Finite Group Databasebeta

← #19212293

Subgroups — #19212293

Order 5888.

630 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 117 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
1D23×#391C211yesmaximal, characteristic
2#15673464C212yesmaximal
3#15671223C211yesmaximal, characteristic, complemented
4#15671222C212yesmaximal, complemented
5C23×#1272C211yesmaximal, characteristic, complemented
6C22×Q8×D23C411yescharacteristic
7C2×C4⋊C4×D23C411yescharacteristic
8C2×C42×D23C2211yescharacteristic
9C2×(C2×D23)⋊C8—22no—
10#13092324C411yescharacteristic
11#13092323C2211yescharacteristic
12#13092322C411yescharacteristic
13#13092321—22no—
14#95×D23—22no—
15#13092172C2212yes—
16#13092171—22no—
17C23×#391C2211yescharacteristic
18C23×#336C2212yes—
19C22×Q8×C23C2×C411yescharacteristic
20C2×Q8×D23—22no—
21C2×Q8×D23—42no—
22C2×Q8×D23—42no—
23C2×Q8×D23C814yescomplemented
24C22×C4×D23—21no—
25C22×C4×D23—21no—
26C22×C4×D23C2×C411yescharacteristic
27C22×C4×D23D412yes—
28C22×Dic46—21no—
29C22×Dic46C2×C411yescharacteristic
30C22×C8×C23—22no—
31C2×C4⋊C4×C23C2×C411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×C4⋊Dic23C2×C411yescharacteristic
34C2×Dic23⋊C4—21no—
35C2×C4×Dic23C2×C411yescharacteristic
36C2×C4×Dic23D412yes—
37C22×C23⋊C8—22no—
38C4⋊C4×D23—42no—
39C42×D23—42no—
40C23×#95—22no—
41C23⋊#95—22no—
42C23⋊#95—22no—
43C23⋊#95—22no—
44(C2×D23)⋊C8—44no—
45C23×D23C22⋊C411yescharacteristic
46C2×Q8×C23—21no—
47C2×Q8×C23—41no—
48C2×Q8×C23—41no—
49C2×Q8×C23C2×C812yes—
50C22×C4×C23—21no—
51C22×C4×C23—21no—
52C22×C4×C23C22×C411yescharacteristic
53C22×C4×C23C2×D412yes—
54C22×Dic23—21no—
55C22×Dic23—21no—
56C22×Dic23C22⋊C412yes—
57C22×Dic23C22⋊C411yescharacteristic
58Q8×D23—48no—
59Q8×D23—48no—
60C2×C4×D23—22no—
61C2×C4×D23—22no—
62C2×C4×D23—24no—
63C2×C4×D23—24no—
64C2×C4×D23—22no—
65C2×C4×D23—22no—
66C2×C4×D23—42no—
67C2×C4×D23—42no—
68C2×C4×D23—42no—
69C2×C4×D23—44no—
70C2×C4×D23—42no—
71C2×C4×D23C2×C812yes—
72C2×C4×D23M1612yes—
73C2×Dic46—21no—
74C2×Dic46—24no—
75C2×Dic46—42no—
76C2×Dic46—42no—
77C2×Dic46—41no—
78C2×Dic46—41no—
79C2×Dic46C2×C812yes—
80C2×C8×C23—42no—
81C2×C8×C23—42no—
82C2×C8×C23—42no—
83C4⋊C4×C23—41no—
84C42×C23—41no—
85C4⋊Dic23—41no—
86Dic23⋊C4—42no—
87C4×Dic23—41no—
88C4×Dic23—42no—
89C2×C23⋊C8—42no—
90C2×C23⋊C8—42no—
91C2×C23⋊C8—42no—
92#7595—231nomaximal, Sylow
93C23×C23C2×C22⋊C411yescharacteristic
94C22×D23—22no—
95C22×D23—22no—
96C22×D23C22⋊C812yes—
97C22×D23#9912yes—
98C22×D23#10012yes—
99Q8×C23—42no—
100Q8×C23—42no—
101C2×C4×C23—22no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—22no—
105C2×C4×C23—22no—
106C2×C4×C23—41no—
107C2×C4×C23—41no—
108C2×C4×C23—41no—
109C2×C4×C23—42no—
110C2×C4×C23C22×C811yescharacteristic
111C2×C4×C23C2×M1611yescharacteristic
112C2×C4×C23#13712yes—
113C2×C4×C23#13712yes—
114C2×Dic23—21no—
115C2×Dic23—21no—
116C2×Dic23—22no—
117C2×Dic23—22no—
118C2×Dic23—22no—
119C2×Dic23—22no—
120C2×Dic23—41no—
121C2×Dic23—41no—
122C2×Dic23—41no—
123C2×Dic23—42no—
124C2×Dic23C22⋊C812yes—
125C4×D23—24no—
126C4×D23—24no—
127C4×D23—44no—
128C4×D23—44no—
129C4×D23—48no—
130C4×D23—84no—
131Dic46—48no—
132Dic46—42no—
133Dic46—42no—
134C8×C23—82no—
135C23⋊C8—82no—
136C2×#391—231no—
137#1817—232no—
138#1272—231no—
139#1272—232no—
140#1272D2311yescharacteristic, complemented
141C22×C23C2×C22⋊C811yescharacteristic
142C22×C23C2×#9911yescharacteristic
143C22×C23C2×#10011yescharacteristic
144C22×C23#41912yes—
145C22×C23#42112yes—
146C2×D23—22no—
147C2×D23—24no—
148C2×D23—24no—
149C2×D23—22no—
150C2×D23#32314yes—
151C4×C23—21no—
152C4×C23—21no—
153C4×C23—22no—
154C4×C23—22no—
155C4×C23—42no—
156C4×C23—81no—
157Dic23—22no—
158Dic23—42no—
159Dic23—42no—
160Dic23—81no—
161C23×Q8—231no—
162C22×C4⋊C4—231no—
163C22×C42—231no—
164C2×C22⋊C8—462no—
165#391—231no—
166#391—231no—
167#391—231no—
168#391—462no—
169#391C2×D2311yescharacteristic
170C2×#95—462no—
171#336—232no—
172#336—462no—
173#336C2×D2312yes—
174C2×C23C2×#32311yescharacteristic
175C2×C23#147912yes—
176C2×C23#151112yes—
177C2×C23#153311yescharacteristic
178C2×C23#155811yescharacteristic
179D23—24no—
180C22×Q8—234no—
181C22×Q8—231no—
182C22×Q8—461no—
183C22×Q8—462no—
184C22×Q8—922no—
185C22×Q8—922no—
186C22×Q8C4×D2311yescharacteristic
187C23×C4—231no—
188C23×C4—232no—
189C23×C4—461no—
190C23×C4—461no—
191C22×C8—22no—
192C22×C8—462no—
193C2×C4⋊C4—231no—
194C2×C4⋊C4—461no—
195C2×C4⋊C4—922no—
196C2×C4⋊C4C4×D2311yescharacteristic
197C2×C42—231no—
198C2×C42—232no—
199C2×C42—922no—
200C2×C42C22×D2311yescharacteristic
201C22⋊C8—924no—
202#95—22no—
203#95—462no—
204#95—462no—
205#95—462no—
206C23#759511yescharacteristic, complemented, Sylow
207C24—231no—
208C2×Q8—21no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—232no—
212C2×Q8—464no—
213C2×Q8—461no—
214C2×Q8—921no—
215C2×Q8—921no—
216C2×Q8—922no—
217C2×Q8—922no—
218C2×Q8—928no—
219C2×Q8—928no—
220C2×Q8C8×D2312yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—231no—
224C22×C4—232no—
225C22×C4—232no—
226C22×C4—232no—
227C22×C4—462no—
228C22×C4—462no—
229C22×C4—464no—
230C22×C4—464no—
231C22×C4—461no—
232C22×C4—462no—
233C22×C4—462no—
234C22×C4—461no—
235C22×C4—922no—
236C22×C4—922no—
237C22×C4—922no—
238C22×C4—922no—
239C22×C4—924no—
240C22×C4C2×C4×D2311yescharacteristic
241C22×C4D4×D2312yes—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—922no—
246C2×C8—922no—
247C2×C8—922no—
248C4⋊C4—41no—
249C4⋊C4—921no—
250C4⋊C4—922no—
251C42—41no—
252C42—922no—
253C42—921no—
254C23—232no—
255C23—232no—
256C23—232no—
257C23—462no—
258C23—462no—
259C23C22⋊C4×D2311yescharacteristic
260Q8—42no—
261Q8—42no—
262Q8—922no—
263Q8—922no—
264Q8—928no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—232no—
275C2×C4—464no—
276C2×C4—464no—
277C2×C4—461no—
278C2×C4—461no—
279C2×C4—462no—
280C2×C4—462no—
281C2×C4—462no—
282C2×C4—462no—
283C2×C4—924no—
284C2×C4—924no—
285C2×C4—928no—
286C2×C4—921no—
287C2×C4—921no—
288C2×C4—921no—
289C2×C4—922no—
290C2×C4—1844no—
291C2×C4C2×C8×D2311yescharacteristic
292C2×C4M16×D2311yescharacteristic
293C2×C4#1062508612yes—
294C2×C4#1062508912yes—
295C8—82no—
296C8—1842no—
297C22—234no—
298C22—462no—
299C22—464no—
300C22—462no—
301C22—464no—
302C22C22⋊C8×D2311yescharacteristic
303C22#99×D2311yescharacteristic
304C22#100×D2311yescharacteristic
305C22#1309242412yes—
306C22#1309243212yes—
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—462no—
314C4—922no—
315C4—922no—
316C4—1841no—
317C2—464no—
318C2D23×#32311yescharacteristic
319C2#1567179012yes—
320C2#1567192812yes—
321C2#1567201911yescharacteristic
322C2#1567212111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7595
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
3. #15671223C2semidirect
4. #15671222C2semidirect
5. C23×#1272C2semidirect
23. C2×Q8×D23C8semidirect
140. #1272D23semidirect
206. C23#7595semidirect