Finite Group Databasebeta

← #29579177

Subgroups — #29579177

Order 15616.

422 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 119 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#21456405C211yesmaximal, characteristic
2#21446762C212yesmaximal
3#21444317C212yesmaximal
4#21444108C211yesmaximal, characteristic
5C4×#106×C61C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840167C411yescharacteristic, complemented
8#16840142C411yescharacteristic, complemented
9#16840113C412yescomplemented
10#16840003—21no—
11#16840003—21no—
12C4×Dic244—21no—
13C4×Dic244—21no—
14#16839815C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16#16839522—24no—
17#16839498—24no—
18#16839484—21no—
19#16839483—21no—
20C2×#106×C61—21no—
21C2×C4×C8×C61C2211yescharacteristic
22C4×C4⋊C4×C61C2212yes—
23C61×#340—21no—
24C2×Dic244—21no—
25C2×Dic244—21no—
26C2×#11758194D412yes—
27#14519777C2×C412yes—
28#14519777C2×C412yes—
29#14519769—22no—
30#14519756—22no—
31#14519756—22no—
32C4×Dic122—22no—
33C4×Dic122—22no—
34#14519736—22no—
35#14519711—21no—
36#14519711—21no—
37C4⋊#92418—21no—
38#14519702—22no—
39#14519702—22no—
40C22⋊#92418D412yes—
41#14519688—21no—
42C4×#92418—21no—
43C4×#92418—21no—
44C22×C8×C61D411yescharacteristic
45C22×C8×C61D411yescharacteristic
46C2×C4⋊C4×C61—22no—
47C2×C42×C61—22no—
48C2×C42×C61C2311yescharacteristic
49#106×C61—24no—
50C4×C8×C61C2×C411yescharacteristic
51C4×C8×C61C2×C411yescharacteristic
52C4×C8×C61D411yescharacteristic
53C4×C8×C61D411yescharacteristic
54#95×C61—22no—
55C22×C4×C61—42no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C2×Dic122—22no—
60C2×Dic122—22no—
61C2×C8×C61—22no—
62C2×C8×C61—41no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C4⋊C4×C61—24no—
68C4⋊C4×C61—42no—
69C42×C61—44no—
70C42×C61C22×C411yescharacteristic
71C42×C61C2×D411yescharacteristic
72C42×C61#4111yescharacteristic
73C42×C61#4111yescharacteristic
74C22⋊Dic61—42no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—42no—
82#11758194—24no—
83C2×#92418—22no—
84C2×#92418—22no—
85Dic244—42no—
86Dic244—42no—
87C23×C61#12711yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—44no—
92C2×C4×C61—82no—
93C2×C4×C61—82no—
94C2×C4×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61C4×D411yescharacteristic
96C2×C4×C61C4×D411yescharacteristic
97C2×C4×C61#12111yescharacteristic
98C2×C4×C61#12111yescharacteristic
99C2×C4×C61#12411yescharacteristic
100C2×C4×C61#13714yes—
101C2×Dic61—42no—
102C2×Dic61—42no—
103Dic122—42no—
104Dic122—42no—
105Dic122—82no—
106C8×C61—21no—
107C8×C61—21no—
108C8×C61—21no—
109C8×C61#10412yes—
110#92418—42no—
111#92418—42no—
112#9720—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61#39011yescharacteristic
116C22×C61#49712yes—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—84no—
121C4×C61C2×#10411yescharacteristic
122C4×C61#42111yescharacteristic
123C4×C61#44112yes—
124C4×C61#47012yes—
125Dic61—82no—
126Dic61—82no—
127#3170—611no—
128#1986—612no—
129C4×#106D6111yescharacteristic
130#1503—612no—
131#1451—611no—
132C2×C61—22no—
133C2×C61#197111yescharacteristic
134C2×C61#197611yescharacteristic
135C2×C61#198011yescharacteristic
136#533—612no—
137#500—611no—
138#494—611no—
139#487—612no—
140#467—1221no—
141#467—1221no—
142C4×Q16—1221no—
143C4×Q16—1221no—
144#431—611no—
145C2×#106—21no—
146C4×M16—611no—
147C2×C4×C8C2×D6111yescharacteristic
148C4×C4⋊C4C2×D6112yes—
149#340—21no—
150#339—1224no—
151#328—1224no—
152#322—1221no—
153#322—1221no—
154C61#972011yescharacteristic, complemented, Sylow
155C2×Q16—1221no—
156C2×Q16—1221no—
157C2×M16—612no—
158C22×C8C22⋊D6111yescharacteristic
159C22×C8C22⋊D6111yescharacteristic
160C4⋊Q8—612no—
161C4⋊Q8—612no—
162#125—1222no—
163C22⋊Q8—1222no—
164C22⋊Q8—1222no—
165C4×Q8—1222no—
166C4×Q8—1222no—
167#117—1222no—
168C2×C4⋊C4—22no—
169C2×C42—22no—
170C2×C42C22×D6111yescharacteristic
171#107—1221no—
172#107—1221no—
173#106—24no—
174C4⋊C8—1221no—
175#103—1222no—
176#103—1222no—
177C22⋊C8—612no—
178#97—1221no—
179C4×C8—1221no—
180C4×C8—1221no—
181C4×C8C4×D6111yescharacteristic
182C4×C8C4×D6111yescharacteristic
183C4×C8D24411yescharacteristic
184C4×C8D24411yescharacteristic
185#95—22no—
186C2×Q8—1222no—
187C2×Q8—1222no—
188C22×C4—42no—
189C22×C4D4×D6111yescharacteristic
190C22×C4D4×D6111yescharacteristic
191C22×C4C2×C22⋊D6111yescharacteristic
192Q16—2442no—
193Q16—2442no—
194M16—1224no—
195C2×C8—22no—
196C2×C8—41no—
197C2×C8—1222no—
198C2×C8—1222no—
199C2×C8#1175819811yescharacteristic
200C2×C8#1175819811yescharacteristic
201C2×C8#1175819811yescharacteristic
202C2×C8#1175819811yescharacteristic
203C4⋊C4—24no—
204C4⋊C4—42no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C4⋊C4—1222no—
208C4⋊C4—1222no—
209C4⋊C4—2442no—
210C4⋊C4—2442no—
211C22⋊C4—2442no—
212C42—44no—
213C42—2442no—
214C42C2×C4×D6111yescharacteristic
215C42C2×D24411yescharacteristic
216C42#1175822611yescharacteristic
217C42#1175822611yescharacteristic
218C23#1451977311yescharacteristic
219Q8—4882no—
220Q8—2442no—
221Q8—2442no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—44no—
226C2×C4—82no—
227C2×C4—82no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4C2×#1175819811yescharacteristic
231C2×C4#1451973911yescharacteristic
232C2×C4#1451973911yescharacteristic
233C2×C4#1451975211yescharacteristic
234C2×C4#1451975211yescharacteristic
235C2×C4#1451976611yescharacteristic
236C2×C4#1451980614yes—
237C8—21no—
238C8—21no—
239C8—21no—
240C8—2442no—
241C8—2442no—
242C8#1451970512yes—
243C22—21no—
244C22—21no—
245C22#1683966311yescharacteristic
246C22#1684015312yes—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—84no—
251C4—4882no—
252C4—4882no—
253C4C2×#1451970511yescharacteristic
254C4#1683978011yescharacteristic
255C4#1683986812yes—
256C4#1684002112yes—
257C2—22no—
258C2#2144668811yescharacteristic
259C2#2144671511yescharacteristic
260C2#2144673711yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#106×C61C2
socleC22×C61#390
prime radicalC23×C61#127
cosocleC2×C42×C61C23
hypercenterC4×#106D61
hypocenterC61#9720
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
7. #16840167C4semidirect
8. #16840142C4semidirect
9. #16840113C4semidirect
154. C61#9720semidirect

Maximal subgroups

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

subgroupindex
#214564052
#214467622
#214443172
#214441082
C4×#106×C612
#972061