Finite Group Databasebeta

← #14568146

Subgroups — #14568146

Order 2432.

436 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597336C211yesmaximal, characteristic
2C2×#10597335C211yesmaximal, characteristic
3#11926484C211yesmaximal, characteristic
4#11926478C211yesmaximal, characteristic
5#11926478C211yesmaximal, characteristic
6#11926441C211yesmaximal, characteristic
7#11926441C211yesmaximal, characteristic
8#11926441C211yesmaximal, characteristic
9#11926439C211yesmaximal, characteristic
10#11926431C211yesmaximal, characteristic
11#11926426C211yesmaximal, characteristic
12#11926413C211yesmaximal, characteristic
13#11926395C211yesmaximal, characteristic
14#11926395C211yesmaximal, characteristic
15C19×#400C211yesmaximal, characteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C4⋊Dic19C2211yescharacteristic
19C2×C4⋊Dic19C2211yescharacteristic
20C2×C4⋊Dic19C2211yescharacteristic
21C2×C4⋊Dic19C2211yescharacteristic
22C2×Dic19⋊C4C2211yescharacteristic
23C2×Dic19⋊C4C2211yescharacteristic
24C2×Dic19⋊C4C2211yescharacteristic
25C2×Dic19⋊C4C2211yescharacteristic
26C2×Dic19⋊C4C2211yescharacteristic
27C2×Dic19⋊C4C2211yescharacteristic
28C2×Dic19⋊C4C2211yescharacteristic
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2211yescharacteristic
32C2×Dic19⋊C4C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×C4×Dic19C2211yescharacteristic
35C2×C4×Dic19C2211yescharacteristic
36C2×C4×Dic19C2211yescharacteristic
37C2×C4×Dic19C2211yescharacteristic
38C2×C4×Dic19C2211yescharacteristic
39#10597336—24no—
40#10597335—24no—
41C19×#95C2211yescharacteristic
42C19×#95C2211yescharacteristic
43C19×#95C2211yescharacteristic
44C19×#95C2211yescharacteristic
45C19×#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C4⋊C4×C19—22no—
69C4⋊C4×C19—22no—
70C4⋊Dic19—22no—
71C4⋊Dic19—22no—
72C4⋊Dic19—22no—
73C4⋊Dic19—22no—
74Dic19⋊C4—22no—
75Dic19⋊C4—22no—
76Dic19⋊C4—22no—
77Dic19⋊C4—22no—
78Dic19⋊C4—22no—
79Dic19⋊C4—22no—
80Dic19⋊C4—22no—
81Dic19⋊C4—22no—
82Dic19⋊C4—22no—
83Dic19⋊C4—22no—
84Dic19⋊C4D414yes—
85Dic19⋊C4Q814yes—
86C4×Dic19—22no—
87C4×Dic19—22no—
88C4×Dic19—22no—
89C4×Dic19—22no—
90C4×Dic19—22no—
91C23×C19C2411yescharacteristic
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19C2×D412yes—
112C2×C4×C19C2×Q812yes—
113C2×Dic19—21no—
114C2×Dic19—21no—
115C2×Dic19—21no—
116C2×Dic19—21no—
117C2×Dic19—21no—
118C2×Dic19—21no—
119C2×Dic19—21no—
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19—21no—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—21no—
127C2×Dic19—21no—
128C2×Dic19—21no—
129C2×Dic19—21no—
130C2×Dic19C2×D412yes—
131C2×Dic19C2×D412yes—
132C2×Dic19C2×Q812yes—
133C2×Dic19C2×Q812yes—
134C2×Dic19#4112yes—
135C2×Dic19#4112yes—
136C2×Dic19#4112yes—
137#2506—191nomaximal, Sylow
138C22×C19C22×D411yescharacteristic
139C22×C19C22×Q811yescharacteristic
140C22×C19C2×#4111yescharacteristic
141C22×C19C2×#4111yescharacteristic
142C22×C19C2×#4111yescharacteristic
143C22×C192−1+411yescharacteristic
144C22×C192−1+411yescharacteristic
145C4×C19—22no—
146C4×C19—22no—
147C4×C19—41no—
148C4×C19—41no—
149C4×C19—41no—
150C4×C19—41no—
151C4×C19—41no—
152Dic19—22no—
153Dic19—22no—
154Dic19—22no—
155Dic19—22no—
156Dic19—41no—
157Dic19—41no—
158Dic19—41no—
159Dic19#12514yescomplemented
160C2×#125—191no—
161C2×#125—191no—
162#400—191no—
163#400D1911yescharacteristic
164#398—191no—
165#398—191no—
166#389—191no—
167#389—191no—
168#389—191no—
169#389—191no—
170#387—191no—
171#387—191no—
172#384—191no—
173C4×C4⋊C4—191no—
174C4×C4⋊C4—191no—
175C2×C19C2×#12511yescharacteristic
176C2×C19#53211yescharacteristic
177C2×C19#54111yescharacteristic
178C2×C19#54711yescharacteristic
179C2×C19D4×Q811yescharacteristic
180C2×C19#55211yescharacteristic
181C2×C19#55711yescharacteristic
182#125—384no—
183#125—384no—
184C2×C4⋊C4—191no—
185C2×C4⋊C4—191no—
186C2×C4⋊C4—191no—
187C2×C4⋊C4—191no—
188C2×C4⋊C4—191no—
189C2×C4⋊C4—191no—
190C2×C4⋊C4—191no—
191C2×C4⋊C4—191no—
192C2×C4⋊C4—191no—
193C2×C4⋊C4—191no—
194C2×C4⋊C4—191no—
195C2×C4⋊C4—191no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4—191no—
198C2×C4⋊C4—191no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4C2×D1911yescharacteristic
201C2×C4⋊C4C2×D1911yescharacteristic
202C2×C42—191no—
203C2×C42—191no—
204C2×C42—191no—
205C2×C42—191no—
206C2×C42—191no—
207#95—191no—
208#95—191no—
209#95—191no—
210#95—191no—
211#95—191no—
212#95—191no—
213#95—191no—
214#95C2×D1911yescharacteristic
215#95C2×D1911yescharacteristic
216#95C2×D1911yescharacteristic
217#95C2×D1911yescharacteristic
218#95C2×D1911yescharacteristic
219C19#250611yescharacteristic, complemented, Sylow
220C22×C4—191no—
221C22×C4—191no—
222C22×C4—191no—
223C22×C4—191no—
224C22×C4—191no—
225C22×C4—191no—
226C22×C4—191no—
227C22×C4—191no—
228C22×C4C22×D1911yescharacteristic
229C22×C4C22×D1911yescharacteristic
230C22×C4C22×D1911yescharacteristic
231C22×C4C22×D1911yescharacteristic
232C22×C4C22×D1911yescharacteristic
233C22×C4C22×D1911yescharacteristic
234C22×C4C22×D1911yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—194no—
238C4⋊C4—194no—
239C4⋊C4—382no—
240C4⋊C4—382no—
241C4⋊C4—382no—
242C4⋊C4—382no—
243C4⋊C4—382no—
244C4⋊C4—382no—
245C4⋊C4—382no—
246C4⋊C4—382no—
247C4⋊C4—382no—
248C4⋊C4—382no—
249C4⋊C4—382no—
250C4⋊C4—382no—
251C4⋊C4—382no—
252C4⋊C4—382no—
253C42—382no—
254C42—382no—
255C42—382no—
256C42—382no—
257C42—382no—
258C23C23×D1911yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—192no—
279C2×C4—192no—
280C2×C4—192no—
281C2×C4—192no—
282C2×C4—192no—
283C2×C4—192no—
284C2×C4—192no—
285C2×C4—381no—
286C2×C4—381no—
287C2×C4—381no—
288C2×C4—381no—
289C2×C4—381no—
290C2×C4—381no—
291C2×C4—381no—
292C2×C4—381no—
293C2×C4—381no—
294C2×C4—381no—
295C2×C4—381no—
296C2×C4—381no—
297C2×C4—381no—
298C2×C4—381no—
299C2×C4—381no—
300C2×C4—381no—
301C2×C4—381no—
302C2×C4D4×D1912yes—
303C2×C4Q8×D1912yes—
304C22C2×D4×D1911yescharacteristic
305C22C2×Q8×D1911yescharacteristic
306C22#41×D1911yescharacteristic
307C22#41×D1911yescharacteristic
308C22#41×D1911yescharacteristic
309C22#1059743611yescharacteristic
310C22#1059743611yescharacteristic
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—194no—
319C4—382no—
320C4—382no—
321C4—382no—
322C4—382no—
323C4—761no—
324C4—761no—
325C4—761no—
326C2#125×D1911yescharacteristic
327C2#1192709311yescharacteristic
328C2#1192715111yescharacteristic
329C2#1192719211yescharacteristic
330C2#1192720711yescharacteristic
331C2#1192723011yescharacteristic
332C2#1192727111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#400C2
hypercenter#400D19
hypocenterC19#2506
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
159. Dic19#125semidirect
219. C19#2506semidirect

Maximal subgroups

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

subgroupindex
C2×#105973362
C2×#105973352
#119264842
#119264782
#119264412
#119264392
#119264312
#119264262
#119264132
#119263952
C19×#4002
#250619