Finite Group Databasebeta

← #30602157

Subgroups — #30602157

Order 15616.

434 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461734C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4×#92420C2212yes—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12C2×#14519768C411yescharacteristic
13#16839660C411yescharacteristic
14#16839647—21no—
15#16839643—21no—
16#16839627C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4×#92420—22no—
27C4×#92420Q814yes—
28#14519768—22no—
29#14519768—22no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
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—
47#14519684—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61M1612yes—
74C42×C61—22no—
75C4⋊Dic61—24no—
76C4⋊Dic61—21no—
77C4⋊Dic61—22no—
78C4⋊Dic61M1612yes—
79#11758196—24no—
80#11758196—42no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—42no—
88C4×Dic61—42no—
89C4×Dic61C2×Q812yes—
90C4×Dic61#4112yes—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C4×Q812yes—
105C2×C4×C61C2×M1611yescharacteristic
106C2×C4×C61C2×M1611yescharacteristic
107C2×C4×C61#13112yes—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61C22⋊Q812yes—
123C2×Dic61#12411yescharacteristic
124C2×Dic61C4⋊Q811yescharacteristic
125C2×Dic61#13512yes—
126C2×Dic61#13512yes—
127#92420—44no—
128#92420—82no—
129#9875—611nomaximal, Sylow
130C22×C61#39111yescharacteristic
131C22×C61#40711yescharacteristic
132C22×C61#40811yescharacteristic
133C22×C61#41611yescharacteristic
134C22×C61#41611yescharacteristic
135C22×C61#42111yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—41no—
138C4×C61—41no—
139C4×C61—42no—
140C4×C61—81no—
141C4×C61#44612yes—
142C4×C61#44612yes—
143Dic61—22no—
144Dic61—41no—
145Dic61—41no—
146Dic61—42no—
147Dic61—81no—
148Dic61#48812yes—
149Dic61#49912yes—
150C4×#125—611no—
151#1831—611no—
152#1744—611no—
153#1279—612no—
154#1279—612no—
155C2×C61#148211yescharacteristic
156C2×C61#148211yescharacteristic
157C2×C61#148811yescharacteristic
158C2×C61#148811yescharacteristic
159C2×C61#198511yescharacteristic
160C2×C61#199111yescharacteristic
161C2×C61#199511yescharacteristic
162C2×#125—611no—
163C2×C4⋊C8—612no—
164C2×C4×C8—612no—
165#389—611no—
166#389#692311yescharacteristic
167#387—1221no—
168#387—1221no—
169#382—611no—
170C4×C4⋊C4—611no—
171C4×C4⋊C4—611no—
172C4×C4⋊C4—1221no—
173C4×C4⋊C4—1221no—
174C43—611no—
175#336—1221no—
176#336—1221no—
177#336—1221no—
178#336—1221no—
179C61#987511yescharacteristic, complemented, Sylow
180C22×C8—1222no—
181C22×C8—1222no—
182#125—1222no—
183#125—1222no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—611no—
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—614no—
203C4×C8—1222no—
204#95—21no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22×#692311yescharacteristic
221C2×C8—1224no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C4⋊C4—21no—
228C4⋊C4—22no—
229C4⋊C4—42no—
230C4⋊C4—612no—
231C4⋊C4—1224no—
232C4⋊C4—1224no—
233C4⋊C4—1221no—
234C4⋊C4—1222no—
235C4⋊C4—2442no—
236C4⋊C4#1175821312yes—
237C42—22no—
238C42—612no—
239C42—612no—
240C42—1222no—
241C42—1222no—
242C42—1221no—
243C42—1221no—
244C42—2441no—
245C42—2441no—
246C42—2442no—
247C42—2442no—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—612no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4Q8×#692312yes—
281C2×C4D61⋊M1611yescharacteristic
282C2×C4C2×#1175821311yescharacteristic
283C2×C4#1451986412yes—
284C8—4882no—
285C8—2444no—
286C22(C2×#6923)⋊Q811yescharacteristic
287C22#1684073311yescharacteristic
288C22#1684073511yescharacteristic
289C22#1684075211yescharacteristic
290C22#1684075211yescharacteristic
291C22#1684076011yescharacteristic
292C22#1684076111yescharacteristic
293C4—41no—
294C4—41no—
295C4—42no—
296C4—81no—
297C4—612no—
298C4—612no—
299C4—1222no—
300C4—4881no—
301C4—2441no—
302C4—2441no—
303C4—2442no—
304C4#1684081212yes—
305C4#1684081412yes—
306C2#2146113011yescharacteristic
307C2#2146113211yescharacteristic
308C2#2146115111yescharacteristic
309C2#2146115311yescharacteristic
310C2#2146199211yescharacteristic
311C2#2146200111yescharacteristic
312C2#2146200711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9875
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
179. C61#9875semidirect

Maximal subgroups

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

subgroupindex
#214617342
#214615342
#214606552
#214483782
#987561