Finite Group Databasebeta

← #29573576

Subgroups — #29573576

Order 15616.

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

normal subgroups only

This group has 498 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#21448729C211yesmaximal, characteristic
2#21444140C211yesmaximal, characteristic
3#21443720C212yesmaximal, complemented
4#21443679C212yesmaximal, complemented
5C61×#1800C211yesmaximal, characteristic
6C2×D4×Dic61—21no—
7#16839815C2212yes—
8#16839661—21no—
9#16839637—22no—
10#16839628C2211yescharacteristic
11#16839622C412yes—
12C4×C4⋊Dic61C2211yescharacteristic
13C2×#14519684C412yes—
14#16839486—22no—
15C2×C4×D4×C61C2211yescharacteristic
16C61×#423C2212yes—
17C2×#100×C61—21no—
18C61×#343—21no—
19C23×Dic61—22no—
20D4×Dic61—42no—
21D4×Dic61—42no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26C2×C4×Dic61—21no—
27C4⋊#92418—22no—
28C22⋊#92418—22no—
29C4×#92418—22no—
30#14519684—22no—
31#14519684—21no—
32#14519684C2×C411yescharacteristic
33#14519684C2×C412yes—
34#14519684C2×C411yescharacteristic
35C22×D4×C61D411yescharacteristic
36C23×C4×C61C2×C412yes—
37C2×M16×C61—22no—
38C4×D4×C61—22no—
39C4×D4×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61D412yes—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—22no—
44C4⋊C8×C61—22no—
45#100×C61—42no—
46C24×C61C22⋊C412yes—
47C2×D4×C61—22no—
48C2×D4×C61—22no—
49C2×D4×C61D812yes—
50C2×D4×C61SD1612yes—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—82no—
54C22×C4×C61C22⋊C412yes—
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—22no—
60C22×Dic61—21no—
61C22×Dic61—44no—
62C22×Dic61—44no—
63C22×Dic61—82no—
64M16×C61—42no—
65M16×C61—42no—
66C2×C8×C61—42no—
67C4⋊C4×C61—22no—
68C22⋊C4×C61—24no—
69C42×C61#4112yes—
70C42×C61#4112yes—
71C22⋊Dic61—44no—
72C4⋊Dic61—42no—
73C4⋊Dic61—41no—
74C4⋊Dic61—41no—
75C4⋊Dic61—82no—
76C4×Dic61—41no—
77C4×Dic61—41no—
78C2×#92418—42no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61#10214yes—
84C23×C61C2×C22⋊C411yescharacteristic
85D4×C61—24no—
86D4×C61—24no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—82no—
92C2×C4×C61—82no—
93C2×C4×C61#11711yescharacteristic
94C2×C4×C61#11711yescharacteristic
95C2×C4×C61#12312yes—
96C2×C4×C61#12312yes—
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61C2×SD1611yescharacteristic
99C2×C4×C61#13712yes—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—88no—
110C8×C61—82no—
111#92418—82no—
112#8764—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—24no—
116C22×C61—44no—
117C22×C61—44no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61#38111yescharacteristic
121C22×C61C2×#10211yescharacteristic
122C22×C61#41911yescharacteristic
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61#48012yes—
128C4×C61#48312yes—
129Dic61—42no—
130Dic61—81no—
131Dic61—82no—
132#2349—611no—
133#1800D6111yescharacteristic
134#1460—611no—
135#1303—612no—
136#1286—612no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—44no—
140C2×C61#182311yescharacteristic
141C2×C61#182711yescharacteristic
142C2×C61#182911yescharacteristic
143C2×C4×D4—1221no—
144C2×C4×D4C2×D6111yescharacteristic
145#431—612no—
146#423C2×D6112yes—
147C2×#100—21no—
148#389—1221no—
149#385—1222no—
150#382—611no—
151#380—612no—
152C4×C4⋊C4—611no—
153C2×#95—612no—
154#343—21no—
155#323—1222no—
156C61#876411yescharacteristic, complemented, Sylow
157C22×D4C22⋊D6111yescharacteristic
158C23×C4—1222no—
159C23×C4C4×D6112yes—
160C2×M16—22no—
161C4×D4—22no—
162C4×D4—22no—
163C4×D4—2442no—
164C4×D4—2442no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4C22⋊D6111yescharacteristic
169C2×C22⋊C4—1222no—
170C2×C22⋊C4D24412yes—
171C2×C42—1221no—
172C2×C42C22×D6111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—1222no—
176#100—42no—
177C22⋊C8—1222no—
178C4×C8—1222no—
179#95—611no—
180#95—612no—
181#95—611no—
182#95—1222no—
183#95—1221no—
184C24#1175819812yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4#1175819912yes—
188C2×D4#1175820112yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—82no—
192C22×C4—1221no—
193C22×C4—1222no—
194C22×C4—1221no—
195C22×C4—4882no—
196C22×C4—2444no—
197C22×C4—2444no—
198C22×C4#1175819812yes—
199C22×C4C2×C4×D6111yescharacteristic
200C22×C4C2×D24411yescharacteristic
201C22×C4C2×C22⋊D6111yescharacteristic
202M16—42no—
203M16—42no—
204C2×C8—42no—
205C2×C8—2442no—
206C4⋊C4—22no—
207C4⋊C4—4882no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—24no—
212C22⋊C4—2444no—
213C42—2441no—
214C42—2441no—
215C42#1175822412yes—
216C42#1175822412yes—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#1451969714yes—
222C23C2×#1175819811yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—1222no—
232C2×C4—4888no—
233C2×C4—2441no—
234C2×C4—2442no—
235C2×C4—2441no—
236C2×C4—2442no—
237C2×C4—2441no—
238C2×C4—2442no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4#1451973311yescharacteristic
242C2×C4#1451973311yescharacteristic
243C2×C4#1451975812yes—
244C2×C4#1451976112yes—
245C2×C4C2×#1175819911yescharacteristic
246C2×C4C2×#1175820111yescharacteristic
247C2×C4#1451980712yes—
248C8—82no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22#1683962311yescharacteristic
258C22C2×#1451969711yescharacteristic
259C22#1683977011yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—4882no—
265C4—4881no—
266C4—2442no—
267C4#1684007312yes—
268C4#1684009012yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#2144590311yescharacteristic
273C2#2144592411yescharacteristic
274C2#2144592811yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1800C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#1800D61
hypocenterC61#8764
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #21443720C2semidirect
4. #21443679C2semidirect
156. C61#8764semidirect

Maximal subgroups

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

subgroupindex
#214487292
#214441402
#214437202
#214436792
C61×#18002
#876461