Finite Group Databasebeta

← #19212179

Subgroups — #19212179

Order 5888.

684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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#15673245C212yesmaximal, complemented
3#15671218C211yesmaximal, characteristic, complemented
4#15671217C212yesmaximal, complemented
5C23×#1270C211yesmaximal, characteristic, complemented
6C2×#10625111C411yescharacteristic
7C2×D4×Dic23C411yescharacteristic
8C2×#10625064C411yescharacteristic
9C2×(C22⋊D23)⋊C4—22no—
10C2×Dic23⋊C8—22no—
11C2×C8×Dic23—22no—
12#13092319C2211yescharacteristic
13#13092317—22no—
14#13092286C411yescharacteristic
15C42×Dic23C2211yescharacteristic
16#13092172C2212yes—
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—
44Dic23⋊C8—28no—
45C8×Dic23—44no—
46C24×C23—21no—
47C23×D23—21no—
48C2×D4×C23—21no—
49C2×D4×C23—41no—
50C2×D4×C23—41no—
51C2×D4×C23C2×C812yes—
52C22×C4×C23—21no—
53C22×C4×C23C22×C411yescharacteristic
54C22×C4×C23C2×D412yes—
55C2×C22⋊D23—28no—
56C2×C22⋊D23—44no—
57C2×C22⋊D23—44no—
58C22×Dic23—21no—
59C22×Dic23—42no—
60C22×Dic23—44no—
61C22×Dic23C22⋊C411yescharacteristic
62C22×Dic23C22⋊C412yes—
63C22×Dic23C22⋊C411yescharacteristic
64C2×D92—21no—
65C2×D92—41no—
66C2×D92—41no—
67C2×D92C2×C812yes—
68C2×C4×D23—42no—
69C2×C4×D23—44no—
70C2×C8×C23—24no—
71C2×C8×C23—42no—
72C2×C8×C23—42no—
73C4⋊C4×C23—41no—
74C22⋊C4×C23—42no—
75C22⋊C4×C23—42no—
76C42×C23—41no—
77C22⋊Dic23—42no—
78(C2×D23)⋊C4—42no—
79(C2×D23)⋊C4—42no—
80(C2×D23)⋊C4—42no—
81C4⋊Dic23—41no—
82Dic23⋊C4—44no—
83C4×Dic23—22no—
84C4×Dic23—24no—
85C4×Dic23C2×C812yes—
86C4×Dic23M1612yes—
87C4×Dic23D814yes—
88C4×Dic23SD1614yes—
89C2×C23⋊C8—24no—
90C2×C23⋊C8—42no—
91C2×C23⋊C8—42no—
92#7569—231nomaximal, Sylow
93C23×C23—22no—
94C23×C23—41no—
95C23×C23—41no—
96C23×C23—42no—
97C23×C23—42no—
98C23×C23C2×C22⋊C411yescharacteristic
99C22×D23—22no—
100C22×D23—41no—
101C22×D23—41no—
102C22×D23—42no—
103C22×D23—42no—
104D4×C23—42no—
105D4×C23—42no—
106C2×C4×C23—22no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—22no—
110C2×C4×C23—41no—
111C2×C4×C23—42no—
112C2×C4×C23C22×C811yescharacteristic
113C2×C4×C23C2×M1611yescharacteristic
114C2×C4×C23C2×D812yes—
115C2×C4×C23C2×SD1612yes—
116C22⋊D23—416no—
117C2×Dic23—21no—
118C2×Dic23—22no—
119C2×Dic23—41no—
120C2×Dic23—42no—
121C2×Dic23—84no—
122C2×Dic23C22⋊C814yes—
123C2×Dic23#10012yes—
124C2×Dic23#10214yes—
125C2×Dic23#10214yes—
126C2×Dic23#10414yes—
127D92—42no—
128D92—42no—
129C4×D23—84no—
130C8×C23—44no—
131C23⋊C8—44no—
132C4×#127—231no—
133C4×C4⋊C8—232no—
134#1270—231no—
135#1270—232no—
136#1270D2311yescharacteristic, complemented
137C22×C23—42no—
138C22×C23—44no—
139C22×C23—81no—
140C22×C23—82no—
141C22×C23—81no—
142C22×C23C2×C22⋊C811yescharacteristic
143C22×C23#41011yescharacteristic
144C22×C23C2×#10011yescharacteristic
145C22×C23C2×#10212yes—
146C22×C23C2×#10412yes—
147C2×D23—42no—
148C2×D23—44no—
149C2×D23—81no—
150C2×D23—82no—
151C2×D23—81no—
152C4×C23—21no—
153C4×C23—21no—
154C4×C23—22no—
155C4×C23—22no—
156C4×C23—81no—
157Dic23—41no—
158Dic23—81no—
159Dic23D4⋊C818yes—
160Dic23#33114yes—
161C2×#127—231no—
162C2×C4×D4—231no—
163C2×C4×D4—231no—
164C2×C4×D4—462no—
165C2×C4⋊C8—462no—
166C2×C4×C8—462no—
167#390—231no—
168#390—462no—
169#390C2×D2311yescharacteristic
170#384—231no—
171C43—231no—
172#336—232no—
173#336C2×D2312yes—
174C2×C23—82no—
175C2×C23#146011yescharacteristic
176C2×C23C2×D4⋊C812yes—
177C2×C23#150212yes—
178C2×C23#152511yescharacteristic
179C2×C23C2×#33111yescharacteristic
180D23—82no—
181C22×D4—231no—
182C22×D4—462no—
183C22×D4C4×D2311yescharacteristic
184C23×C4—461no—
185C23×C4—461no—
186C22×C8—22no—
187C22×C8—462no—
188#127—234no—
189#127—462no—
190C4×D4—924no—
191C4×D4—924no—
192C4×D4—922no—
193C4×D4—922no—
194C2×C4⋊C4—231no—
195C2×C4⋊C4—462no—
196C2×C4⋊C4C4×D2311yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—461no—
199C2×C22⋊C4—461no—
200C2×C22⋊C4—462no—
201C2×C42—231no—
202C2×C42—232no—
203C2×C42—231no—
204C2×C42—232no—
205C2×C42C22×D2311yescharacteristic
206C4⋊C8—468no—
207C4×C8—924no—
208C23#756911yescharacteristic, complemented, Sylow
209C24—21no—
210C24—461no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—232no—
215C2×D4—468no—
216C2×D4—461no—
217C2×D4—921no—
218C2×D4—921no—
219C2×D4—924no—
220C2×D4—924no—
221C2×D4C8×D2312yes—
222C22×C4—21no—
223C22×C4—232no—
224C22×C4—231no—
225C22×C4—231no—
226C22×C4—461no—
227C22×C4—924no—
228C22×C4—922no—
229C22×C4—924no—
230C22×C4—922no—
231C22×C4C2×C4×D2311yescharacteristic
232C22×C4D4×D2312yes—
233C2×C8—24no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—464no—
237C2×C8—922no—
238C2×C8—922no—
239C4⋊C4—41no—
240C4⋊C4—921no—
241C4⋊C4—924no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—922no—
245C22⋊C4—922no—
246C22⋊C4—922no—
247C22⋊C4—922no—
248C42—41no—
249C42—232no—
250C42—232no—
251C42—234no—
252C42—234no—
253C42—464no—
254C42—462no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—462no—
261C23—921no—
262C23—921no—
263C23—922no—
264C23—922no—
265C23C22⋊C4×D2311yescharacteristic
266D4—42no—
267D4—42no—
268D4—922no—
269D4—922no—
270D4—9216no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—234no—
278C2×C4—232no—
279C2×C4—234no—
280C2×C4—234no—
281C2×C4—234no—
282C2×C4—461no—
283C2×C4—462no—
284C2×C4—921no—
285C2×C4—922no—
286C2×C4—1844no—
287C2×C4—1844no—
288C2×C4C2×C8×D2311yescharacteristic
289C2×C4M16×D2311yescharacteristic
290C2×C4D8×D2312yes—
291C2×C4SD16×D2312yes—
292C8—44no—
293C8—924no—
294C22—42no—
295C22—44no—
296C22—82no—
297C22—81no—
298C22—81no—
299C22—922no—
300C22—924no—
301C22—1842no—
302C22—1841no—
303C22—1841no—
304C22C22⋊C8×D2311yescharacteristic
305C22#1309238911yescharacteristic
306C22#100×D2311yescharacteristic
307C22#102×D2312yes—
308C22#104×D2312yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—238no—
315C4—234no—
316C4—921no—
317C4—1841no—
318C2—82no—
319C2—1842no—
320C2#1567171611yescharacteristic
321C2D23×D4⋊C812yes—
322C2#1567189012yes—
323C2#1567198711yescharacteristic
324C2D23×#33111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7569
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. #15673245C2semidirect
3. #15671218C2semidirect
4. #15671217C2semidirect
5. C23×#1270C2semidirect
30. #10625111C8semidirect
136. #1270D23semidirect
208. C23#7569semidirect