Finite Group Databasebeta

← #19212317

Subgroups — #19212317

Order 5888.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 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#15671221C212yesmaximal, complemented
5C23×#1797C211yesmaximal, 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×C4⋊C8—21no—
21C2×C23×C22⋊C8—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×C4⋊C8—42no—
48C23×C22⋊C8—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—21no—
58C22×C4×C23—22no—
59C22×C4×C23—21no—
60C22×C4×C23—41no—
61C22×C4×C23—41no—
62C22×C4×C23—41no—
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×Dic46—21no—
78C2×Dic46—41no—
79C2×Dic46—41no—
80C2×Dic46C2×C812yes—
81C2×C8×C23—42no—
82C2×C8×C23—42no—
83C2×C8×C23—42no—
84C42×C23—22no—
85C42×C23—22no—
86C42×C23—41no—
87C42×C23—41no—
88C22⋊Dic23—24no—
89C22⋊Dic23—42no—
90C4⋊Dic23—21no—
91C4⋊Dic23—41no—
92C4⋊Dic23—41no—
93C4⋊Dic23C2×C812yes—
94Dic23⋊C4—24no—
95Dic23⋊C4—42no—
96Dic23⋊C4—41no—
97Dic23⋊C4—41no—
98C4×Dic23—42no—
99C4×Dic23—42no—
100C2×C23⋊C8—42no—
101C2×C23⋊C8—42no—
102C2×C23⋊C8—42no—
103#7600—231nomaximal, Sylow
104C23×C23—21no—
105C23×C23—21no—
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C22⋊C812yes—
111C23×C23C2×C22⋊C411yescharacteristic
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—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—42no—
126C2×C4×C23—42no—
127C2×C4×C23—44no—
128C2×C4×C23—42no—
129C2×C4×C23—42no—
130C2×C4×C23C22⋊C812yes—
131C2×C4×C23#9912yes—
132C2×C4×C23C22×C811yescharacteristic
133C2×C4×C23C2×M1611yescharacteristic
134C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C23#13712yes—
136C2×C4×C23#13711yescharacteristic
137C2×Dic23—22no—
138C2×Dic23—22no—
139C2×Dic23—41no—
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—
149Dic46—42no—
150Dic46—42no—
151C8×C23—82no—
152C23⋊C8—82no—
153C4×C22⋊Q8—231no—
154#1817—231no—
155#1797D2311yescharacteristic
156#1272—232no—
157#1271—232no—
158C22×C23—22no—
159C22×C23—22no—
160C22×C23—22no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23C2×C22⋊C811yescharacteristic
166C22×C23C2×#9911yescharacteristic
167C22×C23#41311yescharacteristic
168C22×C23#41711yescharacteristic
169C22×C23#41911yescharacteristic
170C22×C23#42111yescharacteristic
171C22×C23#42111yescharacteristic
172C4×C23—21no—
173C4×C23—21no—
174C4×C23—22no—
175C4×C23—22no—
176C4×C23—22no—
177C4×C23—21no—
178C4×C23—21no—
179C4×C23—41no—
180Dic23—42no—
181Dic23—42no—
182Dic23—81no—
183Dic23—81no—
184C2×C22⋊Q8—231no—
185C2×C4×Q8—231no—
186C22×C42C2×D2311yescharacteristic
187C2×C4⋊C8—21no—
188C2×C22⋊C8—21no—
189C2×C22⋊C8—461no—
190#391—231no—
191#389—231no—
192#387—461no—
193#385—461no—
194#380—231no—
195C4×C4⋊C4—231no—
196C4×C4⋊C4—461no—
197C4×C22⋊C4—461no—
198#336—232no—
199#336—461no—
200#336C2×D2312yes—
201C2×C23—42no—
202C2×C23#145911yescharacteristic
203C2×C23#147711yescharacteristic
204C2×C23#147911yescharacteristic
205C2×C23#151111yescharacteristic
206C2×C23#151311yescharacteristic
207C2×C23#153511yescharacteristic
208C2×C23#155911yescharacteristic
209C22×Q8—231no—
210C23×C4C4×D2311yescharacteristic
211C23×C4D9211yescharacteristic
212C23×C4C22⋊D2311yescharacteristic
213C22×C8—22no—
214C22×C8—462no—
215C22⋊Q8—234no—
216C22⋊Q8—462no—
217C4×Q8—922no—
218C2×C4⋊C4—231no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—231no—
221C2×C4⋊C4—461no—
222C2×C4⋊C4—461no—
223C2×C4⋊C4—461no—
224C2×C22⋊C4—461no—
225C2×C22⋊C4—461no—
226C2×C42—42no—
227C2×C42—461no—
228C2×C42—461no—
229C2×C42C4×D2311yescharacteristic
230C2×C42D9211yescharacteristic
231C2×C42C22⋊D2311yescharacteristic
232C2×C42C22×D2311yescharacteristic
233C4⋊C8—42no—
234C22⋊C8—42no—
235C22⋊C8—922no—
236#95—461no—
237#95—461no—
238#95—461no—
239#95—461no—
240#95—461no—
241C23#760011yescharacteristic, complemented, Sylow
242C24(C2×D23)⋊C411yescharacteristic
243C2×Q8—232no—
244C2×Q8—461no—
245C2×Q8—921no—
246C2×Q8—921no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—461no—
257C22×C4—461no—
258C22×C4—461no—
259C22×C4—461no—
260C22×C4C8×D2312yes—
261C22×C4#6726212yes—
262C22×C4(C2×D23)⋊C411yescharacteristic
263C22×C4(C2×D23)⋊C411yescharacteristic
264C22×C4(C2×D23)⋊C411yescharacteristic
265C22×C4C2×C4×D2311yescharacteristic
266C22×C4C2×D9211yescharacteristic
267C22×C4C2×C22⋊D2311yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—922no—
272C2×C8—922no—
273C2×C8—922no—
274C4⋊C4—232no—
275C4⋊C4—461no—
276C4⋊C4—464no—
277C4⋊C4—921no—
278C4⋊C4—921no—
279C4⋊C4—922no—
280C4⋊C4—921no—
281C4⋊C4—921no—
282C22⋊C4—464no—
283C22⋊C4—922no—
284C42—22no—
285C42—22no—
286C42—41no—
287C42—41no—
288C42—922no—
289C42—922no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23(C2×D23)⋊C812yes—
297C23C2×(C2×D23)⋊C411yescharacteristic
298Q8—922no—
299Q8—922no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—462no—
319C2×C4—462no—
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—921no—
329C2×C4—921no—
330C2×C4#1062498812yes—
331C2×C4(C2×D23)⋊C812yes—
332C2×C4C2×C8×D2311yescharacteristic
333C2×C4C2×#6726211yescharacteristic
334C2×C4#1062508012yes—
335C2×C4#1062510311yescharacteristic
336C2×C4#1062511311yescharacteristic
337C8—82no—
338C8—1842no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×(C2×D23)⋊C811yescharacteristic
347C22C2×#1062498811yescharacteristic
348C22#1309239911yescharacteristic
349C22#1309241611yescharacteristic
350C22#1309242711yescharacteristic
351C22#1309243311yescharacteristic
352C22#1309243511yescharacteristic
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—22no—
360C4—41no—
361C4—922no—
362C4—922no—
363C4—1841no—
364C4—1841no—
365C2—42no—
366C2#1567171311yescharacteristic
367C2#1567178211yescharacteristic
368C2#1567179311yescharacteristic
369C2#1567193111yescharacteristic
370C2#1567193811yescharacteristic
371C2#1567202911yescharacteristic
372C2#1567212511yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1797C2
socleC23×C23C2×C22⋊C4
hypercenter#1797D23
hypocenterC23#7600
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #15671222C2semidirect
4. #15671221C2semidirect
39. #10625095C8semidirect
241. C23#7600semidirect