Finite Group Databasebeta

← #19137549

Subgroups — #19137549

Order 5504.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063290C211yesmaximal, characteristic
2#14582803C211yesmaximal, characteristic
3#14582803C211yesmaximal, characteristic
4#14582786C211yesmaximal, characteristic
5#14582785C211yesmaximal, characteristic
6#14582780C211yesmaximal, characteristic
7#14582768C211yesmaximal, characteristic
8#14582763C211yesmaximal, characteristic
9#14582763C211yesmaximal, characteristic
10C4×Dic43⋊C4C211yesmaximal, characteristic
11C4×Dic43⋊C4C211yesmaximal, characteristic
12#14582750C211yesmaximal, characteristic
13#14582750C211yesmaximal, characteristic
14#14582750C211yesmaximal, characteristic
15C43×#387C211yesmaximal, characteristic
16C22×Dic86C2211yescharacteristic
17#13063290C418yescomplemented
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×C4×Dic43C2211yescharacteristic
28C2×C4×Dic43C2211yescharacteristic
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×C42×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×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
67C2×Dic86—22no—
68C2×Dic86—22no—
69C2×Dic86C2×C414yes—
70C4⋊C4×C43—41no—
71C4⋊C4×C43C2×C414yes—
72C42×C43—41no—
73C4⋊Dic43—41no—
74Dic43⋊C4—22no—
75Dic43⋊C4—22no—
76Dic43⋊C4—22no—
77Dic43⋊C4—22no—
78Dic43⋊C4—22no—
79Dic43⋊C4C2×C414yes—
80Dic43⋊C4C2×C414yes—
81Dic43⋊C4Q814yescomplemented
82C4×Dic43—22no—
83C4×Dic43—22no—
84C4×Dic43—41no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87C4×Dic43C2×C414yes—
88C4×Dic43C2×C414yes—
89C4×Dic43C2×C414yes—
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×Dic43C22×C412yes—
128C2×Dic43C22×C412yes—
129C2×Dic43C22×C412yes—
130C2×Dic43C22×C412yes—
131C2×Dic43C2×Q812yes—
132C2×Dic43C2×Q812yes—
133C2×Dic43#4112yes—
134C2×Dic43#4112yes—
135C2×Dic43#4112yes—
136Dic86—28no—
137C22×C43C23×C411yescharacteristic
138C22×C43C22×Q811yescharacteristic
139C22×C43C2×#4111yescharacteristic
140C22×C43C2×#4111yescharacteristic
141C22×C43C2×#4111yescharacteristic
142C22×C43H(5,𝔽2)11yescharacteristic
143C22×C432−1+411yescharacteristic
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—41no—
151Dic43—22no—
152Dic43—22no—
153Dic43—22no—
154Dic43—41no—
155Dic43—41no—
156Dic43—41no—
157Dic43#11714yes—
158Dic43C4×Q814yes—
159#2355—431nomaximal, Sylow
160C2×C43C2×#11711yescharacteristic
161C2×C43C2×C4×Q811yescharacteristic
162C2×C43#52011yescharacteristic
163C2×C43#55411yescharacteristic
164C2×C43#55611yescharacteristic
165C2×C43#55711yescharacteristic
166C2×C43#55911yescharacteristic
167C2×C4×Q8—431no—
168#391—431no—
169#391—431no—
170#387—431no—
171#387—431no—
172#387—431no—
173#387D4311yescharacteristic
174#384—431no—
175#382—431no—
176#382—431no—
177C4×C4⋊C4—431no—
178C4×C4⋊C4—431no—
179C4×C4⋊C4—431no—
180C4×C4⋊C4—431no—
181C4×C4⋊C4—431no—
182C43#235511yescharacteristic, complemented, Sylow
183C22×Q8—431no—
184C4×Q8—438no—
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⋊C4C2×D4311yescharacteristic
195C2×C4⋊C4C2×D4311yescharacteristic
196C2×C42—431no—
197C2×C42—431no—
198C2×C42—431no—
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42C2×D4311yescharacteristic
205#95—431no—
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#95C2×D4311yescharacteristic
216#95C2×D4311yescharacteristic
217#95C2×D4311yescharacteristic
218#95C2×D4311yescharacteristic
219C2×Q8—434no—
220C2×Q8—862no—
221C2×Q8—862no—
222C22×C4—431no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4—431no—
230C22×C4C22×D4311yescharacteristic
231C22×C4C22×D4311yescharacteristic
232C22×C4C22×D4311yescharacteristic
233C22×C4C22×D4311yescharacteristic
234C22×C4C22×D4311yescharacteristic
235C22×C4C22×D4311yescharacteristic
236C22×C4C22×D4311yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—434no—
239C4⋊C4—434no—
240C4⋊C4—434no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C4⋊C4—862no—
244C4⋊C4—862no—
245C4⋊C4—862no—
246C4⋊C4—1721no—
247C4⋊C4C4×D4314yes—
248C42—41no—
249C42—434no—
250C42—434no—
251C42—434no—
252C42—862no—
253C42—862no—
254C42—1721no—
255C42—1721no—
256C42—1721no—
257C23C23×D4311yescharacteristic
258Q8—868no—
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—21no—
275C2×C4—21no—
276C2×C4—432no—
277C2×C4—432no—
278C2×C4—432no—
279C2×C4—432no—
280C2×C4—432no—
281C2×C4—432no—
282C2×C4—432no—
283C2×C4—432no—
284C2×C4—432no—
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×C4—861no—
299C2×C4—861no—
300C2×C4C2×C4×D4312yes—
301C2×C4C2×C4×D4312yes—
302C2×C4C2×C4×D4312yes—
303C2×C4Q8×D4312yes—
304C22C22×C4×D4311yescharacteristic
305C22C2×Q8×D4311yescharacteristic
306C22#41×D4311yescharacteristic
307C22#41×D4311yescharacteristic
308C22#41×D4311yescharacteristic
309C22#1306337011yescharacteristic
310C22#1306337211yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—434no—
319C4—434no—
320C4—862no—
321C4—862no—
322C4—862no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C2#117×D4311yescharacteristic
327C2C4×Q8×D4311yescharacteristic
328C2#1458337811yescharacteristic
329C2#1458360311yescharacteristic
330C2#1458361611yescharacteristic
331C2#1458362611yescharacteristic
332C2#1458363311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#387C2
socleC23×C43C24
hypercenter#387D43
hypocenterC43#2355
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #13063290C4semidirect
81. Dic43⋊C4Q8semidirect
182. C43#2355semidirect