Finite Group Databasebeta

← #30595487

Subgroups — #30595487

Order 15616.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461747C211yesmaximal, characteristic
2#21461747C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×C4×Dic122—21no—
14#16839666—21no—
15#16839661C2211yescharacteristic
16#16839659—21no—
17#16839658C2211yescharacteristic
18#16839631C411yescharacteristic
19C4×#11758196—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22×Dic122—21no—
26#14519776—22no—
27#14519776C814yescomplemented
28C4×Dic122—44no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61—21no—
49C2×C42×C61C2×C411yescharacteristic
50#95×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×Dic122—24no—
63C2×Dic122—42no—
64C2×Dic122—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61C2×C812yes—
74C42×C61—22no—
75C42×C61—42no—
76C4⋊Dic61—21no—
77C4⋊Dic61—42no—
78C4⋊Dic61—41no—
79C4⋊Dic61C2×C812yes—
80#11758196—24no—
81#11758196—42no—
82#11758196—42no—
83#11758196—42no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61—42no—
90C4×Dic61C2×C812yes—
91C4×Dic61M1612yes—
92C23×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#10112yes—
107C2×C4×C61C22×C811yescharacteristic
108C2×C4×C61C2×M1611yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61C22⋊C812yes—
124C2×Dic61C22⋊C812yes—
125C2×Dic61AGL(1,ℤ/8)12yes—
126C2×Dic61#13712yes—
127Dic122—48no—
128#92420—82no—
129#92420—82no—
130#7604—611nomaximal, Sylow
131C22×C61C2×C22⋊C811yescharacteristic
132C22×C61#41011yescharacteristic
133C22×C61C2×#10111yescharacteristic
134C22×C61#41811yescharacteristic
135C22×C61#41911yescharacteristic
136C22×C61#42111yescharacteristic
137C22×C61#42111yescharacteristic
138C4×C61—22no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—42no—
143C4×C61—81no—
144Dic61—22no—
145Dic61—22no—
146Dic61—22no—
147Dic61—22no—
148Dic61—42no—
149Dic61—81no—
150C4×C4⋊Q8—611no—
151#1839—611no—
152#1839—611no—
153#1271—612no—
154#1271—612no—
155C2×C61#146111yescharacteristic
156C2×C61#147811yescharacteristic
157C2×C61#147911yescharacteristic
158C2×C61#151411yescharacteristic
159C2×C61#151511yescharacteristic
160C2×C61#153711yescharacteristic
161C2×C61#155611yescharacteristic
162C2×C4⋊Q8—611no—
163C2×C4×Q8—1221no—
164#391—1221no—
165#389—611no—
166#389—611no—
167#389—1221no—
168#384—611no—
169C4×C4⋊C4—611no—
170C4×C4⋊C4—1221no—
171C4×C4⋊C4#692311yescharacteristic
172C43—611no—
173#336—612no—
174#336—612no—
175#336—1221no—
176#336—1221no—
177#336—1221no—
178#336—1221no—
179C61#760411yescharacteristic, complemented, Sylow
180C22×Q8—1221no—
181C22×C8—1222no—
182C22×C8—1222no—
183C4⋊Q8—614no—
184C4⋊Q8—1222no—
185C4×Q8—2444no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4C2×#692311yescharacteristic
194C2×C4⋊C4C2×#692311yescharacteristic
195C2×C42—21no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—1221no—
203C2×C42C2×#692311yescharacteristic
204#95—21no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208C2×Q8—1224no—
209C2×Q8—2442no—
210C2×Q8—2442no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22⋊#692311yescharacteristic
221C22×C4C22×#692311yescharacteristic
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—612no—
231C4⋊C4—1224no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C4⋊C4—2442no—
237C4⋊C4—2442no—
238C4⋊C4D61⋊C812yes—
239C42—22no—
240C42—42no—
241C42—612no—
242C42—612no—
243C42—1222no—
244C42—1222no—
245C42—2441no—
246C42—2441no—
247C42—2441no—
248C42—2442no—
249C23C2×C22⋊#692311yescharacteristic
250Q8—2448no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—612no—
265C2×C4—612no—
266C2×C4—612no—
267C2×C4—612no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1222no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451983812yes—
283C2×C4C2×D61⋊C811yescharacteristic
284C2×C4D61⋊M1611yescharacteristic
285C8—4882no—
286C8—4882no—
287C22D61⋊(C22⋊C8)11yescharacteristic
288C22#1684074111yescharacteristic
289C22C2×#1451983811yescharacteristic
290C22#1684075411yescharacteristic
291C22#1684075511yescharacteristic
292C22#1684075911yescharacteristic
293C22#1684075911yescharacteristic
294C4—21no—
295C4—21no—
296C4—22no—
297C4—41no—
298C4—42no—
299C4—81no—
300C4—1222no—
301C4—1222no—
302C4—1222no—
303C4—1222no—
304C4—4881no—
305C4—2442no—
306C2#2146106111yescharacteristic
307C2#2146111911yescharacteristic
308C2#2146112211yescharacteristic
309C2#2146123811yescharacteristic
310C2#2146124111yescharacteristic
311C2#2146131011yescharacteristic
312C2#2146134811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
27. #14519776C8semidirect
179. C61#7604semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606382
#214606372
C4×#145197762
#760461