Finite Group Databasebeta

← #29583950

Subgroups — #29583950

Order 15616.

372 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 81 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#21456767C211yesmaximal, characteristic
2#21444610C211yesmaximal, characteristic
3#21444556C211yesmaximal, characteristic
4#21444500C211yesmaximal, characteristic
5#21444241C211yesmaximal, characteristic
6#21443709C211yesmaximal, characteristic
7C61×#1966C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840141—21no—
10#16840112—21no—
11#16839969—21no—
12#16839969—21no—
13#16839918—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16#16839786C2211yescharacteristic
17#16839514—21no—
18#16839512—21no—
19#16839511—22no—
20#16839509—21no—
21#16839507—21no—
22#16839494—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C2×#101×C61—22no—
26C4×M16×C61C2211yescharacteristic
27C2×#11758202—22no—
28C2×#11758202—22no—
29C2×#11758194—21no—
30#14519777D411yescharacteristic
31#14519777D411yescharacteristic
32#14519769—21no—
33#14519756—21no—
34#14519756—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37#14519736—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418D411yescharacteristic
41C4⋊#92418D411yescharacteristic
42C4⋊#92418D412yes—
43#14519701—22no—
44#14519701—22no—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47C4×#92418—21no—
48C4×#92418—21no—
49C22×Q8×C61D412yes—
50C2×M16×C61—21no—
51C2×M16×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61#101×C61—44no—
62#97×C61—21no—
63C4×C8×C61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—22no—
66C2×Q8×C61—42no—
67C2×Q8×C61—42no—
68C22×C4×C61—22no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74M16×C61—22no—
75M16×C61—41no—
76M16×C61—42no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C42×C61C2×D411yescharacteristic
84C42×C61C2×D411yescharacteristic
85C42×C61C2×D411yescharacteristic
86C42×C61#4111yescharacteristic
87C22⋊Dic61—41no—
88#11758202—82no—
89#11758202—82no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—41no—
97#11758194—81no—
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418—22no—
101C2×#92418—41no—
102C23×C61#12311yescharacteristic
103Q8×C61—42no—
104Q8×C61—42no—
105Q8×C61—82no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—44no—
112C2×C4×C61—42no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12111yescharacteristic
116C2×C4×C61#12111yescharacteristic
117C2×C4×C61#12311yescharacteristic
118C2×C4×C61#12411yescharacteristic
119C2×Dic61—41no—
120C2×Dic61—41no—
121Dic122—41no—
122Dic122—41no—
123Dic122—41no—
124Dic122—41no—
125C8×C61—42no—
126C8×C61—81no—
127#92418—41no—
128#92418—41no—
129#92418—42no—
130#92418—81no—
131#10493—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#39411yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—82no—
140C4×C61#45311yescharacteristic
141C4×C61#45511yescharacteristic
142C4×C61#47111yescharacteristic
143C4×C61#47311yescharacteristic
144C4×C61#47312yes—
145Dic61—81no—
146Dic61—81no—
147#3209—611no—
148#1966D6111yescharacteristic
149#1574—611no—
150#1561—611no—
151#1548—611no—
152#1485—611no—
153#1299—611no—
154C2×C61—41no—
155C2×C61#203711yescharacteristic
156C2×C61#204711yescharacteristic
157C2×C61#205211yescharacteristic
158#533—611no—
159C2×C4⋊Q8C2×D6111yescharacteristic
160#494—1221no—
161#487—1221no—
162#462—1221no—
163#462—1221no—
164#451—1222no—
165#431—611no—
166#431—611no—
167#423—611no—
168#423C2×D6111yescharacteristic
169C2×#101—22no—
170C4×M16C2×D6111yescharacteristic
171#335—1221no—
172#334—1221no—
173#333—1222no—
174#332—1221no—
175#332—1221no—
176Q8⋊C8—1222no—
177C61#1049311yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D6112yes—
179C2×Q16—1222no—
180C2×Q16—1222no—
181C2×M16—21no—
182C2×M16—21no—
183C2×M16—1221no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—611no—
189C4⋊Q8—611no—
190#125—1221no—
191C22⋊Q8—1221no—
192C22⋊Q8—1221no—
193C4×Q8—1221no—
194C4×Q8—1221no—
195#117—1221no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C42C22×D6111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—612no—
202C4⋊C8—611no—
203C4⋊C8—611no—
204C4⋊C8—1221no—
205C4⋊C8—1221no—
206#103—1222no—
207#103—1222no—
208#101—44no—
209C22⋊C8—1221no—
210C22⋊C8—1221no—
211#97—21no—
212C4×C8—21no—
213C4×C8—1221no—
214C4×C8—1221no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×Q8—1221no—
220C2×Q8—1221no—
221C22×C4—22no—
222C22×C4#1175822211yescharacteristic
223C22×C4#1175822211yescharacteristic
224C22×C4C2×C22⋊D6111yescharacteristic
225Q16—4882no—
226Q16—4882no—
227M16—22no—
228M16—41no—
229M16—42no—
230M16—4881no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—1222no—
236C2×C8—2441no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—2441no—
248C42—2441no—
249C42D4×D6111yescharacteristic
250C42D4×D6111yescharacteristic
251C42D4×D6111yescharacteristic
252C42#1175822411yescharacteristic
253C23#1451976011yescharacteristic
254Q8—42no—
255Q8—42no—
256Q8—82no—
257Q8—2441no—
258Q8—2441no—
259Q8—2441no—
260Q8—2441no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451974511yescharacteristic
271C2×C4#1451974911yescharacteristic
272C2×C4#1451975011yescharacteristic
273C2×C4#1451975011yescharacteristic
274C2×C4#1451975911yescharacteristic
275C2×C4#1451976311yescharacteristic
276C8—42no—
277C8—81no—
278C8—4881no—
279C8—2441no—
280C8—2442no—
281C8—2441no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1683967711yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—82no—
290C4—4881no—
291C4—4881no—
292C4#1683992911yescharacteristic
293C4#1683993911yescharacteristic
294C4#1684002811yescharacteristic
295C4#1684003612yes—
296C4#1684003611yescharacteristic
297C2—41no—
298C2#2144702911yescharacteristic
299C2#2144708511yescharacteristic
300C2#2144711811yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1966C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1966D61
hypocenterC61#10493
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
177. C61#10493semidirect

Maximal subgroups

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

subgroupindex
#214567672
#214446102
#214445562
#214445002
#214442412
#214437092
C61×#19662
#1049361