Finite Group Databasebeta

← #29577409

Subgroups — #29577409

Order 15616.

514 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 123 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#21454860C211yesmaximal, characteristic
2#21445811C211yesmaximal, characteristic
3#21444500C212yesmaximal, complemented
4#21443722C212yesmaximal, complemented
5C61×#2563C211yesmaximal, characteristic
6#16839840—24no—
7#16839815C2212yes—
8#16839786C2212yes—
9C2×#14519694—21no—
10#16839726—22no—
11#16839531—21no—
12#16839511—24no—
13C2×C4⋊Q8×C61C2211yescharacteristic
14C2×C4×D4×C61C2211yescharacteristic
15C61×#393C414yes—
16C61×#390—21no—
17C61×#382—21no—
18C61×#380—22no—
19C4×C4⋊C4×C61C2211yescharacteristic
20C2×#11758194—24no—
21C2×#11758194—22no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418D414yes—
25#14519694—42no—
26C22⋊#92418—24no—
27C22⋊#92418—22no—
28C4×#92418—22no—
29C22×Q8×C61C2×C412yes—
30C22×D4×C61D411yescharacteristic
31C23×C4×C61D412yes—
32C4⋊Q8×C61—22no—
33C4⋊Q8×C61—22no—
34C4×D4×C61—22no—
35C4×D4×C61—22no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C22⋊C4×C61—24no—
41C2×C22⋊C4×C61C2×C412yes—
42C2×C42×C61—21no—
43C2×C42×C61C2311yescharacteristic
44#95×C61—24no—
45#95×C61C2×C412yes—
46C24×C61C22⋊C412yes—
47C2×Q8×C61—24no—
48C2×Q8×C61—82no—
49C2×D4×C61—22no—
50C2×D4×C61—21no—
51C2×D4×C61—22no—
52C2×D4×C61—21no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—44no—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C4⋊C4×C61—22no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—41no—
67C22⋊C4×C61—24no—
68C22⋊C4×C61—84no—
69C42×C61—41no—
70C42×C61—41no—
71C42×C61C2×D412yes—
72C42×C61#4112yes—
73#11758194—42no—
74#11758194—42no—
75#11758194—84no—
76C2×#92418—24no—
77C2×#92418—42no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84Q8×C61—84no—
85D4×C61—42no—
86D4×C61—42no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—44no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—44no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—82no—
98C2×C4×C61C4×D412yes—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61#12311yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C61#13712yes—
104C2×C4×C61#13711yescharacteristic
105#92418—44no—
106#92418—82no—
107#9399—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—44no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—82no—
115C22×C61#38611yescharacteristic
116C22×C61#41711yescharacteristic
117C22×C61#41911yescharacteristic
118C4×C61—21no—
119C4×C61—22no—
120C4×C61—42no—
121C4×C61—82no—
122C4×C61—82no—
123C4×C61#45512yes—
124C4×C61#46812yes—
125C4×C61#47012yes—
126#2975—611no—
127#2563D6111yescharacteristic
128#1800—611no—
129#1548—612no—
130#1303—612no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61—82no—
134C2×C61#188511yescharacteristic
135C2×C61#189411yescharacteristic
136C2×C61#191411yescharacteristic
137C2×C4⋊Q8C2×D6111yescharacteristic
138C2×C4×D4C2×D6111yescharacteristic
139#436—1224no—
140#431—612no—
141#423—612no—
142C2×#100—1221no—
143#407—1222no—
144#393Dic6114yes—
145#390—21no—
146#382—21no—
147#380—22no—
148C4×C4⋊C4C2×D6111yescharacteristic
149#343—1221no—
150#333—1224no—
151C61#939911yescharacteristic, complemented, Sylow
152C22×Q8C2×Dic6112yes—
153C22×D4C22⋊D6111yescharacteristic
154C23×C4C22⋊D6112yes—
155C2×M16—1224no—
156C2×M16—1222no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4C22⋊D6111yescharacteristic
165C2×C22⋊C4—24no—
166C2×C22⋊C4C2×Dic6112yes—
167C2×C42—21no—
168C2×C42C22×D6111yescharacteristic
169C4⋊C8—614no—
170C4⋊C8—1222no—
171C4⋊C8—1222no—
172#100—2442no—
173C22⋊C8—1224no—
174C22⋊C8—1222no—
175C4×C8—1222no—
176#95—24no—
177#95C2×Dic6112yes—
178C24C22⋊Dic6112yes—
179C2×Q8—24no—
180C2×Q8—82no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—44no—
190C22×C4C22⋊Dic6112yes—
191C22×C4C22×Dic6111yescharacteristic
192C22×C4C2×C22⋊D6111yescharacteristic
193C22×C4C2×C22⋊D6111yescharacteristic
194M16—4884no—
195M16—2442no—
196M16—2442no—
197C2×C8—1224no—
198C2×C8—2442no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C22⋊C4—24no—
205C22⋊C4—84no—
206C42—41no—
207C42—41no—
208C42D4×D6112yes—
209C42#1175822412yes—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊Dic6111yescharacteristic
216Q8—84no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4D4×Dic6112yes—
231C2×C4#1451974511yescharacteristic
232C2×C4#1451974912yes—
233C2×C4#1451975811yescharacteristic
234C2×C4#1451980211yescharacteristic
235C2×C4#1451980711yescharacteristic
236C2×C4#1451980812yes—
237C8—4882no—
238C8—2444no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#1683964211yescharacteristic
247C22#1683976311yescharacteristic
248C22#1683977111yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—82no—
253C4—82no—
254C4#1683993912yes—
255C4#1684001012yes—
256C4#1684001812yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#2144620811yescharacteristic
261C2#2144625311yescharacteristic
262C2#2144636711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2563C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2563D61
hypocenterC61#9399
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #21444500C2semidirect
4. #21443722C2semidirect
151. C61#9399semidirect

Maximal subgroups

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

subgroupindex
#214548602
#214458112
#214445002
#214437222
C61×#25632
#939961