Finite Group Databasebeta

← #29590462

Subgroups — #29590462

Order 15616.

320 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 79 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#21456400C211yesmaximal, characteristic
2#21447619C211yesmaximal, characteristic
3#21445720C211yesmaximal, characteristic
4#21443838C211yesmaximal, characteristic
5#21443837C211yesmaximal, characteristic
6#21443836C211yesmaximal, characteristic
7C61×#1350C211yesmaximal, characteristic
8#16840314—21no—
9#16840166C411yescharacteristic
10#16840140C411yescharacteristic
11#16840111—21no—
12#16840003C2211yescharacteristic
13#16840001—21no—
14Q16×Dic61C411yescharacteristic
15#16839856C411yescharacteristic
16#16839854—21no—
17C2×#14519712—21no—
18M16×Dic61—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839580—21no—
21C22⋊#11758185C2211yescharacteristic
22#16839537—21no—
23#16839527C2211yescharacteristic
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#341C2211yescharacteristic
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C2×#11758194—21no—
30C22×#92418D411yescharacteristic
31#14519776—21no—
32#14519775—21no—
33#14519767—41no—
34#14519756—21no—
35#14519754—41no—
36Q8×Dic61—21no—
37#14519742—21no—
38#14519742—41no—
39#14519733—41no—
40C2×C4×Dic61D411yescharacteristic
41C2×#11758185—21no—
42#14519712—24no—
43#14519711C2×C411yescharacteristic
44#14519710—21no—
45#14519702—21no—
46#14519701—21no—
47#14519700—21no—
48#14519687—41no—
49C8×Dic61—41no—
50C8×Dic61C2×C411yescharacteristic
51C8×Dic61C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C2×Q16×C61C2×C411yescharacteristic
55C2×M16×C61—21no—
56C22×C8×C61C2311yescharacteristic
57C22⋊Q8×C61—21no—
58C2×C16×C61—21no—
59#107×C61C2×C411yescharacteristic
60#103×C61—21no—
61C2×Q8×C61—21no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61SD1611yescharacteristic
64C22×Dic61SD1611yescharacteristic
65C2×Dic122—21no—
66C2×Dic122—41no—
67Q16×C61—41no—
68M16×C61—22no—
69M16×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C22×C411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—41no—
78#11758202—42no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C4×Dic61C22⋊C411yescharacteristic
90C4×Dic61D811yescharacteristic
91C4×Dic61D811yescharacteristic
92#11758194—22no—
93#11758194—41no—
94C2×#92418—22no—
95C2×#92418—41no—
96C2×#92418C22⋊C411yescharacteristic
97C2×#92418C22⋊C411yescharacteristic
98Dic244—41no—
99C16×C61—41no—
100#11758185—41no—
101C23×C61C2×SD1611yescharacteristic
102Q8×C61—41no—
103Q8×C61—41no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×Dic61—22no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61#10211yescharacteristic
115C2×Dic61#10211yescharacteristic
116C2×Dic61#10211yescharacteristic
117C2×Dic61#10211yescharacteristic
118Dic122—41no—
119Dic122—41no—
120Dic122—82no—
121C8×C61—21no—
122C8×C61—21no—
123C8×C61—42no—
124#92418—21no—
125#92418—42no—
126#92418#10412yes—
127#11752—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61C2×#10211yescharacteristic
132C4×C61—21no—
133C4×C61—81no—
134C4×C61—81no—
135C4×C61#41011yescharacteristic
136C4×C61C2×#10411yescharacteristic
137Dic61—21no—
138Dic61—21no—
139Dic61—21no—
140Dic61—81no—
141Dic61—81no—
142Dic61#36212yes—
143#3170—611no—
144#2163—611no—
145C4×#108—611no—
146#1350—611no—
147#1350—611no—
148#1350—611no—
149#1350D6111yescharacteristic
150C2×C61—41no—
151C2×C61#150211yescharacteristic
152C2×C61#214311yescharacteristic
153C2×C61C2×#36211yescharacteristic
154#533—1221no—
155#500—611no—
156#494—611no—
157#487—1221no—
158#467—611no—
159#467—1221no—
160#467C2×D6111yescharacteristic
161C4×Q16—611no—
162C4×Q16—611no—
163C4×Q16—1221no—
164C2×#108—1221no—
165C4×M16—1221no—
166C2×C4×C8—611no—
167C4⋊C16—1221no—
168C22⋊C16—611no—
169C22⋊C16C2×D6111yescharacteristic
170#346—1221no—
171#341—611no—
172#341C2×D6111yescharacteristic
173C61#1175211yescharacteristic, complemented, Sylow
174C2×Q16—611no—
175C2×Q16—1221no—
176C2×Q16C4×D6111yescharacteristic
177C2×M16—21no—
178C2×M16—1221no—
179C22×C8—611no—
180C22×C8C22×D6111yescharacteristic
181C4⋊Q8—1221no—
182C4⋊Q8—1221no—
183#125—2441no—
184C22⋊Q8—21no—
185C22⋊Q8—1221no—
186C22⋊Q8—2441no—
187C4×Q8—1221no—
188C4×Q8—1221no—
189C4×Q8—2441no—
190#117—2441no—
191C2×C42—611no—
192C2×C16—21no—
193C2×C16—1221no—
194#108—1224no—
195#107—611no—
196#107—1221no—
197#107C4×D6111yescharacteristic
198#103—21no—
199#103—1221no—
200#103—1221no—
201#103—1221no—
202#97—2441no—
203C4×C8—611no—
204C4×C8—611no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8—2441no—
208C2×Q8—21no—
209C2×Q8—1221no—
210C2×Q8—2441no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4D4×D6111yescharacteristic
214Q16—41no—
215Q16—2441no—
216Q16—2442no—
217M16—22no—
218M16—41no—
219M16—1222no—
220M16—2441no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—611no—
224C2×C8—611no—
225C2×C8—1222no—
226C2×C8—2441no—
227C2×C8C2×C4×D6111yescharacteristic
228C2×C8D4×D6111yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—1221no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C22⋊C4—41no—
239C22⋊C4—2441no—
240C42—611no—
241C42—611no—
242C42—611no—
243C42—611no—
244C42—2441no—
245C42—2441no—
246C16—41no—
247C16—2441no—
248C23SD16×D6111yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—4882no—
252Q8—2441no—
253Q8—2441no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1222no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4C22⋊C4×D6111yescharacteristic
267C2×C4D8×D6111yescharacteristic
268C8—21no—
269C8—21no—
270C8—42no—
271C8—612no—
272C8—1221no—
273C8—2442no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#102×D6111yescharacteristic
278C4—21no—
279C4—81no—
280C4—81no—
281C4—612no—
282C4—1221no—
283C4—1221no—
284C4—1221no—
285C4—4881no—
286C4—4881no—
287C4#1683973411yescharacteristic
288C4#104×D6111yescharacteristic
289C2—41no—
290C2#2144431211yescharacteristic
291C2#2144754511yescharacteristic
292C2#362×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1350C2
socleC22×C61C2×#102
prime radicalC23×C61C2×SD16
cosocleC22×C8×C61C23
hypercenter#1350D61
hypocenterC61#11752
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
173. C61#11752semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214476192
#214457202
#214438382
#214438372
#214438362
C61×#13502
#1175261