Finite Group Databasebeta

← #29573411

Subgroups — #29573411

Order 15616.

554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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#382×D61C211yesmaximal, characteristic
2#21445582C212yesmaximal
3#21443701C212yesmaximal, complemented
4#21443700C211yesmaximal, characteristic, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D61C411yescharacteristic
7C2×C4⋊C4×D61C411yescharacteristic
8C2×C42×D61C2211yescharacteristic
9C2×#14519689—22no—
10C2×#14519688C2212yes—
11#16839628C2211yescharacteristic
12#16839627C411yescharacteristic
13#16839627C411yescharacteristic
14#16839626—22no—
15#95×D61—22no—
16#16839516—22no—
17C2×#97×C61C2212yes—
18C61×#382C2211yescharacteristic
19C22×C4×D61—21no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D412yes—
23C22×#92418—22no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—21no—
27C2×#11758196—21no—
28C4⋊C4×D61—42no—
29C4⋊C4×D61—42no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D412yes—
32C42×D61—22no—
33C42×D61—21no—
34C42×D61—21no—
35#14519689—28no—
36#14519688—22no—
37#14519688—22no—
38#14519684—22no—
39#14519684—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⋊C412yes—
56C22×Dic61C22⋊C411yescharacteristic
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61—24no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—42no—
65C2×C4×D61—44no—
66C2×C4×D61—42no—
67C2×C4×D61—42no—
68C2×C4×D61—44no—
69C2×C8×C61—24no—
70C2×C8×C61—42no—
71C2×C8×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61#4112yes—
75C42×C61#4111yescharacteristic
76C42×C61#4111yescharacteristic
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C2×#92418—24no—
86C2×#92418—42no—
87C2×#92418—42no—
88C23×C61C2×C22⋊C411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—22no—
92C22×D61#10012yes—
93C22×D61#10414yes—
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—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61#10112yes—
116C4×D61—24no—
117C4×D61—24no—
118C4×D61—44no—
119C4×D61—44no—
120C4×D61—84no—
121C4×D61—84no—
122C8×C61—44no—
123#92418—44no—
124#8718—611nomaximal, Sylow
125C22×C61#38111yescharacteristic
126C22×C61C2×#10011yescharacteristic
127C22×C61C2×#10111yescharacteristic
128C22×C61C2×#10412yes—
129C22×C61#42112yes—
130C2×D61—22no—
131C2×D61—24no—
132C2×D61—24no—
133C2×D61—22no—
134C2×D61#32914yes—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—22no—
138C4×C61—22no—
139C4×C61—81no—
140C4×C61—81no—
141Dic61—22no—
142Dic61—42no—
143Dic61—81no—
144Dic61—81no—
145C2×#382—611no—
146#1749—612no—
147#1295—612no—
148#1295—611no—
149#1295D6111yescharacteristic, complemented
150C2×C61C2×#32911yescharacteristic
151C2×C61#152812yes—
152C2×C61#153311yescharacteristic
153C2×C61#182111yescharacteristic
154C2×C61#182612yes—
155D61—24no—
156C22×C4⋊C4—611no—
157C22×C4⋊C4—611no—
158C22×C42—611no—
159C2×C22⋊C8—1222no—
160C2×#97—612no—
161C2×#97C2×D6112yes—
162#382—611no—
163#382—611no—
164#382—611no—
165#382—1222no—
166#382C2×D6111yescharacteristic
167C2×#95—1222no—
168#336—1222no—
169C61#871811yescharacteristic, complemented, Sylow
170C23×C4—611no—
171C23×C4—612no—
172C23×C4—1221no—
173C23×C4—1221no—
174C22×C8—22no—
175C22×C8—1222no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—2442no—
181C2×C4⋊C4—2442no—
182C2×C4⋊C4C4×D6111yescharacteristic
183C2×C4⋊C4C4×D6111yescharacteristic
184C2×C42—611no—
185C2×C42—612no—
186C2×C42—1222no—
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—
197#95—1222no—
198#95—1222no—
199C24—611no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1224no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—2442no—
214C22×C4—2442no—
215C22×C4—2442no—
216C22×C4—2444no—
217C22×C4—2444no—
218C22×C4C2×C4×D6111yescharacteristic
219C22×C4D4×D6112yes—
220C2×C8—24no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—1224no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2442no—
231C4⋊C4—2442no—
232C42—1221no—
233C42—1221no—
234C42—1222no—
235C42—1222no—
236C42#1175822212yes—
237C42#1175822411yescharacteristic
238C42#1175822611yescharacteristic
239C23—612no—
240C23—614no—
241C23—1221no—
242C23—1222no—
243C23—1221no—
244C23C22⋊C4×D6111yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—612no—
254C2×C4—1224no—
255C2×C4—1224no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—4884no—
262C2×C4—4884no—
263C2×C4—2444no—
264C2×C4—2444no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2442no—
268C2×C4—2442no—
269C2×C4#1451973411yescharacteristic
270C2×C4#1451973511yescharacteristic
271C2×C4#1451975912yes—
272C2×C4#1451976212yes—
273C8—44no—
274C8—2444no—
275C22—614no—
276C22—1222no—
277C22—1224no—
278C22—1224no—
279C22—1222no—
280C22#1683962411yescharacteristic
281C22#100×D6111yescharacteristic
282C22#101×D6111yescharacteristic
283C22#104×D6112yes—
284C22#1683977712yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—1222no—
292C4—4881no—
293C4—4881no—
294C4—2442no—
295C2—1224no—
296C2#329×D6111yescharacteristic
297C2#2144441912yes—
298C2#2144444111yescharacteristic
299C2#2144589811yescharacteristic
300C2#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#8718
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
149. #1295D61semidirect
169. C61#8718semidirect

Maximal subgroups

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

subgroupindex
#382×D612
#214455822
#214437012
#214437002
C61×#12952
#871861