Finite Group Databasebeta

← #19134877

Subgroups — #19134877

Order 5504.

374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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#14583372C211yesmaximal, characteristic
2C2×#13063239C211yesmaximal, characteristic
3#14582776C211yesmaximal, characteristic
4#14582774C211yesmaximal, characteristic, complemented
5#14582771C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C43×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C2211yescharacteristic
9C23×Dic43C2211yescharacteristic
10C4×C22⋊D43—21no—
11C4×C22⋊D43—21no—
12(C22⋊D43)⋊C4—21no—
13(C22⋊D43)⋊C4—21no—
14#13063281—21no—
15C2×C4⋊Dic43—21no—
16C2×Dic43⋊C4—21no—
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2211yescharacteristic
19C2×(C2×D43)⋊C4—21no—
20C22⋊C4×D43—21no—
21#13063239C414yescomplemented
22C43⋊#95—21no—
23C43⋊#95—21no—
24C43⋊#95—21no—
25C2×C22⋊C4×C43C2211yescharacteristic
26C2×C22⋊C4×C43C2211yescharacteristic
27C2×C22⋊C4×C43C2211yescharacteristic
28C24×C43C2311yescharacteristic
29C23×D43D411yescharacteristic
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43D411yescharacteristic
33C22×C4×C43D411yescharacteristic
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C2×C22⋊D43C2×C412yes—
39C2×C22⋊D43Q812yes—
40C22×Dic43—21no—
41C22×Dic43—21no—
42C22×Dic43—21no—
43C22×Dic43—21no—
44C22×Dic43—42no—
45C22×Dic43D411yescharacteristic
46C22×Dic43D411yescharacteristic
47C22×Dic43D411yescharacteristic
48C2×C4×D43—21no—
49C2×C4×D43—21no—
50C22⋊C4×C43—21no—
51C22⋊C4×C43—21no—
52C22⋊C4×C43—21no—
53C22⋊C4×C43—21no—
54C22⋊C4×C43—21no—
55C22⋊C4×C43C2×C412yescomplemented
56C22⋊Dic43—21no—
57C22⋊Dic43—21no—
58C22⋊Dic43—21no—
59C22⋊Dic43C2×C412yescomplemented
60(C2×D43)⋊C4—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—42no—
63C4⋊Dic43—42no—
64Dic43⋊C4—21no—
65Dic43⋊C4—21no—
66Dic43⋊C4—42no—
67C4×Dic43—21no—
68C4×Dic43—21no—
69C23×C43—41no—
70C23×C43—41no—
71C23×C43C22×C411yescharacteristic
72C23×C43C2×D411yescharacteristic
73C23×C43C2×D411yescharacteristic
74C23×C43C2×D411yescharacteristic
75C23×C43C2×Q811yescharacteristic
76C23×C43#4111yescharacteristic
77C23×C43#4111yescharacteristic
78C22×D43—21no—
79C22×D43—21no—
80C22×D43—41no—
81C22×D43—41no—
82C22×D43C4⋊C412yescomplemented
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C22⋊D43—22no—
94C22⋊D43—22no—
95C22⋊D43—22no—
96C22⋊D43—22no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—21no—
104C2×Dic43—21no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43—41no—
113C2×Dic43C4⋊C412yescomplemented
114C4×D43—81no—
115C4×D43—81no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—41no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43C2×C4⋊C411yescharacteristic
127C22×C43C4×D411yescharacteristic
128C22×C43C4×D411yescharacteristic
129C22×C43#12011yescharacteristic
130C22×C43C22⋊Q811yescharacteristic
131C22×C43C22⋊Q811yescharacteristic
132C22×C43#12311yescharacteristic
133C2×D43—22no—
134C2×D43—41no—
135C2×D43—41no—
136C2×D43—42no—
137C2×D43—81no—
138C4×C43—42no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—81no—
142Dic43—22no—
143Dic43—42no—
144Dic43—41no—
145Dic43—42no—
146Dic43—41no—
147#1867—431nomaximal, Sylow
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43#38511yescharacteristic
155C2×C43B(4,𝔽2)11yescharacteristic
156C2×C43#45811yescharacteristic
157D43—42no—
158#518—431no—
159C2×#99—431no—
160#386—431no—
161#385—431no—
162#385—431no—
163#342—431no—
164#342D4311yescharacteristic, complemented
165C43#186711yescharacteristic, complemented, Sylow
166C22×D4—431no—
167C23×C4—431no—
168C4×D4—861no—
169C4×D4—861no—
170C4×D4—861no—
171C4×D4—861no—
172#117—861no—
173C2×C4⋊C4—861no—
174C2×C4⋊C4—861no—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—431no—
177C2×C22⋊C4—861no—
178C2×C22⋊C4—861no—
179C2×C22⋊C4C2×D4311yescharacteristic
180C2×C22⋊C4C2×D4311yescharacteristic
181C2×C22⋊C4C2×D4311yescharacteristic
182#99—434no—
183#95—861no—
184#95—861no—
185#95—861no—
186C24—431no—
187C24C22×D4311yescharacteristic
188C2×D4—432no—
189C2×D4—432no—
190C2×D4—861no—
191C2×D4—861no—
192C2×D4—861no—
193C2×D4—861no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—431no—
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—861no—
200C22×C4—861no—
201C22×C4—861no—
202C22×C4—861no—
203C22×C4—861no—
204C22×C4—861no—
205C22×C4—1722no—
206C22×C4D17211yescharacteristic
207C22×C4D17211yescharacteristic
208C4⋊C4—861no—
209C4⋊C4—861no—
210C4⋊C4—1722no—
211C4⋊C4—1722no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—432no—
218C22⋊C4—861no—
219C22⋊C4—861no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C22⋊C4—861no—
223C22⋊C4—1722no—
224C22⋊C4C4×D4312yescomplemented
225C42—861no—
226C42—861no—
227C23—41no—
228C23—41no—
229C23—432no—
230C23—861no—
231C23—861no—
232C23—1721no—
233C23—1721no—
234C23C2×C4×D4311yescharacteristic
235C23C2×D17211yescharacteristic
236C23#1062189811yescharacteristic
237C23D4×D4311yescharacteristic
238C23D4×D4311yescharacteristic
239C23#1062190011yescharacteristic
240C23Q8×D4311yescharacteristic
241D4—862no—
242D4—862no—
243D4—862no—
244D4—862no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—432no—
256C2×C4—861no—
257C2×C4—861no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—861no—
263C2×C4—861no—
264C2×C4—3441no—
265C2×C4—3441no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—862no—
285C22—3441no—
286C22—1722no—
287C22—1721no—
288C22—1721no—
289C22C4⋊C4×D4311yescharacteristic
290C22(C22⋊D43)⋊C411yescharacteristic
291C22C4×D17211yescharacteristic
292C22#1306329511yescharacteristic
293C22#1306330311yescharacteristic
294C22#1306330511yescharacteristic
295C22#1306330711yescharacteristic
296C4—42no—
297C4—41no—
298C4—41no—
299C4—81no—
300C4—862no—
301C4—1722no—
302C4—1722no—
303C4—1721no—
304C4—1721no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—1722no—
312C2#1458277311yescharacteristic
313C2#1458308711yescharacteristic
314C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43#120
hypercenter#342D43
hypocenterC43#1867
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #14582774C2semidirect
5. #14582771C2semidirect
6. #14582665C2semidirect
7. C43×#342C2semidirect
21. #13063239C4semidirect
55. C22⋊C4×C43C2×C4semidirect
59. C22⋊Dic43C2×C4semidirect
82. C22×D43C4⋊C4semidirect
113. C2×Dic43C4⋊C4semidirect
164. #342D43semidirect
165. C43#1867semidirect
224. C22⋊C4C4×D43semidirect