Finite Group Databasebeta

← #19212157

Subgroups — #19212157

Order 5888.

690 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 121 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#15675886C211yesmaximal, characteristic
2#15673154C212yesmaximal, complemented
3#15671223C211yesmaximal, characteristic, complemented
4#15671217C212yesmaximal, complemented
5C23×#1272C211yesmaximal, characteristic, complemented
6C22×#67292C411yescharacteristic
7C2×#10625063C411yescharacteristic
8C2×C42×D23C2211yescharacteristic
9C2×(C2×D23)⋊C8—22no—
10C2×C8×Dic23—22no—
11#13092324C411yescharacteristic
12#13092319C2211yescharacteristic
13#13092318C411yescharacteristic
14#13092295—22no—
15#13092264—22no—
16#13092172C2212yes—
17C23×#391C2211yescharacteristic
18C23×#336C2212yes—
19C22×Q8×C23C2×C411yescharacteristic
20C2×#67292—22no—
21C2×#67292—42no—
22C2×#67292—42no—
23C2×#67292C814yescomplemented
24C22×D92—21no—
25C22×D92C2×C411yescharacteristic
26C22×C4×D23—21no—
27C22×C4×D23C2×C411yescharacteristic
28C22×C4×D23D412yes—
29C22×C8×C23—22no—
30C2×C4⋊C4×C23C2×C411yescharacteristic
31C2×C42×C23C2311yescharacteristic
32C2×(C2×D23)⋊C4—21no—
33C2×(C2×D23)⋊C4—22no—
34C2×(C2×D23)⋊C4—22no—
35C2×C4⋊Dic23C2×C411yescharacteristic
36C2×C4×Dic23—21no—
37C2×C4×Dic23C2×C411yescharacteristic
38C2×C4×Dic23D412yes—
39C22×C23⋊C8—22no—
40#10625063—42no—
41C42×D23—42no—
42C23×#95—22no—
43C23⋊#95—22no—
44(C2×D23)⋊C8—28no—
45C8×Dic23—44no—
46C23×D23—21no—
47C23×D23C22⋊C411yescharacteristic
48C2×Q8×C23—21no—
49C2×Q8×C23—41no—
50C2×Q8×C23—41no—
51C2×Q8×C23C2×C812yes—
52C22×C4×C23—21no—
53C22×C4×C23—21no—
54C22×C4×C23C22×C411yescharacteristic
55C22×C4×C23C2×D412yes—
56C22×Dic23—21no—
57C22×Dic23C22⋊C412yes—
58C22×Dic23C22⋊C411yescharacteristic
59#67292—48no—
60#67292—48no—
61C2×D92—24no—
62C2×D92—21no—
63C2×D92—41no—
64C2×D92—41no—
65C2×D92—42no—
66C2×D92—42no—
67C2×D92C2×C812yes—
68C2×C4×D23—22no—
69C2×C4×D23—22no—
70C2×C4×D23—22no—
71C2×C4×D23—22no—
72C2×C4×D23—24no—
73C2×C4×D23—24no—
74C2×C4×D23—42no—
75C2×C4×D23—42no—
76C2×C4×D23—42no—
77C2×C4×D23C2×C812yes—
78C2×C4×D23M1612yes—
79C2×C8×C23—24no—
80C2×C8×C23—42no—
81C2×C8×C23—42no—
82C4⋊C4×C23—41no—
83C42×C23—41no—
84(C2×D23)⋊C4—42no—
85(C2×D23)⋊C4—42no—
86(C2×D23)⋊C4—42no—
87(C2×D23)⋊C4—44no—
88C4⋊Dic23—41no—
89C4×Dic23—24no—
90C4×Dic23—41no—
91C4×Dic23—42no—
92C2×C23⋊C8—24no—
93C2×C23⋊C8—42no—
94C2×C23⋊C8—42no—
95#7563—231nomaximal, Sylow
96C23×C23C2×C22⋊C411yescharacteristic
97C22×D23—21no—
98C22×D23—21no—
99C22×D23—22no—
100C22×D23—22no—
101C22×D23—22no—
102C22×D23—41no—
103C22×D23—41no—
104C22×D23—42no—
105C22×D23—42no—
106C22×D23C22⋊C812yes—
107Q8×C23—42no—
108Q8×C23—42no—
109C2×C4×C23—22no—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—22no—
113C2×C4×C23—22no—
114C2×C4×C23—41no—
115C2×C4×C23—41no—
116C2×C4×C23—41no—
117C2×C4×C23—42no—
118C2×C4×C23C22×C811yescharacteristic
119C2×C4×C23C2×M1611yescharacteristic
120C2×C4×C23#13512yes—
121C2×C4×C23#13512yes—
122C2×Dic23—22no—
123C2×Dic23—22no—
124C2×Dic23—41no—
125C2×Dic23—42no—
126C2×Dic23C22⋊C812yes—
127C2×Dic23#9912yes—
128C2×Dic23#10012yes—
129C2×Dic23#10414yes—
130D92—42no—
131D92—42no—
132D92—48no—
133C4×D23—24no—
134C4×D23—24no—
135C4×D23—44no—
136C4×D23—44no—
137C4×D23—48no—
138C8×C23—44no—
139C23⋊C8—44no—
140#2297—231no—
141C4×C22⋊C8—232no—
142#1272—231no—
143#1272D2311yescharacteristic, complemented
144#1270—232no—
145C22×C23C2×C22⋊C811yescharacteristic
146C22×C23C2×#9911yescharacteristic
147C22×C23C2×#10011yescharacteristic
148C22×C23#41612yes—
149C22×C23C2×#10412yes—
150C2×D23—22no—
151C2×D23—24no—
152C2×D23—41no—
153C2×D23—42no—
154C2×D23—41no—
155C2×D23—42no—
156C2×D23—44no—
157C2×D23—81no—
158C2×D23—82no—
159C2×D23—81no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—22no—
163C4×C23—22no—
164C4×C23—42no—
165C4×C23—81no—
166Dic23—24no—
167Dic23—81no—
168Dic23#32314yes—
169C22×#41—231no—
170C2×#117—231no—
171C22×C42—231no—
172C2×C22⋊C8—462no—
173C2×C4×C8—462no—
174#391—231no—
175#391C2×D2311yescharacteristic
176#390—231no—
177#390—231no—
178#386—462no—
179C4×C22⋊C4—462no—
180#336—232no—
181#336C2×D2312yes—
182C2×C23C2×#32311yescharacteristic
183C2×C23#147612yes—
184C2×C23#150112yes—
185C2×C23#152511yescharacteristic
186C2×C23#154311yescharacteristic
187D23—42no—
188D23—82no—
189C2×#41—234no—
190C2×#41—462no—
191C2×#41—922no—
192C2×#41—922no—
193C22×Q8C4×D2311yescharacteristic
194C22×D4—231no—
195C22×D4—461no—
196C23×C4—231no—
197C23×C4—232no—
198C23×C4—461no—
199C22×C8—22no—
200C22×C8—462no—
201#117—922no—
202C2×C4⋊C4—231no—
203C2×C4⋊C4C4×D2311yescharacteristic
204C2×C22⋊C4—462no—
205C2×C22⋊C4—461no—
206C2×C22⋊C4—462no—
207C2×C42—232no—
208C2×C42—231no—
209C2×C42—461no—
210C2×C42—922no—
211C2×C42C22×D2311yescharacteristic
212C22⋊C8—468no—
213C4×C8—924no—
214#95—22no—
215#95—462no—
216C23#756311yescharacteristic, complemented, Sylow
217C24—231no—
218C24—461no—
219#41—928no—
220#41—928no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8C8×D2312yes—
225C2×D4—232no—
226C2×D4—464no—
227C2×D4—461no—
228C2×D4—921no—
229C2×D4—921no—
230C2×D4—922no—
231C2×D4—922no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—231no—
235C22×C4—232no—
236C22×C4—232no—
237C22×C4—232no—
238C22×C4—462no—
239C22×C4—462no—
240C22×C4—464no—
241C22×C4—464no—
242C22×C4—462no—
243C22×C4—462no—
244C22×C4—461no—
245C22×C4—922no—
246C22×C4—922no—
247C22×C4—922no—
248C22×C4C2×C4×D2311yescharacteristic
249C22×C4D4×D2312yes—
250C2×C8—24no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—464no—
254C2×C8—922no—
255C2×C8—922no—
256C4⋊C4—41no—
257C4⋊C4—921no—
258C22⋊C4—924no—
259C22⋊C4—922no—
260C22⋊C4—922no—
261C22⋊C4—922no—
262C42—41no—
263C42—464no—
264C42—921no—
265C42—922no—
266C23—232no—
267C23—461no—
268C23—461no—
269C23—462no—
270C23—462no—
271C23—462no—
272C23—921no—
273C23—921no—
274C23—922no—
275C23—922no—
276C23C22⋊C4×D2311yescharacteristic
277Q8—42no—
278Q8—42no—
279D4—922no—
280D4—922no—
281D4—928no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—232no—
292C2×C4—232no—
293C2×C4—232no—
294C2×C4—234no—
295C2×C4—464no—
296C2×C4—464no—
297C2×C4—462no—
298C2×C4—462no—
299C2×C4—924no—
300C2×C4—924no—
301C2×C4—928no—
302C2×C4—921no—
303C2×C4—922no—
304C2×C4C2×C8×D2311yescharacteristic
305C2×C4M16×D2311yescharacteristic
306C2×C4#1062508712yes—
307C2×C4#1062509012yes—
308C8—44no—
309C8—924no—
310C22—462no—
311C22—464no—
312C22—922no—
313C22—921no—
314C22—921no—
315C22—922no—
316C22—924no—
317C22—1842no—
318C22—1841no—
319C22—1841no—
320C22C22⋊C8×D2311yescharacteristic
321C22#99×D2311yescharacteristic
322C22#100×D2311yescharacteristic
323C22#1309241212yes—
324C22#104×D2312yes—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—234no—
332C4—464no—
333C4—1841no—
334C2—922no—
335C2—1842no—
336C2D23×#32311yescharacteristic
337C2#1567177812yes—
338C2#1567188712yes—
339C2#1567198711yescharacteristic
340C2#1567205811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7563
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
2. #15673154C2semidirect
3. #15671223C2semidirect
4. #15671217C2semidirect
5. C23×#1272C2semidirect
23. C2×#67292C8semidirect
143. #1272D23semidirect
216. C23#7563semidirect