Finite Group Databasebeta

← #29589306

Subgroups — #29589306

Order 15616.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448527C211yesmaximal, characteristic
2#21444136C212yesmaximal
3#21443765C211yesmaximal, characteristic, complemented
4#21443752C212yesmaximal, complemented
5C61×#1325C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic
7C2×#14519742C411yescharacteristic
8C2×#14519739C2211yescharacteristic
9C22⋊C8×D61—22no—
10#16839667C2211yescharacteristic
11#16839663C411yescharacteristic
12#16839652—22no—
13#16839633—22no—
14#16839608C411yescharacteristic
15#16839488C2212yes—
16#16839485—22no—
17C61×#384C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×D244C2×C411yescharacteristic
21C22×C4×D61D412yes—
22C2×C8×D61—42no—
23#14519765—22no—
24#14519765C814yescomplemented
25#14519742—42no—
26#14519739—42no—
27C2×#11758196—21no—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198D412yes—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C22⋊#92418—22no—
35#14519689—42no—
36#14519684—22no—
37#14519684—21no—
38#14519684—21no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2311yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C22⋊C8×C61—22no—
44C23×D61C22⋊C412yes—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22×C411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C2×D244—41no—
54C2×D244—41no—
55C2×D244C2×C812yes—
56C2×D244M1612yes—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—82no—
60C2×Dic122—21no—
61C2×Dic122—41no—
62C2×Dic122—41no—
63C2×Dic122C2×C812yescomplemented
64C2×C8×C61—42no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—82no—
68C42×C61—21no—
69C42×C61C2×C812yescomplemented
70#11758198—28no—
71#11758198—42no—
72#11758198—82no—
73#11758196—42no—
74C4×Dic61—22no—
75C4×Dic61—42no—
76C4×Dic61—41no—
77C2×#92418—42no—
78C8×D61—84no—
79C23×C61C2×C22⋊C411yescharacteristic
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—42no—
83C22×D61—42no—
84C22×D61C22⋊C814yes—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—41no—
94C2×C4×C61C22×C811yescharacteristic
95C2×C4×C61C2×M1611yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61#9912yes—
106D244—42no—
107D244—42no—
108C4×D61—44no—
109C4×D61—82no—
110Dic122—42no—
111Dic122—42no—
112C8×C61—82no—
113#92418—82no—
114#11481—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×C22⋊C811yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C22×C61#41311yescharacteristic
120C2×D61—24no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—44no—
124C2×D61—82no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—42no—
128C4×C61—42no—
129C4×C61—81no—
130Dic61—22no—
131Dic61—41no—
132Dic61—42no—
133Dic61—81no—
134#2326—611no—
135#1459—612no—
136#1325—611no—
137#1325D6111yescharacteristic, complemented
138#1319—612no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#145911yescharacteristic
142C2×C61#212711yescharacteristic
143C2×C61#213511yescharacteristic
144D61—44no—
145C2×#124—611no—
146C2×C4×Q8—611no—
147C2×C4×D4—611no—
148C2×C22⋊C8—1222no—
149#391—611no—
150#390—611no—
151#388—1222no—
152#385—1222no—
153#384C2×D6111yescharacteristic
154#376—611no—
155#324—612no—
156#324C2×D6112yes—
157#323—1222no—
158C61#1148111yescharacteristic, complemented, Sylow
159C22×Q8—611no—
160C22×D4—611no—
161C23×C4—612no—
162C22×C8—2442no—
163#124—614no—
164#124—1222no—
165C4×Q8—2442no—
166C4×D4—2442no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4C4×D6111yescharacteristic
170C2×C4⋊C4C22×D6111yescharacteristic
171C2×C22⋊C4—612no—
172C2×C22⋊C4—1222no—
173C2×C22⋊C4—1222no—
174C2×C42—611no—
175C2×C42—611no—
176C2×C42—1221no—
177C2×C42C4×D6111yescharacteristic
178C22⋊C8—22no—
179C22⋊C8—1222no—
180C22⋊C8—2442no—
181#95—1221no—
182#95—1221no—
183#95—1222no—
184C24—612no—
185C2×Q8—612no—
186C2×Q8—1221no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×D4—612no—
190C2×D4—612no—
191C2×D4—2441no—
192C2×D4—2441no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4—4882no—
202C22×C4C2×C4×D6111yescharacteristic
203C22×C4D4×D6112yes—
204C2×C8—42no—
205C2×C8—4884no—
206C2×C8—2442no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C4⋊C4—2442no—
211C22⋊C4—1228no—
212C22⋊C4—4882no—
213C22⋊C4—2442no—
214C42—21no—
215C42—1222no—
216C42—2441no—
217C42—2442no—
218C42C8×D6112yescomplemented
219C23—614no—
220C23—1222no—
221C23—1222no—
222C23—2442no—
223C23—2442no—
224C23C22⋊C4×D6111yescharacteristic
225Q8—2442no—
226Q8—2442no—
227D4—2442no—
228D4—2442no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—612no—
239C2×C4—1222no—
240C2×C4—1221no—
241C2×C4—4882no—
242C2×C4—2444no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C2×C8×D6111yescharacteristic
251C2×C4M16×D6111yescharacteristic
252C8—82no—
253C8—4882no—
254C22—21no—
255C22—21no—
256C22—1224no—
257C22—4882no—
258C22—2444no—
259C22—2442no—
260C22—2442no—
261C22C22⋊C8×D6111yescharacteristic
262C22#99×D6111yescharacteristic
263C22#1683974511yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—1222no—
270C4—4881no—
271C4—2442no—
272C4—2441no—
273C2—21no—
274C2—21no—
275C2—2444no—
276C2#2144413611yescharacteristic
277C2#2144748511yescharacteristic
278C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11481
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #21443765C2semidirect
4. #21443752C2semidirect
5. C61×#1325C2semidirect
24. #14519765C8semidirect
63. C2×Dic122C2×C8semidirect
69. C42×C61C2×C8semidirect
137. #1325D61semidirect
158. C61#11481semidirect
218. C42C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214485272
#214441362
#214437652
#214437522
C61×#13252
#1148161