Finite Group Databasebeta

← #19212229

Subgroups — #19212229

Order 5888.

500 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675861C211yesmaximal, characteristic
2#15673143C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1839C211yesmaximal, characteristic, complemented
6C2×C4×D92C411yescharacteristic
7C2×#10625043—21no—
8C2×C4×C23⋊C8—21no—
9#13092319C411yescharacteristic
10#13092319C2211yescharacteristic
11#13092315C411yescharacteristic
12#13092315C2211yescharacteristic
13#13092308—21no—
14#13092308—21no—
15C4×C4⋊Dic23C411yescharacteristic
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C43×C23C2211yescharacteristic
20C23×#336—21no—
21C23×#336—21no—
22C23×#336C2212yes—
23C22×D92C2×C411yescharacteristic
24C22×C4×D23—21no—
25C22×C8×C23—22no—
26C2×C42×C23C2×C411yescharacteristic
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23D411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×(C2×D23)⋊C4—21no—
34C2×(C2×D23)⋊C4—21no—
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×C4⋊Dic23C2×C411yescharacteristic
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C22×C23⋊C8—22no—
45C4×D92—22no—
46C4×D92C814yescomplemented
47#10625043—44no—
48C23⋊#95—21no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C4×C23⋊C8—24no—
52C23×D23—21no—
53C22×C4×C23C22⋊C411yescharacteristic
54C22×C4×C23C22⋊C411yescharacteristic
55C22×C4×C23C22⋊C411yescharacteristic
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22×C411yescharacteristic
58C22×C4×C23C2×D411yescharacteristic
59C22×C4×C23C2×D411yescharacteristic
60C22×Dic23—21no—
61C22×Dic23—21no—
62C22×Dic23—21no—
63C2×D92—21no—
64C2×D92—41no—
65C2×D92—41no—
66C2×D92C2×C812yes—
67C2×C4×D23—24no—
68C2×C4×D23—42no—
69C2×C4×D23—42no—
70C2×C8×C23—42no—
71C2×C8×C23—42no—
72C2×C8×C23—42no—
73C42×C23—22no—
74C42×C23—22no—
75C42×C23—22no—
76C42×C23—41no—
77C42×C23—41no—
78C42×C23—41no—
79C42×C23C2×C812yes—
80C42×C23M1612yes—
81(C2×D23)⋊C4—24no—
82(C2×D23)⋊C4—42no—
83(C2×D23)⋊C4—42no—
84(C2×D23)⋊C4—42no—
85(C2×D23)⋊C4—42no—
86C4⋊Dic23—21no—
87C4⋊Dic23—41no—
88C4⋊Dic23—41no—
89C4⋊Dic23C2×C812yes—
90Dic23⋊C4—42no—
91Dic23⋊C4—42no—
92C4×Dic23—42no—
93C2×C23⋊C8—24no—
94C2×C23⋊C8—42no—
95C2×C23⋊C8—42no—
96#7580—231nomaximal, Sylow
97C23×C23C2×C22⋊C411yescharacteristic
98C22×D23—22no—
99C22×D23—41no—
100C22×D23—41no—
101C22×D23—41no—
102C22×D23—41no—
103C22×D23—41no—
104C22×D23—41no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
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×C23C22⋊C812yes—
121C2×C4×C23C22⋊C812yes—
122C2×C4×C23#10412yes—
123C2×C4×C23C22×C811yescharacteristic
124C2×C4×C23C2×M1611yescharacteristic
125C2×C4×C23#13512yes—
126C2×C4×C23AGL(1,ℤ/8)12yes—
127C2×Dic23—22no—
128C2×Dic23—41no—
129C2×Dic23—41no—
130C2×Dic23—41no—
131C2×Dic23—41no—
132C2×Dic23—41no—
133C2×Dic23—41no—
134C2×Dic23—41no—
135C2×Dic23—41no—
136D92—42no—
137D92—42no—
138C4×D23—48no—
139C8×C23—82no—
140C23⋊C8—44no—
141#2293—231no—
142#1839D2311yescharacteristic, complemented
143#1744—231no—
144#1271—232no—
145#1270—232no—
146C22×C23C2×C22⋊C811yescharacteristic
147C22×C23#41011yescharacteristic
148C22×C23#41311yescharacteristic
149C22×C23#41611yescharacteristic
150C22×C23#41811yescharacteristic
151C22×C23C2×#10411yescharacteristic
152C22×C23#42111yescharacteristic
153C2×D23—42no—
154C2×D23—42no—
155C2×D23—42no—
156C2×D23—81no—
157C2×D23—81no—
158C2×D23—81no—
159C2×D23—81no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—22no—
163C4×C23—22no—
164C4×C23—22no—
165C4×C23—22no—
166C4×C23—22no—
167C4×C23—41no—
168Dic23—42no—
169Dic23—81no—
170Dic23—81no—
171C2×C4×D4—231no—
172C2×#117—461no—
173C2×C4×C8—461no—
174#390—231no—
175#390—231no—
176#389—231no—
177#389—231no—
178#388—461no—
179#388—461no—
180C4×C4⋊C4—231no—
181C4×C22⋊C4—461no—
182C43C2×D2311yescharacteristic
183#336—21no—
184#336—21no—
185#336—232no—
186#336—461no—
187#336C2×D2312yes—
188C2×C23#145811yescharacteristic
189C2×C23#147611yescharacteristic
190C2×C23#147811yescharacteristic
191C2×C23#150511yescharacteristic
192C2×C23#152111yescharacteristic
193C2×C23#153211yescharacteristic
194C2×C23#155311yescharacteristic
195D23—82no—
196C22×D4—231no—
197C23×C4—461no—
198C22×C8—22no—
199C22×C8—462no—
200C4×D4—234no—
201C4×D4—462no—
202#117—924no—
203C2×C4⋊C4—231no—
204C2×C4⋊C4—231no—
205C2×C4⋊C4—231no—
206C2×C4⋊C4—461no—
207C2×C4⋊C4—461no—
208C2×C22⋊C4—461no—
209C2×C22⋊C4—461no—
210C2×C22⋊C4—461no—
211C2×C22⋊C4—461no—
212C2×C22⋊C4—461no—
213C2×C42—461no—
214C2×C42C4×D2311yescharacteristic
215C2×C42C4×D2311yescharacteristic
216C2×C42D9211yescharacteristic
217C2×C42D9211yescharacteristic
218C2×C42C22⋊D2311yescharacteristic
219C2×C42C22⋊D2311yescharacteristic
220C2×C42C22×D2311yescharacteristic
221C4×C8—464no—
222#95—461no—
223#95—461no—
224#95—461no—
225C23#758011yescharacteristic, complemented, Sylow
226C24—461no—
227C2×D4—232no—
228C2×D4—461no—
229C2×D4—921no—
230C2×D4—921no—
231C22×C4—461no—
232C22×C4—464no—
233C22×C4—461no—
234C22×C4—461no—
235C22×C4—922no—
236C22×C4—922no—
237C22×C4(C2×D23)⋊C411yescharacteristic
238C22×C4(C2×D23)⋊C411yescharacteristic
239C22×C4(C2×D23)⋊C411yescharacteristic
240C22×C4(C2×D23)⋊C411yescharacteristic
241C22×C4C2×C4×D2311yescharacteristic
242C22×C4C2×D9211yescharacteristic
243C22×C4C2×C22⋊D2311yescharacteristic
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—464no—
248C2×C8—922no—
249C2×C8—922no—
250C4⋊C4—232no—
251C4⋊C4—461no—
252C4⋊C4—921no—
253C4⋊C4—921no—
254C4⋊C4—922no—
255C4⋊C4—922no—
256C22⋊C4—464no—
257C22⋊C4—922no—
258C22⋊C4—922no—
259C22⋊C4—922no—
260C22⋊C4—922no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—922no—
268C42C8×D2312yes—
269C42#6726212yes—
270C23—462no—
271C23—921no—
272C23—921no—
273C23—921no—
274C23—921no—
275C23—921no—
276C23—921no—
277C23C2×(C2×D23)⋊C411yescharacteristic
278D4—922no—
279D4—922no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—462no—
296C2×C4—928no—
297C2×C4—921no—
298C2×C4—921no—
299C2×C4—921no—
300C2×C4—921no—
301C2×C4—921no—
302C2×C4—921no—
303C2×C4—921no—
304C2×C4—921no—
305C2×C4(C2×D23)⋊C812yes—
306C2×C4(C2×D23)⋊C812yes—
307C2×C4#1062500712yes—
308C2×C4C2×C8×D2311yescharacteristic
309C2×C4C2×#6726211yescharacteristic
310C2×C4#1062507912yes—
311C2×C4#1062512112yes—
312C8—82no—
313C8—924no—
314C22—922no—
315C22—922no—
316C22—922no—
317C22—1841no—
318C22—1841no—
319C22—1841no—
320C22—1841no—
321C22C2×(C2×D23)⋊C811yescharacteristic
322C22#1309239011yescharacteristic
323C22#1309239911yescharacteristic
324C22#1309241111yescharacteristic
325C22#1309242311yescharacteristic
326C22C2×#1062500711yescharacteristic
327C22#1309243511yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—22no—
335C4—41no—
336C4—922no—
337C4—1841no—
338C4—1841no—
339C2—1842no—
340C2#1567170911yescharacteristic
341C2#1567177711yescharacteristic
342C2#1567178911yescharacteristic
343C2#1567190611yescharacteristic
344C2#1567197211yescharacteristic
345C2#1567201811yescharacteristic
346C2#1567210311yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1839C2
socleC23×C23C2×C22⋊C4
hypercenter#1839D23
hypocenterC23#7580
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #15673143C2semidirect
3. #15671219C2semidirect
5. C23×#1839C2semidirect
46. C4×D92C8semidirect
142. #1839D23semidirect
225. C23#7580semidirect