Finite Group Databasebeta

← #29577444

Subgroups — #29577444

Order 15616.

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

normal subgroups only

This group has 554 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#21454904C211yesmaximal, characteristic, complemented
2#21445815C211yesmaximal, characteristic, complemented
3#21444487C212yesmaximal
4#21443722C212yesmaximal, complemented
5C61×#2548C211yesmaximal, characteristic
6#16839893—24no—
7#16839819—22no—
8#16839815C2212yes—
9#16839786C2212yes—
10C2×#14519696—21no—
11#16839531—21no—
12#16839506—24no—
13C2×#127×C61C2211yescharacteristic
14C2×#124×C61—21no—
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#394C414yes—
17C61×#390—21no—
18C61×#390—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—
27#14519688—24no—
28C4×#92418—22no—
29C22×Q8×C61D411yescharacteristic
30C22×D4×C61—21no—
31C22×D4×C61—21no—
32C22×D4×C61C2×C412yes—
33#127×C61—22no—
34#127×C61—22no—
35#124×C61—44no—
36C4×Q8×C61—22no—
37C4×Q8×C61—22no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61—24no—
42C2×C22⋊C4×C61—24no—
43C2×C42×C61—21no—
44C2×C42×C61D412yes—
45C2×C42×C61C2311yescharacteristic
46#95×C61C2×C412yes—
47C24×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—21no—
51C2×Q8×C61—21no—
52C2×D4×C61—24no—
53C2×D4×C61—44no—
54C2×D4×C61—41no—
55C2×D4×C61—42no—
56C2×D4×C61—41no—
57C2×D4×C61—42no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61—82no—
61C22×C4×C61—22no—
62C22×C4×C61C22⋊C412yes—
63C22×C4×C61C22⋊C412yes—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C4⋊C4×C61—24no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—42no—
70C22⋊C4×C61—48no—
71C22⋊C4×C61—84no—
72C42×C61—22no—
73C42×C61—22no—
74C42×C61—42no—
75C42×C61C2×D412yes—
76C42×C61#4112yes—
77#11758194—42no—
78#11758194—42no—
79C2×#92418—24no—
80C2×#92418—42no—
81C23×C61—44no—
82C23×C61—44no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61—42no—
86C23×C61C2×C22⋊C411yescharacteristic
87Q8×C61—42no—
88Q8×C61—42no—
89D4×C61—84no—
90D4×C61—82no—
91D4×C61—82no—
92D4×C61—82no—
93D4×C61—82no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61C4×D412yes—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61#12112yes—
107C2×C4×C61#12311yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)12yes—
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C61#13711yescharacteristic
111#92418—44no—
112#92418—82no—
113#9406—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—84no—
117C22×C61—84no—
118C22×C61—82no—
119C22×C61—82no—
120C22×C61—82no—
121C22×C61#38611yescharacteristic
122C22×C61#41711yescharacteristic
123C22×C61#41811yescharacteristic
124C4×C61—21no—
125C4×C61—22no—
126C4×C61—42no—
127C4×C61—42no—
128C4×C61—82no—
129C4×C61#45412yes—
130C4×C61#46812yes—
131C4×C61#46912yes—
132#2983—611no—
133#2548D6111yescharacteristic
134#1801—611no—
135#1545—612no—
136#1303—612no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—162no—
140C2×C61#188811yescharacteristic
141C2×C61#189511yescharacteristic
142C2×C61#191411yescharacteristic
143C2×#127C2×D6111yescharacteristic
144C2×#124—21no—
145C2×C4×Q8C2×D6111yescharacteristic
146#446—1224no—
147#432—1222no—
148#431—612no—
149#423—612no—
150C2×#101—1221no—
151#394Dic6114yes—
152#390—21no—
153#390—22no—
154C4×C4⋊C4C2×D6111yescharacteristic
155#343—1221no—
156#331—1224no—
157C61#940611yescharacteristic, complemented, Sylow
158C22×Q8C22⋊D6111yescharacteristic
159C22×D4—21no—
160C22×D4—21no—
161C22×D4C2×Dic6112yes—
162C2×M16—1222no—
163#127—22no—
164#127—22no—
165#124—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×Dic6112yes—
170C2×C4⋊C4C22⋊D6111yescharacteristic
171C2×C22⋊C4—24no—
172C2×C22⋊C4—24no—
173C2×C42—21no—
174C2×C42C22⋊D6112yes—
175C2×C42C22×D6111yescharacteristic
176C4⋊C8—614no—
177C4⋊C8—1224no—
178C4⋊C8—1222no—
179C4⋊C8—1222no—
180#101—2442no—
181C22⋊C8—1222no—
182#97—1224no—
183C4×C8—1222no—
184#95C2×Dic6112yes—
185C24—22no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×D4—24no—
191C2×D4—44no—
192C2×D4—41no—
193C2×D4—42no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—42no—
197C2×D4—41no—
198C2×D4—82no—
199C22×C4—22no—
200C22×C4C22⋊Dic6112yes—
201C22×C4C22⋊Dic6112yes—
202C22×C4C22×Dic6111yescharacteristic
203C22×C4C2×C22⋊D6111yescharacteristic
204C22×C4C2×C22⋊D6111yescharacteristic
205M16—2442no—
206M16—2442no—
207C2×C8—1224no—
208C2×C8—2442no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—42no—
212C22⋊C4—48no—
213C22⋊C4—84no—
214C42—22no—
215C42—22no—
216C42—42no—
217C42D4×D6112yes—
218C42#1175822412yes—
219C23—44no—
220C23—44no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23C2×C22⋊Dic6111yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—84no—
228D4—82no—
229D4—82no—
230D4—82no—
231D4—82no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4D4×Dic6112yes—
243C2×C4#1451974511yescharacteristic
244C2×C4#1451974912yes—
245C2×C4#1451975811yescharacteristic
246C2×C4#1451980211yescharacteristic
247C2×C4#1451980312yes—
248C2×C4#1451980711yescharacteristic
249C8—4882no—
250C8—2444no—
251C22—21no—
252C22—21no—
253C22—84no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22#1683964211yescharacteristic
259C22#1683976311yescharacteristic
260C22#1683976711yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4#1683993412yes—
267C4#1684000612yes—
268C4#1684001312yes—
269C2—21no—
270C2—21no—
271C2—162no—
272C2#2144622311yescharacteristic
273C2#2144625811yescharacteristic
274C2#2144636711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2548C2
socleC22×C61#386
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#2548D61
hypocenterC61#9406
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #21454904C2semidirect
2. #21445815C2semidirect
4. #21443722C2semidirect
157. C61#9406semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214458152
#214444872
#214437222
C61×#25482
#940661