Finite Group Databasebeta

← #29599483

Subgroups — #29599483

Order 15616.

444 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#16839561C212yesmaximal
2#21446213C212yesmaximal
3#21446033C211yesmaximal, characteristic
4#21443946C211yesmaximal, characteristic
5C61×#2734C211yesmaximal, characteristic
6#16840240C2211yescharacteristic
7#16839802—21no—
8#16839771—22no—
9C2×#14519696C2212yes—
10C2×#14519696C2211yescharacteristic
11#16839561—24no—
12#16839522—22no—
13#16839522—21no—
14C2×C4⋊Q8×C61C2212yes—
15C61×#398—21no—
16C61×#395—22no—
17C61×#391C2211yescharacteristic
18C61×#389—21no—
19C61×#387—22no—
20C2×#11758194—21no—
21C2×#11758194—22no—
22Q8×Dic61—41no—
23Q8×Dic61—41no—
24#14519736—22no—
25#14519736—21no—
26#14519710—41no—
27#14519708—41no—
28#14519701—42no—
29#14519701—42no—
30#14519696—21no—
31#14519696—22no—
32#14519696—22no—
33#14519696D412yes—
34C22×Q8×C61D412yes—
35C22×Q8×C61C2311yescharacteristic
36C4⋊Q8×C61—22no—
37C4⋊Q8×C61—22no—
38C4⋊Q8×C61—22no—
39C4⋊Q8×C61—22no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61D412yes—
47C2×C42×C61D411yescharacteristic
48#95×C61—21no—
49#95×C61—22no—
50#95×C61—22no—
51#95×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—22no—
54C2×Q8×C61—41no—
55C2×Q8×C61—41no—
56C2×Q8×C61—42no—
57C2×Q8×C61—42no—
58C2×Q8×C61C2×D411yescharacteristic
59C2×Q8×C61#4111yescharacteristic
60C2×Q8×C61#4112yes—
61C22×C4×C61—21no—
62C22×C4×C61—22no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61C2×D412yes—
66C22×C4×C61C2×D411yescharacteristic
67C4⋊C4×C61—24no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—81no—
74C4⋊C4×C61—81no—
75C42×C61—22no—
76C42×C61—22no—
77C42×C61—41no—
78C22⋊Dic61—41no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4×Dic61—41no—
84C4×Dic61—42no—
85#11758194—22no—
86#11758194—41no—
87#11758194—42no—
88#11758194—42no—
89C2×#92418—41no—
90C2×#92418—42no—
91C23×C61#12011yescharacteristic
92Q8×C61—41no—
93Q8×C61—41no—
94Q8×C61—42no—
95Q8×C61—44no—
96Q8×C61—82no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—24no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61#12111yescharacteristic
113C2×C4×C61#12112yes—
114C2×C4×C61#12312yes—
115C2×C4×C61#12411yescharacteristic
116C2×Dic61—41no—
117C2×Dic61—41no—
118#92418—42no—
119#92418—82no—
120#13428—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#39411yescharacteristic
124C22×C61B(4,𝔽2)11yescharacteristic
125C22×C61#45811yescharacteristic
126C4×C61—21no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—44no—
131C4×C61—42no—
132C4×C61—81no—
133C4×C61—82no—
134Dic61—81no—
135Dic61—81no—
136#2734D6111yescharacteristic
137C2×#356—612no—
138#1886—612no—
139#1857—611no—
140#1394—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61#204411yescharacteristic
144C2×C61#220311yescharacteristic
145C2×C61#220511yescharacteristic
146C2×C4⋊Q8C2×D6112yes—
147#519—611no—
148#428—1221no—
149#419—1222no—
150C2×#101—611no—
151C2×#101—612no—
152#398—21no—
153#395—22no—
154#391C2×D6111yescharacteristic
155#389—21no—
156#387—22no—
157#356—1224no—
158#339—1221no—
159#339—1222no—
160C61#1342811yescharacteristic, complemented, Sylow
161C22×Q8C22⋊D6112yes—
162C22×Q8C22×D6111yescharacteristic
163C2×M16—1221no—
164C2×M16—1222no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4×Q8—2441no—
170C4×Q8—2441no—
171#117—1222no—
172#117—1221no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C22⋊D6111yescharacteristic
179C2×C42C22⋊D6112yes—
180C2×C42C22⋊D6111yescharacteristic
181#107—2441no—
182#106—2441no—
183#103—2442no—
184#103—2442no—
185#101—612no—
186#101—1221no—
187#101—1222no—
188#101—1222no—
189#95—21no—
190#95—22no—
191#95—22no—
192#95—22no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8D4×D6111yescharacteristic
200C2×Q8#1175822411yescharacteristic
201C2×Q8#1175822412yes—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×C22⋊D6111yescharacteristic
207C22×C4C2×C22⋊D6112yes—
208M16—1222no—
209M16—2442no—
210M16—2442no—
211M16—2441no—
212C2×C8—2442no—
213C2×C8—2441no—
214C4⋊C4—24no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—1222no—
223C4⋊C4—1222no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C22⋊C4—2441no—
227C42—22no—
228C42—22no—
229C42—41no—
230C42—2441no—
231C42—2442no—
232C23#1451974611yescharacteristic
233Q8—41no—
234Q8—42no—
235Q8—41no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4#1451974811yescharacteristic
256C2×C4#1451974912yes—
257C2×C4#1451975812yes—
258C2×C4#1451976411yescharacteristic
259C8—4882no—
260C8—2442no—
261C22—21no—
262C22—21no—
263C22#1683967611yescharacteristic
264C22#1683994911yescharacteristic
265C22#1683995211yescharacteristic
266C4—22no—
267C4—21no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—4881no—
275C4—4881no—
276C2—21no—
277C2—21no—
278C2#2144706711yescharacteristic
279C2#2144784011yescharacteristic
280C2#2144784911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#2734C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2734D61
hypocenterC61#13428
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2734

Complements

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

NH ≅ G/Ntype
160. C61#13428semidirect

Maximal subgroups

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

subgroupindex
C2×#168395612
#214462132
#214460332
#214439462
C61×#27342
#1342861