Finite Group Databasebeta

← #19212249

Subgroups — #19212249

Order 5888.

510 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625046C211yesmaximal, characteristic
2C4×C4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#15671222C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1839C211yesmaximal, characteristic, complemented
6C2×#10625046C411yescharacteristic
7C2×C4×Dic46C411yescharacteristic
8C2×C4×D92C411yescharacteristic
9C2×C4⋊(C23⋊C8)—21no—
10C2×C4×C23⋊C8—21no—
11#13092323C2211yescharacteristic
12#13092319C2211yescharacteristic
13#13092308—21no—
14#13092308—21no—
15#13092283C411yescharacteristic
16C4×(C2×D23)⋊C4—21no—
17C4×(C2×D23)⋊C4—21no—
18#13092172C2212yes—
19C43×C23C2211yescharacteristic
20C23×#336—21no—
21C23×#336—21no—
22C23×#336C2212yes—
23C22×D92C2×C411yescharacteristic
24C22×C4×D23—21no—
25C22×Dic46C2×C411yescharacteristic
26C22×C8×C23—22no—
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23C2×C411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23D411yescharacteristic
33C2×C42×C23C2311yescharacteristic
34C2×(C2×D23)⋊C4—21no—
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×(C2×D23)⋊C4—21no—
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×C4×Dic23—21no—
43C22×C23⋊C8—22no—
44#10625046—22no—
45#10625046C814yescomplemented
46C4×D92—42no—
47C4×Dic46—42no—
48C23⋊#95—21no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C4⋊(C23⋊C8)—24no—
53C4×C23⋊C8—42no—
54C23×D23—21no—
55C22×C4×C23C22⋊C411yescharacteristic
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C22⋊C411yescharacteristic
59C22×C4×C23C22×C411yescharacteristic
60C22×C4×C23C2×D411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×Dic23—21no—
63C22×Dic23—21no—
64C22×Dic23—21no—
65C2×D92—21no—
66C2×D92—41no—
67C2×D92—41no—
68C2×D92C2×C812yes—
69C2×C4×D23—42no—
70C2×C4×D23—42no—
71C2×C4×D23—42no—
72C2×Dic46—21no—
73C2×Dic46—41no—
74C2×Dic46—41no—
75C2×Dic46C2×C812yes—
76C2×C8×C23—42no—
77C2×C8×C23—42no—
78C2×C8×C23—42no—
79C42×C23—22no—
80C42×C23—22no—
81C42×C23—22no—
82C42×C23—21no—
83C42×C23—21no—
84C42×C23—41no—
85C42×C23—41no—
86C42×C23C2×C812yes—
87C42×C23M1612yes—
88(C2×D23)⋊C4—24no—
89(C2×D23)⋊C4—24no—
90(C2×D23)⋊C4—42no—
91(C2×D23)⋊C4—42no—
92(C2×D23)⋊C4—41no—
93(C2×D23)⋊C4—41no—
94C4⋊Dic23—41no—
95C4⋊Dic23—41no—
96Dic23⋊C4—42no—
97C4×Dic23—42no—
98C2×C23⋊C8—24no—
99C2×C23⋊C8—42no—
100C2×C23⋊C8—42no—
101#7584—231nomaximal, Sylow
102C23×C23C2×C22⋊C411yescharacteristic
103C22×D23—22no—
104C22×D23—41no—
105C22×D23—41no—
106C22×D23—41no—
107C22×D23—41no—
108C22×D23—41no—
109C22×D23—41no—
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—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C22⋊C812yes—
125C2×C4×C23C22⋊C812yes—
126C2×C4×C23#10012yes—
127C2×C4×C23#10412yes—
128C2×C4×C23C22×C811yescharacteristic
129C2×C4×C23C2×M1611yescharacteristic
130C2×C4×C23#13512yes—
131C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C23#13711yescharacteristic
133C2×Dic23—22no—
134C2×Dic23—41no—
135C2×Dic23—41no—
136C2×Dic23—41no—
137C2×Dic23—41no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142D92—42no—
143D92—42no—
144C4×D23—84no—
145Dic46—42no—
146Dic46—42no—
147C8×C23—82no—
148C23⋊C8—44no—
149C4×#124—231no—
150#1839D2311yescharacteristic, complemented
151C4×C4⋊C8—231no—
152#1272—232no—
153#1270—232no—
154C22×C23C2×C22⋊C811yescharacteristic
155C22×C23#41011yescharacteristic
156C22×C23C2×#10011yescharacteristic
157C22×C23#41611yescharacteristic
158C22×C23#41711yescharacteristic
159C22×C23C2×#10411yescharacteristic
160C22×C23#42111yescharacteristic
161C2×D23—42no—
162C2×D23—42no—
163C2×D23—42no—
164C2×D23—81no—
165C2×D23—81no—
166C2×D23—81no—
167C2×D23—81no—
168C4×C23—22no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—22no—
172C4×C23—22no—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—22no—
176C4×C23—22no—
177Dic23—42no—
178Dic23—81no—
179Dic23—81no—
180C2×#124—231no—
181C2×C4×Q8—231no—
182C2×C4×D4—231no—
183C2×C4⋊C8—461no—
184C2×C4×C8—461no—
185#391—231no—
186#390—231no—
187#388—461no—
188#388—461no—
189#382—231no—
190C4×C22⋊C4—461no—
191C4×C22⋊C4—461no—
192C43C2×D2311yescharacteristic
193#336—21no—
194#336—21no—
195#336—232no—
196#336C2×D2312yes—
197C2×C23#146011yescharacteristic
198C2×C23#147611yescharacteristic
199C2×C23#147711yescharacteristic
200C2×C23#150911yescharacteristic
201C2×C23#152111yescharacteristic
202C2×C23#152711yescharacteristic
203C2×C23#155111yescharacteristic
204D23—82no—
205C22×Q8—231no—
206C22×D4—231no—
207C23×C4—461no—
208C22×C8—22no—
209C22×C8—462no—
210#124—234no—
211#124—462no—
212C4×Q8—922no—
213C4×D4—922no—
214C2×C4⋊C4—231no—
215C2×C4⋊C4—231no—
216C2×C4⋊C4—461no—
217C2×C22⋊C4—461no—
218C2×C22⋊C4—461no—
219C2×C22⋊C4—461no—
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222C2×C42—461no—
223C2×C42C4×D2311yescharacteristic
224C2×C42C4×D2311yescharacteristic
225C2×C42D9211yescharacteristic
226C2×C42D9211yescharacteristic
227C2×C42C22⋊D2311yescharacteristic
228C2×C42C22⋊D2311yescharacteristic
229C2×C42C22×D2311yescharacteristic
230C4⋊C8—464no—
231C4×C8—922no—
232#95—461no—
233#95—461no—
234#95—461no—
235#95—461no—
236C23#758411yescharacteristic, complemented, Sylow
237C24—461no—
238C2×Q8—232no—
239C2×Q8—461no—
240C2×Q8—921no—
241C2×Q8—921no—
242C2×D4—232no—
243C2×D4—461no—
244C2×D4—921no—
245C2×D4—921no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4—461no—
249C22×C4—922no—
250C22×C4—922no—
251C22×C4—922no—
252C22×C4(C2×D23)⋊C411yescharacteristic
253C22×C4(C2×D23)⋊C411yescharacteristic
254C22×C4(C2×D23)⋊C411yescharacteristic
255C22×C4(C2×D23)⋊C411yescharacteristic
256C22×C4C2×C4×D2311yescharacteristic
257C22×C4C2×D9211yescharacteristic
258C22×C4C2×C22⋊D2311yescharacteristic
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—464no—
263C2×C8—922no—
264C2×C8—922no—
265C4⋊C4—921no—
266C4⋊C4—921no—
267C4⋊C4—922no—
268C22⋊C4—464no—
269C22⋊C4—464no—
270C22⋊C4—921no—
271C22⋊C4—921no—
272C22⋊C4—922no—
273C22⋊C4—922no—
274C42—21no—
275C42—21no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—922no—
282C42C8×D2312yes—
283C42#6726212yes—
284C23—462no—
285C23—921no—
286C23—921no—
287C23—921no—
288C23—921no—
289C23—921no—
290C23—921no—
291C23C2×(C2×D23)⋊C411yescharacteristic
292Q8—922no—
293Q8—922no—
294D4—922no—
295D4—922no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
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—462no—
311C2×C4—921no—
312C2×C4—921no—
313C2×C4—921no—
314C2×C4—921no—
315C2×C4—921no—
316C2×C4—921no—
317C2×C4—921no—
318C2×C4—921no—
319C2×C4—1844no—
320C2×C4(C2×D23)⋊C812yes—
321C2×C4(C2×D23)⋊C812yes—
322C2×C4#1062500512yes—
323C2×C4#1062500712yes—
324C2×C4C2×C8×D2311yescharacteristic
325C2×C4C2×#6726211yescharacteristic
326C2×C4#1062507911yescharacteristic
327C2×C4#1062508011yescharacteristic
328C2×C4#1062512112yes—
329C8—82no—
330C8—924no—
331C22—922no—
332C22—922no—
333C22—922no—
334C22—1841no—
335C22—1841no—
336C22—1841no—
337C22—1841no—
338C22C2×(C2×D23)⋊C811yescharacteristic
339C22#1309239011yescharacteristic
340C22C2×#1062500511yescharacteristic
341C22#1309241111yescharacteristic
342C22#1309241911yescharacteristic
343C22C2×#1062500711yescharacteristic
344C22#1309243511yescharacteristic
345C4—22no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—922no—
355C4—1841no—
356C4—1841no—
357C2—1842no—
358C2#1567171711yescharacteristic
359C2#1567177711yescharacteristic
360C2#1567178511yescharacteristic
361C2#1567192311yescharacteristic
362C2#1567197211yescharacteristic
363C2#1567199611yescharacteristic
364C2#1567209311yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1839C2
socleC23×C23C2×C22⋊C4
hypercenter#1839D23
hypocenterC23#7584
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. C4×C4⋊(C23⋊C8)C2semidirect
3. #15671222C2semidirect
5. C23×#1839C2semidirect
45. #10625046C8semidirect
150. #1839D23semidirect
236. C23#7584semidirect