Finite Group Databasebeta

← #29656312

Subgroups — #29656312

Order 15616.

918 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16840492C211yesmaximal, characteristic
2#21455945C212yesmaximal
3#21445037C218yesmaximal, complemented
4#21444545C211yesmaximal, characteristic
5#21444267C212yesmaximal
6C61×#3139C211yesmaximal, characteristic
7#16840492—24no—
8#16840492—22no—
9#16840492C2214yes—
10C2×#14519776—22no—
11C2×#14519775—22no—
12C2×C4×Dic122C2212yes—
13C2×#14519742—22no—
14#16840090—22no—
15#16840044C2214yes—
16#16839969C2214yes—
17#16839917—22no—
18#16839867—24no—
19#16839819C2212yes—
20#16839511C2214yes—
21#16839494C2218yes—
22C61×#533C2211yescharacteristic
23C2×C4⋊Q8×C61C2211yescharacteristic
24C61×#491—22no—
25C61×#487C2214yes—
26C61×#419—22no—
27C4×M16×C61C2211yescharacteristic
28C22×Dic122—22no—
29C22×Dic122D412yes—
30C2×#11758202—24no—
31#14519776—28no—
32#14519776—28no—
33#14519775—28no—
34#14519775—28no—
35C4×Dic122—22no—
36C4×Dic122—22no—
37C4×Dic122D414yes—
38C4×Dic122C2314yes—
39#14519742—28no—
40#14519742—28no—
41C2×C4⋊Dic61D412yes—
42C2×#11758196—24no—
43C2×#11758196—22no—
44C2×C4×Dic61—22no—
45C2×C4×Dic61—22no—
46#14519708—24no—
47C4⋊#92418C2314yes—
48#14519701—24no—
49#14519700—24no—
50C22⋊#92418—22no—
51#14519688—22no—
52C22×Q8×C61D412yes—
53C2×M16×C61—21no—
54C4⋊Q8×C61—22no—
55C4⋊Q8×C61D412yes—
56C4⋊Q8×C61C2312yes—
57C4⋊Q8×C61C2312yes—
58#125×C61—21no—
59C22⋊Q8×C61—22no—
60C4×Q8×C61—22no—
61#117×C61—21no—
62C2×C4⋊C4×C61—22no—
63C2×C42×C61C2311yescharacteristic
64#103×C61—28no—
65#97×C61—21no—
66C4×C8×C61C2312yes—
67C2×Q8×C61—22no—
68C2×Q8×C61—22no—
69C2×Q8×C61—44no—
70C2×Q8×C61C2×D414yes—
71C22×C4×C61—22no—
72C22×C4×C61C2×D412yes—
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—22no—
75C22×Dic61—22no—
76C2×Dic122—22no—
77C2×Dic122—28no—
78C2×Dic122—28no—
79C2×Dic122—84no—
80C2×Dic122C2×D414yes—
81M16×C61—42no—
82C2×C8×C61—22no—
83C4⋊C4×C61—24no—
84C4⋊C4×C61—24no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—42no—
88C22⋊C4×C61—41no—
89C42×C61—41no—
90C42×C61C2×D412yes—
91C42×C61C2×D411yescharacteristic
92C42×C61C2411yescharacteristic
93#11758202—48no—
94C4⋊Dic61—22no—
95C4⋊Dic61C2×D414yes—
96#11758196—216no—
97#11758196—24no—
98#11758196—24no—
99C4×Dic61—28no—
100C4×Dic61—24no—
101C4×Dic61—24no—
102C2×#92418—24no—
103C23×C61#12011yescharacteristic
104Q8×C61—44no—
105Q8×C61—44no—
106Q8×C61—82no—
107C2×C4×C61—22no—
108C2×C4×C61—24no—
109C2×C4×C61—24no—
110C2×C4×C61—44no—
111C2×C4×C61—42no—
112C2×C4×C61#12012yes—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61C22×D411yescharacteristic
115C2×C4×C61C22×D412yes—
116C2×Dic61—28no—
117C2×Dic61—24no—
118C2×Dic61—24no—
119C2×Dic61—44no—
120Dic122—28no—
121Dic122—24no—
122Dic122—88no—
123Dic122#13718yes—
124C8×C61—42no—
125#92418—44no—
126#18551—611nomaximal, Sylow
127C22×C61—22no—
128C22×C61#45512yes—
129C22×C61C2×#12011yescharacteristic
130C4×C61—22no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—44no—
134C4×C61—82no—
135C4×C61C2×#13714yes—
136Dic61—28no—
137Dic61—44no—
138C2×Q82—611no—
139#3139D6111yescharacteristic
140#3113—612no—
141#1645—618no—
142#1558—611no—
143#1491—612no—
144C2×C61—22no—
145C2×C61#300412yes—
146C2×C61C2×#45511yescharacteristic
147Q82—614no—
148Q82—1224no—
149Q82—1222no—
150#533C2×D6111yescharacteristic
151C2×C4⋊Q8—1222no—
152C2×C4⋊Q8—1222no—
153C2×C4⋊Q8C2×D6111yescharacteristic
154C2×C4×Q8—612no—
155C2×C4×Q8—1222no—
156#491—22no—
157#487C2×D6114yes—
158#483—1222no—
159#475—614no—
160#462—614no—
161#451—1222no—
162#441—1224no—
163#432—612no—
164#419—22no—
165C4×M16C2×D6111yescharacteristic
166#333—614no—
167Q8⋊C8—618no—
168C61#1855111yescharacteristic, complemented, Sylow
169C22×Q8—612no—
170C22×Q8—1222no—
171C22×Q8C22⋊D6112yes—
172C2×Q16—1224no—
173C2×M16—21no—
174C4⋊Q8—22no—
175C4⋊Q8—1228no—
176C4⋊Q8—1228no—
177C4⋊Q8—1228no—
178C4⋊Q8—1228no—
179C4⋊Q8C22⋊D6112yes—
180C4⋊Q8C22×D6112yes—
181C4⋊Q8C22×D6112yes—
182#125—21no—
183C22⋊Q8—22no—
184C4×Q8—22no—
185C4×Q8—614no—
186C4×Q8—614no—
187C4×Q8—1228no—
188C4×Q8—1228no—
189C4×Q8—1222no—
190C4×Q8—1222no—
191#117—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—612no—
194C2×C4⋊C4—1224no—
195C2×C4⋊C4—1222no—
196C2×C42—1222no—
197C2×C42—1222no—
198C2×C42C22×D6111yescharacteristic
199#106—1224no—
200C4⋊C8—614no—
201#103—28no—
202#103—1224no—
203#103—1224no—
204C22⋊C8—1222no—
205#97—21no—
206#97—1222no—
207C4×C8C22×D6112yes—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—44no—
211C2×Q8—614no—
212C2×Q8—1228no—
213C2×Q8—1228no—
214C2×Q8—1222no—
215C2×Q8—4884no—
216C2×Q8C2×C22⋊D6114yes—
217C22×C4—22no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4D4×D6112yes—
221C22×C4C2×C22⋊D6111yescharacteristic
222Q16—2448no—
223M16—42no—
224C2×C8—22no—
225C2×C8—1224no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—614no—
232C4⋊C4—12216no—
233C4⋊C4—1224no—
234C4⋊C4—1222no—
235C4⋊C4—1224no—
236C22⋊C4—41no—
237C42—41no—
238C42—1228no—
239C42—1224no—
240C42—1224no—
241C42D4×D6112yes—
242C42C2×C22⋊D6111yescharacteristic
243C42C23×D6111yescharacteristic
244C23#1451974511yescharacteristic
245Q8—44no—
246Q8—44no—
247Q8—82no—
248Q8—618no—
249Q8—1228no—
250Q8—1224no—
251Q8—4888no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—1228no—
258C2×C4—1224no—
259C2×C4—1224no—
260C2×C4—2444no—
261C2×C4#1451974511yescharacteristic
262C2×C4#1451974512yes—
263C2×C4C2×D4×D6112yes—
264C2×C4C22×C22⋊D6111yescharacteristic
265C8—42no—
266C8—2444no—
267C22—22no—
268C22#1683993912yes—
269C22C2×#1451974511yescharacteristic
270C4—21no—
271C4—21no—
272C4—22no—
273C4—44no—
274C4—82no—
275C4—1228no—
276C4—2444no—
277C4#137×D6114yes—
278C2—22no—
279C2#2145505112yes—
280C2C2×#1683993911yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3139C2
socleC22×C61C2×#120
prime radicalC23×C61#120
hypercenter#3139D61
hypocenterC61#18551
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
3. #21445037C2semidirect
168. C61#18551semidirect

Maximal subgroups

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

subgroupindex
C2×#168404922
#214559452
#214450372
#214445452
#214442672
C61×#31392
#1855161