Finite Group Databasebeta

← #29577384

Subgroups — #29577384

Order 15616.

506 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 139 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#21454900C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21444491C212yesmaximal
4#21443722C212yesmaximal
5C61×#2546C211yesmaximal, characteristic
6Q8×#92418—24no—
7#16839815—22no—
8#16839815C2212yes—
9#16839786C2212yes—
10C2×#14519696—21no—
11#16839531—21no—
12#16839508—24no—
13C2×C4⋊Q8×C61—21no—
14C2×C4⋊Q8×C61C2211yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#398C414yes—
17C61×#391—21no—
18C61×#389—22no—
19C4×C4⋊C4×C61C2211yescharacteristic
20C2×#11758194—22no—
21C4⋊#92418—24no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418D414yes—
25#14519696—42no—
26C22⋊#92418—22no—
27C4×#92418—24no—
28C4×#92418—22no—
29C22×Q8×C61—21no—
30C22×Q8×C61D411yescharacteristic
31C4⋊Q8×C61—22no—
32C4⋊Q8×C61—22no—
33C4⋊Q8×C61—42no—
34C4⋊Q8×C61—42no—
35C4×Q8×C61—22no—
36C4×Q8×C61—22no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—24no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61C2×C412yes—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C42×C61—21no—
44C2×C42×C61D412yes—
45C2×C42×C61C2311yescharacteristic
46#95×C61—24no—
47#95×C61C2×C412yes—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—42no—
51C2×Q8×C61—41no—
52C2×Q8×C61—41no—
53C2×Q8×C61—42no—
54C2×Q8×C61D812yes—
55C2×Q8×C61SD1612yes—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61C22×C411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C4⋊C4×C61—24no—
64C4⋊C4×C61—24no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61—24no—
67C4⋊C4×C61—48no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61—22no—
71C42×C61—22no—
72C42×C61—41no—
73C42×C61—41no—
74C42×C61C2×D412yes—
75C42×C61#4112yes—
76#11758194—42no—
77#11758194—42no—
78C2×#92418—24no—
79C2×#92418—42no—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—24no—
82Q8×C61—24no—
83Q8×C61—82no—
84Q8×C61—82no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—24no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61#10214yes—
98C2×C4×C61C4×D412yes—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61#12311yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61C2×SD1611yescharacteristic
104C2×C4×C61#13512yes—
105#92418—44no—
106#92418—82no—
107#9394—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#38611yescharacteristic
111C22×C61C2×#10211yescharacteristic
112C22×C61#41611yescharacteristic
113C4×C61—21no—
114C4×C61—24no—
115C4×C61—22no—
116C4×C61—44no—
117C4×C61—42no—
118C4×C61—82no—
119C4×C61#45612yes—
120C4×C61#46512yes—
121C4×C61#46612yes—
122#2982—611no—
123#2546D6111yescharacteristic
124#1801—611no—
125#1546—612no—
126#1303—612no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#188611yescharacteristic
130C2×C61#189311yescharacteristic
131C2×C61#191511yescharacteristic
132C2×C4⋊Q8—21no—
133C2×C4⋊Q8C2×D6111yescharacteristic
134C2×C4×Q8C2×D6111yescharacteristic
135C8×Q8—1224no—
136#431—612no—
137#431—1222no—
138#423—612no—
139C2×#101—1221no—
140#398Dic6114yes—
141#391—21no—
142#389—22no—
143C4×C4⋊C4C2×D6111yescharacteristic
144#343—1221no—
145#332—1224no—
146C61#939411yescharacteristic, complemented, Sylow
147C22×Q8—21no—
148C22×Q8C22⋊D6111yescharacteristic
149C2×M16—1222no—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4⋊Q8—42no—
153C4⋊Q8—42no—
154C4×Q8—22no—
155C4×Q8—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×Dic6112yes—
160C2×C4⋊C4C2×Dic6112yes—
161C2×C4⋊C4C22⋊D6111yescharacteristic
162C2×C42—21no—
163C2×C42C22⋊D6112yes—
164C2×C42C22×D6111yescharacteristic
165C4⋊C8—614no—
166C4⋊C8—1224no—
167C4⋊C8—1222no—
168C4⋊C8—1222no—
169#101—2442no—
170C22⋊C8—1222no—
171C4×C8—1224no—
172C4×C8—1222no—
173#95—24no—
174#95C2×Dic6112yes—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8#1175819912yes—
182C2×Q8#1175820012yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C22⋊Dic6112yes—
186C22×C4C22⋊Dic6112yes—
187C22×C4C22×Dic6111yescharacteristic
188C22×C4C2×C22⋊D6111yescharacteristic
189C22×C4C2×C22⋊D6111yescharacteristic
190M16—2442no—
191M16—2442no—
192C2×C8—1224no—
193C2×C8—2442no—
194C4⋊C4—24no—
195C4⋊C4—24no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—48no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C42—22no—
202C42—22no—
203C42—41no—
204C42—41no—
205C42D4×D6112yes—
206C42#1175822412yes—
207C23C2×C22⋊Dic6111yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#1451969814yes—
225C2×C4D4×Dic6112yes—
226C2×C4#1451974511yescharacteristic
227C2×C4#1451974912yes—
228C2×C4#1451975811yescharacteristic
229C2×C4C2×#1175819911yescharacteristic
230C2×C4C2×#1175820011yescharacteristic
231C2×C4#1451979712yes—
232C8—4882no—
233C8—2444no—
234C22—21no—
235C22—21no—
236C22#1683964211yescharacteristic
237C22C2×#1451969811yescharacteristic
238C22#1683975811yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4#1683994412yes—
246C4#1683998912yes—
247C4#1683999612yes—
248C2—21no—
249C2—21no—
250C2#2144621311yescharacteristic
251C2#2144624811yescharacteristic
252C2#2144637211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2546C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2546D61
hypocenterC61#9394
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
146. C61#9394semidirect

Maximal subgroups

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

subgroupindex
#214549002
#214458152
#214444912
#214437222
C61×#25462
#939461