no—
259C4⋊C4—196no—
260C4⋊C4—193no—
261C4⋊C4—191no—
262C4⋊C4—193no—
263C4⋊C4C22×D1913yes—
264C4⋊C4C22×D1913yes—
265C4⋊C4C22×D1913yes—
266C4⋊C4C22×D1916yes—
267C4⋊C4C22×D1913yes—
268C4⋊C4C22×D1911yescharacteristic
269C4⋊C4C22×D1913yes—
270C22⋊C4—193no—
271C22⋊C4—193no—
272C22⋊C4—196no—
273C22⋊C4—193no—
274C22⋊C4—193no—
275C42—191no—
276C42—193no—
277C42—193no—
278C42—193no—
279C42—193no—
280C42C22×D1913yes—
281C42C22×D1913yes—
282C42C22×D1913yes—
283C23—193no—
284Q8—43no—
285Q8—763no—
286Q8—763no—
287Q8—763no—
288Q8Q8×D1914yes—
289D4—1912no—
290C2×C4—191no—
291C2×C4—1912no—
292C2×C4—191no—
293C2×C4—191no—
294C2×C4—191no—
295C2×C4—193no—
296C2×C4—193no—
297C2×C4—193no—
298C2×C4—766no—
299C2×C4—763no—
300C2×C4—763no—
301C2×C4—766no—
302C2×C4C23×D1911yescharacteristic
303C2×C4C23×D1913yes—
304C2×C4C23×D1911yescharacteristic
305C2×C4C23×D1911yescharacteristic
306C2×C4C23×D1913yes—
307C2×C4C23×D1913yes—
308C2×C4C23×D1913yes—
309C22—196no—
310C22—383no—
311C22—383no—
312C22C24×D1911yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—192no—
320C4—381no—
321C4—383no—
322C4—381no—
323C4—383no—
324C4—383no—
325C4—381no—
326C4C2×Q8×D1916yes—
327C2—386no—
328C2C22×Q8×D1911yescharacteristic
329C2#1192738011yescharacteristic
330C2#1192738111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#557C2
prime radicalC2×#64545C22
hypercenter#557D19
hypocenterC19#3504
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #11927273C2semidirect
2. #11927270C2semidirect
3. #11927270C2semidirect
4. #11927255C2semidirect
5. #11927254C2semidirect
6. #11927250C2semidirect
7. #11927250C2semidirect
8. #11927174C2semidirect
9. #11927171C2semidirect
10. #11927098C2semidirect
11. #125×D19C2semidirect
15. C19×#557C2semidirect
68. #64545Q8semidirect
165. #557D19semidirect
231. C19#3504semidirect

Maximal subgroups

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

subgroupindex
#119272732
#119272702
#119272552
#119272542
#119272502
#119271742
#119271712
#119270982
#125×D192
#119270262
C4×#645452
C19×#5572
#350419