Finite Group Databasebeta

← #30595424

Subgroups — #30595424

Order 15616.

426 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461746C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460638C212yesmaximal
5#21448374C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519769C411yescharacteristic
13#16839658C2211yescharacteristic
14#16839658C2211yescharacteristic
15#16839644—21no—
16#16839644—21no—
17C4⋊C4×Dic61C411yescharacteristic
18C4⋊C4×Dic61C411yescharacteristic
19#16839613—21no—
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#382C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4×#92420—42no—
27#14519769—22no—
28#14519769C814yescomplemented
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—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—
46#14519684—21no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50#95×C61—21no—
51#95×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×#92420—24no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C2×C812yes—
72C42×C61M1612yes—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2×C812yes—
76C4⋊Dic61C2×C812yes—
77#11758196—24no—
78#11758196—24no—
79#11758196—42no—
80#11758196—41no—
81#11758196—41no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61—42no—
90C4×Dic61—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C22⋊C812yes—
105C2×C4×C61C22⋊C812yes—
106C2×C4×C61C22×C811yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61#10112yes—
123C2×Dic61#10412yes—
124C2×Dic61#13512yes—
125C2×Dic61AGL(1,ℤ/8)11yescharacteristic
126C2×Dic61#13711yescharacteristic
127#92420—44no—
128#92420—82no—
129#7585—611nomaximal, Sylow
130C22×C61C2×C22⋊C811yescharacteristic
131C22×C61#41011yescharacteristic
132C22×C61C2×#10111yescharacteristic
133C22×C61#41611yescharacteristic
134C22×C61#41711yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—81no—
142C4×C61—81no—
143Dic61—22no—
144Dic61—21no—
145Dic61—21no—
146Dic61—22no—
147Dic61—22no—
148Dic61—42no—
149Dic61—42no—
150C4×#125—611no—
151#1839—611no—
152C4×C4⋊C8—611no—
153#1271—612no—
154#1271—612no—
155C2×C61#146111yescharacteristic
156C2×C61#147611yescharacteristic
157C2×C61#147711yescharacteristic
158C2×C61#150911yescharacteristic
159C2×C61#152111yescharacteristic
160C2×C61#152811yescharacteristic
161C2×C61#155211yescharacteristic
162C2×#125—611no—
163C2×C4⋊C8—1221no—
164C2×C4×C8—1221no—
165#389—611no—
166#389—611no—
167#387—1221no—
168#387—1221no—
169#382#692311yescharacteristic
170C4×C4⋊C4—611no—
171C4×C4⋊C4—611no—
172C4×C4⋊C4—1221no—
173C4×C4⋊C4—1221no—
174C43—611no—
175#336—612no—
176#336—612no—
177#336—1221no—
178#336—1221no—
179C61#758511yescharacteristic, complemented, Sylow
180C22×C8—1222no—
181C22×C8—1222no—
182#125—614no—
183#125—1222no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4C2×#692311yescharacteristic
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—1221no—
199C2×C42—1221no—
200C2×C42C2×#692311yescharacteristic
201C4⋊C8—1224no—
202C4×C8—2442no—
203#95—21no—
204#95—21no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4C22⋊#692311yescharacteristic
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22×#692311yescharacteristic
220C2×C8—1224no—
221C2×C8—2442no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—612no—
229C4⋊C4—612no—
230C4⋊C4—1224no—
231C4⋊C4—1224no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—2442no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C42—1221no—
238C42—1222no—
239C42—1222no—
240C42—1222no—
241C42—1221no—
242C42—2441no—
243C42—2441no—
244C42—2442no—
245C42—2442no—
246C42D61⋊C812yes—
247C42#1175821312yes—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—612no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4#1451983412yes—
281C2×C4#1451983412yes—
282C2×C4C2×D61⋊C811yescharacteristic
283C2×C4C2×#1175821311yescharacteristic
284C8—4882no—
285C8—2444no—
286C22C2×#1451983411yescharacteristic
287C22#1684074211yescharacteristic
288C22D61⋊#10111yescharacteristic
289C22#1684075211yescharacteristic
290C22#1684075311yescharacteristic
291C22D61⋊#10411yescharacteristic
292C22#1684075911yescharacteristic
293C4—21no—
294C4—21no—
295C4—22no—
296C4—22no—
297C4—81no—
298C4—81no—
299C4—1222no—
300C4—1222no—
301C4—1222no—
302C4—1221no—
303C4—1221no—
304C4—2442no—
305C4—2442no—
306C2#2146106311yescharacteristic
307C2#2146111211yescharacteristic
308C2#2146111611yescharacteristic
309C2#2146122011yescharacteristic
310C2#2146126011yescharacteristic
311C2#2146128211yescharacteristic
312C2#2146134111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#7585
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
28. #14519769C8semidirect
179. C61#7585semidirect

Maximal subgroups

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

subgroupindex
#214617462
C4×C4⋊#924202
#214606382
#214483742
#758561