Finite Group Databasebeta

← #14566378

Subgroups — #14566378

Order 2432.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597390C211yesmaximal, characteristic
2#11926451C211yesmaximal, characteristic
3#11926448C211yesmaximal, characteristic
4#11926448C211yesmaximal, characteristic
5#11926441C211yesmaximal, characteristic
6#11926439C211yesmaximal, characteristic
7#11926431C211yesmaximal, characteristic
8#11926428C211yesmaximal, characteristic
9#11926426C211yesmaximal, characteristic
10#11926425C211yesmaximal, characteristic
11#11926408C211yesmaximal, characteristic
12C4×Dic19⋊C4C211yesmaximal, characteristic
13#11926395C211yesmaximal, characteristic
14#11926389C211yesmaximal, characteristic
15C19×#391C211yesmaximal, characteristic
16C22×Q8×C19C2211yescharacteristic
17C22×Dic38C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C42×C19C2211yescharacteristic
20#10597390C418yescomplemented
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×C4×Dic19C2211yescharacteristic
31C2×C4×Dic19C2211yescharacteristic
32C2×C4×Dic19C2211yescharacteristic
33C2×C4×Dic19C2211yescharacteristic
34C2×C4×Dic19C2211yescharacteristic
35C2×C4×Dic19C2211yescharacteristic
36C19×#95C2211yescharacteristic
37C19×#95C2211yescharacteristic
38C19×#95C2211yescharacteristic
39C19×#95C2211yescharacteristic
40C19⋊#95C2211yescharacteristic
41C19⋊#95C2211yescharacteristic
42C19⋊#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C2×Q8×C19—41no—
53C2×Q8×C19—41no—
54C2×Q8×C19C2×C414yes—
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C22×Dic19C2311yescharacteristic
70C2×Dic38—41no—
71C2×Dic38—41no—
72C2×Dic38C2×C414yes—
73C4⋊C4×C19—41no—
74C42×C19—41no—
75C4⋊Dic19—41no—
76Dic19⋊C4—22no—
77Dic19⋊C4—22no—
78Dic19⋊C4—41no—
79Dic19⋊C4—41no—
80Dic19⋊C4C2×C414yes—
81Dic19⋊C4C2×C414yes—
82Dic19⋊C4C2×C414yes—
83Dic19⋊C4C2×C414yes—
84C4×Dic19—22no—
85C4×Dic19—41no—
86C4×Dic19—41no—
87C4×Dic19—41no—
88C4×Dic19C2×C414yes—
89C4×Dic19Q814yescomplemented
90C23×C19C2411yescharacteristic
91Q8×C19—44no—
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×C19C22×C412yes—
110C2×C4×C19C22×C412yes—
111C2×C4×C19C22×C412yes—
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×Dic19C22×C412yes—
131C2×Dic19C22×C412yes—
132C2×Dic19C22×C412yes—
133C2×Dic19C22×C412yes—
134C2×Dic19C2×Q812yes—
135C2×Dic19C2×Q812yes—
136C2×Dic19#4112yes—
137Dic38—44no—
138#2331—191nomaximal, Sylow
139C22×C19C23×C411yescharacteristic
140C22×C19C22×Q811yescharacteristic
141C22×C19C2×#4111yescharacteristic
142C22×C19H(5,𝔽2)11yescharacteristic
143C22×C19H(5,𝔽2)11yescharacteristic
144C22×C192−1+411yescharacteristic
145C22×C192−1+411yescharacteristic
146C4×C19—22no—
147C4×C19—22no—
148C4×C19—22no—
149C4×C19—22no—
150C4×C19—41no—
151C4×C19—41no—
152C4×C19—41no—
153Dic19—22no—
154Dic19—22no—
155Dic19—22no—
156Dic19—22no—
157Dic19—41no—
158Dic19—41no—
159Dic19—41no—
160Dic19C4×Q814yes—
161C2×C4⋊Q8—191no—
162#391—191no—
163#391—191no—
164#391—191no—
165#391D1911yescharacteristic
166#389—191no—
167#389—191no—
168#387—191no—
169#387—191no—
170#387—191no—
171#387—191no—
172#382—191no—
173C4×C4⋊C4—191no—
174C4×C4⋊C4—191no—
175#376—191no—
176C2×C19C2×C4×Q811yescharacteristic
177C2×C19#51811yescharacteristic
178C2×C19#51911yescharacteristic
179C2×C19#54211yescharacteristic
180C2×C19#54211yescharacteristic
181C2×C19#54411yescharacteristic
182C2×C19#54411yescharacteristic
183C22×Q8—191no—
184C22×Q8C2×D1911yescharacteristic
185C4⋊Q8—198no—
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⋊C4C2×D1911yescharacteristic
196C2×C42—191no—
197C2×C42—191no—
198C2×C42—191no—
199C2×C42—191no—
200C2×C42—191no—
201C2×C42—191no—
202C2×C42C2×D1911yescharacteristic
203#95—191no—
204#95—191no—
205#95—191no—
206#95—191no—
207#95—191no—
208#95—191no—
209#95—191no—
210#95—191no—
211#95—191no—
212#95—191no—
213#95—191no—
214#95—191no—
215#95C2×D1911yescharacteristic
216#95C2×D1911yescharacteristic
217#95C2×D1911yescharacteristic
218#95C2×D1911yescharacteristic
219C19#233111yescharacteristic, complemented, Sylow
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—194no—
223C2×Q8—761no—
224C2×Q8—761no—
225C2×Q8C4×D1914yes—
226C22×C4—191no—
227C22×C4—191no—
228C22×C4—191no—
229C22×C4—191no—
230C22×C4—191no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—191no—
234C22×C4C22×D1911yescharacteristic
235C22×C4C22×D1911yescharacteristic
236C22×C4C22×D1911yescharacteristic
237C22×C4C22×D1911yescharacteristic
238C22×C4C22×D1911yescharacteristic
239C22×C4C22×D1911yescharacteristic
240C22×C4C22×D1911yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—194no—
243C4⋊C4—194no—
244C4⋊C4—194no—
245C4⋊C4—194no—
246C4⋊C4—382no—
247C4⋊C4—382no—
248C4⋊C4—761no—
249C4⋊C4—761no—
250C4⋊C4—761no—
251C42—41no—
252C42—194no—
253C42—194no—
254C42—382no—
255C42—761no—
256C42—761no—
257C42—761no—
258C23C23×D1911yescharacteristic
259Q8—44no—
260Q8—764no—
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×C4C2×C4×D1912yes—
303C2×C4C2×C4×D1912yes—
304C2×C4C2×C4×D1912yes—
305C2×C4Q8×D1912yes—
306C22C22×C4×D1911yescharacteristic
307C22#1059743011yescharacteristic
308C22#1059743011yescharacteristic
309C22C2×Q8×D1911yescharacteristic
310C22#1059743311yescharacteristic
311C22#41×D1911yescharacteristic
312C22#1059743611yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—194no—
321C4—382no—
322C4—382no—
323C4—382no—
324C4—382no—
325C4—761no—
326C4—761no—
327C4—761no—
328C2C4×Q8×D1911yescharacteristic
329C2#1192701711yescharacteristic
330C2#1192702011yescharacteristic
331C2#1192715811yescharacteristic
332C2#1192716411yescharacteristic
333C2#1192717111yescharacteristic
334C2#1192717311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#391C2
socle, prime radical, cosocleC23×C19C24
hypercenter#391D19
hypocenterC19#2331
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
20. #10597390C4semidirect
89. C4×Dic19Q8semidirect
219. C19#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
#119264512
#119264482
#119264412
#119264392
#119264312
#119264282
#119264262
#119264252
#119264082
C4×Dic19⋊C42
#119263952
#119263892
C19×#3912
#233119