Finite Group Databasebeta

← #29577419

Subgroups — #29577419

Order 15616.

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

normal subgroups only

This group has 534 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#21444491C212yesmaximal, complemented
4#21443722C212yesmaximal, complemented
5C61×#2547C211yesmaximal, characteristic
6#16839840—24no—
7#16839815C2212yes—
8#16839786C2212yes—
9C2×#14519694—21no—
10#16839726—22no—
11#16839531—21no—
12#16839508—24no—
13C2×C4⋊Q8×C61C2211yescharacteristic
14C2×#124×C61—21no—
15C2×C4×D4×C61C2211yescharacteristic
16C61×#397C414yes—
17C61×#391—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×C61—21no—
30C22×D4×C61D411yescharacteristic
31C23×C4×C61D412yes—
32C4⋊Q8×C61—22no—
33C4⋊Q8×C61—22no—
34#124×C61—44no—
35C4×D4×C61—22no—
36C4×D4×C61—22no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61—24no—
42C2×C22⋊C4×C61C2×C412yes—
43C2×C42×C61—21no—
44C2×C42×C61C2311yescharacteristic
45#95×C61—24no—
46#95×C61C2×C412yes—
47C24×C61C22⋊C412yes—
48C2×Q8×C61—42no—
49C2×Q8×C61—42no—
50C2×Q8×C61—41no—
51C2×Q8×C61—41no—
52C2×D4×C61—22no—
53C2×D4×C61—22no—
54C2×D4×C61—21no—
55C2×D4×C61—21no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—44no—
61C22×C4×C61C22⋊C412yes—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C4⋊C4×C61—22no—
66C4⋊C4×C61—24no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C22⋊C4×C61—24no—
71C22⋊C4×C61—48no—
72C42×C61—42no—
73C42×C61C2×D412yes—
74C42×C61#4112yes—
75#11758194—42no—
76#11758194—42no—
77#11758194—84no—
78C2×#92418—24no—
79C2×#92418—42no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—82no—
87Q8×C61—82no—
88D4×C61—42no—
89D4×C61—42no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61—44no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—82no—
102C2×C4×C61C4×D412yes—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61#12112yes—
105C2×C4×C61#12311yescharacteristic
106C2×C4×C61AGL(1,ℤ/8)12yes—
107C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C61#13711yescharacteristic
109#92418—44no—
110#92418—82no—
111#9401—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—44no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—82no—
119C22×C61#38611yescharacteristic
120C22×C61#41711yescharacteristic
121C22×C61#41811yescharacteristic
122C4×C61—21no—
123C4×C61—22no—
124C4×C61—42no—
125C4×C61—82no—
126C4×C61—82no—
127C4×C61#45512yes—
128C4×C61#46812yes—
129C4×C61#46912yes—
130#2975—611no—
131#2547D6111yescharacteristic
132#1800—611no—
133#1546—612no—
134#1303—612no—
135C2×C61—21no—
136C2×C61—21no—
137C2×C61—82no—
138C2×C61#188511yescharacteristic
139C2×C61#189511yescharacteristic
140C2×C61#191511yescharacteristic
141C2×C4⋊Q8C2×D6111yescharacteristic
142C2×#124—21no—
143C2×C4×D4C2×D6111yescharacteristic
144#436—1224no—
145#431—612no—
146#423—612no—
147C2×#100—1221no—
148#407—1222no—
149#397Dic6114yes—
150#391—21no—
151#380—22no—
152C4×C4⋊C4C2×D6111yescharacteristic
153#343—1221no—
154#332—1224no—
155C61#940111yescharacteristic, complemented, Sylow
156C22×Q8—21no—
157C22×D4C22⋊D6111yescharacteristic
158C23×C4C22⋊D6112yes—
159C2×M16—1224no—
160C2×M16—1222no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163#124—44no—
164C4×D4—22no—
165C4×D4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×Dic6112yes—
169C2×C4⋊C4C22⋊D6111yescharacteristic
170C2×C22⋊C4—24no—
171C2×C22⋊C4C2×Dic6112yes—
172C2×C42—21no—
173C2×C42C22×D6111yescharacteristic
174C4⋊C8—614no—
175C4⋊C8—1222no—
176C4⋊C8—1222no—
177#100—2442no—
178C22⋊C8—1224no—
179C22⋊C8—1222no—
180C4×C8—1222no—
181#95—24no—
182#95C2×Dic6112yes—
183C24C22⋊Dic6112yes—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—41no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—44no—
197C22×C4C22⋊Dic6112yes—
198C22×C4C22×Dic6111yescharacteristic
199C22×C4C2×C22⋊D6111yescharacteristic
200C22×C4C2×C22⋊D6111yescharacteristic
201M16—4884no—
202M16—2442no—
203M16—2442no—
204C2×C8—1224no—
205C2×C8—2442no—
206C4⋊C4—22no—
207C4⋊C4—24no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C22⋊C4—24no—
212C22⋊C4—48no—
213C42—42no—
214C42D4×D6112yes—
215C42#1175822412yes—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C2×C22⋊Dic6111yescharacteristic
222Q8—82no—
223Q8—82no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4D4×Dic6112yes—
239C2×C4#1451974511yescharacteristic
240C2×C4#1451974912yes—
241C2×C4#1451975811yescharacteristic
242C2×C4#1451980211yescharacteristic
243C2×C4#1451980312yes—
244C2×C4#1451980711yescharacteristic
245C8—4882no—
246C8—2444no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—82no—
254C22#1683964211yescharacteristic
255C22#1683976311yescharacteristic
256C22#1683976711yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—82no—
261C4—82no—
262C4#1683993912yes—
263C4#1684000612yes—
264C4#1684001312yes—
265C2—21no—
266C2—21no—
267C2—82no—
268C2#2144620811yescharacteristic
269C2#2144625811yescharacteristic
270C2#2144637211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2547C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2547D61
hypocenterC61#9401
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2547

Complements

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

NH ≅ G/Ntype
3. #21444491C2semidirect
4. #21443722C2semidirect
155. C61#9401semidirect

Maximal subgroups

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

subgroupindex
#214548602
#214458112
#214444912
#214437222
C61×#25472
#940161