Finite Group Databasebeta

← #29591167

Subgroups — #29591167

Order 15616.

372 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 103 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#21445815C211yesmaximal, characteristic
2#21444143C211yesmaximal, characteristic
3#21443849C212yesmaximal
4#21443846C212yesmaximal
5C61×#2581C211yesmaximal, characteristic
6#16839815—21no—
7#16839786—21no—
8C2×#14519696—21no—
9#16839531C2212yes—
10#16839488—21no—
11#16839488C2212yes—
12C2×C4×Q8×C61C411yescharacteristic
13C2×C4×Q8×C61C2211yescharacteristic
14C61×#400C411yescharacteristic
15C61×#400C2211yescharacteristic
16C61×#395C411yescharacteristic
17C61×#395C2211yescharacteristic
18C61×#391—21no—
19C61×#389—21no—
20C61×#387—21no—
21C61×#387—21no—
22C61×#382C411yescharacteristic
23C2×#11758194—22no—
24C4⋊#92418—41no—
25C4⋊#92418—41no—
26C4⋊#92418—41no—
27#14519696—42no—
28C22⋊#92418—22no—
29C4×#92418—41no—
30C22×Q8×C61C2×C411yescharacteristic
31C22×Q8×C61D411yescharacteristic
32C4×Q8×C61—41no—
33C4×Q8×C61—41no—
34C4×Q8×C61—41no—
35C4×Q8×C61—41no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C42×C61—21no—
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C2×Q8×C61—41no—
58C2×Q8×C61—41no—
59C2×Q8×C61—42no—
60C2×Q8×C61—41no—
61C2×Q8×C61SD1612yes—
62C2×Q8×C61Q1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—42no—
90#11758194—42no—
91#11758194—42no—
92C2×#92418—42no—
93C2×#92418—42no—
94C23×C61C2×C22⋊C411yescharacteristic
95Q8×C61—42no—
96Q8×C61—42no—
97Q8×C61—42no—
98Q8×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#9911yescharacteristic
124C2×C4×C61#9911yescharacteristic
125C2×C4×C61#10312yes—
126C2×C4×C61#10312yes—
127C2×C4×C61C2×SD1611yescharacteristic
128C2×C4×C61C2×Q1611yescharacteristic
129#92418—82no—
130#92418—82no—
131#11905—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10311yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—42no—
146C4×C61—41no—
147C4×C61—81no—
148C4×C61—81no—
149C4×C61—81no—
150#2581D6111yescharacteristic
151#1801—611no—
152#1461—611no—
153#1354—612no—
154#1353—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61#152011yescharacteristic
158C2×C61#212011yescharacteristic
159C2×C61#213311yescharacteristic
160C2×C4×Q8Dic6111yescharacteristic
161C2×C4×Q8C2×D6111yescharacteristic
162#431—1221no—
163#423—1221no—
164C2×#101—1221no—
165#400Dic6111yescharacteristic
166#400C2×D6111yescharacteristic
167#395Dic6111yescharacteristic
168#395C2×D6111yescharacteristic
169#391—21no—
170#389—21no—
171#387—21no—
172#387—21no—
173#382Dic6111yescharacteristic
174#343—612no—
175#324—612no—
176#324—1221no—
177C61#1190511yescharacteristic, complemented, Sylow
178C22×Q8C2×Dic6111yescharacteristic
179C22×Q8C22⋊D6111yescharacteristic
180C2×M16—1222no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic6111yescharacteristic
190C2×C4⋊C4C2×Dic6111yescharacteristic
191C2×C4⋊C4C22⋊D6111yescharacteristic
192C2×C4⋊C4C22×D6111yescharacteristic
193C2×C42—21no—
194C2×C42C2×Dic6111yescharacteristic
195C2×C42C22⋊D6111yescharacteristic
196C2×C42C22⋊D6111yescharacteristic
197C4⋊C8—2441no—
198C4⋊C8—2441no—
199C4⋊C8—2441no—
200#101—2442no—
201C22⋊C8—1222no—
202C4×C8—2441no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95C2×Dic6111yescharacteristic
211#95C2×Dic6111yescharacteristic
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C2×Q8#1175820112yes—
217C2×Q8#1175820212yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic6111yescharacteristic
223C22×C4C22⋊Dic6111yescharacteristic
224C22×C4C22⋊Dic6111yescharacteristic
225C22×C4C22⋊Dic6111yescharacteristic
226C22×C4C22×Dic6111yescharacteristic
227C22×C4C2×C22⋊D6111yescharacteristic
228C22×C4C2×C22⋊D6111yescharacteristic
229M16—2442no—
230M16—2442no—
231C2×C8—2442no—
232C2×C8—2442no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—42no—
249C23C2×C22⋊Dic6111yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#1451969211yescharacteristic
279C2×C4#1451969211yescharacteristic
280C2×C4#1451970112yes—
281C2×C4#1451970112yes—
282C2×C4C2×#1175820111yescharacteristic
283C2×C4C2×#1175820211yescharacteristic
284C8—4882no—
285C8—4882no—
286C22—21no—
287C22—21no—
288C22C2×#1451969211yescharacteristic
289C22C2×#1451970111yescharacteristic
290C22#1683977911yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—42no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2#2144439111yescharacteristic
307C2#2144746011yescharacteristic
308C2#2144750811yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2581C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2581D61
hypocenterC61#11905
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
177. C61#11905semidirect

Maximal subgroups

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

subgroupindex
#214458152
#214441432
#214438492
#214438462
C61×#25812
#1190561