Finite Group Databasebeta

← #30595899

Subgroups — #30595899

Order 15616.

528 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461747C211yesmaximal, characteristic, complemented
2#21461735C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4#21454177C211yesmaximal, characteristic
5C2×#14519844—21no—
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519774C411yescharacteristic
12C2×#14519766—21no—
13C2×#14519766—21no—
14#16839663—21no—
15#16839663—21no—
16#16839663C412yes—
17#16839663C2212yes—
18C42×Dic61C2211yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23C22×D244—21no—
24C22×D244—21no—
25C22×D244C2×C412yes—
26#14519774—42no—
27#14519766—44no—
28#14519766—42no—
29#14519766—42no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40C22×Q8×C61—21no—
41C4⋊Q8×C61—42no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C42×C61C2×C411yescharacteristic
45C23×D61—22no—
46C2×Q8×C61—42no—
47C2×Q8×C61—42no—
48C2×Q8×C61—42no—
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C2×D244—24no—
58C2×D244—42no—
59C2×D244—42no—
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—42no—
65C2×D244—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—42no—
74C42×C61—22no—
75#11758198—44no—
76#11758198—44no—
77#11758198—42no—
78#11758198—42no—
79#11758198—44no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—41no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61D812yes—
86C4×Dic61SD1612yes—
87C23×C61C2×C22⋊C411yescharacteristic
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95Q8×C61—84no—
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—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61#10012yes—
106C2×C4×C61#10212yes—
107C2×C4×C61#13112yes—
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—21no—
117C2×Dic61#10212yes—
118C2×Dic61C2×D811yescharacteristic
119C2×Dic61C2×SD1611yescharacteristic
120C2×Dic61AGL(1,ℤ/8)12yes—
121D244—84no—
122D244—84no—
123D244—84no—
124#92420—82no—
125#92420—82no—
126#7719—611nomaximal, Sylow
127C22×C61#40811yescharacteristic
128C22×C61#41011yescharacteristic
129C22×C61C2×#10011yescharacteristic
130C22×C61C2×#10211yescharacteristic
131C22×C61#41811yescharacteristic
132C22×C61#42111yescharacteristic
133C22×C61#42111yescharacteristic
134C2×D61—82no—
135C2×D61—82no—
136C2×D61—82no—
137C2×D61—82no—
138C2×D61—82no—
139C2×D61—82no—
140C2×D61—82no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—82no—
145Dic61—22no—
146Dic61—22no—
147Dic61—21no—
148Dic61—21no—
149Dic61—41no—
150#2858—611no—
151#1839—611no—
152#1831—611no—
153#1270—614no—
154C2×C61#146911yescharacteristic
155C2×C61#148011yescharacteristic
156C2×C61#149611yescharacteristic
157C2×C61#151411yescharacteristic
158C2×C61#151711yescharacteristic
159C2×C61#153311yescharacteristic
160C2×C61#154511yescharacteristic
161D61—162no—
162C2×C4⋊Q8#692311yescharacteristic
163C2×#127—611no—
164C2×#124—1221no—
165C2×#124—1221no—
166C2×C4⋊C8—1221no—
167#390—612no—
168#390—612no—
169#390—1221no—
170#390—1221no—
171C43—611no—
172#336—612no—
173#336—612no—
174#336—1221no—
175#336—1221no—
176#336—1221no—
177C61#771911yescharacteristic, complemented, Sylow
178C22×Q8—21no—
179C22×D4—612no—
180C22×D4—1221no—
181C22×D4—1221no—
182C22×C8—1222no—
183C22×C8—1222no—
184C4⋊Q8—42no—
185#127—2442no—
186#124—2442no—
187#124—2442no—
188#124—2444no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×#692312yes—
191C2×C22⋊C4—1222no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1222no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42C2×#692311yescharacteristic
202C4⋊C8—2442no—
203C24—1222no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×D4—1224no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2442no—
214C2×D4—2442no—
215C2×D4—2442no—
216C22×C4—22no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22⋊#692311yescharacteristic
223C22×C4C22×#692311yescharacteristic
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C2×C8—2442no—
229C2×C8—2442no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—2444no—
233C22⋊C4—2442no—
234C22⋊C4—2442no—
235C22⋊C4—2444no—
236C22⋊C4—2444no—
237C42—22no—
238C42—612no—
239C42—612no—
240C42—1222no—
241C42—1222no—
242C42—2441no—
243C42—2441no—
244C42—2441no—
245C23—2442no—
246C23—2442no—
247C23—2442no—
248C23—2442no—
249C23—2442no—
250C23—2442no—
251C23—2442no—
252C23C2×C22⋊#692311yescharacteristic
253Q8—84no—
254D4—4884no—
255D4—4884no—
256D4—4884no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—612no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—612no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4#1451983712yes—
280C2×C4#1451983912yes—
281C2×C4#1451986512yes—
282C8—4882no—
283C8—4882no—
284C22—4882no—
285C22—4882no—
286C22—4882no—
287C22—4882no—
288C22—4882no—
289C22—4882no—
290C22—4882no—
291C22#1684073711yescharacteristic
292C22#1684074311yescharacteristic
293C22C2×#1451983711yescharacteristic
294C22C2×#1451983911yescharacteristic
295C22#1684075411yescharacteristic
296C22#1684076111yescharacteristic
297C22#1684076111yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—82no—
302C4—1221no—
303C4—1221no—
304C4—1222no—
305C4—1222no—
306C4—2441no—
307C2—9762no—
308C2#2146109011yescharacteristic
309C2#2146112611yescharacteristic
310C2#2146118011yescharacteristic
311C2#2146124011yescharacteristic
312C2#2146125011yescharacteristic
313C2#2146130011yescharacteristic
314C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7719
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21461735C2semidirect
3. #21460636C2semidirect
177. C61#7719semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617352
#214606362
#214541772
#771961