Finite Group Databasebeta

← #29583966

Subgroups — #29583966

Order 15616.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#21456972C211yesmaximal, characteristic
2#21446807C211yesmaximal, characteristic
3#21444556C211yesmaximal, characteristic
4#21444490C211yesmaximal, characteristic
5#21444239C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic
7C61×#1574C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840167—21no—
11#16840113—21no—
12#16840098—22no—
13#16840058—21no—
14#16840058—21no—
15#16839786C2211yescharacteristic
16C4×#11758194C2211yescharacteristic
17#16839530—22no—
18#16839509—21no—
19#16839507—21no—
20#16839507—22no—
21#16839492—22no—
22C61×#431C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#335—21no—
26C61×#334—21no—
27C22×Dic122—21no—
28C2×#11758194—21no—
29C2×#11758194—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777D411yescharacteristic
35#14519777D411yescharacteristic
36#14519769—21no—
37#14519756—21no—
38#14519756—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D412yes—
44#14519711—22no—
45#14519711—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519702—22no—
49#14519702—22no—
50#14519688—21no—
51C4×#92418—21no—
52C2×M16×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61D412yes—
57C4⋊C8×C61D411yescharacteristic
58C4⋊C8×C61D411yescharacteristic
59C22⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×C4×C61#4111yescharacteristic
66C22×Dic61—22no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122—81no—
72C2×Dic122—81no—
73M16×C61—42no—
74C2×C8×C61—21no—
75C2×C8×C61—21no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C42×C61C2×D411yescharacteristic
79C42×C61C2×D411yescharacteristic
80C42×C61C2×D411yescharacteristic
81C42×C61#4111yescharacteristic
82C22⋊Dic61—41no—
83C4⋊Dic61—22no—
84C4⋊Dic61—21no—
85C4⋊Dic61—22no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—41no—
94#11758194—22no—
95#11758194—41no—
96#11758194—81no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61#12311yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61#12111yescharacteristic
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12111yescharacteristic
109C2×C4×C61#12311yescharacteristic
110C2×C4×C61#12411yescharacteristic
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—82no—
115Dic122—41no—
116Dic122—41no—
117Dic122—41no—
118Dic122—41no—
119Dic122—82no—
120Dic122—81no—
121Dic122—81no—
122C8×C61—41no—
123C8×C61—41no—
124C8×C61—42no—
125C8×C61—81no—
126#92418—42no—
127#92418—81no—
128#10495—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61#39411yescharacteristic
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61#45411yescharacteristic
137C4×C61#45611yescharacteristic
138C4×C61#47111yescharacteristic
139C4×C61#47211yescharacteristic
140C4×C61#47312yes—
141Dic61—81no—
142Dic61—82no—
143Dic61—81no—
144#3230—611no—
145#1997—611no—
146#1574D6111yescharacteristic
147#1561—611no—
148#1546—611no—
149#1485—611no—
150#1299—611no—
151C2×C61—41no—
152C2×C61#203811yescharacteristic
153C2×C61#204711yescharacteristic
154C2×C61#205111yescharacteristic
155#533—611no—
156C2×C4⋊Q8—611no—
157#500—1221no—
158#487—1221no—
159#484—1222no—
160#477—1221no—
161#477—1221no—
162#431C2×D6111yescharacteristic
163#431C2×D6111yescharacteristic
164#423—611no—
165#423C2×D6111yescharacteristic
166C4×M16—611no—
167#343—1222no—
168#335—21no—
169#334—21no—
170#332—1221no—
171#332—1221no—
172#332—1222no—
173Q8⋊C8—1222no—
174C61#1049511yescharacteristic, complemented, Sylow
175C22×Q8—1221no—
176C2×M16—21no—
177C2×M16—1221no—
178C2×M16—1221no—
179C4⋊Q8—611no—
180C4⋊Q8—611no—
181C4⋊Q8—1221no—
182C4⋊Q8—1221no—
183C4⋊Q8—1221no—
184C4⋊Q8—1221no—
185#125—1221no—
186C22⋊Q8—1221no—
187C22⋊Q8—1221no—
188C4×Q8—1221no—
189C4×Q8—1221no—
190#117—1221no—
191C2×C4⋊C4—612no—
192C2×C4⋊C4—1221no—
193C2×C42C22×D6111yescharacteristic
194#107—1222no—
195#107—1222no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—1221no—
199C4⋊C8—1221no—
200C4⋊C8D24412yes—
201C4⋊C8C22⋊D6111yescharacteristic
202C4⋊C8C22⋊D6111yescharacteristic
203#103—1222no—
204#103—1222no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207#97—1221no—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—1221no—
211C2×Q8—1221no—
212C2×Q8—1221no—
213C2×Q8—4881no—
214C2×Q8—4881no—
215C2×Q8—2441no—
216C2×Q8—2441no—
217C22×C4—1222no—
218C22×C4#1175822211yescharacteristic
219C22×C4D4×D6111yescharacteristic
220C22×C4#1175822611yescharacteristic
221M16—42no—
222M16—1222no—
223M16—4881no—
224M16—2441no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—2441no—
230C2×C8—2441no—
231C4⋊C4—1222no—
232C4⋊C4—1221no—
233C4⋊C4—1222no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C4⋊C4—1221no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C22⋊C4—2441no—
242C42—2441no—
243C42C2×D24411yescharacteristic
244C42D4×D6111yescharacteristic
245C42#1175822611yescharacteristic
246C42C2×C22⋊D6111yescharacteristic
247C23#1451976211yescharacteristic
248Q8—4882no—
249Q8—4881no—
250Q8—4881no—
251Q8—2441no—
252Q8—2441no—
253Q8—2441no—
254Q8—2441no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—4882no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2442no—
264C2×C4#1451974511yescharacteristic
265C2×C4#1451975111yescharacteristic
266C2×C4#1451975211yescharacteristic
267C2×C4#1451975211yescharacteristic
268C2×C4#1451976211yescharacteristic
269C2×C4#1451976611yescharacteristic
270C8—41no—
271C8—42no—
272C8—41no—
273C8—81no—
274C8—4881no—
275C8—2442no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1683967911yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—4881no—
284C4—4882no—
285C4—4881no—
286C4#1683993311yescharacteristic
287C4#1683994311yescharacteristic
288C4#1684002611yescharacteristic
289C4#1684003311yescharacteristic
290C4#1684003712yes—
291C2—41no—
292C2#2144703811yescharacteristic
293C2#2144708711yescharacteristic
294C2#2144711311yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1574C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1574D61
hypocenterC61#10495
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
174. C61#10495semidirect

Maximal subgroups

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

subgroupindex
#214569722
#214468072
#214445562
#214444902
#214442392
#214437102
C61×#15742
#1049561