Finite Group Databasebeta

← #14569021

Subgroups — #14569021

Order 2432.

468 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597335C211yesmaximal, characteristic
2C2×#10597333C211yesmaximal, characteristic
3#11926478C211yesmaximal, characteristic
4#11926477C211yesmaximal, characteristic
5#11926465C211yesmaximal, characteristic
6#11926464C211yesmaximal, characteristic
7#11926442C211yesmaximal, characteristic
8#11926441C211yesmaximal, characteristic
9#11926441C211yesmaximal, characteristic
10#11926439C211yesmaximal, characteristic
11#11926439C211yesmaximal, characteristic
12#11926439C211yesmaximal, characteristic
13#11926439C211yesmaximal, characteristic
14C4×Dic19⋊C4C211yesmaximal, characteristic
15C19×#389C211yesmaximal, characteristic
16C22×Dic38C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C42×C19C2211yescharacteristic
22C2×C4⋊Dic19C2211yescharacteristic
23C2×C4⋊Dic19C2211yescharacteristic
24C2×C4⋊Dic19C2211yescharacteristic
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×Dic19⋊C4C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×C4×Dic19C2211yescharacteristic
38C2×C4×Dic19C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41#10597335—24no—
42#10597333—24no—
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
68C2×Dic38—22no—
69C2×Dic38—22no—
70C2×Dic38—22no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—41no—
75C42×C19—41no—
76C4⋊Dic19—22no—
77C4⋊Dic19—22no—
78C4⋊Dic19—41no—
79Dic19⋊C4—22no—
80Dic19⋊C4—22no—
81Dic19⋊C4—22no—
82Dic19⋊C4—22no—
83Dic19⋊C4—22no—
84Dic19⋊C4—22no—
85Dic19⋊C4—22no—
86Dic19⋊C4—22no—
87Dic19⋊C4—41no—
88Dic19⋊C4—41no—
89Dic19⋊C4Q814yescomplemented
90Dic19⋊C4Q814yescomplemented
91C4×Dic19—22no—
92C4×Dic19—22no—
93C4×Dic19—41no—
94C4×Dic19D414yes—
95C23×C19C2411yescharacteristic
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×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19C2×D412yes—
114C2×C4×C19C2×Q812yes—
115C2×C4×C19C2×Q812yes—
116C2×C4×C19#4112yes—
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×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19C2×D412yes—
135C2×Dic19C2×D412yes—
136C2×Dic19C2×Q812yes—
137C2×Dic19C2×Q812yes—
138C2×Dic19C2×Q812yes—
139C2×Dic19C2×Q812yes—
140C2×Dic19#4112yes—
141Dic38—28no—
142#2584—191nomaximal, Sylow
143C22×C19C22×D411yescharacteristic
144C22×C19C22×Q811yescharacteristic
145C22×C19C22×Q811yescharacteristic
146C22×C19C2×#4111yescharacteristic
147C22×C19C2×#4111yescharacteristic
148C22×C19H(5,𝔽2)11yescharacteristic
149C22×C192−1+411yescharacteristic
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—41no—
157Dic19—22no—
158Dic19—22no—
159Dic19—22no—
160Dic19—22no—
161Dic19—41no—
162Dic19—41no—
163Dic19—41no—
164Dic19C4⋊Q814yes—
165C2×#125—191no—
166C2×C4×Q8—191no—
167#398—191no—
168#398—191no—
169#395—191no—
170#395—191no—
171#389—191no—
172#389—191no—
173#389—191no—
174#389—191no—
175#389—191no—
176#389—191no—
177#389—191no—
178#389D1911yescharacteristic
179C4×C4⋊C4—191no—
180C2×C19#52511yescharacteristic
181C2×C19C2×C4⋊Q811yescharacteristic
182C2×C19#53711yescharacteristic
183C2×C19#55411yescharacteristic
184C2×C19#55411yescharacteristic
185C2×C19#55711yescharacteristic
186C2×C19#55711yescharacteristic
187C22×Q8—191no—
188#125—384no—
189C4×Q8—384no—
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⋊C4—191no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4C2×D1911yescharacteristic
206C2×C4⋊C4C2×D1911yescharacteristic
207C2×C4⋊C4C2×D1911yescharacteristic
208C2×C4⋊C4C2×D1911yescharacteristic
209C2×C42—191no—
210C2×C42—191no—
211C2×C42—191no—
212C2×C42—191no—
213C2×C42C2×D1911yescharacteristic
214#95—191no—
215#95—191no—
216#95—191no—
217#95—191no—
218#95—191no—
219#95—191no—
220#95—191no—
221#95—191no—
222#95C2×D1911yescharacteristic
223#95C2×D1911yescharacteristic
224C19#258411yescharacteristic, complemented, Sylow
225C2×Q8—382no—
226C2×Q8—382no—
227C2×Q8—382no—
228C22×C4—191no—
229C22×C4—191no—
230C22×C4—191no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—191no—
234C22×C4—191no—
235C22×C4—191no—
236C22×C4C22×D1911yescharacteristic
237C22×C4C22×D1911yescharacteristic
238C22×C4C22×D1911yescharacteristic
239C22×C4C22×D1911yescharacteristic
240C22×C4C22×D1911yescharacteristic
241C22×C4C22×D1911yescharacteristic
242C22×C4C22×D1911yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—194no—
248C4⋊C4—194no—
249C4⋊C4—382no—
250C4⋊C4—382no—
251C4⋊C4—382no—
252C4⋊C4—382no—
253C4⋊C4—382no—
254C4⋊C4—382no—
255C4⋊C4—382no—
256C4⋊C4—382no—
257C4⋊C4—382no—
258C4⋊C4—382no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C42—41no—
263C42—194no—
264C42—382no—
265C42—382no—
266C42—761no—
267C23C23×D1911yescharacteristic
268Q8—388no—
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—192no—
287C2×C4—192no—
288C2×C4—192no—
289C2×C4—192no—
290C2×C4—192no—
291C2×C4—192no—
292C2×C4—192no—
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×C4—381no—
303C2×C4—381no—
304C2×C4—381no—
305C2×C4—381no—
306C2×C4—381no—
307C2×C4—381no—
308C2×C4—381no—
309C2×C4—381no—
310C2×C4#6454112yes—
311C2×C4D4×D1912yes—
312C2×C4Q8×D1912yes—
313C2×C4Q8×D1912yes—
314C22C2×#6454111yescharacteristic
315C22C2×D4×D1911yescharacteristic
316C22#1059743011yescharacteristic
317C22C2×Q8×D1911yescharacteristic
318C22C2×Q8×D1911yescharacteristic
319C22#41×D1911yescharacteristic
320C22#1059743611yescharacteristic
321C4—22no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—194no—
329C4—382no—
330C4—382no—
331C4—382no—
332C4—382no—
333C4—761no—
334C4—761no—
335C4—761no—
336C2#1192705311yescharacteristic
337C2C4⋊Q8×D1911yescharacteristic
338C2#1192712111yescharacteristic
339C2#1192724811yescharacteristic
340C2#1192724911yescharacteristic
341C2#1192727111yescharacteristic
342C2#1192727211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#389C2
hypercenter#389D19
hypocenterC19#2584
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
89. Dic19⋊C4Q8semidirect
90. Dic19⋊C4Q8semidirect
224. C19#2584semidirect

Maximal subgroups

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

subgroupindex
C2×#105973352
C2×#105973332
#119264782
#119264772
#119264652
#119264642
#119264422
#119264412
#119264392
C4×Dic19⋊C42
C19×#3892
#258419