Finite Group Databasebeta

← #19212301

Subgroups — #19212301

Order 5888.

654 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675884C211yesmaximal, characteristic
2#15673376C212yesmaximal, complemented
3#15671222C212yesmaximal, complemented
4#15671218C211yesmaximal, characteristic, complemented
5C23×#1270C211yesmaximal, characteristic, complemented
6C22×#67290C411yescharacteristic
7C2×#10625063C411yescharacteristic
8C2×C42×D23C2211yescharacteristic
9C2×Dic23⋊C8—22no—
10C2×(C2×D23)⋊C8—22no—
11#13092323C2211yescharacteristic
12#13092322C411yescharacteristic
13#13092320C411yescharacteristic
14#13092293—22no—
15C22⋊C4×Dic23—22no—
16#13092172C2212yes—
17C23×#390C2211yescharacteristic
18C23×#336C2212yes—
19C22×D4×C23C2×C411yescharacteristic
20C22×C22⋊D23—21no—
21C23×Dic23—21no—
22C2×#67290—22no—
23C2×#67290—42no—
24C2×#67290—42no—
25C2×#67290C814yescomplemented
26C22×C4×D23C2×C411yescharacteristic
27C22×C4×D23D412yes—
28C22×Dic46C2×C411yescharacteristic
29C22×C8×C23—22no—
30C2×C4⋊C4×C23C2×C411yescharacteristic
31C2×C22⋊C4×C23—22no—
32C2×C42×C23C2311yescharacteristic
33C2×C22⋊Dic23—22no—
34C2×(C2×D23)⋊C4—21no—
35C2×C4⋊Dic23C2×C411yescharacteristic
36C2×C4×Dic23—21no—
37C2×C4×Dic23C2×C411yescharacteristic
38C2×C4×Dic23D412yes—
39C22×C23⋊C8—22no—
40#10625063—42no—
41C42×D23—42no—
42C23⋊#95—22no—
43C23⋊#95—22no—
44(C2×D23)⋊C8—44no—
45Dic23⋊C8—44no—
46C24×C23—21no—
47C23×D23C22⋊C411yescharacteristic
48C2×D4×C23—21no—
49C2×D4×C23—41no—
50C2×D4×C23—41no—
51C2×D4×C23C2×C812yes—
52C22×C4×C23—21no—
53C22×C4×C23C22×C411yescharacteristic
54C22×C4×C23C2×D412yes—
55C2×C22⋊D23—24no—
56C2×C22⋊D23—42no—
57C2×C22⋊D23—42no—
58C22×Dic23—21no—
59C22×Dic23—24no—
60C22×Dic23—21no—
61C22×Dic23—42no—
62C22×Dic23—42no—
63C22×Dic23C22⋊C412yes—
64C22×Dic23C22⋊C411yescharacteristic
65#67290—48no—
66#67290—48no—
67C2×C4×D23—22no—
68C2×C4×D23—22no—
69C2×C4×D23—22no—
70C2×C4×D23—22no—
71C2×C4×D23—42no—
72C2×C4×D23—42no—
73C2×C4×D23C2×C812yes—
74C2×C4×D23M1612yes—
75C2×Dic46—21no—
76C2×Dic46—41no—
77C2×Dic46—41no—
78C2×Dic46C2×C812yes—
79C2×C8×C23—42no—
80C2×C8×C23—42no—
81C2×C8×C23—42no—
82C4⋊C4×C23—41no—
83C22⋊C4×C23—42no—
84C22⋊C4×C23—42no—
85C42×C23—41no—
86C22⋊Dic23—44no—
87(C2×D23)⋊C4—42no—
88C4⋊Dic23—41no—
89C4×Dic23—24no—
90C4×Dic23—41no—
91C4×Dic23—42no—
92C2×C23⋊C8—42no—
93C2×C23⋊C8—42no—
94C2×C23⋊C8—42no—
95#7597—231nomaximal, Sylow
96C23×C23—22no—
97C23×C23—41no—
98C23×C23—41no—
99C23×C23—42no—
100C23×C23—42no—
101C23×C23C2×C22⋊C411yescharacteristic
102C22×D23—21no—
103C22×D23—21no—
104C22×D23—22no—
105C22×D23—22no—
106C22×D23C22⋊C812yes—
107D4×C23—42no—
108D4×C23—42no—
109C2×C4×C23—22no—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—22no—
113C2×C4×C23—41no—
114C2×C4×C23—42no—
115C2×C4×C23C22×C811yescharacteristic
116C2×C4×C23C2×M1611yescharacteristic
117C2×C4×C23AGL(1,ℤ/8)12yes—
118C2×C4×C23#13712yes—
119C22⋊D23—48no—
120C2×Dic23—22no—
121C2×Dic23—22no—
122C2×Dic23—22no—
123C2×Dic23—22no—
124C2×Dic23—41no—
125C2×Dic23—41no—
126C2×Dic23—48no—
127C2×Dic23—41no—
128C2×Dic23—42no—
129C2×Dic23C22⋊C812yes—
130C2×Dic23#9912yes—
131C2×Dic23#10012yes—
132C4×D23—24no—
133C4×D23—24no—
134C4×D23—44no—
135C4×D23—44no—
136Dic46—42no—
137Dic46—42no—
138C8×C23—82no—
139C23⋊C8—82no—
140#2297—231no—
141#1797—232no—
142#1272—232no—
143#1270—231no—
144#1270D2311yescharacteristic, complemented
145C22×C23—42no—
146C22×C23—44no—
147C22×C23—81no—
148C22×C23—81no—
149C22×C23—82no—
150C22×C23C2×C22⋊C811yescharacteristic
151C22×C23C2×#9911yescharacteristic
152C22×C23C2×#10011yescharacteristic
153C22×C23#41712yes—
154C22×C23#42112yes—
155C2×D23—22no—
156C2×D23—24no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—42no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—22no—
163C4×C23—22no—
164C4×C23—81no—
165Dic23—42no—
166Dic23—42no—
167Dic23—81no—
168Dic23#32314yes—
169C22×#41—231no—
170C2×#117—231no—
171C22×C42—231no—
172C2×C4⋊C8—462no—
173C2×C22⋊C8—462no—
174#391—231no—
175#391—231no—
176#390—231no—
177#390C2×D2311yescharacteristic
178#386—462no—
179C4×C22⋊C4—462no—
180#336—232no—
181#336C2×D2312yes—
182C2×C23—82no—
183C2×C23C2×#32311yescharacteristic
184C2×C23#147712yes—
185C2×C23#151312yes—
186C2×C23#153611yescharacteristic
187C2×C23#156011yescharacteristic
188D23—42no—
189C2×#41—234no—
190C2×#41—462no—
191C2×#41—922no—
192C2×#41—922no—
193C22×Q8—231no—
194C22×D4—461no—
195C22×D4C4×D2311yescharacteristic
196C23×C4—231no—
197C23×C4—232no—
198C23×C4—461no—
199C22×C8—22no—
200C22×C8—462no—
201#117—922no—
202C2×C4⋊C4—231no—
203C2×C4⋊C4C4×D2311yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—461no—
206C2×C22⋊C4—462no—
207C2×C42—232no—
208C2×C42—231no—
209C2×C42—461no—
210C2×C42—922no—
211C2×C42C22×D2311yescharacteristic
212C4⋊C8—924no—
213C22⋊C8—924no—
214#95—462no—
215#95—462no—
216C23#759711yescharacteristic, complemented, Sylow
217C24—21no—
218C24—231no—
219#41—928no—
220#41—928no—
221C2×Q8—232no—
222C2×Q8—461no—
223C2×Q8—921no—
224C2×Q8—921no—
225C2×D4—21no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—464no—
229C2×D4—922no—
230C2×D4—922no—
231C2×D4C8×D2312yes—
232C22×C4—21no—
233C22×C4—231no—
234C22×C4—232no—
235C22×C4—232no—
236C22×C4—232no—
237C22×C4—462no—
238C22×C4—462no—
239C22×C4—464no—
240C22×C4—461no—
241C22×C4—462no—
242C22×C4—462no—
243C22×C4—461no—
244C22×C4—922no—
245C22×C4—922no—
246C22×C4—922no—
247C22×C4—922no—
248C22×C4C2×C4×D2311yescharacteristic
249C22×C4D4×D2312yes—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—922no—
254C2×C8—922no—
255C2×C8—922no—
256C4⋊C4—41no—
257C4⋊C4—921no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—922no—
261C22⋊C4—924no—
262C42—41no—
263C42—464no—
264C42—921no—
265C42—922no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—232no—
272C23—461no—
273C23—461no—
274C23—462no—
275C23—462no—
276C23C22⋊C4×D2311yescharacteristic
277Q8—922no—
278Q8—922no—
279D4—42no—
280D4—42no—
281D4—928no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—232no—
289C2×C4—232no—
290C2×C4—232no—
291C2×C4—464no—
292C2×C4—464no—
293C2×C4—462no—
294C2×C4—462no—
295C2×C4—462no—
296C2×C4—462no—
297C2×C4—924no—
298C2×C4—924no—
299C2×C4—928no—
300C2×C4—921no—
301C2×C4—921no—
302C2×C4—921no—
303C2×C4—922no—
304C2×C4C2×C8×D2311yescharacteristic
305C2×C4M16×D2311yescharacteristic
306C2×C4#1062508212yes—
307C2×C4#1062508612yes—
308C8—82no—
309C8—1842no—
310C22—42no—
311C22—44no—
312C22—81no—
313C22—82no—
314C22—81no—
315C22—462no—
316C22—464no—
317C22—921no—
318C22—922no—
319C22—921no—
320C22C22⋊C8×D2311yescharacteristic
321C22#99×D2311yescharacteristic
322C22#100×D2311yescharacteristic
323C22#1309241512yes—
324C22#1309243212yes—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—234no—
331C4—922no—
332C4—922no—
333C4—1841no—
334C2—82no—
335C2—922no—
336C2D23×#32311yescharacteristic
337C2#1567178112yes—
338C2#1567193712yes—
339C2#1567203011yescharacteristic
340C2#1567212911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7597
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673376C2semidirect
3. #15671222C2semidirect
4. #15671218C2semidirect
5. C23×#1270C2semidirect
25. C2×#67290C8semidirect
144. #1270D23semidirect
216. C23#7597semidirect