Finite Group Databasebeta

← #19212328

Subgroups — #19212328

Order 5888.

440 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#15675968C211yesmaximal, characteristic
2#15673539C211yesmaximal, characteristic
3#15673539C211yesmaximal, characteristic
4#15671221C211yesmaximal, characteristic
5#15671220C211yesmaximal, characteristic
6#15671219C211yesmaximal, characteristic
7C23×#1271C211yesmaximal, characteristic
8C2×#10625059C411yescharacteristic
9C2×#10625058—21no—
10#13092321—21no—
11#13092315C2211yescharacteristic
12#13092312—21no—
13#13092286C411yescharacteristic
14C4⋊C4×Dic23C411yescharacteristic
15C4⋊C4×Dic23C411yescharacteristic
16#13092268—21no—
17C42×Dic23C2211yescharacteristic
18#13092172C2211yescharacteristic
19#13092172C2211yescharacteristic
20#13092171—21no—
21#13092171—21no—
22#13092171—21no—
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×Dic46—21no—
28C22×C8×C23—21no—
29C22×C8×C23—21no—
30C2×C4⋊C4×C23—21no—
31C2×C4⋊C4×C23C2×C411yescharacteristic
32C2×C4⋊C4×C23C2×C411yescharacteristic
33C2×C42×C23C2311yescharacteristic
34C2×C4⋊Dic23C2×C411yescharacteristic
35C2×C4⋊Dic23C2×C411yescharacteristic
36C2×Dic23⋊C4—21no—
37C2×Dic23⋊C4—21no—
38C2×Dic23⋊C4—21no—
39C2×Dic23⋊C4—21no—
40C2×C4×Dic23—21no—
41C2×C4×Dic23—21no—
42C2×C4×Dic23C2×C411yescharacteristic
43C2×C4×Dic23C2×C411yescharacteristic
44C2×C4×Dic23D411yescharacteristic
45C2×C4×Dic23D411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C22×C23⋊C8—21no—
49C22×C23⋊C8—21no—
50#10625059—22no—
51#10625059C814yescomplemented
52#10625058—42no—
53#10625058—42no—
54C23×#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58C22×C4×C23—21no—
59C22×C4×C23—21no—
60C22×C4×C23C22×C411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×C4×C23C2×D411yescharacteristic
63C22×Dic23—21no—
64C22×Dic23—21no—
65C22×Dic23C22⋊C411yescharacteristic
66C22×Dic23C22⋊C411yescharacteristic
67C22×Dic23C22⋊C411yescharacteristic
68C22×Dic23C22⋊C411yescharacteristic
69C2×Dic46—24no—
70C2×Dic46—42no—
71C2×Dic46—42no—
72C2×C8×C23—41no—
73C2×C8×C23—41no—
74C2×C8×C23—41no—
75C2×C8×C23—41no—
76C2×C8×C23—41no—
77C2×C8×C23—41no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23—41no—
80C4⋊C4×C23—41no—
81C4⋊C4×C23—41no—
82C4⋊C4×C23C2×C812yes—
83C42×C23—41no—
84C4⋊Dic23—21no—
85C4⋊Dic23—41no—
86C4⋊Dic23C2×C812yes—
87Dic23⋊C4—24no—
88Dic23⋊C4—42no—
89Dic23⋊C4—42no—
90Dic23⋊C4—41no—
91Dic23⋊C4—41no—
92C4×Dic23—21no—
93C4×Dic23—21no—
94C4×Dic23—21no—
95C4×Dic23—21no—
96C4×Dic23—22no—
97C4×Dic23—41no—
98C4×Dic23—41no—
99C4×Dic23—42no—
100C4×Dic23—42no—
101C4×Dic23C2×C812yes—
102C4×Dic23M1612yes—
103C2×C23⋊C8—41no—
104C2×C23⋊C8—41no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8—41no—
108C2×C23⋊C8—41no—
109#7604—231nomaximal, Sylow
110C23×C23C2×C22⋊C411yescharacteristic
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—22no—
118C2×C4×C23—41no—
119C2×C4×C23—41no—
120C2×C4×C23—41no—
121C2×C4×C23—41no—
122C2×C4×C23—41no—
123C2×C4×C23C22×C811yescharacteristic
124C2×C4×C23C2×M1611yescharacteristic
125C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C23#13711yescharacteristic
128C2×C4×C23#13711yescharacteristic
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—22no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23C22⋊C812yes—
145C2×Dic23C22⋊C812yes—
146C2×Dic23#10112yes—
147Dic46—48no—
148C8×C23—81no—
149C8×C23—81no—
150C23⋊C8—81no—
151C23⋊C8—81no—
152C4×C4⋊Q8—231no—
153#1839—231no—
154#1839—231no—
155#1271—231no—
156#1271—231no—
157#1271—231no—
158#1271D2311yescharacteristic
159C22×C23C2×C22⋊C811yescharacteristic
160C22×C23#41011yescharacteristic
161C22×C23C2×#10111yescharacteristic
162C22×C23#41811yescharacteristic
163C22×C23#41911yescharacteristic
164C22×C23#42111yescharacteristic
165C22×C23#42111yescharacteristic
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—21no—
172C4×C23—42no—
173C4×C23—81no—
174Dic23—22no—
175Dic23—22no—
176Dic23—22no—
177Dic23—41no—
178Dic23—42no—
179Dic23—81no—
180C2×C4⋊Q8—231no—
181C2×C4×Q8—461no—
182#391—461no—
183#389—231no—
184#389—461no—
185#389C2×D2311yescharacteristic
186#384—231no—
187C4×C4⋊C4—231no—
188C4×C4⋊C4—231no—
189C4×C4⋊C4—461no—
190C43—231no—
191#336—231no—
192#336—231no—
193#336—461no—
194#336—461no—
195#336—461no—
196#336—461no—
197#336C2×D2311yescharacteristic
198#336C2×D2311yescharacteristic
199C2×C23#146111yescharacteristic
200C2×C23#147811yescharacteristic
201C2×C23#147911yescharacteristic
202C2×C23#151411yescharacteristic
203C2×C23#151511yescharacteristic
204C2×C23#153711yescharacteristic
205C2×C23#155611yescharacteristic
206C22×Q8—461no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—461no—
210C22×C8—461no—
211C4⋊Q8—234no—
212C4⋊Q8—462no—
213C4×Q8—922no—
214C4×Q8—922no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—231no—
217C2×C4⋊C4—231no—
218C2×C4⋊C4—461no—
219C2×C4⋊C4—461no—
220C2×C4⋊C4—461no—
221C2×C4⋊C4—461no—
222C2×C4⋊C4C4×D2311yescharacteristic
223C2×C4⋊C4C4×D2311yescharacteristic
224C2×C42—231no—
225C2×C42—231no—
226C2×C42—231no—
227C2×C42—231no—
228C2×C42—231no—
229C2×C42—231no—
230C2×C42—461no—
231C2×C42—461no—
232C2×C42C22×D2311yescharacteristic
233#95—21no—
234#95—461no—
235#95—461no—
236#95—461no—
237C23#760411yescharacteristic, complemented, Sylow
238C2×Q8—464no—
239C2×Q8—922no—
240C2×Q8—922no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—231no—
244C22×C4—231no—
245C22×C4—231no—
246C22×C4—231no—
247C22×C4—461no—
248C22×C4—461no—
249C22×C4C2×C4×D2311yescharacteristic
250C22×C4D4×D2311yescharacteristic
251C22×C4D4×D2311yescharacteristic
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—921no—
259C2×C8—921no—
260C2×C8—921no—
261C2×C8—921no—
262C2×C8—921no—
263C2×C8—921no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—232no—
269C4⋊C4—464no—
270C4⋊C4—461no—
271C4⋊C4—921no—
272C4⋊C4—922no—
273C4⋊C4—922no—
274C4⋊C4—921no—
275C4⋊C4—921no—
276C4⋊C4C8×D2312yes—
277C42—41no—
278C42—232no—
279C42—232no—
280C42—462no—
281C42—461no—
282C42—461no—
283C42—461no—
284C42—461no—
285C42—921no—
286C42—921no—
287C42—922no—
288C42—922no—
289C23C22⋊C4×D2311yescharacteristic
290Q8—928no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—232no—
304C2×C4—232no—
305C2×C4—232no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—461no—
312C2×C4—462no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—921no—
317C2×C4—921no—
318C2×C4—921no—
319C2×C4—921no—
320C2×C4—921no—
321C2×C4C2×C8×D2311yescharacteristic
322C2×C4M16×D2311yescharacteristic
323C2×C4#1062508211yescharacteristic
324C2×C4#1062508511yescharacteristic
325C2×C4#1062508611yescharacteristic
326C2×C4#1062508911yescharacteristic
327C8—81no—
328C8—81no—
329C8—1841no—
330C8—1841no—
331C22C22⋊C8×D2311yescharacteristic
332C22#1309238911yescharacteristic
333C22#101×D2311yescharacteristic
334C22#1309242011yescharacteristic
335C22#1309242411yescharacteristic
336C22#1309243211yescharacteristic
337C22#1309243211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—42no—
345C4—81no—
346C4—462no—
347C4—462no—
348C4—462no—
349C4—921no—
350C4—922no—
351C4—1841no—
352C2#1567171911yescharacteristic
353C2#1567178611yescharacteristic
354C2#1567179011yescharacteristic
355C2#1567194211yescharacteristic
356C2#1567194611yescharacteristic
357C2#1567203311yescharacteristic
358C2#1567211211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7604
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
51. #10625059C8semidirect
237. C23#7604semidirect