Finite Group Databasebeta

← #14568633

Subgroups — #14568633

Order 2432.

676 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597386C211yesmaximal, characteristic
2C2×#10597331C212yesmaximal, complemented
3C2×#10597333C211yesmaximal, characteristic, complemented
4#11926462C211yesmaximal, characteristic, complemented
5#11926461C211yesmaximal, characteristic, complemented
6#11926458C211yesmaximal, characteristic, complemented
7#11926444C212yesmaximal, complemented
8#11926444C212yesmaximal, complemented
9#11926444C212yesmaximal, complemented
10#11926395C211yesmaximal, characteristic, complemented
11C19×#394C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2212yes—
15C22×D76C2211yescharacteristic
16C22×Dic38C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22#10597386—24no—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2211yescharacteristic
29C2×Dic19⋊C4C2211yescharacteristic
30C2×C4×Dic19C2212yes—
31C2×C4×Dic19C2211yescharacteristic
32C2×C4×Dic19C2211yescharacteristic
33C2×C4×Dic19C2211yescharacteristic
34#10597333—24no—
35#10597331—28no—
36C19×#95C2211yescharacteristic
37C19⋊#95C2211yescharacteristic
38C24×C19C2312yes—
39C23×D19C2312yes—
40C2×D4×C19—22no—
41C2×D4×C19—42no—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2312yes—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—24no—
47C2×C22⋊D19—24no—
48C2×C22⋊D19—24no—
49C2×C22⋊D19—24no—
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2311yescharacteristic
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2311yescharacteristic
57C2×D76—22no—
58C2×D76—42no—
59C2×Dic38—22no—
60C2×Dic38—22no—
61C2×Dic38D414yescomplemented
62C4⋊C4×C19—22no—
63C22⋊C4×C19—24no—
64C22⋊C4×C19—42no—
65C22⋊Dic19—24no—
66C22⋊Dic19—42no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—24no—
69(C2×D19)⋊C4—42no—
70(C2×D19)⋊C4—42no—
71Dic19⋊C4—22no—
72Dic19⋊C4—22no—
73Dic19⋊C4—24no—
74C4×Dic19—24no—
75C4×Dic19—22no—
76C4×Dic19—22no—
77C4×Dic19D414yes—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19C2411yescharacteristic
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—22no—
89C22×D19—22no—
90C22×D19—22no—
91C22×D19—22no—
92C22×D19—22no—
93D4×C19—44no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19C2×D412yes—
103C2×C4×C19C2×D412yes—
104C22⋊D19—48no—
105C22⋊D19—48no—
106C2×Dic19—21no—
107C2×Dic19—21no—
108C2×Dic19—21no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19C2×D412yes—
114C2×Dic19C2×D412yes—
115C2×Dic19C2×D412yes—
116C2×Dic19C2×D412yes—
117C2×Dic19#4112yes—
118C2×Dic19#4114yes—
119D76—44no—
120Dic38—28no—
121#2548—191nomaximal, Sylow
122C22×C19—42no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19C22×D411yescharacteristic
130C22×C19C22×D411yescharacteristic
131C22×C19C2×#4111yescharacteristic
132C22×C19C2×#4112yes—
133C22×C19H(5,𝔽2)12yes—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19—42no—
139C2×D19—42no—
140C2×D19—42no—
141C4×C19—22no—
142C4×C19—22no—
143C4×C19—41no—
144C4×C19—42no—
145Dic19—22no—
146Dic19—41no—
147Dic19—42no—
148Dic19#12114yes—
149Dic19#12414yescomplemented
150C2×#127—191no—
151C2×#124—192no—
152C2×C4×Q8—191no—
153#394—191no—
154#394—191no—
155#394—191no—
156#394D1911yescharacteristic, complemented
157#390—192no—
158#390—192no—
159#390—192no—
160C4×C4⋊C4—191no—
161C2×C19—82no—
162C2×C19C2×#12111yescharacteristic
163C2×C19C2×#12411yescharacteristic
164C2×C19#53511yescharacteristic
165C2×C19#55012yes—
166C2×C19#55912yes—
167D19—82no—
168C22×Q8—191no—
169C22×D4—192no—
170C22×D4—192no—
171C22×D4—191no—
172C22×D4C2×D1911yescharacteristic
173#127—384no—
174#124—388no—
175C4×Q8—384no—
176C2×C4⋊C4—191no—
177C2×C4⋊C4—191no—
178C2×C4⋊C4—192no—
179C2×C4⋊C4C2×D1911yescharacteristic
180C2×C22⋊C4—192no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—192no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4C2×D1912yes—
187C2×C22⋊C4C2×D1912yes—
188C2×C42—191no—
189C2×C42—191no—
190C2×C42—191no—
191C2×C42—192no—
192#95—191no—
193#95C2×D1911yescharacteristic
194C19#254811yescharacteristic, complemented, Sylow
195C24—192no—
196C24C22×D1912yes—
197C2×Q8—194no—
198C2×Q8—382no—
199C2×Q8—382no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—384no—
203C2×D4—384no—
204C2×D4—384no—
205C2×D4—384no—
206C2×D4—384no—
207C2×D4—384no—
208C2×D4—382no—
209C2×D4—762no—
210C22×C4—191no—
211C22×C4—191no—
212C22×C4—191no—
213C22×C4—192no—
214C22×C4—191no—
215C22×C4C22×D1912yes—
216C22×C4C22×D1911yescharacteristic
217C22×C4C22×D1911yescharacteristic
218C22×C4C22×D1911yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—384no—
221C4⋊C4—382no—
222C4⋊C4—382no—
223C22⋊C4—24no—
224C22⋊C4—42no—
225C22⋊C4—384no—
226C22⋊C4—384no—
227C22⋊C4—384no—
228C22⋊C4—762no—
229C22⋊C4—762no—
230C22⋊C4—762no—
231C42—194no—
232C42—382no—
233C42—382no—
234C42—384no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—382no—
243C23—382no—
244C23—382no—
245C23—382no—
246C23—382no—
247C23—382no—
248C23—382no—
249C23C23×D1911yescharacteristic
250Q8—388no—
251D4—44no—
252D4—764no—
253D4—768no—
254D4—768no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—192no—
264C2×C4—192no—
265C2×C4—192no—
266C2×C4—194no—
267C2×C4—192no—
268C2×C4—192no—
269C2×C4—381no—
270C2×C4—381no—
271C2×C4—382no—
272C2×C4—381no—
273C2×C4—382no—
274C2×C4—382no—
275C2×C4—382no—
276C2×C4D4×D1912yes—
277C2×C4D4×D1912yes—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—762no—
286C22—762no—
287C22—762no—
288C22—762no—
289C22—762no—
290C22—762no—
291C22—762no—
292C22C2×D4×D1911yescharacteristic
293C22C2×D4×D1911yescharacteristic
294C22#1059743012yes—
295C22#41×D1912yes—
296C22#41×D1911yescharacteristic
297C4—22no—
298C4—22no—
299C4—41no—
300C4—42no—
301C4—194no—
302C4—194no—
303C4—382no—
304C4—761no—
305C4—762no—
306C2—82no—
307C2—1522no—
308C2#121×D1911yescharacteristic
309C2#124×D1911yescharacteristic
310C2#1192710911yescharacteristic
311C2#1192721212yes—
312C2#1192727812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC2×#10597386C2
hypercenter#394D19
hypocenterC19#2548
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#10597331C2semidirect
3. C2×#10597333C2semidirect
4. #11926462C2semidirect
5. #11926461C2semidirect
6. #11926458C2semidirect
7. #11926444C2semidirect
8. #11926444C2semidirect
9. #11926444C2semidirect
10. #11926395C2semidirect
11. C19×#394C2semidirect
61. C2×Dic38D4semidirect
149. Dic19#124semidirect
156. #394D19semidirect
194. C19#2548semidirect

Maximal subgroups

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

subgroupindex
C2×#105973862
C2×#105973312
C2×#105973332
#119264622
#119264612
#119264582
#119264442
#119263952
C19×#3942
#254819