Finite Group Databasebeta

← #30595694

Subgroups — #30595694

Order 15616.

426 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461735C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5#21454178C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519767—21no—
13#16839661C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839659—21no—
16#16839658C2211yescharacteristic
17#16839657—21no—
18#16839631C411yescharacteristic
19#16839631C411yescharacteristic
20#16839626—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4⋊#92420—24no—
27C4×#92420—42no—
28#14519767—42no—
29#14519767—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—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—
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—22no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—42no—
73C42×C61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—42no—
79#11758196—42no—
80#11758196—42no—
81#11758196—42no—
82#11758196—42no—
83#11758196—41no—
84#11758196—41no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61D812yes—
90C4×Dic61SD1612yes—
91C4×Dic61SD1612yes—
92C4×Dic61Q1612yes—
93C23×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#10212yes—
107C2×C4×C61#10312yes—
108C2×C4×C61#13112yes—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61#10112yes—
122C2×Dic61#10212yes—
123C2×Dic61#10312yes—
124C2×Dic61#10412yes—
125C2×Dic61C2×D811yescharacteristic
126C2×Dic61C2×SD1611yescharacteristic
127C2×Dic61C2×SD1611yescharacteristic
128C2×Dic61C2×Q1611yescharacteristic
129#92420—44no—
130#92420—82no—
131#7663—611nomaximal, Sylow
132C22×C61#40811yescharacteristic
133C22×C61#41011yescharacteristic
134C22×C61C2×#10111yescharacteristic
135C22×C61C2×#10211yescharacteristic
136C22×C61C2×#10311yescharacteristic
137C22×C61C2×#10411yescharacteristic
138C22×C61#42111yescharacteristic
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—81no—
143C4×C61—81no—
144Dic61—21no—
145Dic61—21no—
146Dic61—21no—
147Dic61—21no—
148Dic61—22no—
149Dic61—81no—
150Dic61—81no—
151Dic61#33214yes—
152#2859—611no—
153#1831—611no—
154C4×C4⋊C8—611no—
155#1271—612no—
156#1271—612no—
157C2×C61#147011yescharacteristic
158C2×C61#148011yescharacteristic
159C2×C61#149311yescharacteristic
160C2×C61#150211yescharacteristic
161C2×C61#151811yescharacteristic
162C2×C61#152811yescharacteristic
163C2×C61C2×#33211yescharacteristic
164C2×#125—1221no—
165C2×C4⋊C8—1221no—
166C2×C4⋊C8—1221no—
167C2×C4×C8—1221no—
168#389—611no—
169#389—611no—
170#389—611no—
171#389—1221no—
172#389—1221no—
173#389#692311yescharacteristic
174#384—611no—
175#384—611no—
176#382—1221no—
177C43—611no—
178#336—612no—
179#336—612no—
180#336—1221no—
181C61#766311yescharacteristic, complemented, Sylow
182C22×C8—1222no—
183C22×C8—1222no—
184#125—2442no—
185#125—2442no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42C2×#692311yescharacteristic
205C4⋊C8—1224no—
206C4⋊C8—2442no—
207C4×C8—2442no—
208#95—21no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4C22⋊#692311yescharacteristic
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22×#692311yescharacteristic
223C2×C8—1224no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C2×C8—2442no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—1222no—
233C4⋊C4—2441no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C4⋊C4—2442no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C42—22no—
244C42—612no—
245C42—612no—
246C42—612no—
247C42—612no—
248C42—1222no—
249C42—1222no—
250C42—2441no—
251C42—2441no—
252C23C2×C22⋊#692311yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—612no—
266C2×C4—612no—
267C2×C4—612no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—612no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4#1451983912yes—
286C2×C4#1451984012yes—
287C2×C4#1451986412yes—
288C8—4882no—
289C8—2444no—
290C22#1684073511yescharacteristic
291C22#1684074111yescharacteristic
292C22D61⋊#10111yescharacteristic
293C22C2×#1451983911yescharacteristic
294C22C2×#1451984011yescharacteristic
295C22D61⋊#10411yescharacteristic
296C22#1684075911yescharacteristic
297C4—22no—
298C4—22no—
299C4—22no—
300C4—81no—
301C4—81no—
302C4—614no—
303C4—1221no—
304C4—1221no—
305C4—1222no—
306C4—1221no—
307C4—1221no—
308C4—4881no—
309C4—4881no—
310C2#2146109111yescharacteristic
311C2#2146112411yescharacteristic
312C2#2146116711yescharacteristic
313C2#2146119811yescharacteristic
314C2#2146125211yescharacteristic
315C2#2146128211yescharacteristic
316C2D61⋊#33211yescharacteristic
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#7663
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
181. C61#7663semidirect

Maximal subgroups

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

subgroupindex
#214617352
C4×C4⋊#924202
#214606382
#214606372
#214541782
#766361