Finite Group Databasebeta

← #29573422

Subgroups — #29573422

Order 15616.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#21448225C211yesmaximal, characteristic
2#21445582C212yesmaximal
3#21443701C212yesmaximal, complemented
4#21443700C211yesmaximal, characteristic, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×#14519735C411yescharacteristic
7C2×#14519735C411yescharacteristic
8C2×C42×D61C2211yescharacteristic
9C2×#14519689—22no—
10C2×#14519688C2212yes—
11#16839631C411yescharacteristic
12#16839631C411yescharacteristic
13#16839628C2211yescharacteristic
14#16839621—22no—
15#16839613—22no—
16#16839516—22no—
17C2×#97×C61C2212yes—
18C61×#382C2211yescharacteristic
19C22×C4×D61C2×C411yescharacteristic
20C22×C4×D61D412yes—
21C22×#92418—22no—
22#14519735—42no—
23#14519735—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—22no—
27C2×#11758196—22no—
28C2×#11758198—21no—
29C2×#11758198—21no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61D412yes—
34C42×D61—22no—
35C42×D61—21no—
36C42×D61—21no—
37#14519689—28no—
38#14519688—22no—
39#14519688—22no—
40#14519684—22no—
41C22×C8×C61—22no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C42×C61C2311yescharacteristic
45#97×C61—22no—
46#97×C61—22no—
47#95×C61—22no—
48C23×D61C22⋊C411yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61C22×C411yescharacteristic
52C22×C4×C61C2×D412yes—
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C412yes—
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—24no—
64C2×C4×D61—42no—
65C2×C8×C61—24no—
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61#4112yes—
71C42×C61#4111yescharacteristic
72C42×C61#4111yescharacteristic
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77#11758196—44no—
78#11758196—44no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61—42no—
84C4×Dic61—42no—
85C2×#92418—24no—
86C2×#92418—42no—
87C2×#92418—42no—
88C23×C61C2×C22⋊C411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61#10112yes—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61#11711yescharacteristic
103C2×C4×C61#11711yescharacteristic
104C2×C4×C61#12312yes—
105C2×C4×C61#12312yes—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61#10012yes—
115C2×Dic61#10414yes—
116C4×D61—24no—
117C4×D61—24no—
118C4×D61—44no—
119C4×D61—44no—
120C8×C61—44no—
121#92418—44no—
122#8721—611nomaximal, Sylow
123C22×C61#38111yescharacteristic
124C22×C61C2×#10011yescharacteristic
125C22×C61C2×#10111yescharacteristic
126C22×C61C2×#10412yes—
127C22×C61#42112yes—
128C2×D61—22no—
129C2×D61—24no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—22no—
136C4×C61—22no—
137C4×C61—81no—
138C4×C61—81no—
139Dic61—22no—
140Dic61—24no—
141Dic61—81no—
142Dic61—81no—
143#2285—611no—
144#1749—612no—
145#1295—612no—
146#1295—611no—
147#1295D6111yescharacteristic, complemented
148C2×C61#152511yescharacteristic
149C2×C61#153112yes—
150C2×C61#153611yescharacteristic
151C2×C61#182111yescharacteristic
152C2×C61#182612yes—
153D61—42no—
154C2×#117—611no—
155C2×#117—611no—
156C22×C42—611no—
157C2×C22⋊C8—1222no—
158C2×#97—612no—
159C2×#97C2×D6112yes—
160#384—611no—
161#384—611no—
162#382—611no—
163#382C2×D6111yescharacteristic
164#380—1222no—
165C4×C4⋊C4—1222no—
166#336—1222no—
167C61#872111yescharacteristic, complemented, Sylow
168C23×C4—611no—
169C23×C4—612no—
170C22×C8—22no—
171C22×C8—1222no—
172#117—2442no—
173#117—2442no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—1222no—
177C2×C4⋊C4—1222no—
178C2×C4⋊C4C4×D6111yescharacteristic
179C2×C4⋊C4C4×D6111yescharacteristic
180C2×C22⋊C4—1221no—
181C2×C22⋊C4—1221no—
182C2×C42—611no—
183C2×C42—612no—
184C2×C42—1222no—
185C2×C42—1221no—
186C2×C42—1221no—
187C2×C42—1221no—
188C2×C42—1221no—
189C2×C42C22×D6111yescharacteristic
190C22⋊C8—1228no—
191#97—22no—
192#97—22no—
193#97—1222no—
194#97—1222no—
195#95—22no—
196#95—1222no—
197C24—611no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—611no—
201C22×C4—612no—
202C22×C4—1222no—
203C22×C4—1224no—
204C22×C4—1222no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—2442no—
212C22×C4C2×C4×D6111yescharacteristic
213C22×C4D4×D6112yes—
214C2×C8—24no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—1224no—
218C2×C8—2442no—
219C2×C8—2442no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2444no—
225C4⋊C4—2444no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C42—1221no—
229C42—1221no—
230C42—1222no—
231C42—1222no—
232C42—2442no—
233C42—2442no—
234C42#1175822212yes—
235C42#1175822411yescharacteristic
236C42#1175822611yescharacteristic
237C23—612no—
238C23—1221no—
239C23—1222no—
240C23—1222no—
241C23—1221no—
242C23C22⋊C4×D6111yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—612no—
252C2×C4—614no—
253C2×C4—1224no—
254C2×C4—1224no—
255C2×C4—1221no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—2444no—
260C2×C4—2444no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4#1451973411yescharacteristic
266C2×C4#1451973511yescharacteristic
267C2×C4#1451975912yes—
268C2×C4#1451976212yes—
269C8—44no—
270C8—2444no—
271C22—1222no—
272C22—1224no—
273C22—2442no—
274C22—2441no—
275C22—2441no—
276C22#1683962411yescharacteristic
277C22#100×D6111yescharacteristic
278C22#101×D6111yescharacteristic
279C22#104×D6112yes—
280C22#1683977712yes—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—81no—
286C4—81no—
287C4—1222no—
288C4—1224no—
289C4—4881no—
290C4—4881no—
291C2—2442no—
292C2#2144440911yescharacteristic
293C2#2144443212yes—
294C2#2144445211yescharacteristic
295C2#2144589811yescharacteristic
296C2#2144591712yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #21443701C2semidirect
4. #21443700C2semidirect
5. C61×#1295C2semidirect
147. #1295D61semidirect
167. C61#8721semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214482252
#214455822
#214437012
#214437002
C61×#12952
#872161