Finite Group Databasebeta

← #30604267

Subgroups — #30604267

Order 15616.

398 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461068C211yesmaximal, characteristic
2D61⋊#324C211yesmaximal, characteristic
3#21460760C212yesmaximal, complemented
4#21460750C212yesmaximal, complemented
5#21450301C211yesmaximal, characteristic
6#16840733—21no—
7D61⋊(C22⋊C8)—21no—
8#16840608—21no—
9#16840608—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C2×#14519757C411yescharacteristic
13C2×C4⋊C4×D61C2211yescharacteristic
14#16839704—21no—
15#16839704—21no—
16#16839668C2211yescharacteristic
17#16839667C411yescharacteristic
18#16839627C2211yescharacteristic
19#16839624—21no—
20#16839624—21no—
21C4×#11758198C411yescharacteristic
22C61×#382C411yescharacteristic
23C2×#11758213—41no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C22×Dic122C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519757—41no—
34#14519757—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2311yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×#11758196D411yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56C23×D61C22⋊C411yescharacteristic
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×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—22no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×Dic122—22no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×#92420—42no—
81C2×#92420—42no—
82#11758213—82no—
83D61⋊C8—82no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—41no—
87#11758198—42no—
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—22no—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—22no—
99C22×D61—41no—
100C22×D61#9911yescharacteristic
101C22×D61#9911yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
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—42no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#13112yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
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—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61—42no—
130C4×D61—42no—
131C4×D61—81no—
132C4×D61—81no—
133Dic122—82no—
134#92420—82no—
135#92420—82no—
136#11551—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#40811yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C22×C61#41311yescharacteristic
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—42no—
148C2×D61—42no—
149C2×D61#35412yes—
150C4×C61—22no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—81no—
154C4×C61—81no—
155Dic61—41no—
156Dic61—41no—
157Dic61—41no—
158Dic61—81no—
159Dic61—81no—
160#2503—611no—
161#1463—611no—
162C2×#324—611no—
163#1324—612no—
164#1319—612no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61#146811yescharacteristic
168C2×C61C2×#35411yescharacteristic
169C2×C61#213311yescharacteristic
170D61—22no—
171D61—41no—
172C2×C22⋊Q8—611no—
173C22×C4⋊C4—611no—
174#407—1221no—
175C2×C22⋊C8—1221no—
176#400—1221no—
177#400—1221no—
178#391—611no—
179#391—611no—
180#382—611no—
181#382#692311yescharacteristic
182#381—1221no—
183#381—1221no—
184C4×C22⋊C4—611no—
185#324—612no—
186#324—612no—
187#324—1221no—
188#324—1221no—
189C61#1155111yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C23×C4—611no—
192C23×C4—611no—
193C23×C4—611no—
194C2×M16—2441no—
195C22×C8—2441no—
196C22⋊Q8—2441no—
197C22⋊Q8—2441no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—2441no—
203C2×C4⋊C4—2441no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C22⋊C4—1221no—
207C2×C22⋊C4—1221no—
208C2×C42—611no—
209C2×C42C2×#692311yescharacteristic
210C22⋊C8—1222no—
211C22⋊C8—1222no—
212C22⋊C8—2441no—
213C22⋊C8—2441no—
214#95—21no—
215#95—21no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223C24—611no—
224C2×Q8—1222no—
225C2×Q8—2441no—
226C2×Q8—2441no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1222no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—2441no—
242C22×C4—2442no—
243C22×C4—2442no—
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22×#692311yescharacteristic
247M16—4882no—
248C2×C8—4882no—
249C2×C8—2442no—
250C2×C8—2442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2442no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C22⋊C4—2442no—
260C42—41no—
261C42—1222no—
262C23—611no—
263C23—611no—
264C23—1222no—
265C23—1221no—
266C23—1221no—
267C23—2441no—
268C23C2×C22⋊#692311yescharacteristic
269Q8—4882no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—4881no—
287C2×C4—4881no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451986512yes—
301C8—4882no—
302C8—4882no—
303C22—21no—
304C22—21no—
305C22—612no—
306C22—1221no—
307C22—1221no—
308C22—1221no—
309C22—1221no—
310C22—1221no—
311C22—2442no—
312C22—2442no—
313C22#1684073711yescharacteristic
314C22D61⋊#9911yescharacteristic
315C22#1684074811yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—81no—
320C4—81no—
321C4—4881no—
322C4—4881no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C2—21no—
327C2—21no—
328C2—1222no—
329C2—2441no—
330C2#2146108711yescharacteristic
331C2D61⋊#35411yescharacteristic
332C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#382#6923
hypocenterC61#11551
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #21460760C2semidirect
4. #21460750C2semidirect
189. C61#11551semidirect

Maximal subgroups

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

subgroupindex
#214610682
D61⋊#3242
#214607602
#214607502
#214503012
#1155161