Finite Group Databasebeta

← #19137809

Subgroups — #19137809

Order 5504.

944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C22×#10621900C211yesmaximal, characteristic, complemented
2C2×#13063287C211yesmaximal, characteristic, complemented
3C2×(C22⋊D43)⋊C4C212yesmaximal, complemented
4#14582819C211yesmaximal, characteristic, complemented
5#14582814C212yesmaximal, complemented
6#14582812C211yesmaximal, characteristic, complemented
7#14582808C212yesmaximal, complemented
8#14582807C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic43C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C2×#10621900—28no—
13C2×#10621900—24no—
14C22×Dic86C2211yescharacteristic
15C22×D172C2211yescharacteristic
16C22×C22⋊D43C2212yes—
17C22×C22⋊D43C2212yes—
18C23×Dic43C2212yes—
19C22×C4×D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21#13063287—24no—
22(C22⋊D43)⋊C4—28no—
23C2×Dic43⋊C4C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×C4×Dic43C2212yes—
30C2×C4×Dic43C2211yescharacteristic
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C43⋊#95C2212yes—
34C22×D4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2212yes—
38#95×C43C2211yescharacteristic
39C24×C43C2312yes—
40C23×D43C2311yescharacteristic
41C23×D43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—24no—
44C22×C4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—24no—
53C2×C22⋊D43—24no—
54C22×Dic43—24no—
55C22×Dic43—24no—
56C22×Dic43D418yescomplemented
57C22×Dic43C2311yescharacteristic
58C22×Dic43C2312yes—
59C22×Dic43C2312yes—
60C22×Dic43C2311yescharacteristic
61#10621900—232no—
62C2×D172—22no—
63C2×D172—22no—
64C2×D172—22no—
65C2×C4×D43—24no—
66C2×C4×D43—24no—
67C2×C4×D43—22no—
68C2×C4×D43D414yescomplemented
69C2×Dic86—22no—
70C2×Dic86—24no—
71C4⋊C4×C43—22no—
72C22⋊C4×C43—24no—
73C22⋊C4×C43—24no—
74C22⋊Dic43—24no—
75(C2×D43)⋊C4—22no—
76(C2×D43)⋊C4—24no—
77(C2×D43)⋊C4—24no—
78(C2×D43)⋊C4—22no—
79Dic43⋊C4—24no—
80C4×Dic43—24no—
81C4×Dic43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43C2×D414yes—
89C23×C43C2411yescharacteristic
90C22×D43—21no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—21no—
95C22×D43—21no—
96C22×D43—21no—
97C22×D43—22no—
98C22×D43C2×D412yes—
99C22×D43#4112yescomplemented
100D4×C43—28no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43C2×D412yes—
110C2×C4×C43#4112yescomplemented
111C22⋊D43—216no—
112C22⋊D43—216no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—216no—
118C2×Dic43—21no—
119C2×Dic43—22no—
120C2×Dic43C2×D414yes—
121C2×Dic43C2×D414yes—
122C2×Dic43C2×D412yes—
123C2×Dic43#4114yescomplemented
124D172—28no—
125C4×D43—28no—
126C4×D43—44no—
127Dic86—28no—
128C22×C43—24no—
129C22×C43—24no—
130C22×C43—24no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43C22×D412yes—
136C22×C43C22×D411yescharacteristic
137C22×C43C2×#4111yescharacteristic
138C22×C43C2×#4112yes—
139C22×C43C2×#4111yescharacteristic
140C2×D43—22no—
141C2×D43—22no—
142C2×D43—22no—
143C2×D43—24no—
144C2×D43—22no—
145C2×D43—41no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—42no—
149C2×D43—41no—
150C4×C43—22no—
151C4×C43—22no—
152C4×C43—41no—
153C4×C43—42no—
154Dic43—24no—
155Dic43—24no—
156Dic43—41no—
157Dic43#12014yes—
158#2388—431nomaximal, Sylow
159C2×C43—44no—
160C2×C43C2×#12011yescharacteristic
161C2×C43#52512yes—
162C2×C43#52511yescharacteristic
163C2×C43#53212yes—
164C2×C43#53211yescharacteristic
165D43—42no—
166D43—42no—
167C22×#41—431no—
168C2×C4×D4—431no—
169C2×C4×D4—432no—
170#395—431no—
171#394—432no—
172#394D4311yescharacteristic, complemented
173#393—431no—
174#392—431no—
175#392—432no—
176C4×C22⋊C4—432no—
177C4×C22⋊C4—431no—
178C43#238811yescharacteristic, complemented, Sylow
179C2×#41—868no—
180C2×#41—864no—
181C22×Q8—431no—
182C22×D4—432no—
183C22×D4—432no—
184C22×D4—431no—
185C22×D4C2×D4311yescharacteristic
186C23×C4—432no—
187C23×C4—431no—
188C23×C4—431no—
189C4×D4—868no—
190C4×D4—864no—
191C2×C4⋊C4—432no—
192C2×C4⋊C4C2×D4311yescharacteristic
193C2×C22⋊C4—432no—
194C2×C22⋊C4—432no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—431no—
197C2×C22⋊C4—432no—
198C2×C22⋊C4C2×D4312yes—
199C2×C22⋊C4C2×D4312yes—
200C2×C42—432no—
201C2×C42—431no—
202#95—431no—
203#95—432no—
204#95—432no—
205#95C2×D4311yescharacteristic
206C24—431no—
207C24—431no—
208C24C22×D4312yes—
209#41—8632no—
210C2×Q8—864no—
211C2×Q8—862no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—862no—
215C2×D4—862no—
216C2×D4—864no—
217C2×D4—864no—
218C2×D4—864no—
219C2×D4—864no—
220C2×D4—864no—
221C2×D4—864no—
222C2×D4—862no—
223C22×C4—431no—
224C22×C4—438no—
225C22×C4—432no—
226C22×C4—432no—
227C22×C4—434no—
228C22×C4—431no—
229C22×C4—864no—
230C22×C4—864no—
231C22×C4—862no—
232C22×C4—864no—
233C22×C4—864no—
234C22×C4C22×D4312yes—
235C22×C4C22×D4311yescharacteristic
236C22×C4C22×D4311yescharacteristic
237C22×C4C22×D4311yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—864no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—864no—
243C22⋊C4—864no—
244C22⋊C4—862no—
245C22⋊C4—864no—
246C22⋊C4—862no—
247C42—862no—
248C42—864no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—432no—
256C23—432no—
257C23—862no—
258C23—861no—
259C23—862no—
260C23—862no—
261C23—862no—
262C23—861no—
263C23—861no—
264C23—861no—
265C23D4×D4314yes—
266C23C23×D4311yescharacteristic
267Q8—868no—
268D4—28no—
269D4—868no—
270D4—8616no—
271D4—8616no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—434no—
281C2×C4—432no—
282C2×C4—434no—
283C2×C4—434no—
284C2×C4—868no—
285C2×C4—8616no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—861no—
291C2×C4—862no—
292C2×C4—1724no—
293C2×C4D4×D4312yes—
294C2×C4#1062190012yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—862no—
303C22—864no—
304C22—862no—
305C22—862no—
306C22—862no—
307C22—1721no—
308C22—1722no—
309C22—1722no—
310C22—1722no—
311C22—1721no—
312C22C2×D4×D4312yes—
313C22C2×D4×D4311yescharacteristic
314C22#41×D4311yescharacteristic
315C22#41×D4312yes—
316C22C2×#1062190011yescharacteristic
317C4—22no—
318C4—22no—
319C4—41no—
320C4—42no—
321C4—434no—
322C4—864no—
323C4—864no—
324C4—1721no—
325C2—44no—
326C2—1722no—
327C2—1722no—
328C2#120×D4311yescharacteristic
329C2#1458340712yes—
330C2#1458340911yescharacteristic
331C2#1458344412yes—
332C2#1458344811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2388
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#10621900C2semidirect
2. C2×#13063287C2semidirect
3. C2×(C22⋊D43)⋊C4C2semidirect
4. #14582819C2semidirect
5. #14582814C2semidirect
6. #14582812C2semidirect
7. #14582808C2semidirect
8. #14582807C2semidirect
9. C22⋊C4×Dic43C2semidirect
10. #14582746C2semidirect
11. C43×#394C2semidirect
56. C22×Dic43D4semidirect
68. C2×C4×D43D4semidirect
99. C22×D43#41semidirect
110. C2×C4×C43#41semidirect
123. C2×Dic43#41semidirect
172. #394D43semidirect
178. C43#2388semidirect
294. C2×C4#10621900semidirect