Finite Group Databasebeta

← #30594149

Subgroups — #30594149

Order 15616.

412 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 76 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#21460657C211yesmaximal, characteristic
2#21460657C211yesmaximal, characteristic
3#21444082C211yesmaximal, characteristic
4C2×C22⋊#92420—21no—
5C2×C22⋊#92420—21no—
6C22×#11758196—21no—
7C2×#14519684—21no—
8C2×#14519684C411yescharacteristic
9C2×#14519684C2211yescharacteristic
10C22×C4⋊C4×C61C411yescharacteristic
11C22×#92420—41no—
12C22×#92420—41no—
13C22⋊#92420—22no—
14C22⋊#92420—22no—
15C22⋊#92420—41no—
16C22⋊#92420—41no—
17C23×Dic61—21no—
18C23×Dic61D411yescharacteristic
19C23×Dic61D411yescharacteristic
20C2×#11758196—42no—
21C2×#11758196—42no—
22C2×#11758196—41no—
23C2×#11758196—41no—
24#14519684—21no—
25#14519684—41no—
26#14519684—42no—
27#14519684C812yescomplemented
28C23×C4×C61—21no—
29C23×C4×C61C2×C411yescharacteristic
30C2×C4⋊C4×C61—41no—
31C2×C4⋊C4×C61—42no—
32C24×C61C22⋊C411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61—22no—
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61—41no—
39C22×C4×C61—41no—
40C22×C4×C61—41no—
41C22×C4×C61—41no—
42C22×C4×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61C2×C811yescharacteristic
45C22×C4×C61M1611yescharacteristic
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61—41no—
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61—41no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61D811yescharacteristic
62C22×Dic61SD1611yescharacteristic
63C22×Dic61SD1611yescharacteristic
64C22×Dic61Q1611yescharacteristic
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—81no—
68C2×#92420—81no—
69C2×#92420—81no—
70C2×#92420—81no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73#11758196—44no—
74#11758196—44no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61C22⋊C811yescharacteristic
80C23×C61#9911yescharacteristic
81C23×C61#10111yescharacteristic
82C23×C61#10211yescharacteristic
83C23×C61#10311yescharacteristic
84C23×C61#10411yescharacteristic
85C23×C61#10411yescharacteristic
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—81no—
97C2×C4×C61—81no—
98C2×C4×C61—81no—
99C2×C4×C61—81no—
100C2×Dic61—24no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—81no—
120C2×Dic61—81no—
121#92420—82no—
122#92420—82no—
123#7123—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61#32411yescharacteristic
137C22×C61D4⋊C811yescharacteristic
138C22×C61Q8⋊C811yescharacteristic
139C22×C61#32711yescharacteristic
140C22×C61#32811yescharacteristic
141C22×C61#33011yescharacteristic
142C22×C61#33211yescharacteristic
143C22×C61AΣL(1,𝔽16)11yescharacteristic
144C22×C61#35211yescharacteristic
145C22×C61#35311yescharacteristic
146C22×C61#35611yescharacteristic
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—82no—
150Dic61—44no—
151Dic61—41no—
152Dic61—41no—
153Dic61—41no—
154Dic61—41no—
155#1444—611no—
156#1280—611no—
157#1280—611no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#127111yescharacteristic
163C2×C61#132511yescharacteristic
164C2×C61#132611yescharacteristic
165C2×C61#134311yescharacteristic
166C2×C61#134611yescharacteristic
167C2×C61#135211yescharacteristic
168C2×C61#135411yescharacteristic
169C22×C4⋊C4—1221no—
170C22×C4⋊C4#692311yescharacteristic
171C2×C22⋊C8—1221no—
172C2×C22⋊C8—1221no—
173C2×#95—611no—
174C2×#95—611no—
175C2×#95—1221no—
176C61#712311yescharacteristic, complemented, Sylow
177C23×C4—21no—
178C23×C4—611no—
179C23×C4—611no—
180C23×C4—1221no—
181C23×C4C2×#692311yescharacteristic
182C22×C8—2441no—
183C22×C8—2441no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—2442no—
187C2×C4⋊C4—2441no—
188C2×C4⋊C4—2441no—
189C2×C4⋊C4—2442no—
190C22⋊C8—1222no—
191C22⋊C8—1222no—
192C22⋊C8—2441no—
193C22⋊C8—2441no—
194#95—612no—
195#95—1221no—
196#95—2441no—
197#95—2442no—
198C24C22⋊#692311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1222no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—2441no—
222C22×C4—2441no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4—2441no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4D61⋊C811yescharacteristic
230C22×C4#1175821311yescharacteristic
231C2×C8—4881no—
232C2×C8—4881no—
233C2×C8—4881no—
234C2×C8—4881no—
235C2×C8—2442no—
236C2×C8—2442no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—2444no—
240C4⋊C4—2444no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23#1451983411yescharacteristic
246C23#1451983511yescharacteristic
247C23#1451983811yescharacteristic
248C23#1451983911yescharacteristic
249C23#1451984011yescharacteristic
250C23#1451984111yescharacteristic
251C23#1451984211yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—1224no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—4881no—
272C2×C4—4881no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2442no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C8—4882no—
288C8—4882no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22#1684060811yescharacteristic
302C22#1684061011yescharacteristic
303C22#1684061211yescharacteristic
304C22#1684061311yescharacteristic
305C22#1684061611yescharacteristic
306C22#1684061911yescharacteristic
307C22#1684062111yescharacteristic
308C22#1684066211yescharacteristic
309C22#1684066411yescharacteristic
310C22#1684066611yescharacteristic
311C22#1684067211yescharacteristic
312C4—41no—
313C4—41no—
314C4—82no—
315C4—2444no—
316C4—2441no—
317C4—2441no—
318C4—2441no—
319C4—2441no—
320C2—21no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2#2146063811yescharacteristic
325C2#2146076211yescharacteristic
326C2#2146076411yescharacteristic
327C2#2146079711yescharacteristic
328C2#2146080311yescharacteristic
329C2#2146081611yescharacteristic
330C2#2146082011yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#14519684C22
hypercenterC22×C4⋊C4#6923
hypocenterC61#7123
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
27. #14519684C8semidirect
176. C61#7123semidirect

Maximal subgroups

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

subgroupindex
#214606572
#214440822
#712361