Finite Group Databasebeta

← #19212173

Subgroups — #19212173

Order 5888.

528 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625046C211yesmaximal, characteristic
2#15673143C211yesmaximal, characteristic, complemented
3#15671222C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1744C211yesmaximal, characteristic, complemented
6C2×#10625046C411yescharacteristic
7C2×C4×Dic46C411yescharacteristic
8C2×C4×D92C411yescharacteristic
9C2×C4×C23⋊C8—21no—
10#13092323C2211yescharacteristic
11#13092319C2211yescharacteristic
12#13092308—21no—
13#13092308—21no—
14#13092283C411yescharacteristic
15C4×(C2×D23)⋊C4—21no—
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C2×C4×C8×C23—21no—
20C43×C23C2211yescharacteristic
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—
48C4×C8×C23—24no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C4×C23⋊C8—24no—
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—24no—
77C2×C8×C23—42no—
78C2×C8×C23—42no—
79C42×C23—22no—
80C42×C23—22no—
81C42×C23—22no—
82C42×C23—22no—
83C42×C23—22no—
84C42×C23—41no—
85C42×C23C2×C812yes—
86C42×C23M1612yes—
87(C2×D23)⋊C4—24no—
88(C2×D23)⋊C4—24no—
89(C2×D23)⋊C4—42no—
90(C2×D23)⋊C4—42no—
91(C2×D23)⋊C4—42no—
92C4⋊Dic23—41no—
93C4⋊Dic23—41no—
94Dic23⋊C4—42no—
95C4×Dic23—42no—
96C2×C23⋊C8—24no—
97C2×C23⋊C8—42no—
98C2×C23⋊C8—42no—
99#7567—231nomaximal, Sylow
100C23×C23C2×C22⋊C411yescharacteristic
101C22×D23—22no—
102C22×D23—41no—
103C22×D23—41no—
104C22×D23—41no—
105C22×D23—41no—
106C22×D23—41no—
107C22×D23—41no—
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×C23—21no—
121C2×C4×C23C22⋊C812yes—
122C2×C4×C23C22⋊C812yes—
123C2×C4×C23#10012yes—
124C2×C4×C23#10412yes—
125C2×C4×C23#10412yes—
126C2×C4×C23C22×C811yescharacteristic
127C2×C4×C23C2×M1611yescharacteristic
128C2×C4×C23#13512yes—
129C2×C4×C23#13512yes—
130C2×Dic23—22no—
131C2×Dic23—41no—
132C2×Dic23—41no—
133C2×Dic23—41no—
134C2×Dic23—41no—
135C2×Dic23—41no—
136C2×Dic23—41no—
137C2×Dic23—41no—
138C2×Dic23—41no—
139D92—42no—
140D92—42no—
141C4×D23—84no—
142Dic46—42no—
143Dic46—42no—
144C8×C23—44no—
145C23⋊C8—44no—
146C4×#124—231no—
147#1744—231no—
148#1744D2311yescharacteristic, complemented
149#1272—232no—
150#1270—232no—
151C22×C23C2×C22⋊C811yescharacteristic
152C22×C23#41011yescharacteristic
153C22×C23C2×#10011yescharacteristic
154C22×C23#41611yescharacteristic
155C22×C23#41611yescharacteristic
156C22×C23C2×#10411yescharacteristic
157C22×C23C2×#10411yescharacteristic
158C2×D23—42no—
159C2×D23—42no—
160C2×D23—42no—
161C2×D23—81no—
162C2×D23—81no—
163C2×D23—81no—
164C2×D23—81no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—22no—
168C4×C23—22no—
169C4×C23—22no—
170C4×C23—22no—
171C4×C23—41no—
172C4×C23#32914yes—
173Dic23—42no—
174Dic23—81no—
175Dic23—81no—
176C2×#124—231no—
177C2×C4×Q8—231no—
178C2×C4×D4—231no—
179C2×C4×C8—21no—
180C2×C4×C8—461no—
181#391—231no—
182#390—231no—
183#388—461no—
184#388—461no—
185#382—231no—
186C4×C22⋊C4—461no—
187C4×C22⋊C4—461no—
188C43C2×D2311yescharacteristic
189#336—21no—
190#336—232no—
191#336—461no—
192#336C2×D2312yes—
193C2×C23#146011yescharacteristic
194C2×C23#147611yescharacteristic
195C2×C23#147611yescharacteristic
196C2×C23#150011yescharacteristic
197C2×C23#150011yescharacteristic
198C2×C23C2×#32911yescharacteristic
199C2×C23#154311yescharacteristic
200D23—82no—
201C22×Q8—231no—
202C22×D4—231no—
203C23×C4—461no—
204C22×C8—22no—
205C22×C8—462no—
206#124—234no—
207#124—462no—
208C4×Q8—922no—
209C4×D4—922no—
210C2×C4⋊C4—231no—
211C2×C4⋊C4—231no—
212C2×C4⋊C4—461no—
213C2×C22⋊C4—461no—
214C2×C22⋊C4—461no—
215C2×C22⋊C4—461no—
216C2×C22⋊C4—461no—
217C2×C22⋊C4—461no—
218C2×C42—461no—
219C2×C42C4×D2311yescharacteristic
220C2×C42C4×D2311yescharacteristic
221C2×C42D9211yescharacteristic
222C2×C42D9211yescharacteristic
223C2×C42C22⋊D2311yescharacteristic
224C2×C42C22⋊D2311yescharacteristic
225C2×C42C22×D2311yescharacteristic
226C4×C8—24no—
227C4×C8—464no—
228#95—461no—
229#95—461no—
230#95—461no—
231#95—461no—
232C23#756711yescharacteristic, complemented, Sylow
233C24—461no—
234C2×Q8—232no—
235C2×Q8—461no—
236C2×Q8—921no—
237C2×Q8—921no—
238C2×D4—232no—
239C2×D4—461no—
240C2×D4—921no—
241C2×D4—921no—
242C22×C4—461no—
243C22×C4—461no—
244C22×C4—461no—
245C22×C4—922no—
246C22×C4—922no—
247C22×C4—922no—
248C22×C4(C2×D23)⋊C411yescharacteristic
249C22×C4(C2×D23)⋊C411yescharacteristic
250C22×C4(C2×D23)⋊C411yescharacteristic
251C22×C4(C2×D23)⋊C411yescharacteristic
252C22×C4C2×C4×D2311yescharacteristic
253C22×C4C2×D9211yescharacteristic
254C22×C4C2×C22⋊D2311yescharacteristic
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—464no—
259C2×C8—922no—
260C2×C8—922no—
261C4⋊C4—921no—
262C4⋊C4—921no—
263C4⋊C4—922no—
264C22⋊C4—464no—
265C22⋊C4—464no—
266C22⋊C4—922no—
267C22⋊C4—922no—
268C22⋊C4—922no—
269C42—22no—
270C42—22no—
271C42—22no—
272C42—22no—
273C42—22no—
274C42—41no—
275C42—922no—
276C42C8×D2312yes—
277C42#6726212yes—
278C23—462no—
279C23—921no—
280C23—921no—
281C23—921no—
282C23—921no—
283C23—921no—
284C23—921no—
285C23C2×(C2×D23)⋊C411yescharacteristic
286Q8—922no—
287Q8—922no—
288D4—922no—
289D4—922no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—462no—
304C2×C4—921no—
305C2×C4—921no—
306C2×C4—921no—
307C2×C4—921no—
308C2×C4—921no—
309C2×C4—921no—
310C2×C4—921no—
311C2×C4—921no—
312C2×C4—1844no—
313C2×C4#1062498712yes—
314C2×C4(C2×D23)⋊C812yes—
315C2×C4(C2×D23)⋊C812yes—
316C2×C4#1062500512yes—
317C2×C4#1062500712yes—
318C2×C4C2×C8×D2311yescharacteristic
319C2×C4C2×#6726211yescharacteristic
320C2×C4#1062507512yes—
321C2×C4#1062512112yes—
322C8—44no—
323C8—924no—
324C22—922no—
325C22—922no—
326C22—922no—
327C22—1841no—
328C22—1841no—
329C22—1841no—
330C22—1841no—
331C22C2×(C2×D23)⋊C811yescharacteristic
332C22#1309239011yescharacteristic
333C22C2×#1062500511yescharacteristic
334C22#1309241111yescharacteristic
335C22#1309241411yescharacteristic
336C22C2×#1062500711yescharacteristic
337C22C2×#1062498711yescharacteristic
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—922no—
346C4—1841no—
347C4—1841no—
348C4#1309215614yes—
349C2—1842no—
350C2#1567171711yescharacteristic
351C2#1567177711yescharacteristic
352C2#1567178011yescharacteristic
353C2#1567188111yescharacteristic
354C2#1567188411yescharacteristic
355C2C2×#1309215611yescharacteristic
356C2#1567205711yescharacteristic
subgroupG/H
centerC22×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1744C2
socleC23×C23C2×C22⋊C4
hypercenter#1744D23
hypocenterC23#7567
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #15673143C2semidirect
3. #15671222C2semidirect
5. C23×#1744C2semidirect
45. #10625046C8semidirect
148. #1744D23semidirect
232. C23#7567semidirect