Finite Group Databasebeta

← #19212289

Subgroups — #19212289

Order 5888.

482 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675861C211yesmaximal, characteristic
2#15673540C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D92C411yescharacteristic
7C2×#10625043—21no—
8#13092319C411yescharacteristic
9#13092319C2211yescharacteristic
10#13092315C411yescharacteristic
11#13092315C2211yescharacteristic
12#13092308—21no—
13#13092308—21no—
14C4×C4⋊Dic23C411yescharacteristic
15C4×(C2×D23)⋊C4—21no—
16#13092172—21no—
17#13092172—21no—
18#13092172C2212yes—
19C2×C23×C4⋊C8—21no—
20C43×C23C2211yescharacteristic
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×C4⋊C8—42no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C23⋊#95—21no—
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—21no—
74C42×C23—22no—
75C42×C23—21no—
76C42×C23—41no—
77C42×C23—41no—
78C42×C23—41no—
79C42×C23—41no—
80C42×C23C2×C812yes—
81C42×C23M1612yes—
82(C2×D23)⋊C4—24no—
83(C2×D23)⋊C4—42no—
84(C2×D23)⋊C4—42no—
85(C2×D23)⋊C4—42no—
86(C2×D23)⋊C4—41no—
87(C2×D23)⋊C4—41no—
88C4⋊Dic23—21no—
89C4⋊Dic23—41no—
90C4⋊Dic23—41no—
91C4⋊Dic23C2×C812yes—
92Dic23⋊C4—42no—
93Dic23⋊C4—42no—
94C4×Dic23—42no—
95C2×C23⋊C8—42no—
96C2×C23⋊C8—42no—
97C2×C23⋊C8—42no—
98#7594—231nomaximal, Sylow
99C23×C23C2×C22⋊C411yescharacteristic
100C22×D23—22no—
101C22×D23—41no—
102C22×D23—41no—
103C22×D23—41no—
104C22×D23—41no—
105C22×D23—41no—
106C22×D23—41no—
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×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C22⋊C812yes—
124C2×C4×C23C22⋊C812yes—
125C2×C4×C23C22×C811yescharacteristic
126C2×C4×C23C2×M1611yescharacteristic
127C2×C4×C23AGL(1,ℤ/8)12yes—
128C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C23#13711yescharacteristic
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—48no—
142C8×C23—82no—
143C23⋊C8—82no—
144#2293—231no—
145#1839—231no—
146#1831D2311yescharacteristic, complemented
147#1271—232no—
148#1270—232no—
149C22×C23C2×C22⋊C811yescharacteristic
150C22×C23#41011yescharacteristic
151C22×C23#41311yescharacteristic
152C22×C23#41711yescharacteristic
153C22×C23#41811yescharacteristic
154C22×C23#42111yescharacteristic
155C22×C23#42111yescharacteristic
156C2×D23—42no—
157C2×D23—42no—
158C2×D23—42no—
159C2×D23—81no—
160C2×D23—81no—
161C2×D23—81no—
162C2×D23—81no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—22no—
166C4×C23—22no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—22no—
170C4×C23—41no—
171C4×C23—41no—
172Dic23—42no—
173Dic23—81no—
174Dic23—81no—
175C2×C4×D4—231no—
176C2×#117—461no—
177C2×C4⋊C8—21no—
178#390—231no—
179#390—231no—
180#389—231no—
181#389—231no—
182#388—461no—
183#388—461no—
184C4×C4⋊C4—231no—
185C4×C22⋊C4—461no—
186C43C2×D2311yescharacteristic
187#336—21no—
188#336—232no—
189#336—461no—
190#336—461no—
191#336C2×D2312yes—
192C2×C23#145811yescharacteristic
193C2×C23#147711yescharacteristic
194C2×C23#147811yescharacteristic
195C2×C23#151211yescharacteristic
196C2×C23#151411yescharacteristic
197C2×C23#153511yescharacteristic
198C2×C23#155711yescharacteristic
199D23—82no—
200C22×D4—231no—
201C23×C4—461no—
202C22×C8—22no—
203C22×C8—462no—
204C4×D4—234no—
205C4×D4—462no—
206#117—924no—
207C2×C4⋊C4—231no—
208C2×C4⋊C4—231no—
209C2×C4⋊C4—231no—
210C2×C4⋊C4—461no—
211C2×C4⋊C4—461no—
212C2×C22⋊C4—461no—
213C2×C22⋊C4—461no—
214C2×C22⋊C4—461no—
215C2×C22⋊C4—461no—
216C2×C22⋊C4—461no—
217C2×C42—461no—
218C2×C42C4×D2311yescharacteristic
219C2×C42C4×D2311yescharacteristic
220C2×C42D9211yescharacteristic
221C2×C42D9211yescharacteristic
222C2×C42C22⋊D2311yescharacteristic
223C2×C42C22⋊D2311yescharacteristic
224C2×C42C22×D2311yescharacteristic
225C4⋊C8—42no—
226#95—461no—
227#95—461no—
228#95—461no—
229C23#759411yescharacteristic, complemented, Sylow
230C24—461no—
231C2×D4—232no—
232C2×D4—461no—
233C2×D4—921no—
234C2×D4—921no—
235C22×C4—461no—
236C22×C4—464no—
237C22×C4—461no—
238C22×C4—461no—
239C22×C4—922no—
240C22×C4—922no—
241C22×C4(C2×D23)⋊C411yescharacteristic
242C22×C4(C2×D23)⋊C411yescharacteristic
243C22×C4(C2×D23)⋊C411yescharacteristic
244C22×C4(C2×D23)⋊C411yescharacteristic
245C22×C4C2×C4×D2311yescharacteristic
246C22×C4C2×D9211yescharacteristic
247C22×C4C2×C22⋊D2311yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—922no—
252C2×C8—922no—
253C2×C8—922no—
254C4⋊C4—232no—
255C4⋊C4—461no—
256C4⋊C4—921no—
257C4⋊C4—921no—
258C4⋊C4—922no—
259C4⋊C4—922no—
260C22⋊C4—464no—
261C22⋊C4—922no—
262C22⋊C4—922no—
263C22⋊C4—922no—
264C22⋊C4—921no—
265C22⋊C4—921no—
266C42—22no—
267C42—21no—
268C42—21no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—922no—
274C42C8×D2312yes—
275C42#6726212yes—
276C23—462no—
277C23—921no—
278C23—921no—
279C23—921no—
280C23—921no—
281C23—921no—
282C23—921no—
283C23C2×(C2×D23)⋊C411yescharacteristic
284D4—922no—
285D4—922no—
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—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—462no—
303C2×C4—928no—
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(C2×D23)⋊C812yes—
313C2×C4(C2×D23)⋊C812yes—
314C2×C4C2×C8×D2311yescharacteristic
315C2×C4C2×#6726211yescharacteristic
316C2×C4#1062507912yes—
317C2×C4#1062510311yescharacteristic
318C2×C4#1062511311yescharacteristic
319C8—82no—
320C8—1842no—
321C22—922no—
322C22—922no—
323C22—922no—
324C22—1841no—
325C22—1841no—
326C22—1841no—
327C22—1841no—
328C22C2×(C2×D23)⋊C811yescharacteristic
329C22#1309239011yescharacteristic
330C22#1309239911yescharacteristic
331C22#1309241611yescharacteristic
332C22#1309242311yescharacteristic
333C22#1309243311yescharacteristic
334C22#1309243511yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—922no—
345C4—1841no—
346C4—1841no—
347C2—1842no—
348C2#1567170911yescharacteristic
349C2#1567178211yescharacteristic
350C2#1567178911yescharacteristic
351C2#1567193311yescharacteristic
352C2#1567194511yescharacteristic
353C2#1567202611yescharacteristic
354C2#1567211711yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1831C2
socleC23×C23C2×C22⋊C4
hypercenter#1831D23
hypocenterC23#7594
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #15673540C2semidirect
3. #15671219C2semidirect
5. C23×#1831C2semidirect
46. C4×D92C8semidirect
146. #1831D23semidirect
229. C23#7594semidirect