Finite Group Databasebeta

← #20248406

Subgroups — #20248406

Order 6016.

468 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094022C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic
4#15689054C211yesmaximal, characteristic
5#15689044C211yesmaximal, characteristic
6#15689042C211yesmaximal, characteristic
7#15689027C211yesmaximal, characteristic
8#15689021C211yesmaximal, characteristic
9#15689020C211yesmaximal, characteristic
10#15689020C211yesmaximal, characteristic
11#15689020C211yesmaximal, characteristic
12#15688987C211yesmaximal, characteristic
13C4×Dic47⋊C4C211yesmaximal, characteristic
14#15688974C211yesmaximal, characteristic
15C47×#391C211yesmaximal, 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×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×Q8×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×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—
75C42×C47—41no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—41no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—41no—
89Dic47⋊C4D414yes—
90Dic47⋊C4Q814yescomplemented
91C4×Dic47—22no—
92C4×Dic47—22no—
93C4×Dic47—41no—
94C4×Dic47Q814yescomplemented
95C23×C47C2411yescharacteristic
96Q8×C47—44no—
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×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D412yes—
115C2×C4×C47C2×Q812yes—
116C2×C4×C47C2×Q812yes—
117C2×C4×C47#4112yes—
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×Dic47—21no—
135C2×Dic47C2×D412yes—
136C2×Dic47C2×D412yes—
137C2×Dic47C2×Q812yes—
138C2×Dic47C2×Q812yes—
139C2×Dic47C2×Q812yes—
140C2×Dic47C2×Q812yes—
141C2×Dic47#4112yes—
142Dic94—44no—
143C22×C47C22×D411yescharacteristic
144C22×C47C22×Q811yescharacteristic
145C22×C47C22×Q811yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47H(5,𝔽2)11yescharacteristic
149C22×C472−1+411yescharacteristic
150C4×C47—22no—
151C4×C47—22no—
152C4×C47—22no—
153C4×C47—22no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157Dic47—22no—
158Dic47—22no—
159Dic47—22no—
160Dic47—22no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47C4⋊Q814yes—
165#2550—471nomaximal, Sylow
166C2×C47C2×C4⋊Q811yescharacteristic
167C2×C47#53311yescharacteristic
168C2×C47#54411yescharacteristic
169C2×C47#54611yescharacteristic
170C2×C47#54811yescharacteristic
171C2×C47#55411yescharacteristic
172C2×C47#55711yescharacteristic
173C2×C4⋊Q8—471no—
174C2×#125—471no—
175#398—471no—
176#398—471no—
177#395—471no—
178#395—471no—
179#391—471no—
180#391D4711yescharacteristic
181#389—471no—
182#389—471no—
183#389—471no—
184#389—471no—
185#382—471no—
186C4×C4⋊C4—471no—
187C4×C4⋊C4—471no—
188C47#255011yescharacteristic, complemented, Sylow
189C22×Q8—471no—
190C22×Q8C2×D4711yescharacteristic
191C4⋊Q8—944no—
192#125—944no—
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⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4C2×D4711yescharacteristic
209C2×C42—471no—
210C2×C42—471no—
211C2×C42—471no—
212C2×C42—471no—
213C2×C42C2×D4711yescharacteristic
214#95—471no—
215#95—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95—471no—
220#95—471no—
221#95—471no—
222#95C2×D4711yescharacteristic
223#95C2×D4711yescharacteristic
224#95C2×D4711yescharacteristic
225#95C2×D4711yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—942no—
230C2×Q8—942no—
231C2×Q8—1881no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4C22×D4711yescharacteristic
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243C22×C4C22×D4711yescharacteristic
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—474no—
249C4⋊C4—474no—
250C4⋊C4—942no—
251C4⋊C4—942no—
252C4⋊C4—942no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—942no—
257C4⋊C4—942no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C42—41no—
264C42—474no—
265C42—942no—
266C42—942no—
267C42—1881no—
268C23C23×D4711yescharacteristic
269Q8—44no—
270Q8—1884no—
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—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—472no—
289C2×C4—472no—
290C2×C4—472no—
291C2×C4—472no—
292C2×C4—472no—
293C2×C4—472no—
294C2×C4—472no—
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×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4#1062535012yes—
313C2×C4D4×D4712yes—
314C2×C4Q8×D4712yes—
315C2×C4Q8×D4712yes—
316C22C2×D4×D4711yescharacteristic
317C22C2×Q8×D4711yescharacteristic
318C22C2×Q8×D4711yescharacteristic
319C22#41×D4711yescharacteristic
320C22C2×#1062535011yescharacteristic
321C22#1309406911yescharacteristic
322C22#1309407111yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—474no—
331C4—942no—
332C4—942no—
333C4—942no—
334C4—942no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C2C4⋊Q8×D4711yescharacteristic
339C2#1568967711yescharacteristic
340C2#1568975211yescharacteristic
341C2#1568976311yescharacteristic
342C2#1568978111yescharacteristic
343C2#1568982711yescharacteristic
344C2#1568985111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2550
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
90. Dic47⋊C4Q8semidirect
94. C4×Dic47Q8semidirect
188. C47#2550semidirect