Finite Group Databasebeta

← #19137925

Subgroups — #19137925

Order 5504.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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
2C2×#13063307C212yesmaximal, complemented
3C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#14582820C211yesmaximal, characteristic, complemented
5#14582819C211yesmaximal, characteristic, complemented
6#14582813C211yesmaximal, characteristic, complemented
7#14582775C212yesmaximal, complemented
8#14582774C212yesmaximal, complemented
9#14582771C212yesmaximal, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C2×#10621900—28no—
13C2×#10621900—24no—
14C22×Dic86C2211yescharacteristic
15C22×C22⋊D43C2212yes—
16C23×Dic43C2212yes—
17C22×C4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20#13063307—28no—
21C2×C4⋊Dic43C2212yes—
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2212yes—
25C2×Dic43⋊C4C2211yescharacteristic
26C4⋊C4×D43—24no—
27C2×C22⋊Dic43C2212yes—
28C2×C22⋊Dic43C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
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
41C2×D4×C43—22no—
42C2×D4×C43—24no—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—24no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43D418yes—
50C22×Dic43—24no—
51C22×Dic43—24no—
52C22×Dic43—24no—
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58#10621900—232no—
59C2×C4×D43—22no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×C4×D43—24no—
63C2×C4×D43—22no—
64C2×C4×D43—24no—
65C2×C4×D43D414yes—
66C2×Dic86—22no—
67C2×Dic86—24no—
68C4⋊C4×C43—22no—
69C22⋊C4×C43—24no—
70C22⋊C4×C43—24no—
71C22⋊Dic43—24no—
72C22⋊Dic43—24no—
73(C2×D43)⋊C4—24no—
74C4⋊Dic43—22no—
75C4⋊Dic43—24no—
76Dic43⋊C4—22no—
77Dic43⋊C4—22no—
78Dic43⋊C4—24no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43C2×D414yes—
86C23×C43C2411yescharacteristic
87C22×D43—21no—
88C22×D43—21no—
89C22×D43—22no—
90C22×D43C2×D414yes—
91C22×D43C2×D412yes—
92D4×C43—28no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43C2×D412yes—
102C2×C4×C43#4112yescomplemented
103C22⋊D43—216no—
104C2×Dic43—216no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43C2×D414yes—
116C2×Dic43C2×D412yes—
117C2×Dic43#4112yescomplemented
118C4×D43—28no—
119C4×D43—28no—
120C4×D43—44no—
121Dic86—28no—
122C22×C43—24no—
123C22×C43—24no—
124C22×C43—24no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43C22×D411yescharacteristic
130C22×C43C22×D412yes—
131C22×C43C2×#4111yescharacteristic
132C22×C43C2×#4111yescharacteristic
133C22×C432−1+412yes—
134C2×D43—22no—
135C2×D43—22no—
136C2×D43—24no—
137C2×D43—24no—
138C2×D43#12014yes—
139C4×C43—22no—
140C4×C43—22no—
141C4×C43—41no—
142C4×C43—42no—
143Dic43—24no—
144Dic43—22no—
145Dic43—22no—
146Dic43—41no—
147Dic43—42no—
148#2406—431nomaximal, Sylow
149C2×C43—44no—
150C2×C43C2×#12011yescharacteristic
151C2×C43#52511yescharacteristic
152C2×C43#53611yescharacteristic
153C2×C43#54712yes—
154C2×C43#54712yes—
155D43—24no—
156C22×#41—431no—
157C2×#123—432no—
158C22×C4⋊C4—431no—
159#395—431no—
160#395—431no—
161#394—431no—
162#394D4311yescharacteristic, complemented
163#386—432no—
164#385—432no—
165#385—432no—
166#381—431no—
167C43#240611yescharacteristic, complemented, Sylow
168C2×#41—864no—
169C2×#41—868no—
170C22×Q8—431no—
171C22×D4—432no—
172C22×D4C2×D4311yescharacteristic
173C23×C4—431no—
174C23×C4—432no—
175C23×C4—431no—
176C23×C4—431no—
177#123—868no—
178C2×C4⋊C4—431no—
179C2×C4⋊C4—431no—
180C2×C4⋊C4—431no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—864no—
184C2×C4⋊C4C2×D4311yescharacteristic
185C2×C22⋊C4—432no—
186C2×C22⋊C4—432no—
187C2×C22⋊C4—432no—
188C2×C22⋊C4C2×D4312yes—
189C2×C22⋊C4C2×D4312yes—
190#95—432no—
191#95—431no—
192#95—432no—
193#95—432no—
194#95C2×D4311yescharacteristic
195C24—431no—
196C24C22×D4312yes—
197#41—8632no—
198C2×Q8—864no—
199C2×Q8—862no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—438no—
203C2×D4—864no—
204C2×D4—864no—
205C22×C4—431no—
206C22×C4—431no—
207C22×C4—432no—
208C22×C4—434no—
209C22×C4—432no—
210C22×C4—431no—
211C22×C4—862no—
212C22×C4—862no—
213C22×C4—864no—
214C22×C4—862no—
215C22×C4—864no—
216C22×C4—864no—
217C22×C4—864no—
218C22×C4—864no—
219C22×C4—862no—
220C22×C4C22×D4312yes—
221C22×C4C22×D4311yescharacteristic
222C22×C4C22×D4311yescharacteristic
223C22×C4C22×D4311yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—862no—
226C4⋊C4—862no—
227C4⋊C4—864no—
228C4⋊C4—864no—
229C4⋊C4—862no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C22⋊C4—864no—
233C22⋊C4—864no—
234C22⋊C4—864no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—434no—
242C23—432no—
243C23—861no—
244C23—861no—
245C23—862no—
246C23D4×D4314yes—
247C23C23×D4311yescharacteristic
248Q8—868no—
249D4—28no—
250D4—8616no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—432no—
260C2×C4—434no—
261C2×C4—432no—
262C2×C4—868no—
263C2×C4—868no—
264C2×C4—8616no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—861no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—861no—
273C2×C4—862no—
274C2×C4—862no—
275C2×C4—1724no—
276C2×C4D4×D4312yes—
277C2×C4#1062190012yescomplemented
278C22—24no—
279C22—24no—
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—434no—
286C22—862no—
287C22—862no—
288C22—864no—
289C22—864no—
290C22C2×D4×D4311yescharacteristic
291C22C2×D4×D4312yes—
292C22#41×D4311yescharacteristic
293C22C2×#1062190011yescharacteristic
294C22#1306337212yes—
295C4—22no—
296C4—22no—
297C4—41no—
298C4—42no—
299C4—862no—
300C4—864no—
301C4—862no—
302C4—1721no—
303C4—1722no—
304C2—44no—
305C2—864no—
306C2#120×D4311yescharacteristic
307C2#1458340911yescharacteristic
308C2#1458346911yescharacteristic
309C2#1458354712yes—
310C2#1458354912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2406
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13063307C2semidirect
3. C2×C4⋊C4×D43C2semidirect
4. #14582820C2semidirect
5. #14582819C2semidirect
6. #14582813C2semidirect
7. #14582775C2semidirect
8. #14582774C2semidirect
9. #14582771C2semidirect
10. #14582761C2semidirect
11. C43×#394C2semidirect
102. C2×C4×C43#41semidirect
117. C2×Dic43#41semidirect
162. #394D43semidirect
167. C43#2406semidirect
277. C2×C4#10621900semidirect