Finite Group Databasebeta

← #19137333

Subgroups — #19137333

Order 5504.

444 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063315C211yesmaximal, characteristic
2#14582796C211yesmaximal, characteristic
3#14582795C211yesmaximal, characteristic
4#14582794C211yesmaximal, characteristic
5#14582794C211yesmaximal, characteristic
6#14582794C211yesmaximal, characteristic
7#14582785C211yesmaximal, characteristic
8#14582783C211yesmaximal, characteristic
9#14582782C211yesmaximal, characteristic
10#14582780C211yesmaximal, characteristic
11#14582768C211yesmaximal, characteristic
12C4×Dic43⋊C4C211yesmaximal, characteristic
13#14582750C211yesmaximal, characteristic
14#14582744C211yesmaximal, characteristic
15C43×#389C211yesmaximal, characteristic
16#13063315C418yescomplemented
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×C4×Dic43C2211yescharacteristic
30C2×C4×Dic43C2211yescharacteristic
31C2×C4×Dic43C2211yescharacteristic
32C2×C4×Dic43C2211yescharacteristic
33C2×C4×Dic43C2211yescharacteristic
34C2×C4×Dic43C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C2×C4⋊C4×C43C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C42×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52C22×C4×C43C2311yescharacteristic
53C22×C4×C43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C22×Dic43C2311yescharacteristic
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43C2×C414yes—
71C42×C43—41no—
72C4⋊Dic43—41no—
73C4⋊Dic43C2×C414yes—
74Dic43⋊C4—22no—
75Dic43⋊C4—22no—
76Dic43⋊C4—41no—
77Dic43⋊C4—41no—
78Dic43⋊C4—41no—
79Dic43⋊C4—41no—
80Dic43⋊C4C2×C414yes—
81Dic43⋊C4C2×C414yes—
82Dic43⋊C4C2×C414yes—
83Dic43⋊C4C2×C414yes—
84C4×Dic43—22no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87C4×Dic43—41no—
88C4×Dic43C2×C414yes—
89C4×Dic43Q814yes—
90C23×C43C2411yescharacteristic
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43C22×C412yes—
109C2×C4×C43C22×C412yes—
110C2×C4×C43C22×C412yes—
111C2×C4×C43C2×Q812yes—
112C2×Dic43—21no—
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43C22×C412yes—
130C2×Dic43C22×C412yes—
131C2×Dic43C22×C412yes—
132C2×Dic43C22×C412yes—
133C2×Dic43C2×Q812yes—
134C2×Dic43C2×Q812yes—
135C2×Dic43#4112yes—
136C22×C43C23×C411yescharacteristic
137C22×C43C22×Q811yescharacteristic
138C22×C43C2×#4111yescharacteristic
139C22×C43H(5,𝔽2)11yescharacteristic
140C22×C43H(5,𝔽2)11yescharacteristic
141C22×C432−1+411yescharacteristic
142C22×C432−1+411yescharacteristic
143C4×C43—22no—
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150Dic43—22no—
151Dic43—22no—
152Dic43—22no—
153Dic43—22no—
154Dic43—41no—
155Dic43—41no—
156Dic43—41no—
157Dic43C4×Q814yes—
158#2330—431nomaximal, Sylow
159C2×C43C2×C4×Q811yescharacteristic
160C2×C43#52011yescharacteristic
161C2×C43#52011yescharacteristic
162C2×C43#54011yescharacteristic
163C2×C43#54111yescharacteristic
164C2×C43#54411yescharacteristic
165C2×C43#54411yescharacteristic
166C2×#125—431no—
167#389—431no—
168#389—431no—
169#389—431no—
170#389—431no—
171#389—431no—
172#389D4311yescharacteristic
173#387—431no—
174#387—431no—
175#387—431no—
176#387—431no—
177#384—431no—
178C4×C4⋊C4—431no—
179C4×C4⋊C4—431no—
180#376—431no—
181C43#233011yescharacteristic, complemented, Sylow
182#125—438no—
183C2×C4⋊C4—431no—
184C2×C4⋊C4—431no—
185C2×C4⋊C4—431no—
186C2×C4⋊C4—431no—
187C2×C4⋊C4—431no—
188C2×C4⋊C4—431no—
189C2×C4⋊C4—431no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4C2×D4311yescharacteristic
196C2×C4⋊C4C2×D4311yescharacteristic
197C2×C4⋊C4C2×D4311yescharacteristic
198C2×C4⋊C4C2×D4311yescharacteristic
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42—431no—
205C2×C42C2×D4311yescharacteristic
206#95—431no—
207#95—431no—
208#95—431no—
209#95—431no—
210#95—431no—
211#95—431no—
212#95—431no—
213#95—431no—
214#95—431no—
215#95—431no—
216#95C2×D4311yescharacteristic
217#95C2×D4311yescharacteristic
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—431no—
222C22×C4—431no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4C22×D4311yescharacteristic
227C22×C4C22×D4311yescharacteristic
228C22×C4C22×D4311yescharacteristic
229C22×C4C22×D4311yescharacteristic
230C22×C4C22×D4311yescharacteristic
231C22×C4C22×D4311yescharacteristic
232C22×C4C22×D4311yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—434no—
237C4⋊C4—434no—
238C4⋊C4—434no—
239C4⋊C4—434no—
240C4⋊C4—434no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C4⋊C4—1721no—
248C4⋊C4C4×D4314yes—
249C42—41no—
250C42—434no—
251C42—434no—
252C42—862no—
253C42—1721no—
254C42—1721no—
255C42—1721no—
256C23C23×D4311yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—432no—
275C2×C4—432no—
276C2×C4—432no—
277C2×C4—432no—
278C2×C4—432no—
279C2×C4—432no—
280C2×C4—432no—
281C2×C4—861no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—861no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4C2×C4×D4312yes—
299C2×C4C2×C4×D4312yes—
300C2×C4C2×C4×D4312yes—
301C2×C4Q8×D4312yes—
302C22C22×C4×D4311yescharacteristic
303C22C2×Q8×D4311yescharacteristic
304C22#41×D4311yescharacteristic
305C22#1306337011yescharacteristic
306C22#1306337011yescharacteristic
307C22#1306337211yescharacteristic
308C22#1306337311yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—434no—
317C4—862no—
318C4—862no—
319C4—862no—
320C4—862no—
321C4—1721no—
322C4—1721no—
323C4—1721no—
324C2C4×Q8×D4311yescharacteristic
325C2#1458337811yescharacteristic
326C2#1458338011yescharacteristic
327C2#1458349911yescharacteristic
328C2#1458350811yescharacteristic
329C2#1458352611yescharacteristic
330C2#1458352811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#389C2
socleC23×C43C24
hypercenter#389D43
hypocenterC43#2330
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
16. #13063315C4semidirect
181. C43#2330semidirect