Finite Group Databasebeta

← #19212341

Subgroups — #19212341

Order 5888.

612 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15673465C211yesmaximal, characteristic
2#15673091C211yesmaximal, characteristic
3#15671220C214yesmaximal, complemented
4C2×C23×#389C211yesmaximal, characteristic
5C22×#67267—21no—
6C2×C22⋊(C23⋊C8)—21no—
7#13092172—21no—
8#13092172—21no—
9#13092172C2212yes—
10#13092172C2212yes—
11C22×C4⋊C4×C23—21no—
12C22×C4⋊C4×C23C411yescharacteristic
13C22×C4⋊C4×C23C411yescharacteristic
14C22×C42×C23C2211yescharacteristic
15C23×#389—21no—
16C23×#389—21no—
17C23×#389C412yes—
18C23×#389C2212yes—
19C2×C23×#95—21no—
20C23×C4×C23—21no—
21C23×C4×C23—21no—
22C23×C4×C23C2×C411yescharacteristic
23C23×C4×C23D411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C2×C4⋊C4×C23—21no—
26C2×C4⋊C4×C23—24no—
27C2×C4⋊C4×C23—21no—
28C2×C4⋊C4×C23—22no—
29C2×C4⋊C4×C23—22no—
30C2×C4⋊C4×C23—42no—
31C2×C4⋊C4×C23—44no—
32C2×C4⋊C4×C23C2×C412yes—
33C2×C4⋊C4×C23C2×C412yes—
34C2×C42×C23—42no—
35C2×C42×C23C2×C411yescharacteristic
36C2×C42×C23D411yescharacteristic
37C2×C42×C23D411yescharacteristic
38C2×C42×C23C2311yescharacteristic
39C2×#67267—24no—
40C2×#67267—42no—
41C2×#67267—42no—
42C22×C23⋊C8—22no—
43C22×C23⋊C8—22no—
44C23×#95—22no—
45C23×#95—22no—
46C22⋊(C23⋊C8)—42no—
47C24×C23C22⋊C411yescharacteristic
48C22×C4×C23—22no—
49C22×C4×C23—22no—
50C22×C4×C23—22no—
51C22×C4×C23—22no—
52C22×C4×C23—22no—
53C22×C4×C23—24no—
54C22×C4×C23—22no—
55C22×C4×C23—22no—
56C22×C4×C23—22no—
57C22×C4×C23—22no—
58C22×C4×C23—41no—
59C22×C4×C23—42no—
60C22×C4×C23—42no—
61C22×C4×C23—42no—
62C22×C4×C23—42no—
63C22×C4×C23—42no—
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23SD1612yes—
68C22×C4×C23Q1612yes—
69C22×C4×C23C22×C411yescharacteristic
70C22×C4×C23C2×D411yescharacteristic
71C22×C4×C23C2×D411yescharacteristic
72C4⋊C4×C23—24no—
73C4⋊C4×C23—22no—
74C4⋊C4×C23—42no—
75C4⋊C4×C23—42no—
76C4⋊C4×C23—44no—
77C4⋊C4×C23—44no—
78C4⋊C4×C23M1614yescomplemented
79C42×C23—41no—
80C42×C23—41no—
81C42×C23—41no—
82C42×C23—41no—
83#67267—48no—
84C2×C23⋊C8—24no—
85C2×C23⋊C8—42no—
86C2×C23⋊C8—42no—
87C2×C23⋊C8—42no—
88C2×C23⋊C8—42no—
89C2×C23⋊C8—42no—
90#7607—231nomaximal, Sylow
91C23×C23—21no—
92C23×C23—21no—
93C23×C23—21no—
94C23×C23—21no—
95C23×C23#9912yes—
96C23×C23#10312yes—
97C23×C23#10412yes—
98C23×C23C2×C22⋊C411yescharacteristic
99C2×C4×C23—28no—
100C2×C4×C23—24no—
101C2×C4×C23—24no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
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—24no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—44no—
117C2×C4×C23—48no—
118C2×C4×C23—42no—
119C2×C4×C23—42no—
120C2×C4×C23—42no—
121C2×C4×C23—42no—
122C2×C4×C23—42no—
123C2×C4×C23—84no—
124C2×C4×C23#10112yes—
125C2×C4×C23#10312yes—
126C2×C4×C23C2×M1612yes—
127C2×C4×C23C2×SD1611yescharacteristic
128C2×C4×C23C2×Q1611yescharacteristic
129C2×C4×C23AGL(1,ℤ/8)12yes—
130C23⋊C8—44no—
131C23⋊C8—82no—
132C2×#389D2311yescharacteristic
133#1817—231no—
134#1728—231no—
135#1271—234no—
136C22×C23—22no—
137C22×C23—22no—
138C22×C23—22no—
139C22×C23—22no—
140C22×C23—22no—
141C22×C23—22no—
142C22×C23#32814yes—
143C22×C23#40711yescharacteristic
144C22×C23C2×#9911yescharacteristic
145C22×C23C2×#10111yescharacteristic
146C22×C23C2×#10311yescharacteristic
147C22×C23#41811yescharacteristic
148C22×C23C2×#10411yescharacteristic
149C22×C23#42111yescharacteristic
150C4×C23—22no—
151C4×C23—22no—
152C4×C23—21no—
153C4×C23—22no—
154C4×C23—21no—
155C4×C23—22no—
156C4×C23—44no—
157C4×C23—41no—
158C4×C23—82no—
159C22×M16—461no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4Dic2311yescharacteristic
162C22×C4⋊C4Dic2311yescharacteristic
163C22×C42C2×D2311yescharacteristic
164C2×C22⋊C8—461no—
165#389—21no—
166#389—21no—
167#389Dic2312yes—
168#389C2×D2312yes—
169C2×#95—21no—
170#336—232no—
171#336—232no—
172#336—461no—
173#336—461no—
174C2×C23—24no—
175C2×C23#146311yescharacteristic
176C2×C23#148711yescharacteristic
177C2×C23#149011yescharacteristic
178C2×C23C2×#32811yescharacteristic
179C2×C23#151011yescharacteristic
180C2×C23#152811yescharacteristic
181C2×C23#154911yescharacteristic
182C23×C4—21no—
183C23×C4—21no—
184C23×C4C2×Dic2311yescharacteristic
185C23×C4C22⋊D2311yescharacteristic
186C23×C4C22⋊D2311yescharacteristic
187C2×M16—464no—
188C2×M16—922no—
189C2×M16—922no—
190C22×C8—462no—
191C22×C8—462no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4C2×Dic2312yes—
200C2×C4⋊C4C2×Dic2312yes—
201C2×C42—42no—
202C2×C42C2×Dic2311yescharacteristic
203C2×C42C22⋊D2311yescharacteristic
204C2×C42C22⋊D2311yescharacteristic
205C2×C42C22×D2311yescharacteristic
206C22⋊C8—922no—
207#95—22no—
208#95—22no—
209C23#760711yescharacteristic, complemented, Sylow
210C24C22⋊Dic2311yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4#6727412yes—
228C22×C4#6727512yes—
229C22×C4C22⋊Dic2311yescharacteristic
230C22×C4C22⋊Dic2311yescharacteristic
231C22×C4C22⋊Dic2311yescharacteristic
232C22×C4C22×Dic2311yescharacteristic
233C22×C4C2×C22⋊D2311yescharacteristic
234C22×C4C2×C22⋊D2311yescharacteristic
235M16—928no—
236C2×C8—464no—
237C2×C8—922no—
238C2×C8—922no—
239C2×C8—922no—
240C2×C8—922no—
241C2×C8—922no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—44no—
247C4⋊C4—44no—
248C4⋊C4#6726714yescomplemented
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#1062501612yes—
258C23#1062501712yes—
259C23#1062501912yes—
260C23C2×C22⋊Dic2311yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—44no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4#1062501712yes—
287C2×C4#1062501812yes—
288C2×C4C2×#6726712yes—
289C2×C4#1062510312yes—
290C2×C4C2×#6727411yescharacteristic
291C2×C4C2×#6727511yescharacteristic
292C8—924no—
293C8—1842no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22#1309215414yes—
301C22#1309238111yescharacteristic
302C22C2×#1062501611yescharacteristic
303C22C2×#1062501811yescharacteristic
304C22C2×#1062501711yescharacteristic
305C22#1309242211yescharacteristic
306C22C2×#1062501911yescharacteristic
307C22#1309243411yescharacteristic
308C4—21no—
309C4—21no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—44no—
315C4—41no—
316C4—82no—
317C2—24no—
318C2#1567172711yescharacteristic
319C2#1567182611yescharacteristic
320C2#1567184011yescharacteristic
321C2C2×#1309215411yescharacteristic
322C2#1567192611yescharacteristic
323C2#1567199911yescharacteristic
324C2#1567208211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic23
commutatorC22×C4×C23C22×C4
FrattiniC2×C42C22×D23
FittingC2×C23×#389C2
socleC23×C23C2×C22⋊C4
hypercenterC2×#389D23
hypocenterC23#7607
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #15671220C2semidirect
78. C4⋊C4×C23M16semidirect
209. C23#7607semidirect
248. C4⋊C4#67267semidirect