Finite Group Databasebeta

← #19212241

Subgroups — #19212241

Order 5888.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625095C211yesmaximal, characteristic
2#15673465C211yesmaximal, characteristic
3#15671222C212yesmaximal, complemented
4#15671219C212yesmaximal, complemented
5C4×C23×C22⋊C8C211yesmaximal, characteristic
6C2×#10625095C411yescharacteristic
7C2×C4×Dic46C411yescharacteristic
8C2×C22⋊(C23⋊C8)—21no—
9#13092323C2211yescharacteristic
10#13092315C2211yescharacteristic
11#13092301—21no—
12#13092290—21no—
13#13092277C411yescharacteristic
14C4×Dic23⋊C4—21no—
15C4×C4⋊Dic23C411yescharacteristic
16C4×C22⋊Dic23—21no—
17#13092172—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C2×C4×C8×C23—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×Dic46C2×C411yescharacteristic
27C22×C8×C23—22no—
28C2×C42×C23—42no—
29C2×C42×C23C2×C411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×C22⋊Dic23—21no—
34C2×C22⋊Dic23—21no—
35C2×C4⋊Dic23C2×C411yescharacteristic
36C2×C4⋊Dic23C2×C411yescharacteristic
37C2×C4⋊Dic23C2×C411yescharacteristic
38#10625095—22no—
39#10625095C814yescomplemented
40C2×Dic23⋊C4—21no—
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C2×C4×Dic23—21no—
45C22×C23⋊C8—22no—
46C4×Dic46—42no—
47C23×C22⋊C8—24no—
48C4×C8×C23—42no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C22⋊(C23⋊C8)—42no—
55C24×C23C22⋊C411yescharacteristic
56C22×C4×C23—22no—
57C22×C4×C23—22no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—41no—
61C22×C4×C23—41no—
62C22×C4×C23—41no—
63C22×C4×C23—41no—
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C2×C812yes—
68C22×C4×C23M1612yes—
69C22×C4×C23C22×C411yescharacteristic
70C22×C4×C23C2×D411yescharacteristic
71C22×C4×C23C2×D411yescharacteristic
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C2×Dic46—21no—
77C2×Dic46—41no—
78C2×Dic46—41no—
79C2×Dic46C2×C812yes—
80C2×C8×C23—24no—
81C2×C8×C23—42no—
82C2×C8×C23—42no—
83C42×C23—22no—
84C42×C23—22no—
85C42×C23—41no—
86C42×C23—41no—
87C22⋊Dic23—24no—
88C22⋊Dic23—42no—
89C4⋊Dic23—21no—
90C4⋊Dic23—41no—
91C4⋊Dic23—41no—
92C4⋊Dic23C2×C812yes—
93Dic23⋊C4—24no—
94Dic23⋊C4—42no—
95Dic23⋊C4—42no—
96C4×Dic23—42no—
97C4×Dic23—42no—
98C2×C23⋊C8—42no—
99C2×C23⋊C8—42no—
100C2×C23⋊C8—42no—
101#7583—231nomaximal, Sylow
102C23×C23—21no—
103C23×C23—21no—
104C23×C23—21no—
105C23×C23—21no—
106C23×C23—21no—
107C23×C23—21no—
108C23×C23C22⋊C812yes—
109C23×C23C2×C22⋊C411yescharacteristic
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—42no—
123C2×C4×C23—42no—
124C2×C4×C23—44no—
125C2×C4×C23—44no—
126C2×C4×C23C22⋊C812yes—
127C2×C4×C23#9912yes—
128C2×C4×C23#10412yes—
129C2×C4×C23C22×C811yescharacteristic
130C2×C4×C23C2×M1611yescharacteristic
131C2×C4×C23#13512yes—
132C2×C4×C23#13712yes—
133C2×Dic23—22no—
134C2×Dic23—22no—
135C2×Dic23—41no—
136C2×Dic23—41no—
137C2×Dic23—41no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23—41no—
145Dic46—42no—
146Dic46—42no—
147C8×C23—44no—
148C23⋊C8—82no—
149C4×C22⋊Q8—231no—
150#1817—231no—
151C4×C22⋊C8D2311yescharacteristic
152#1272—232no—
153#1271—232no—
154C22×C23—22no—
155C22×C23—22no—
156C22×C23—22no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23C2×C22⋊C811yescharacteristic
162C22×C23C2×#9911yescharacteristic
163C22×C23#41311yescharacteristic
164C22×C23#41611yescharacteristic
165C22×C23#41911yescharacteristic
166C22×C23C2×#10411yescharacteristic
167C22×C23#42111yescharacteristic
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—22no—
171C4×C23—22no—
172C4×C23—22no—
173C4×C23—22no—
174C4×C23—22no—
175Dic23—42no—
176Dic23—42no—
177Dic23—81no—
178Dic23—81no—
179C2×C22⋊Q8—231no—
180C2×C4×Q8—231no—
181C22×C42C2×D2311yescharacteristic
182C2×C22⋊C8—21no—
183C2×C22⋊C8—461no—
184C2×C4×C8—21no—
185#391—231no—
186#389—231no—
187#387—461no—
188#385—461no—
189#380—231no—
190C4×C4⋊C4—231no—
191C4×C4⋊C4—461no—
192C4×C22⋊C4—461no—
193#336—232no—
194#336—461no—
195#336C2×D2312yes—
196C2×C23—42no—
197C2×C23#145911yescharacteristic
198C2×C23#147611yescharacteristic
199C2×C23#147911yescharacteristic
200C2×C23#150811yescharacteristic
201C2×C23#151611yescharacteristic
202C2×C23#152911yescharacteristic
203C2×C23#155411yescharacteristic
204C22×Q8—231no—
205C23×C4C4×D2311yescharacteristic
206C23×C4D9211yescharacteristic
207C23×C4C22⋊D2311yescharacteristic
208C22×C8—22no—
209C22×C8—462no—
210C22⋊Q8—234no—
211C22⋊Q8—462no—
212C4×Q8—922no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—231no—
215C2×C4⋊C4—231no—
216C2×C4⋊C4—461no—
217C2×C4⋊C4—461no—
218C2×C4⋊C4—461no—
219C2×C22⋊C4—461no—
220C2×C22⋊C4—461no—
221C2×C42—42no—
222C2×C42—461no—
223C2×C42—461no—
224C2×C42C4×D2311yescharacteristic
225C2×C42D9211yescharacteristic
226C2×C42C22⋊D2311yescharacteristic
227C2×C42C22×D2311yescharacteristic
228C22⋊C8—24no—
229C22⋊C8—922no—
230C4×C8—42no—
231#95—461no—
232#95—461no—
233#95—461no—
234#95—461no—
235#95—461no—
236C23#758311yescharacteristic, complemented, Sylow
237C24(C2×D23)⋊C411yescharacteristic
238C2×Q8—232no—
239C2×Q8—461no—
240C2×Q8—921no—
241C2×Q8—921no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4C8×D2312yes—
255C22×C4#6726212yes—
256C22×C4(C2×D23)⋊C411yescharacteristic
257C22×C4(C2×D23)⋊C411yescharacteristic
258C22×C4(C2×D23)⋊C411yescharacteristic
259C22×C4C2×C4×D2311yescharacteristic
260C22×C4C2×D9211yescharacteristic
261C22×C4C2×C22⋊D2311yescharacteristic
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—922no—
266C2×C8—922no—
267C2×C8—922no—
268C4⋊C4—232no—
269C4⋊C4—461no—
270C4⋊C4—464no—
271C4⋊C4—921no—
272C4⋊C4—921no—
273C4⋊C4—922no—
274C4⋊C4—922no—
275C22⋊C4—464no—
276C22⋊C4—922no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—922no—
282C42—922no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23(C2×D23)⋊C812yes—
290C23C2×(C2×D23)⋊C411yescharacteristic
291Q8—922no—
292Q8—922no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—462no—
310C2×C4—462no—
311C2×C4—921no—
312C2×C4—921no—
313C2×C4—921no—
314C2×C4—921no—
315C2×C4—921no—
316C2×C4—921no—
317C2×C4—921no—
318C2×C4—921no—
319C2×C4—921no—
320C2×C4—921no—
321C2×C4#1062498712yes—
322C2×C4#1062498812yes—
323C2×C4(C2×D23)⋊C812yes—
324C2×C4C2×C8×D2311yescharacteristic
325C2×C4C2×#6726211yescharacteristic
326C2×C4#1062507512yes—
327C2×C4#1062512212yes—
328C8—44no—
329C8—1842no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×(C2×D23)⋊C811yescharacteristic
338C22C2×#1062498811yescharacteristic
339C22#1309239911yescharacteristic
340C22#1309241411yescharacteristic
341C22#1309242511yescharacteristic
342C22C2×#1062498711yescharacteristic
343C22#1309243311yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—22no—
348C4—21no—
349C4—21no—
350C4—22no—
351C4—922no—
352C4—922no—
353C4—1841no—
354C4—1841no—
355C2—42no—
356C2#1567171311yescharacteristic
357C2#1567178011yescharacteristic
358C2#1567179111yescharacteristic
359C2#1567191611yescharacteristic
360C2#1567195411yescharacteristic
361C2#1567200211yescharacteristic
362C2#1567210511yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC4×C23×C22⋊C8C2
socleC23×C23C2×C22⋊C4
hypercenterC4×C22⋊C8D23
hypocenterC23#7583
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #15671222C2semidirect
4. #15671219C2semidirect
39. #10625095C8semidirect
236. C23#7583semidirect