Finite Group Databasebeta

← #20249281

Subgroups — #20249281

Order 6016.

620 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093999C211yesmaximal, characteristic, complemented
2C2×#13093986C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689041C212yesmaximal, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689033C212yesmaximal, complemented
7#15689033C211yesmaximal, characteristic, complemented
8#15689012C212yesmaximal, complemented
9#15689001C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#400C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×D188C2212yes—
14C22×D188C2211yescharacteristic
15C22×D188C2212yes—
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13093999—24no—
19#13093986—24no—
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2211yescharacteristic
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C23×D47C2312yes—
38C23×D47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×D188—22no—
49C2×D188—22no—
50C2×D188—22no—
51C2×D188—24no—
52C2×D188—24no—
53C2×D188—22no—
54C2×D188—42no—
55C2×D188—42no—
56C2×D188—42no—
57C2×D188—42no—
58C2×D188—42no—
59C2×C4×D47—22no—
60C2×C4×D47—42no—
61C2×C4×D47—42no—
62C2×C4×D47D414yescomplemented
63C4⋊C4×C47—22no—
64C4⋊C4×C47—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—24no—
68(C2×D47)⋊C4—24no—
69(C2×D47)⋊C4—42no—
70(C2×D47)⋊C4—42no—
71(C2×D47)⋊C4—42no—
72(C2×D47)⋊C4—42no—
73Dic47⋊C4—42no—
74C4×Dic47—22no—
75C23×C47C2411yescharacteristic
76C22×D47—21no—
77C22×D47—21no—
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—22no—
90C22×D47—22no—
91C22×D47C2×D412yes—
92C22×D47#4112yes—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47C2×D412yes—
105C2×C4×C47#4112yes—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47C2×D412yes—
113D188—28no—
114D188—44no—
115D188—48no—
116D188—48no—
117C4×D47—44no—
118C4×D47—44no—
119C22×C47C22×D411yescharacteristic
120C22×C47C2×#4111yescharacteristic
121C22×C47C2×#4111yescharacteristic
122C22×C47H(5,𝔽2)12yes—
123C22×C47H(5,𝔽2)12yes—
124C2×D47—22no—
125C2×D47—22no—
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—24no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—42no—
141C4×C47—22no—
142C4×C47—22no—
143C4×C47—41no—
144C4×C47—42no—
145C4×C47—42no—
146Dic47—22no—
147Dic47—41no—
148Dic47—42no—
149#2635—471nomaximal, Sylow
150C2×C47#52511yescharacteristic
151C2×C47#53411yescharacteristic
152C2×C47#53511yescharacteristic
153C2×C47#53812yes—
154C2×C47#54012yes—
155D47—42no—
156D47—42no—
157D47—82no—
158C2×#121—471no—
159C2×C4×D4—471no—
160#400D4711yescharacteristic, complemented
161#399—471no—
162#394—471no—
163#394—472no—
164#392—471no—
165#392—472no—
166#388—472no—
167#386—472no—
168#381—471no—
169C47#263511yescharacteristic, complemented, Sylow
170C22×D4—471no—
171C22×D4—472no—
172C22×D4—471no—
173C22×D4—472no—
174C23×C4—471no—
175C23×C4—471no—
176#121—944no—
177C4×D4—944no—
178C2×C4⋊C4—472no—
179C2×C4⋊C4C2×D4711yescharacteristic
180C2×C4⋊C4C2×D4711yescharacteristic
181C2×C22⋊C4—471no—
182C2×C22⋊C4—471no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4—472no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4—472no—
187C2×C22⋊C4—472no—
188C2×C22⋊C4—472no—
189C2×C42—471no—
190#95—472no—
191#95—471no—
192#95C2×D4711yescharacteristic
193#95C2×D4712yes—
194#95C2×D4712yes—
195C24—471no—
196C24—471no—
197C24—472no—
198C2×D4—942no—
199C2×D4—942no—
200C2×D4—944no—
201C2×D4—944no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—1882no—
205C2×D4—1882no—
206C2×D4—1882no—
207C2×D4—1882no—
208C2×D4—1882no—
209C22×C4—471no—
210C22×C4—474no—
211C22×C4—472no—
212C22×C4—471no—
213C22×C4—942no—
214C22×C4—1882no—
215C22×C4—1882no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218C22×C4C22×D4712yes—
219C22×C4C22×D4711yescharacteristic
220C22×C4C22×D4711yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—1882no—
224C22⋊C4—944no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C22⋊C4—944no—
228C22⋊C4—1882no—
229C22⋊C4—1882no—
230C22⋊C4—1882no—
231C22⋊C4—1882no—
232C42—942no—
233C23—472no—
234C23—472no—
235C23—941no—
236C23—941no—
237C23—941no—
238C23—941no—
239C23—942no—
240C23—942no—
241C23—942no—
242C23—942no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—942no—
247C23—942no—
248C23—942no—
249C23—942no—
250C23C23×D4711yescharacteristic
251D4—948no—
252D4—1884no—
253D4—1888no—
254D4—1888no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—472no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—1884no—
274C2×C4—1884no—
275C2×C4D4×D4712yes—
276C2×C4#1062535412yes—
277C22—942no—
278C22—942no—
279C22—942no—
280C22—942no—
281C22—944no—
282C22—1882no—
283C22—1882no—
284C22—1882no—
285C22—1882no—
286C22—1882no—
287C22—1882no—
288C22—1882no—
289C22—1882no—
290C22—1882no—
291C22—1881no—
292C22—1881no—
293C22—1882no—
294C22C2×D4×D4711yescharacteristic
295C22#41×D4711yescharacteristic
296C22C2×#1062535411yescharacteristic
297C22#1309407012yes—
298C22#1309407012yes—
299C4—22no—
300C4—22no—
301C4—41no—
302C4—42no—
303C4—42no—
304C4—942no—
305C4—1882no—
306C4—1881no—
307C2—3762no—
308C2—1882no—
309C2—1882no—
310C2#1568963611yescharacteristic
311C2#1568968411yescharacteristic
312C2#1568969111yescharacteristic
313C2#1568971212yes—
314C2#1568972912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2635
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13093999C2semidirect
2. C2×#13093986C2semidirect
3. #15689058C2semidirect
4. #15689041C2semidirect
5. #15689040C2semidirect
6. #15689033C2semidirect
7. #15689033C2semidirect
8. #15689012C2semidirect
9. #15689001C2semidirect
10. #15688985C2semidirect
11. C47×#400C2semidirect
62. C2×C4×D47D4semidirect
160. #400D47semidirect
169. C47#2635semidirect