Finite Group Databasebeta

← #19212224

Subgroups — #19212224

Order 5888.

568 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675880C211yesmaximal, characteristic
2C2×#13092172C211yesmaximal, characteristic
3#15671221C212yesmaximal, complemented
4#15671219C212yesmaximal, complemented
5C23×#1817C211yesmaximal, characteristic
6C23×C23⋊C8—21no—
7C2×#10625097C411yescharacteristic
8C2×#10625097C411yescharacteristic
9#13092315C411yescharacteristic
10#13092315C411yescharacteristic
11#13092315C2211yescharacteristic
12#13092315C2211yescharacteristic
13#13092290—21no—
14#13092290—21no—
15C4×Dic23⋊C4—21no—
16C4×Dic23⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C23×#336—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—24no—
48C22×C23⋊C8—22no—
49C22×C23⋊C8—42no—
50C22×C23⋊C8—42no—
51C23×C22⋊C8—42no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C24×C23C22⋊C411yescharacteristic
57C22×C4×C23—22no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23—21no—
62C22×C4×C23—21no—
63C22×C4×C23—22no—
64C22×C4×C23—22no—
65C22×C4×C23—41no—
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C22⋊C411yescharacteristic
68C22×C4×C23C22⋊C411yescharacteristic
69C22×C4×C23C2×C812yes—
70C22×C4×C23M1612yes—
71C22×C4×C23C22×C411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23—21no—
77C22×Dic23—21no—
78C2×C8×C23—42no—
79C2×C8×C23—42no—
80C2×C8×C23—42no—
81C42×C23—41no—
82C42×C23—41no—
83C42×C23—41no—
84C42×C23—41no—
85C22⋊Dic23—24no—
86C22⋊Dic23—42no—
87C4⋊Dic23—21no—
88C4⋊Dic23—21no—
89C4⋊Dic23—41no—
90C4⋊Dic23—41no—
91C4⋊Dic23C2×C812yescomplemented
92C4⋊Dic23C2×C812yescomplemented
93Dic23⋊C4—42no—
94Dic23⋊C4—42no—
95Dic23⋊C4—42no—
96Dic23⋊C4—41no—
97Dic23⋊C4—41no—
98C4×Dic23—24no—
99C4×Dic23—42no—
100C2×C23⋊C8—24no—
101C2×C23⋊C8—48no—
102C2×C23⋊C8—42no—
103C2×C23⋊C8—42no—
104#7579—231nomaximal, Sylow
105C23×C23—21no—
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C23×C23C22⋊C812yes—
110C23×C23#9912yes—
111C23×C23#10112yes—
112C23×C23C2×C22⋊C411yescharacteristic
113C2×C4×C23—24no—
114C2×C4×C23—24no—
115C2×C4×C23—24no—
116C2×C4×C23—24no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—44no—
131C2×C4×C23C22⋊C812yes—
132C2×C4×C23#10412yes—
133C2×C4×C23C22×C811yescharacteristic
134C2×C4×C23C2×M1611yescharacteristic
135C2×C4×C23#13512yes—
136C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C23#13711yescharacteristic
138C2×Dic23—22no—
139C2×Dic23—22no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23—41no—
145C2×Dic23—41no—
146C2×Dic23—41no—
147C2×Dic23—41no—
148C2×Dic23—41no—
149C2×Dic23—41no—
150C8×C23—82no—
151C23⋊C8—44no—
152#2296—231no—
153#1817D2311yescharacteristic
154C2×#336—231no—
155#1271—232no—
156#1271—232no—
157C22×C23—22no—
158C22×C23—22no—
159C22×C23—22no—
160C22×C23—22no—
161C22×C23—22no—
162C22×C23—22no—
163C22×C23#32414yes—
164C22×C23C2×C22⋊C811yescharacteristic
165C22×C23C2×#9911yescharacteristic
166C22×C23C2×#10111yescharacteristic
167C22×C23#41611yescharacteristic
168C22×C23#41711yescharacteristic
169C22×C23C2×#10411yescharacteristic
170C22×C23#42111yescharacteristic
171C4×C23—22no—
172C4×C23—21no—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—22no—
176C4×C23—21no—
177C4×C23—22no—
178C4×C23—41no—
179Dic23—42no—
180Dic23—42no—
181Dic23—81no—
182Dic23—81no—
183C23×C8—461no—
184C2×#117—231no—
185C2×#117—231no—
186C22×C42C2×D2311yescharacteristic
187C2×C22⋊C8—21no—
188#389—231no—
189#389—231no—
190#389—231no—
191#389—231no—
192#385—461no—
193#385—461no—
194C4×C4⋊C4—461no—
195C4×C4⋊C4—461no—
196#336—21no—
197#336—232no—
198#336—461no—
199#336C2×D2312yes—
200C2×C23—24no—
201C2×C23C2×#32411yescharacteristic
202C2×C23#147611yescharacteristic
203C2×C23#147711yescharacteristic
204C2×C23#150411yescharacteristic
205C2×C23#151611yescharacteristic
206C2×C23#153111yescharacteristic
207C2×C23#155211yescharacteristic
208C23×C4C4×D2311yescharacteristic
209C23×C4D9211yescharacteristic
210C23×C4C22⋊D2311yescharacteristic
211C22×C8—22no—
212C22×C8—464no—
213C22×C8—462no—
214C22×C8—922no—
215C22×C8—922no—
216#117—234no—
217#117—462no—
218#117—922no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—231no—
221C2×C4⋊C4—231no—
222C2×C4⋊C4—231no—
223C2×C4⋊C4—461no—
224C2×C4⋊C4—461no—
225C2×C4⋊C4—461no—
226C2×C4⋊C4—461no—
227C2×C22⋊C4—461no—
228C2×C22⋊C4—461no—
229C2×C42—42no—
230C2×C42—461no—
231C2×C42—461no—
232C2×C42C4×D2311yescharacteristic
233C2×C42D9211yescharacteristic
234C2×C42C22⋊D2311yescharacteristic
235C2×C42C22×D2311yescharacteristic
236C22⋊C8—42no—
237#95—461no—
238#95—461no—
239#95—461no—
240#95—461no—
241C23#757911yescharacteristic, complemented, Sylow
242C24(C2×D23)⋊C411yescharacteristic
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4C8×D2312yes—
257C22×C4#6726212yes—
258C22×C4(C2×D23)⋊C411yescharacteristic
259C22×C4(C2×D23)⋊C411yescharacteristic
260C22×C4(C2×D23)⋊C411yescharacteristic
261C22×C4C2×C4×D2311yescharacteristic
262C22×C4C2×D9211yescharacteristic
263C22×C4C2×C22⋊D2311yescharacteristic
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—464no—
268C2×C8—928no—
269C2×C8—922no—
270C2×C8—922no—
271C4⋊C4—232no—
272C4⋊C4—232no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—921no—
276C4⋊C4—921no—
277C4⋊C4—922no—
278C4⋊C4—921no—
279C4⋊C4—921no—
280C4⋊C4—922no—
281C4⋊C4—922no—
282C22⋊C4—464no—
283C22⋊C4—922no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—464no—
289C42—922no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1062498812yes—
295C23(C2×D23)⋊C812yes—
296C23#1062500612yes—
297C23C2×(C2×D23)⋊C411yescharacteristic
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—44no—
316C2×C4—462no—
317C2×C4—462no—
318C2×C4—921no—
319C2×C4—921no—
320C2×C4—921no—
321C2×C4—921no—
322C2×C4—921no—
323C2×C4—921no—
324C2×C4—921no—
325C2×C4—921no—
326C2×C4—921no—
327C2×C4—921no—
328C2×C4(C2×D23)⋊C812yes—
329C2×C4#1062500712yes—
330C2×C4C2×C8×D2311yescharacteristic
331C2×C4C2×#6726211yescharacteristic
332C2×C4#1062507911yescharacteristic
333C2×C4#1062508011yescharacteristic
334C2×C4#1062512112yes—
335C8—82no—
336C8—924no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22#1309214214yes—
344C22C2×(C2×D23)⋊C811yescharacteristic
345C22C2×#1062498811yescharacteristic
346C22C2×#1062500611yescharacteristic
347C22#1309241111yescharacteristic
348C22#1309241911yescharacteristic
349C22C2×#1062500711yescharacteristic
350C22#1309243511yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—41no—
359C4—922no—
360C4—922no—
361C4—1841no—
362C4—1841no—
363C2—24no—
364C2C2×#1309214211yescharacteristic
365C2#1567177711yescharacteristic
366C2#1567178511yescharacteristic
367C2#1567190211yescharacteristic
368C2#1567195111yescharacteristic
369C2#1567201311yescharacteristic
370C2#1567209811yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1817C2
socleC23×C23C2×C22⋊C4
hypercenter#1817D23
hypocenterC23#7579
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #15671221C2semidirect
4. #15671219C2semidirect
36. #10625097C8semidirect
91. C4⋊Dic23C2×C8semidirect
92. C4⋊Dic23C2×C8semidirect
241. C23#7579semidirect