Finite Group Databasebeta

← #30604333

Subgroups — #30604333

Order 15616.

480 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461076C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460762C214yesmaximal, complemented
4#21450773C211yesmaximal, characteristic
5#16840733—21no—
6D61⋊(C22⋊C8)—21no—
7#16840607C2212yes—
8#16840607C2212yes—
9#16840606—21no—
10#16840606—21no—
11C2×#14519753—21no—
12C2×#14519753—21no—
13C2×C4×D244C2211yescharacteristic
14#16839697—21no—
15#16839697—21no—
16#16839663C412yes—
17#16839631C2212yes—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758213—41no—
21C2×D61⋊C8—41no—
22#14519834—41no—
23#14519834—41no—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26C22×D244C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519753—44no—
30#14519753—44no—
31C4×D244—41no—
32C4×D244—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2311yescharacteristic
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198D411yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61C2×C412yes—
42#14519684—21no—
43C22×Q8×C61—21no—
44C4⋊Q8×C61—41no—
45C4⋊Q8×C61—41no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C412yes—
48C2×C42×C61C2×C411yescharacteristic
49C23×D61C22⋊C411yescharacteristic
50C23×D61C22⋊C411yescharacteristic
51C2×Q8×C61—42no—
52C2×Q8×C61—42no—
53C2×Q8×C61—41no—
54C2×Q8×C61—41no—
55C22×C4×C61—22no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—22no—
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×D244—22no—
63C2×D244—22no—
64C2×D244—41no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73#11758213—82no—
74D61⋊C8—82no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—21no—
79#11758198—41no—
80#11758198—41no—
81#11758198—44no—
82#11758198—44no—
83C4⋊Dic61—24no—
84C4⋊Dic61—41no—
85#11758196—44no—
86#11758196—44no—
87C4×Dic61—24no—
88C23×C61C2×C22⋊C411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—41no—
95C22×D61—41no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61#10112yes—
99Q8×C61—82no—
100Q8×C61—82no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61#9911yescharacteristic
111C2×C4×C61#13112yes—
112C2×Dic61—24no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119D244—44no—
120C4×D61—42no—
121C4×D61—42no—
122C4×D61—81no—
123C4×D61—81no—
124#92420—82no—
125#92420—82no—
126#11570—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61#40811yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C22×C61C2×#10111yescharacteristic
132C2×D61—22no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—81no—
141C2×D61—81no—
142C4×C61—21no—
143C4×C61—22no—
144C4×C61—41no—
145C4×C61—82no—
146C4×C61#35312yes—
147Dic61—44no—
148Dic61—41no—
149Dic61—41no—
150#2542—611no—
151#1465—611no—
152#1459—611no—
153#1325—614no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#147211yescharacteristic
157C2×C61C2×#35311yescharacteristic
158C2×C61#213511yescharacteristic
159D61—42no—
160D61—81no—
161C2×C4⋊Q8#692311yescharacteristic
162C2×C22⋊Q8—1221no—
163C2×C22⋊Q8—1221no—
164C2×C4×D4—611no—
165#407—1221no—
166C2×C22⋊C8—1221no—
167#399—1221no—
168#399—1221no—
169#390—612no—
170#384—612no—
171C4×C4⋊C4—611no—
172#324—612no—
173#324—612no—
174#323—1221no—
175#323—1221no—
176C61#1157011yescharacteristic, complemented, Sylow
177C22×Q8—21no—
178C22×D4—611no—
179C23×C4—611no—
180C23×C4—611no—
181C2×M16—2441no—
182C22×C8—2441no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185C22⋊Q8—2444no—
186C22⋊Q8—2444no—
187C4×D4—2441no—
188C4×D4—2441no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1222no—
193C2×C4⋊C4—1222no—
194C2×C4⋊C4C2×#692312yes—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—1222no—
198C2×C22⋊C4—1222no—
199C2×C42—612no—
200C2×C42C2×#692311yescharacteristic
201C22⋊C8—1222no—
202C22⋊C8—1222no—
203C22⋊C8—2441no—
204C22⋊C8—2441no—
205#95—1221no—
206C24—611no—
207C24—611no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×D4—1222no—
213C2×D4—1222no—
214C2×D4—2441no—
215C22×C4—22no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1222no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—2442no—
224C22×C4—2442no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228M16—4882no—
229C2×C8—4882no—
230C2×C8—2442no—
231C2×C8—2442no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—1224no—
235C4⋊C4—2441no—
236C4⋊C4—2444no—
237C4⋊C4—2444no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2444no—
241C22⋊C4—2444no—
242C42—21no—
243C42—21no—
244C42—1224no—
245C23—612no—
246C23—1221no—
247C23—1221no—
248C23—1221no—
249C23—1221no—
250C23—1221no—
251C23—2441no—
252C23—2441no—
253C23—2441no—
254C23—2441no—
255C23C2×C22⋊#692311yescharacteristic
256Q8—82no—
257Q8—82no—
258D4—2444no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—1224no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—4881no—
271C2×C4—4881no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451983511yescharacteristic
279C2×C4#1451983511yescharacteristic
280C2×C4#1451986512yes—
281C8—4882no—
282C8—4882no—
283C22—21no—
284C22—21no—
285C22—1222no—
286C22—4881no—
287C22—4881no—
288C22—2442no—
289C22—2442no—
290C22—2441no—
291C22—2441no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22#1684073711yescharacteristic
296C22C2×#1451983511yescharacteristic
297C22D61⋊#10111yescharacteristic
298C4—21no—
299C4—22no—
300C4—41no—
301C4—82no—
302C4—2444no—
303C4—2441no—
304C4—2441no—
305C4#1684066612yes—
306C2—21no—
307C2—21no—
308C2—4881no—
309C2—2442no—
310C2#2146109911yescharacteristic
311C2C2×#1684066611yescharacteristic
312C2#2146212111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11570
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460762C2semidirect
176. C61#11570semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214610562
#214607622
#214507732
#1157061