Finite Group Databasebeta

← #29596023

Subgroups — #29596023

Order 15616.

432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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#21448537C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal
3#21445813C212yesmaximal
4#21443946C211yesmaximal, characteristic
5C61×#1394C211yesmaximal, characteristic
6C2×#14519775C2211yescharacteristic
7C2×Q8×Dic61C2211yescharacteristic
8C2×#14519742C411yescharacteristic
9#16839785—22no—
10C2×#14519696C2212yes—
11#16839668C411yescharacteristic
12#16839649—22no—
13#16839644—22no—
14#16839627C411yescharacteristic
15#16839608C411yescharacteristic
16#16839560—24no—
17#16839530—22no—
18C2×#101×C61C2212yes—
19C61×#391C2211yescharacteristic
20C22×Dic122C2×C411yescharacteristic
21C2×#11758194—22no—
22#14519775—22no—
23#14519775D412yes—
24#14519775Q812yes—
25Q8×Dic61—42no—
26#14519742—42no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35#14519706—44no—
36#14519696—22no—
37#14519696—22no—
38#14519684—21no—
39#14519684—21no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61C2311yescharacteristic
43C2×M16×C61—22no—
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46#101×C61—22no—
47#101×C61—22no—
48#95×C61—22no—
49C2×Q8×C61—41no—
50C2×Q8×C61—41no—
51C2×Q8×C61C2×D411yescharacteristic
52C2×Q8×C61C2×Q811yescharacteristic
53C2×Q8×C61#4112yes—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D412yes—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×Dic122C4⋊C412yes—
67M16×C61—42no—
68M16×C61—42no—
69C2×C8×C61—42no—
70C4⋊C4×C61—41no—
71C42×C61—41no—
72C4⋊Dic61—41no—
73C4⋊Dic61—42no—
74#11758196—24no—
75#11758196—24no—
76#11758196—42no—
77C4×Dic61—21no—
78C4×Dic61—24no—
79C4×Dic61—22no—
80C4×Dic61—42no—
81C4×Dic61C4⋊C412yes—
82#11758194—42no—
83#11758194—42no—
84C2×#92418—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—41no—
87Q8×C61—41no—
88Q8×C61—42no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61C2×C4⋊C411yescharacteristic
99C2×C4×C61#11711yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61C22⋊Q812yes—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—42no—
112C2×Dic61—41no—
113C2×Dic61#9912yes—
114Dic122—42no—
115Dic122—42no—
116C8×C61—82no—
117#92418—82no—
118#12804—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61#38011yescharacteristic
122C22×C61C2×#9911yescharacteristic
123C22×C61#41011yescharacteristic
124C4×C61—22no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—22no—
128C4×C61—81no—
129C4×C61—81no—
130Dic61—22no—
131Dic61—42no—
132Dic61—42no—
133Dic61—41no—
134Dic61—42no—
135#2327—611no—
136C2×#356—612no—
137#1801—612no—
138#1394—611no—
139#1394D6111yescharacteristic
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#179911yescharacteristic
143C2×C61#213311yescharacteristic
144C2×C61#213511yescharacteristic
145C2×C4⋊Q8—611no—
146C2×C4×Q8—611no—
147C2×C4×Q8—611no—
148#423—1222no—
149C2×#101—612no—
150C2×#101C2×D6112yes—
151#391—611no—
152#391C2×D6111yescharacteristic
153#387—1222no—
154#387—1222no—
155#382—611no—
156#376—611no—
157#356—1224no—
158#343—1222no—
159C61#1280411yescharacteristic, complemented, Sylow
160C22×Q8—611no—
161C22×Q8C22×D6111yescharacteristic
162C2×M16—22no—
163C2×M16—1222no—
164C4⋊Q8—612no—
165C4⋊Q8—612no—
166C4⋊Q8—1222no—
167C4×Q8—2442no—
168C4×Q8—2442no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1222no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4C4×D6111yescharacteristic
174C2×C42—611no—
175C2×C42—611no—
176C2×C42—612no—
177C2×C42—1221no—
178C2×C42C4×D6111yescharacteristic
179C4⋊C8—2444no—
180#101—22no—
181#101—22no—
182#101—1222no—
183#101—1222no—
184#95—22no—
185#95—1221no—
186#95—1221no—
187#95—1222no—
188#95—1222no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—612no—
192C2×Q8—1221no—
193C2×Q8—2441no—
194C2×Q8—2441no—
195C2×Q8#1175822212yes—
196C2×Q8D4×D6111yescharacteristic
197C2×Q8Q8×D6111yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—611no—
201C22×C4—612no—
202C22×C4—611no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4C2×C4×D6111yescharacteristic
206C22×C4D4×D6112yes—
207M16—42no—
208M16—42no—
209M16—2442no—
210M16—2442no—
211C2×C8—42no—
212C2×C8—2442no—
213C4⋊C4—41no—
214C4⋊C4—1224no—
215C4⋊C4—1224no—
216C4⋊C4—2441no—
217C4⋊C4—2442no—
218C4⋊C4—2442no—
219C42—41no—
220C42—612no—
221C42—1224no—
222C42—1222no—
223C42—1221no—
224C42—2442no—
225C23C22⋊C4×D6111yescharacteristic
226Q8—42no—
227Q8—41no—
228Q8—41no—
229Q8—2442no—
230Q8—2442no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—612no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2442no—
251C2×C4—2441no—
252C2×C4C4⋊C4×D6111yescharacteristic
253C2×C4#1451973411yescharacteristic
254C2×C4#1451975012yes—
255C2×C4#1451975512yes—
256C8—82no—
257C8—4882no—
258C22—21no—
259C22—21no—
260C22#1683962111yescharacteristic
261C22#99×D6111yescharacteristic
262C22#1683973411yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—81no—
268C4—81no—
269C4—1222no—
270C4—2442no—
271C4—2441no—
272C4—2442no—
273C4—2442no—
274C2—21no—
275C2—21no—
276C2#2144580611yescharacteristic
277C2#2144750511yescharacteristic
278C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#12804
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
159. C61#12804semidirect

Maximal subgroups

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

subgroupindex
#214485372
C2×#168395602
#214458132
#214439462
C61×#13942
#1280461