Finite Group Databasebeta

← #29583952

Subgroups — #29583952

Order 15616.

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

normal subgroups only

This group has 372 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#21456769C211yesmaximal, characteristic
2#21446662C211yesmaximal, characteristic
3#21444556C211yesmaximal, characteristic
4#21444499C211yesmaximal, characteristic
5#21444239C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic
7C61×#1574C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840142—21no—
11#16840113—21no—
12#16839973—21no—
13#16839973—21no—
14#16839920—22no—
15#16839786C2211yescharacteristic
16C2×#14519695—22no—
17C4×#11758194C2211yescharacteristic
18#16839510—22no—
19#16839509—21no—
20#16839507—21no—
21#16839492—22no—
22C61×#431C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#335—21no—
26C61×#334—21no—
27C22×Dic122D412yes—
28C2×Dic244—22no—
29C2×Dic244—22no—
30C2×#11758194—21no—
31C2×#11758194—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519702—22no—
49#14519702—22no—
50#14519695—44no—
51#14519688—21no—
52C4×#92418—21no—
53C2×M16×C61—21no—
54C2×C42×C61C2311yescharacteristic
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61D412yes—
58C4⋊C8×C61D411yescharacteristic
59C4⋊C8×C61D411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63C4×C8×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61#4111yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—22no—
68C2×Dic122—22no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—22no—
72C2×Dic122—42no—
73C2×Dic122—42no—
74M16×C61—42no—
75C2×C8×C61—21no—
76C2×C8×C61—21no—
77C2×C8×C61—22no—
78C2×C8×C61—41no—
79C42×C61C2×D411yescharacteristic
80C42×C61C2×D411yescharacteristic
81C42×C61C2×D411yescharacteristic
82C42×C61#4111yescharacteristic
83C22⋊Dic61—41no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—41no—
95#11758194—22no—
96#11758194—41no—
97#11758194—81no—
98C2×#92418—41no—
99C2×#92418—41no—
100Dic244—82no—
101Dic244—82no—
102C23×C61#12311yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61#12111yescharacteristic
110C2×C4×C61#12111yescharacteristic
111C2×C4×C61#12111yescharacteristic
112C2×C4×C61#12311yescharacteristic
113C2×C4×C61#12411yescharacteristic
114C2×Dic61—44no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118Dic122—41no—
119Dic122—42no—
120Dic122—41no—
121Dic122—42no—
122Dic122—41no—
123Dic122—41no—
124Dic122—82no—
125C8×C61—41no—
126C8×C61—41no—
127C8×C61—42no—
128C8×C61—81no—
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#45311yescharacteristic
140C4×C61#45511yescharacteristic
141C4×C61#47111yescharacteristic
142C4×C61#47312yes—
143C4×C61#47311yescharacteristic
144Dic61—81no—
145Dic61—82no—
146Dic61—81no—
147#3209—611no—
148#1966—611no—
149#1574D6111yescharacteristic
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⋊Q8—611no—
160#494—1221no—
161#487—1221no—
162#462—1221no—
163#462—1221no—
164#451—1222no—
165#431C2×D6111yescharacteristic
166#431C2×D6111yescharacteristic
167#423—611no—
168#423C2×D6111yescharacteristic
169C2×#101—1222no—
170C4×M16—611no—
171#335—21no—
172#334—21no—
173#333—1222no—
174#332—1221no—
175#332—1221no—
176Q8⋊C8—1222no—
177C61#1049311yescharacteristic, complemented, Sylow
178C22×Q8—612no—
179C2×Q16—1222no—
180C2×Q16—1222no—
181C2×M16—21no—
182C2×M16—1221no—
183C2×M16—1221no—
184C4⋊Q8—611no—
185C4⋊Q8—611no—
186C4⋊Q8—1221no—
187C4⋊Q8—1221no—
188C4⋊Q8—1221no—
189C4⋊Q8—1221no—
190#125—1221no—
191C22⋊Q8—1221no—
192C22⋊Q8—1221no—
193C4×Q8—1221no—
194C4×Q8—1221no—
195#117—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C42C22×D6111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—1221no—
202C4⋊C8—1221no—
203C4⋊C8D24412yes—
204C4⋊C8C22⋊D6111yescharacteristic
205C4⋊C8C22⋊D6111yescharacteristic
206#103—1222no—
207#103—1222no—
208#101—2444no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211#97—1221no—
212C4×C8—21no—
213C4×C8—21no—
214C4×C8—1221no—
215C2×Q8—1222no—
216C2×Q8—1221no—
217C2×Q8—1222no—
218C2×Q8—1221no—
219C2×Q8—2442no—
220C2×Q8—2442no—
221C22×C4—1222no—
222C22×C4#1175822211yescharacteristic
223C22×C4D4×D6111yescharacteristic
224C22×C4#1175822611yescharacteristic
225Q16—4882no—
226Q16—4882no—
227M16—42no—
228M16—1222no—
229M16—4881no—
230M16—2441no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—2441no—
236C2×C8—2441no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—2441no—
248C42—2441no—
249C42C2×D24411yescharacteristic
250C42D4×D6111yescharacteristic
251C42#1175822611yescharacteristic
252C42C2×C22⋊D6111yescharacteristic
253C23#1451976211yescharacteristic
254Q8—4882no—
255Q8—2441no—
256Q8—2442no—
257Q8—2441no—
258Q8—2441no—
259Q8—2441no—
260Q8—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—2444no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2442no—
270C2×C4#1451974511yescharacteristic
271C2×C4#1451975111yescharacteristic
272C2×C4#1451975211yescharacteristic
273C2×C4#1451975211yescharacteristic
274C2×C4#1451976211yescharacteristic
275C2×C4#1451976611yescharacteristic
276C8—41no—
277C8—42no—
278C8—41no—
279C8—81no—
280C8—4881no—
281C8—2442no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1683967911yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—4882no—
290C4—4881no—
291C4—4881no—
292C4#1683992811yescharacteristic
293C4#1683993811yescharacteristic
294C4#1684002611yescharacteristic
295C4#1684003712yes—
296C4#1684003811yescharacteristic
297C2—41no—
298C2#2144703111yescharacteristic
299C2#2144708711yescharacteristic
300C2#2144712011yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1574C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1574D61
hypocenterC61#10493
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
177. C61#10493semidirect

Maximal subgroups

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

subgroupindex
#214567692
#214466622
#214445562
#214444992
#214442392
#214437102
C61×#15742
#1049361