Finite Group Databasebeta

← #20250171

Subgroups — #20250171

Order 6016.

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×#13094022C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic
3#15689064C211yesmaximal, characteristic
4#15689064C211yesmaximal, characteristic
5#15689056C211yesmaximal, characteristic
6#15689056C211yesmaximal, characteristic
7#15689043C211yesmaximal, characteristic
8#15689030C211yesmaximal, characteristic
9#15689027C211yesmaximal, characteristic
10#15689019C211yesmaximal, characteristic
11#15689010C211yesmaximal, characteristic
12#15689009C211yesmaximal, characteristic
13#15689008C211yesmaximal, characteristic
14#15689006C211yesmaximal, characteristic
15C47×#395C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17#13094022—24no—
18#13094014—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×Q8×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C2×Q8×C47—22no—
54C2×Q8×C47—22no—
55C2×Q8×C47—41no—
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×Dic94—22no—
72C2×Dic94—22no—
73C2×Dic94—41no—
74C4⋊C4×C47—22no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—41no—
77C4⋊Dic47—22no—
78C4⋊Dic47—41no—
79C4⋊Dic47Q814yescomplemented
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—41no—
87Dic47⋊C4D414yes—
88C4×Dic47—22no—
89C4×Dic47—22no—
90C4×Dic47—41no—
91C23×C47C2411yescharacteristic
92Q8×C47—44no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47C2×D412yes—
112C2×C4×C47C2×Q812yes—
113C2×C4×C47#4112yes—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47C2×D412yes—
135C2×Dic47C2×D412yes—
136C2×Dic47C2×Q812yes—
137C2×Dic47C2×Q812yes—
138Dic94—44no—
139C22×C47C22×D411yescharacteristic
140C22×C47C22×Q811yescharacteristic
141C22×C47C2×#4111yescharacteristic
142C22×C47H(5,𝔽2)11yescharacteristic
143C22×C472−1+411yescharacteristic
144C22×C472−1+411yescharacteristic
145C22×C472−1+411yescharacteristic
146C4×C47—22no—
147C4×C47—22no—
148C4×C47—22no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153Dic47—22no—
154Dic47—22no—
155Dic47—22no—
156Dic47—22no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#2713—471nomaximal, Sylow
162C2×C47#53611yescharacteristic
163C2×C47#54111yescharacteristic
164C2×C47#54411yescharacteristic
165C2×C47#54611yescharacteristic
166C2×C47D4×Q811yescharacteristic
167C2×C47#55711yescharacteristic
168C2×C47#56311yescharacteristic
169C2×C4⋊Q8—471no—
170C2×#125—471no—
171#400—471no—
172#400—471no—
173#398—471no—
174#398—471no—
175#395—471no—
176#395D4711yescharacteristic
177#391—471no—
178#391—471no—
179#389—471no—
180#387—471no—
181#387—471no—
182#387—471no—
183#387—471no—
184C47#271311yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C22×Q8C2×D4711yescharacteristic
187C4⋊Q8—944no—
188#125—944no—
189C2×C4⋊C4—471no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—471no—
195C2×C4⋊C4—471no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4C2×D4711yescharacteristic
201C2×C4⋊C4C2×D4711yescharacteristic
202C2×C4⋊C4C2×D4711yescharacteristic
203C2×C42—471no—
204C2×C42—471no—
205C2×C42—471no—
206#95—471no—
207#95—471no—
208#95—471no—
209#95—471no—
210#95—471no—
211#95—471no—
212#95—471no—
213#95—471no—
214#95—471no—
215#95—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95C2×D4711yescharacteristic
220#95C2×D4711yescharacteristic
221#95C2×D4711yescharacteristic
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—942no—
226C2×Q8—942no—
227C2×Q8—1881no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4711yescharacteristic
238C22×C4C22×D4711yescharacteristic
239C22×C4C22×D4711yescharacteristic
240C22×C4C22×D4711yescharacteristic
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—474no—
247C4⋊C4—474no—
248C4⋊C4—942no—
249C4⋊C4—942no—
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—942no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C42—942no—
258C42—942no—
259C42—1881no—
260C23C23×D4711yescharacteristic
261Q8—44no—
262Q8—1884no—
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—21no—
280C2×C4—21no—
281C2×C4—472no—
282C2×C4—472no—
283C2×C4—472no—
284C2×C4—472no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4D4×D4712yes—
306C2×C4#1062535212yes—
307C2×C4Q8×D4712yes—
308C22C2×D4×D4711yescharacteristic
309C22C2×Q8×D4711yescharacteristic
310C22C2×#1062535211yescharacteristic
311C22#1309406911yescharacteristic
312C22#1309407111yescharacteristic
313C22#1309407211yescharacteristic
314C22#1309407211yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—942no—
323C4—942no—
324C4—942no—
325C4—942no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C2#1568969611yescharacteristic
331C2#1568973311yescharacteristic
332C2#1568975211yescharacteristic
333C2#1568976011yescharacteristic
334C2#1568978811yescharacteristic
335C2#1568984811yescharacteristic
336C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2713
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
79. C4⋊Dic47Q8semidirect
184. C47#2713semidirect