Finite Group Databasebeta

← #30595525

Subgroups — #30595525

Order 15616.

428 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461735C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3#21460639C212yesmaximal
4#21460637C212yesmaximal
5#21448297C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—21no—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839669C411yescharacteristic
13#16839669C2211yescharacteristic
14#16839661C411yescharacteristic
15#16839661C2211yescharacteristic
16#16839648—21no—
17#16839648—21no—
18C4×C4⋊Dic61—21no—
19C4×C4⋊Dic61C411yescharacteristic
20#16839608—21no—
21C42×Dic61C2211yescharacteristic
22C2×C4×Q8×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519844—42no—
27#14519832—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×Q8×C61C2×C411yescharacteristic
47C4×Q8×C61—22no—
48C4×Q8×C61—22no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53C2×Q8×C61—21no—
54C2×Q8×C61—41no—
55C2×Q8×C61—41no—
56C2×Q8×C61M1612yes—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×#92420—24no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—24no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61M1612yes—
77C42×C61—24no—
78C42×C61—21no—
79C42×C61—21no—
80C4⋊Dic61—42no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4×Dic61—22no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C4×Dic61—42no—
92C4×Dic61SD1612yes—
93C4×Dic61Q1612yes—
94C23×C61C2×C22⋊C411yescharacteristic
95Q8×C61—42no—
96Q8×C61—42no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#10312yes—
111C2×C4×C61C2×M1611yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61#10312yes—
128C2×Dic61#10412yes—
129C2×Dic61C2×SD1611yescharacteristic
130C2×Dic61C2×Q1611yescharacteristic
131C2×Dic61AGL(1,ℤ/8)11yescharacteristic
132C2×Dic61#13711yescharacteristic
133#92420—44no—
134#92420—82no—
135#7615—611nomaximal, Sylow
136C22×C61#40711yescharacteristic
137C22×C61#41011yescharacteristic
138C22×C61#41311yescharacteristic
139C22×C61C2×#10311yescharacteristic
140C22×C61#41711yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—42no—
149Dic61—22no—
150Dic61—21no—
151Dic61—21no—
152Dic61—21no—
153Dic61—21no—
154Dic61—22no—
155Dic61—81no—
156Dic61—81no—
157#2295—611no—
158#1831—611no—
159#1767—611no—
160#1272—612no—
161#1271—612no—
162C2×C61#146411yescharacteristic
163C2×C61#148711yescharacteristic
164C2×C61#148911yescharacteristic
165C2×C61#150311yescharacteristic
166C2×C61#151211yescharacteristic
167C2×C61#153211yescharacteristic
168C2×C61#155011yescharacteristic
169C2×C4×Q8#692311yescharacteristic
170C2×C4⋊C8—1221no—
171C2×C4⋊C8—1221no—
172C2×#97—1221no—
173#391—611no—
174#391—611no—
175#389—611no—
176#389—611no—
177#387—1221no—
178#387—1221no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4—1221no—
181#376—1221no—
182C43—611no—
183#336—612no—
184#336—612no—
185#336—1221no—
186C61#761511yescharacteristic, complemented, Sylow
187C22×Q8C2×#692311yescharacteristic
188C22×C8—1222no—
189C22×C8—1222no—
190C4×Q8—22no—
191C4×Q8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—21no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—1221no—
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—1224no—
208C4⋊C8—2442no—
209#97—2442no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—21no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8#1175821712yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22×#692311yescharacteristic
232C2×C8—1224no—
233C2×C8—2442no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—24no—
239C4⋊C4—21no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4#1175821712yes—
246C42—24no—
247C42—21no—
248C42—21no—
249C42—612no—
250C42—612no—
251C42—1222no—
252C42—1221no—
253C42—1221no—
254C42—2441no—
255C42—2441no—
256C42—2441no—
257C42—2442no—
258C23C2×C22⋊#692311yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—612no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—612no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4#1451984012yes—
295C2×C4C2×#1175821711yescharacteristic
296C2×C4C2×#1175821711yescharacteristic
297C8—4882no—
298C8—2444no—
299C22#1684073211yescharacteristic
300C22#1684074111yescharacteristic
301C22#1684074811yescharacteristic
302C22C2×#1451984011yescharacteristic
303C22#1684075311yescharacteristic
304C22D61⋊#10411yescharacteristic
305C22#1684076111yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—1222no—
313C4—1222no—
314C4—1221no—
315C4—1221no—
316C4—1221no—
317C4—1221no—
318C4—4881no—
319C4—4881no—
320C2#2146107011yescharacteristic
321C2#2146114711yescharacteristic
322C2#2146115411yescharacteristic
323C2#2146120111yescharacteristic
324C2#2146123211yescharacteristic
325C2#2146129611yescharacteristic
326C2#2146133611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
186. C61#7615semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214616042
#214606392
#214606372
#214482972
#761561