Finite Group Databasebeta

← #29577441

Subgroups — #29577441

Order 15616.

554 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 115 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#21454904C211yesmaximal, characteristic, complemented
2#21450818C211yesmaximal, characteristic
3#21444488C212yesmaximal
4#21443720C212yesmaximal, complemented
5C61×#1801C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7C2×#14519766—21no—
8#16839893—24no—
9#16839819—22no—
10#16839815C2212yes—
11#16839679C414yes—
12#16839664—22no—
13#16839663—21no—
14C4×C4⋊Dic61C2211yescharacteristic
15#16839505—24no—
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#423C2212yes—
18C2×#101×C61—21no—
19C61×#343—21no—
20C22×D244—21no—
21C22×D244—21no—
22C22×D244C2×C412yes—
23#14519774—22no—
24#14519774—22no—
25#14519766—44no—
26C2×C4⋊Dic61—21no—
27C2×#11758198—24no—
28C2×#11758198—24no—
29C2×C4×Dic61—21no—
30C4⋊#92418—24no—
31C4⋊#92418D414yes—
32C22⋊#92418—22no—
33#14519688—24no—
34C4×#92418—22no—
35#14519684C2×C412yes—
36C22×Q8×C61D411yescharacteristic
37C2×M16×C61—22no—
38C4×Q8×C61—22no—
39C4×Q8×C61—22no—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C42×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44C4⋊C8×C61—22no—
45C4⋊C8×C61—22no—
46#101×C61—42no—
47C23×D61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—21no—
50C2×Q8×C61—22no—
51C2×Q8×C61—21no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22⋊C412yes—
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×Dic61—22no—
58C2×D244—24no—
59C2×D244—44no—
60C2×D244—41no—
61C2×D244—42no—
62C2×D244—41no—
63C2×D244—41no—
64C2×D244—42no—
65C2×D244—41no—
66C2×D244—82no—
67M16×C61—42no—
68M16×C61—42no—
69C2×C8×C61—42no—
70C4⋊C4×C61—24no—
71C4⋊C4×C61—22no—
72C42×C61—22no—
73C42×C61—22no—
74C42×C61C2×D412yes—
75C42×C61#4112yes—
76#11758198—48no—
77#11758198—84no—
78C4⋊Dic61—42no—
79C4×Dic61—42no—
80C2×#92418—24no—
81C23×C61C2×C22⋊C411yescharacteristic
82C22×D61—44no—
83C22×D61—44no—
84C22×D61—42no—
85C22×D61—42no—
86C22×D61—42no—
87Q8×C61—42no—
88Q8×C61—42no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61C4×D412yes—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61#12112yes—
99C2×C4×C61#12311yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)12yes—
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C61#13711yescharacteristic
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106D244—84no—
107D244—82no—
108D244—82no—
109D244—82no—
110D244—82no—
111C8×C61—82no—
112#92418—44no—
113#9406—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61#38611yescharacteristic
117C22×C61#41711yescharacteristic
118C22×C61#41811yescharacteristic
119C2×D61—84no—
120C2×D61—84no—
121C2×D61—82no—
122C2×D61—82no—
123C2×D61—82no—
124C4×C61—21no—
125C4×C61—22no—
126C4×C61—42no—
127C4×C61—42no—
128C4×C61#45412yes—
129C4×C61#46812yes—
130C4×C61#46912yes—
131Dic61—82no—
132#2983—611no—
133#2548—611no—
134#1801D6111yescharacteristic, complemented
135#1545—612no—
136#1303—612no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#188811yescharacteristic
140C2×C61#189511yescharacteristic
141C2×C61#191411yescharacteristic
142D61—162no—
143C2×#127—611no—
144C2×#124—1221no—
145C2×C4×Q8C2×D6111yescharacteristic
146#446—1224no—
147#432—1222no—
148#431—612no—
149#423C2×D6112yes—
150C2×#101—21no—
151#394—614no—
152#390—1221no—
153#390—1222no—
154C4×C4⋊C4—611no—
155#343—21no—
156#331—1224no—
157C61#940611yescharacteristic, complemented, Sylow
158C22×Q8C22⋊D6111yescharacteristic
159C22×D4—612no—
160C22×D4—1221no—
161C22×D4—1221no—
162C2×M16—22no—
163#127—1222no—
164#127—1222no—
165#124—2444no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4C4×D6112yes—
170C2×C4⋊C4C22⋊D6111yescharacteristic
171C2×C22⋊C4—1224no—
172C2×C22⋊C4—1224no—
173C2×C42—1221no—
174C2×C42D24412yes—
175C2×C42C22×D6111yescharacteristic
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—614no—
179C4⋊C8—1224no—
180#101—42no—
181C22⋊C8—1222no—
182#97—1224no—
183C4×C8—1222no—
184#95—612no—
185C24—1222no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×D4—1224no—
191C2×D4—4882no—
192C2×D4—2444no—
193C2×D4—2441no—
194C2×D4—2441no—
195C2×D4—2442no—
196C2×D4—2441no—
197C2×D4—2442no—
198C2×D4—2441no—
199C22×C4—1222no—
200C22×C4#1175819812yes—
201C22×C4#1175819812yes—
202C22×C4C2×C4×D6111yescharacteristic
203C22×C4C2×D24411yescharacteristic
204C22×C4C2×C22⋊D6111yescharacteristic
205M16—42no—
206M16—42no—
207C2×C8—42no—
208C2×C8—1224no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—2442no—
212C22⋊C4—4884no—
213C22⋊C4—2448no—
214C42—22no—
215C42—22no—
216C42—2442no—
217C42D4×D6112yes—
218C42#1175822412yes—
219C23—2444no—
220C23—2444no—
221C23—2442no—
222C23—2442no—
223C23—2442no—
224C23C2×#1175819811yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—4884no—
228D4—4882no—
229D4—4882no—
230D4—4882no—
231D4—4882no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4#1451973712yes—
243C2×C4#1451974711yescharacteristic
244C2×C4#1451974912yes—
245C2×C4#1451976111yescharacteristic
246C2×C4#1451980212yes—
247C2×C4#1451980311yescharacteristic
248C2×C4#1451980811yescharacteristic
249C8—82no—
250C8—2444no—
251C22—21no—
252C22—21no—
253C22—4884no—
254C22—4884no—
255C22—4882no—
256C22—4882no—
257C22—4882no—
258C22#1683963911yescharacteristic
259C22#1683976111yescharacteristic
260C22#1683976611yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—4882no—
266C4#1683993712yes—
267C4#1684001012yes—
268C4#1684001312yes—
269C2—21no—
270C2—21no—
271C2—9762no—
272C2#2144622011yescharacteristic
273C2#2144625511yescharacteristic
274C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1801C2
socleC22×C61#386
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1801D61
hypocenterC61#9406
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #21454904C2semidirect
4. #21443720C2semidirect
5. C61×#1801C2semidirect
134. #1801D61semidirect
157. C61#9406semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214508182
#214444882
#214437202
C61×#18012
#940661