Finite Group Databasebeta

← #30597785

Subgroups — #30597785

Order 15616.

444 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 116 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#21461536C211yesmaximal, characteristic
2#21461536C211yesmaximal, characteristic
3C2×#16840619C212yesmaximal
4#21460695C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×#14519832C2212yes—
7C2×#14519832C2212yes—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840619C418yescomplemented
13C2×#14519768C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839647—21no—
16#16839643—21no—
17#16839627C2211yescharacteristic
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519832—22no—
27#14519832—22no—
28#14519832C2×C414yes—
29#14519832C2×C414yes—
30#14519768—22no—
31#14519768C2×C414yes—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×#92420—24no—
67C2×#92420—24no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61C4212yes—
76C42×C61—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—24no—
79C4⋊Dic61—41no—
80C4⋊Dic61C4212yes—
81#11758196—24no—
82#11758196—42no—
83C4×Dic61—22no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61—42no—
89C4×Dic61—42no—
90C4×Dic61C22×C412yes—
91C4×Dic61#4112yes—
92C23×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61C2×C4211yescharacteristic
108C2×C4×C61#11711yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61#10112yes—
125C2×Dic61C4×D412yes—
126C2×Dic61C4×D412yes—
127#92420—44no—
128#92420—44no—
129#8225—611nomaximal, Sylow
130C22×C61C4×C22⋊C411yescharacteristic
131C22×C61C2×#10111yescharacteristic
132C22×C61#41311yescharacteristic
133C22×C61#42111yescharacteristic
134C22×C61#42111yescharacteristic
135C22×C61#42111yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—42no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—81no—
143Dic61—22no—
144Dic61—22no—
145Dic61—22no—
146Dic61—41no—
147Dic61—42no—
148Dic61—81no—
149C4×#125—611no—
150#1745—611no—
151#1745—611no—
152C2×#330—612no—
153#1295—612no—
154C2×C61#153411yescharacteristic
155C2×C61#153511yescharacteristic
156C2×C61#153511yescharacteristic
157C2×C61#153711yescharacteristic
158C2×C61C4×#10111yescharacteristic
159C2×C61#175911yescharacteristic
160C2×C61#175911yescharacteristic
161C2×#125—611no—
162C2×#97—612no—
163C2×#97—612no—
164#389—611no—
165#389#692311yescharacteristic
166#387—1221no—
167#387—1221no—
168#382—611no—
169C4×C4⋊C4—611no—
170C4×C4⋊C4—611no—
171C4×C4⋊C4—1221no—
172C4×C4⋊C4—1221no—
173C43—611no—
174#336—1221no—
175#336—1221no—
176#336—1221no—
177#336—1221no—
178#330—618no—
179C61#822511yescharacteristic, complemented, Sylow
180C22×C8—1222no—
181C22×C8—1222no—
182#125—614no—
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
201#97—614no—
202#97—614no—
203#97—1222no—
204#97—1222no—
205#95—21no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
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—1224no—
223C2×C8—1224no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—612no—
232C4⋊C4—1224no—
233C4⋊C4—1224no—
234C4⋊C4—1221no—
235C4⋊C4—2441no—
236C4⋊C4—2442no—
237C4⋊C4C4×#692312yes—
238C42—41no—
239C42—612no—
240C42—612no—
241C42—1222no—
242C42—2441no—
243C42—2441no—
244C42—2441no—
245C42—2441no—
246C42—2442no—
247C42—2442no—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—612no—
264C2×C4—612no—
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—1221no—
275C2×C4—1222no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4C2×C4×#692311yescharacteristic
282C2×C4#1451985611yescharacteristic
283C8—2444no—
284C8—2444no—
285C22C4×C22⋊#692311yescharacteristic
286C22D61⋊#10111yescharacteristic
287C22#1684074911yescharacteristic
288C22#1684075911yescharacteristic
289C22#1684075911yescharacteristic
290C22#1684076011yescharacteristic
291C22#1684076111yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—42no—
297C4—81no—
298C4—1222no—
299C4—1222no—
300C4—1222no—
301C4—4881no—
302C4—2441no—
303C4—2442no—
304C2#2146130211yescharacteristic
305C2#2146130411yescharacteristic
306C2#2146130611yescharacteristic
307C2#2146131111yescharacteristic
308C2#2146157211yescharacteristic
309C2#2146158211yescharacteristic
310C2#2146158311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8225
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. #16840619C4semidirect
179. C61#8225semidirect

Maximal subgroups

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

subgroupindex
#214615362
C2×#168406192
#214606952
#214483782
#822561