Finite Group Databasebeta

← #19141370

Subgroups — #19141370

Order 5504.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063315C211yesmaximal, characteristic
2#14582838C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic
4#14582832C211yesmaximal, characteristic
5#14582830C211yesmaximal, characteristic
6#14582818C211yesmaximal, characteristic
7#14582818C211yesmaximal, characteristic
8#14582806C211yesmaximal, characteristic
9#14582806C211yesmaximal, characteristic
10#14582794C211yesmaximal, characteristic
11#14582785C211yesmaximal, characteristic
12#14582783C211yesmaximal, characteristic
13#14582783C211yesmaximal, characteristic
14#14582780C211yesmaximal, characteristic
15C2×C4⋊Q8×C43C211yesmaximal, characteristic
16#13063315—24no—
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×C4×Dic43C2211yescharacteristic
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2211yescharacteristic
33C43⋊#95C2211yescharacteristic
34C43⋊#95C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C22×Q8×C43C2211yescharacteristic
46C22×Q8×C43C2211yescharacteristic
47C4⋊Q8×C43—24no—
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C4⋊C4×C43C2211yescharacteristic
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C42×C43C2211yescharacteristic
53C2×Q8×C43—22no—
54C2×Q8×C43—22no—
55C2×Q8×C43—22no—
56C2×Q8×C43—22no—
57C2×Q8×C43—41no—
58C2×Q8×C43—41no—
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C4⋊C4×C43—22no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43D414yes—
78C42×C43—22no—
79C4⋊Dic43—22no—
80C4⋊Dic43—41no—
81Dic43⋊C4—22no—
82Dic43⋊C4—22no—
83Dic43⋊C4—22no—
84Dic43⋊C4—22no—
85Dic43⋊C4—22no—
86Dic43⋊C4—41no—
87Dic43⋊C4—41no—
88Dic43⋊C4Q814yescomplemented
89C4×Dic43—22no—
90C4×Dic43—41no—
91C23×C43C2411yescharacteristic
92Q8×C43—44no—
93Q8×C43—44no—
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×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43C2×D412yes—
111C2×C4×C43C2×D412yes—
112C2×C4×C43C2×D412yes—
113C2×C4×C43C2×Q812yes—
114C2×C4×C43#4112yes—
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×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43C2×Q812yes—
138C2×Dic43C2×Q812yes—
139C22×C43C22×D411yescharacteristic
140C22×C43C22×Q811yescharacteristic
141C22×C43C2×#4111yescharacteristic
142C22×C43H(5,𝔽2)11yescharacteristic
143C22×C432−1+411yescharacteristic
144C22×C432−1+411yescharacteristic
145C22×C432−1+411yescharacteristic
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—41no—
152C4×C43—41no—
153Dic43—22no—
154Dic43—22no—
155Dic43—41no—
156Dic43—41no—
157Dic43—41no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161#2713—431nomaximal, Sylow
162C2×C43#53611yescharacteristic
163C2×C43#54111yescharacteristic
164C2×C43#54411yescharacteristic
165C2×C43#54611yescharacteristic
166C2×C43D4×Q811yescharacteristic
167C2×C43#55711yescharacteristic
168C2×C43#56311yescharacteristic
169C2×C4⋊Q8D4311yescharacteristic
170C2×#125—431no—
171#400—431no—
172#400—431no—
173#398—431no—
174#398—431no—
175#395—431no—
176#395—431no—
177#391—431no—
178#391—431no—
179#389—431no—
180#387—431no—
181#387—431no—
182#387—431no—
183#387—431no—
184C43#271311yescharacteristic, complemented, Sylow
185C22×Q8C2×D4311yescharacteristic
186C22×Q8C2×D4311yescharacteristic
187C4⋊Q8—24no—
188#125—864no—
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⋊C4—431no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4C2×D4311yescharacteristic
200C2×C4⋊C4C2×D4311yescharacteristic
201C2×C4⋊C4C2×D4311yescharacteristic
202C2×C4⋊C4C2×D4311yescharacteristic
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#95—431no—
217#95—431no—
218#95—431no—
219#95—431no—
220#95—431no—
221#95—431no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C22×C4—431no—
229C22×C4—431no—
230C22×C4—431no—
231C22×C4—431no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—431no—
235C22×C4—431no—
236C22×C4C22×D4311yescharacteristic
237C22×C4C22×D4311yescharacteristic
238C22×C4C22×D4311yescharacteristic
239C22×C4C22×D4311yescharacteristic
240C22×C4C22×D4311yescharacteristic
241C22×C4C22×D4311yescharacteristic
242C22×C4C22×D4311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—434no—
247C4⋊C4—862no—
248C4⋊C4—862no—
249C4⋊C4—862no—
250C4⋊C4—862no—
251C4⋊C4—862no—
252C4⋊C4—862no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4C22⋊D4314yes—
257C42—22no—
258C42—862no—
259C42—1721no—
260C23C23×D4311yescharacteristic
261Q8—44no—
262Q8—44no—
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—21no—
277C2×C4—21no—
278C2×C4—21no—
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×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4#1062190012yes—
304C2×C4Q8×D4312yes—
305C2×C4C2×C22⋊D4312yes—
306C2×C4C2×C22⋊D4312yes—
307C2×C4C2×C22⋊D4312yes—
308C22C22×C22⋊D4311yescharacteristic
309C22C2×Q8×D4311yescharacteristic
310C22C2×#1062190011yescharacteristic
311C22#1306337011yescharacteristic
312C22#1306337311yescharacteristic
313C22#1306337311yescharacteristic
314C22#1306337311yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—862no—
323C4—862no—
324C4—1721no—
325C4—1721no—
326C4—1721no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C2#1458347311yescharacteristic
331C2#1458351011yescharacteristic
332C2#1458352611yescharacteristic
333C2#1458354311yescharacteristic
334C2Q8×C22⋊D4311yescharacteristic
335C2#1458362411yescharacteristic
336C2#1458364811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C4⋊Q8×C43C2
hypercenterC2×C4⋊Q8D43
hypocenterC43#2713
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
88. Dic43⋊C4Q8semidirect
184. C43#2713semidirect