Finite Group Databasebeta

← #19212325

Subgroups — #19212325

Order 5888.

608 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#15675961C211yesmaximal, characteristic
2#15673539C212yesmaximal, complemented
3#15671218C211yesmaximal, characteristic, complemented
4#15671217C212yesmaximal, complemented
5C23×#1270C211yesmaximal, characteristic, complemented
6C2×#10625111C411yescharacteristic
7C2×D4×Dic23C411yescharacteristic
8C2×#10625064C411yescharacteristic
9C2×(C22⋊D23)⋊C4—22no—
10#13092319C2211yescharacteristic
11#13092317—22no—
12#13092286C411yescharacteristic
13C42×Dic23C2211yescharacteristic
14#13092172C2212yes—
15#13092171—22no—
16#13092171—22no—
17C23×#390C2211yescharacteristic
18C23×#336C2212yes—
19C22×D4×C23C2×C411yescharacteristic
20C22×C22⋊D23—22no—
21C23×Dic23—21no—
22C22×D92C2×C411yescharacteristic
23C22×C4×D23—21no—
24C22×C8×C23—22no—
25C2×C4⋊C4×C23C2×C411yescharacteristic
26C2×C22⋊C4×C23—22no—
27C2×C42×C23C2311yescharacteristic
28C2×C22⋊Dic23—21no—
29#10625111—22no—
30#10625111C814yescomplemented
31D4×Dic23—42no—
32C2×(C2×D23)⋊C4—22no—
33C2×(C2×D23)⋊C4—21no—
34C2×C4⋊Dic23C2×C411yescharacteristic
35C2×Dic23⋊C4—22no—
36C2×C4×Dic23C2×C411yescharacteristic
37C2×C4×Dic23C2×C411yescharacteristic
38C2×C4×Dic23D412yes—
39C2×C4×Dic23D412yes—
40C22×C23⋊C8—22no—
41#10625064—42no—
42(C22⋊D23)⋊C4—44no—
43(C22⋊D23)⋊C4—44no—
44C24×C23—21no—
45C23×D23—21no—
46C2×D4×C23—21no—
47C2×D4×C23—41no—
48C2×D4×C23—41no—
49C2×D4×C23C2×C812yes—
50C22×C4×C23—21no—
51C22×C4×C23C22×C411yescharacteristic
52C22×C4×C23C2×D412yes—
53C2×C22⋊D23—28no—
54C2×C22⋊D23—44no—
55C2×C22⋊D23—44no—
56C22×Dic23—21no—
57C22×Dic23—44no—
58C22×Dic23—42no—
59C22×Dic23C22⋊C411yescharacteristic
60C22×Dic23C22⋊C412yes—
61C22×Dic23C22⋊C411yescharacteristic
62C2×D92—21no—
63C2×D92—41no—
64C2×D92—41no—
65C2×D92C2×C812yes—
66C2×C4×D23—44no—
67C2×C4×D23—42no—
68C2×C8×C23—42no—
69C2×C8×C23—42no—
70C2×C8×C23—42no—
71C4⋊C4×C23—41no—
72C22⋊C4×C23—42no—
73C22⋊C4×C23—42no—
74C42×C23—41no—
75C22⋊Dic23—42no—
76(C2×D23)⋊C4—42no—
77(C2×D23)⋊C4—42no—
78(C2×D23)⋊C4—42no—
79C4⋊Dic23—41no—
80Dic23⋊C4—44no—
81C4×Dic23—22no—
82C4×Dic23—22no—
83C4×Dic23—22no—
84C4×Dic23—42no—
85C4×Dic23C2×C812yes—
86C4×Dic23M1612yes—
87C2×C23⋊C8—42no—
88C2×C23⋊C8—42no—
89C2×C23⋊C8—42no—
90#7603—231nomaximal, Sylow
91C23×C23—22no—
92C23×C23—41no—
93C23×C23—41no—
94C23×C23—42no—
95C23×C23—42no—
96C23×C23C2×C22⋊C411yescharacteristic
97C22×D23—22no—
98C22×D23—41no—
99C22×D23—41no—
100C22×D23—42no—
101C22×D23—42no—
102D4×C23—42no—
103D4×C23—42no—
104C2×C4×C23—22no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—22no—
108C2×C4×C23—41no—
109C2×C4×C23—42no—
110C2×C4×C23C22×C811yescharacteristic
111C2×C4×C23C2×M1611yescharacteristic
112C2×C4×C23AGL(1,ℤ/8)12yes—
113C2×C4×C23AGL(1,ℤ/8)12yes—
114C22⋊D23—416no—
115C2×Dic23—22no—
116C2×Dic23—22no—
117C2×Dic23—22no—
118C2×Dic23—21no—
119C2×Dic23—22no—
120C2×Dic23—41no—
121C2×Dic23—42no—
122C2×Dic23—84no—
123C2×Dic23C22⋊C814yes—
124C2×Dic23#10012yes—
125D92—42no—
126D92—42no—
127C4×D23—84no—
128C8×C23—82no—
129C23⋊C8—82no—
130C4×#127—231no—
131#1839—232no—
132#1270—231no—
133#1270—232no—
134#1270D2311yescharacteristic, complemented
135C22×C23—42no—
136C22×C23—44no—
137C22×C23—81no—
138C22×C23—81no—
139C22×C23—82no—
140C22×C23C2×C22⋊C811yescharacteristic
141C22×C23#41011yescharacteristic
142C22×C23C2×#10011yescharacteristic
143C22×C23#41812yes—
144C22×C23#42112yes—
145C2×D23—42no—
146C2×D23—44no—
147C2×D23—81no—
148C2×D23—81no—
149C2×D23—82no—
150C4×C23—21no—
151C4×C23—21no—
152C4×C23—22no—
153C4×C23—22no—
154C4×C23—81no—
155Dic23—22no—
156Dic23—24no—
157Dic23—41no—
158Dic23—81no—
159C2×#127—231no—
160C2×C4×D4—231no—
161C2×C4×D4—231no—
162C2×C4×D4—462no—
163#390—231no—
164#390—462no—
165#390C2×D2311yescharacteristic
166#384—231no—
167C43—231no—
168#336—232no—
169#336—462no—
170#336—462no—
171#336C2×D2312yes—
172C2×C23—82no—
173C2×C23#146011yescharacteristic
174C2×C23#147812yes—
175C2×C23#151412yes—
176C2×C23#153611yescharacteristic
177C2×C23#155511yescharacteristic
178D23—82no—
179C22×D4—231no—
180C22×D4—462no—
181C22×D4C4×D2311yescharacteristic
182C23×C4—461no—
183C23×C4—461no—
184C22×C8—22no—
185C22×C8—462no—
186#127—234no—
187#127—462no—
188C4×D4—924no—
189C4×D4—924no—
190C4×D4—922no—
191C4×D4—922no—
192C2×C4⋊C4—231no—
193C2×C4⋊C4—462no—
194C2×C4⋊C4C4×D2311yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—461no—
197C2×C22⋊C4—461no—
198C2×C22⋊C4—462no—
199C2×C42—231no—
200C2×C42—231no—
201C2×C42—232no—
202C2×C42—232no—
203C2×C42C22×D2311yescharacteristic
204C23#760311yescharacteristic, complemented, Sylow
205C24—21no—
206C24—461no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—232no—
211C2×D4—468no—
212C2×D4—461no—
213C2×D4—921no—
214C2×D4—921no—
215C2×D4—924no—
216C2×D4—924no—
217C2×D4C8×D2312yes—
218C22×C4—21no—
219C22×C4—232no—
220C22×C4—231no—
221C22×C4—231no—
222C22×C4—461no—
223C22×C4—922no—
224C22×C4—924no—
225C22×C4—922no—
226C22×C4—924no—
227C22×C4C2×C4×D2311yescharacteristic
228C22×C4D4×D2312yes—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—922no—
233C2×C8—922no—
234C2×C8—922no—
235C4⋊C4—41no—
236C4⋊C4—921no—
237C4⋊C4—924no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—922no—
241C22⋊C4—922no—
242C22⋊C4—922no—
243C22⋊C4—922no—
244C42—41no—
245C42—232no—
246C42—232no—
247C42—462no—
248C42—462no—
249C42—462no—
250C42—922no—
251C23—22no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—462no—
257C23—921no—
258C23—921no—
259C23—922no—
260C23—922no—
261C23C22⋊C4×D2311yescharacteristic
262D4—42no—
263D4—42no—
264D4—922no—
265D4—922no—
266D4—9216no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—234no—
274C2×C4—232no—
275C2×C4—462no—
276C2×C4—462no—
277C2×C4—462no—
278C2×C4—461no—
279C2×C4—462no—
280C2×C4—921no—
281C2×C4—922no—
282C2×C4—1844no—
283C2×C4—1844no—
284C2×C4C2×C8×D2311yescharacteristic
285C2×C4M16×D2311yescharacteristic
286C2×C4#1062508212yes—
287C2×C4#1062508512yes—
288C8—82no—
289C8—1842no—
290C22—42no—
291C22—44no—
292C22—81no—
293C22—82no—
294C22—81no—
295C22—922no—
296C22—924no—
297C22—1841no—
298C22—1842no—
299C22—1841no—
300C22C22⋊C8×D2311yescharacteristic
301C22#1309238911yescharacteristic
302C22#100×D2311yescharacteristic
303C22#1309242012yes—
304C22#1309243212yes—
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—462no—
311C4—464no—
312C4—921no—
313C4—1841no—
314C2—82no—
315C2—1842no—
316C2#1567171611yescharacteristic
317C2#1567178612yes—
318C2#1567194212yes—
319C2#1567203011yescharacteristic
320C2#1567210911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7603
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673539C2semidirect
3. #15671218C2semidirect
4. #15671217C2semidirect
5. C23×#1270C2semidirect
30. #10625111C8semidirect
134. #1270D23semidirect
204. C23#7603semidirect