Finite Group Databasebeta

← #19212160

Subgroups — #19212160

Order 5888.

550 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675880C211yesmaximal, characteristic
2C4×C22⋊(C23⋊C8)C211yesmaximal, characteristic
3#15671221C212yesmaximal, complemented
4#15671219C212yesmaximal, complemented
5C4×C23×C22⋊C8C211yesmaximal, characteristic
6C2×#10625097C411yescharacteristic
7C2×#10625097C411yescharacteristic
8C2×C22⋊(C23⋊C8)—21no—
9C2×C4×C23⋊C8—21no—
10#13092315C411yescharacteristic
11#13092315C411yescharacteristic
12#13092315C2211yescharacteristic
13#13092315C2211yescharacteristic
14#13092290—21no—
15#13092290—21no—
16C4×Dic23⋊C4—21no—
17C4×Dic23⋊C4—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×C8×C23—22no—
27C2×C42×C23—42no—
28C2×C42×C23C2×C411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23C2311yescharacteristic
32C2×C22⋊Dic23—21no—
33C2×C22⋊Dic23—21no—
34#10625097—22no—
35#10625097—42no—
36#10625097C814yescomplemented
37C2×C4⋊Dic23C2×C411yescharacteristic
38C2×C4⋊Dic23C2×C411yescharacteristic
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×Dic23⋊C4—21no—
44C2×Dic23⋊C4—21no—
45C2×C4×Dic23—21no—
46C2×C4×Dic23—21no—
47C22×C23⋊C8—22no—
48C23×C22⋊C8—24no—
49C4×C8×C23—42no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C22⋊(C23⋊C8)—24no—
55C4×C23⋊C8—42no—
56C24×C23C22⋊C411yescharacteristic
57C22×C4×C23—22no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23—41no—
64C22×C4×C23—41no—
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C22⋊C411yescharacteristic
68C22×C4×C23C2×C812yes—
69C22×C4×C23M1612yes—
70C22×C4×C23C22×C411yescharacteristic
71C22×C4×C23C2×D411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23—21no—
77C2×C8×C23—24no—
78C2×C8×C23—42no—
79C2×C8×C23—42no—
80C42×C23—22no—
81C42×C23—22no—
82C42×C23—41no—
83C42×C23—41no—
84C22⋊Dic23—24no—
85C22⋊Dic23—42no—
86C4⋊Dic23—21no—
87C4⋊Dic23—21no—
88C4⋊Dic23—41no—
89C4⋊Dic23—41no—
90C4⋊Dic23C2×C812yes—
91C4⋊Dic23C2×C812yes—
92Dic23⋊C4—42no—
93Dic23⋊C4—42no—
94Dic23⋊C4—42no—
95Dic23⋊C4—42no—
96C4×Dic23—24no—
97C4×Dic23—42no—
98C2×C23⋊C8—24no—
99C2×C23⋊C8—42no—
100C2×C23⋊C8—42no—
101#7564—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—24no—
121C2×C4×C23—24no—
122C2×C4×C23—44no—
123C2×C4×C23—44no—
124C2×C4×C23C22⋊C812yes—
125C2×C4×C23#9912yes—
126C2×C4×C23#10112yes—
127C2×C4×C23#10412yes—
128C2×C4×C23#10412yes—
129C2×C4×C23C22×C811yescharacteristic
130C2×C4×C23C2×M1611yescharacteristic
131C2×C4×C23#13512yes—
132C2×C4×C23#13512yes—
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—
145C8×C23—44no—
146C23⋊C8—44no—
147#2296—231no—
148C4×C22⋊C8—231no—
149C4×C22⋊C8D2311yescharacteristic
150#1271—232no—
151#1271—232no—
152C22×C23—22no—
153C22×C23—22no—
154C22×C23—22no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23C2×C22⋊C811yescharacteristic
160C22×C23C2×#9911yescharacteristic
161C22×C23C2×#10111yescharacteristic
162C22×C23#41611yescharacteristic
163C22×C23#41611yescharacteristic
164C22×C23C2×#10411yescharacteristic
165C22×C23C2×#10411yescharacteristic
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—22no—
169C4×C23—22no—
170C4×C23—22no—
171C4×C23—22no—
172C4×C23#32414yes—
173Dic23—42no—
174Dic23—42no—
175Dic23—81no—
176Dic23—81no—
177C2×#117—231no—
178C2×#117—231no—
179C22×C42C2×D2311yescharacteristic
180C2×C22⋊C8—21no—
181C2×C22⋊C8—461no—
182C2×C4×C8—21no—
183C2×C4×C8—461no—
184#389—231no—
185#389—231no—
186#389—231no—
187#389—231no—
188#385—461no—
189#385—461no—
190C4×C4⋊C4—461no—
191C4×C4⋊C4—461no—
192#336—232no—
193#336C2×D2312yes—
194C2×C23—42no—
195C2×C23C2×#32411yescharacteristic
196C2×C23#147611yescharacteristic
197C2×C23#147611yescharacteristic
198C2×C23#150111yescharacteristic
199C2×C23#150111yescharacteristic
200C2×C23#152611yescharacteristic
201C2×C23#154411yescharacteristic
202C23×C4C4×D2311yescharacteristic
203C23×C4D9211yescharacteristic
204C23×C4C22⋊D2311yescharacteristic
205C22×C8—22no—
206C22×C8—462no—
207#117—234no—
208#117—462no—
209#117—922no—
210C2×C4⋊C4—231no—
211C2×C4⋊C4—231no—
212C2×C4⋊C4—231no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—461no—
215C2×C4⋊C4—461no—
216C2×C4⋊C4—461no—
217C2×C4⋊C4—461no—
218C2×C22⋊C4—461no—
219C2×C22⋊C4—461no—
220C2×C42—42no—
221C2×C42—461no—
222C2×C42—461no—
223C2×C42C4×D2311yescharacteristic
224C2×C42D9211yescharacteristic
225C2×C42C22⋊D2311yescharacteristic
226C2×C42C22×D2311yescharacteristic
227C22⋊C8—24no—
228C22⋊C8—464no—
229C4×C8—42no—
230C4×C8—922no—
231#95—461no—
232#95—461no—
233#95—461no—
234#95—461no—
235C23#756411yescharacteristic, complemented, Sylow
236C24(C2×D23)⋊C411yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4—461no—
249C22×C4C8×D2312yes—
250C22×C4#6726212yes—
251C22×C4(C2×D23)⋊C411yescharacteristic
252C22×C4(C2×D23)⋊C411yescharacteristic
253C22×C4(C2×D23)⋊C411yescharacteristic
254C22×C4C2×C4×D2311yescharacteristic
255C22×C4C2×D9211yescharacteristic
256C22×C4C2×C22⋊D2311yescharacteristic
257C2×C8—24no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—464no—
261C2×C8—922no—
262C2×C8—922no—
263C4⋊C4—232no—
264C4⋊C4—232no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4—921no—
268C4⋊C4—921no—
269C4⋊C4—922no—
270C4⋊C4—922no—
271C4⋊C4—922no—
272C4⋊C4—922no—
273C22⋊C4—464no—
274C22⋊C4—922no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—464no—
280C42—922no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23(C2×D23)⋊C812yes—
288C23C2×(C2×D23)⋊C411yescharacteristic
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—462no—
304C2×C4—462no—
305C2×C4—921no—
306C2×C4—921no—
307C2×C4—921no—
308C2×C4—921no—
309C2×C4—921no—
310C2×C4—921no—
311C2×C4—921no—
312C2×C4—921no—
313C2×C4—921no—
314C2×C4—921no—
315C2×C4#1062498712yes—
316C2×C4#1062498812yes—
317C2×C4(C2×D23)⋊C812yes—
318C2×C4#1062500612yes—
319C2×C4#1062500712yes—
320C2×C4C2×C8×D2311yescharacteristic
321C2×C4C2×#6726211yescharacteristic
322C2×C4#1062507512yes—
323C2×C4#1062512112yes—
324C8—44no—
325C8—924no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22C2×(C2×D23)⋊C811yescharacteristic
334C22C2×#1062498811yescharacteristic
335C22C2×#1062500611yescharacteristic
336C22#1309241111yescharacteristic
337C22#1309241411yescharacteristic
338C22C2×#1062500711yescharacteristic
339C22C2×#1062498711yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—922no—
347C4—922no—
348C4—1841no—
349C4—1841no—
350C4#1309214214yes—
351C2—42no—
352C2C2×#1309214211yescharacteristic
353C2#1567177711yescharacteristic
354C2#1567178011yescharacteristic
355C2#1567188611yescharacteristic
356C2#1567188911yescharacteristic
357C2#1567199111yescharacteristic
358C2#1567206111yescharacteristic
subgroupG/H
centerC22×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC4×C23×C22⋊C8C2
socleC23×C23C2×C22⋊C4
hypercenterC4×C22⋊C8D23
hypocenterC23#7564
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #15671221C2semidirect
4. #15671219C2semidirect
36. #10625097C8semidirect
235. C23#7564semidirect