Finite Group Databasebeta

← #30595774

Subgroups — #30595774

Order 15616.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#14519834C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21460638C214yesmaximal, complemented
4#21454166C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×#14519834—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519753—21no—
12C2×C42×D61C2211yescharacteristic
13#16839669—21no—
14#16839658—21no—
15#16839658C2212yes—
16#16839632C411yescharacteristic
17#16839619—21no—
18#16839619C412yes—
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758213—24no—
21C2×#11758213—42no—
22C2×#11758213—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26C4×#92420—42no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519753—42no—
31#14519753—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C412yes—
35C2×#11758196—22no—
36C2×#11758198—22no—
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40C42×D61—42no—
41#14519684—22no—
42#14519684—22no—
43C22×Q8×C61—21no—
44C4⋊Q8×C61—42no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C42×C61C2×C411yescharacteristic
48C23×D61C22⋊C411yescharacteristic
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C2×Q8×C61—42no—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×C4×D61D812yes—
69C2×C4×D61SD1612yes—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76#11758213—48no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79C42×C61—22no—
80#11758198—44no—
81C4⋊Dic61—24no—
82C4⋊Dic61—42no—
83C4⋊Dic61—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—22no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61#10212yes—
97Q8×C61—84no—
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#9912yes—
106C2×C4×C61#10212yes—
107C2×C4×C61#10412yes—
108C2×C4×C61#10412yes—
109C2×C4×C61#13112yes—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61#10112yes—
120C2×Dic61C2×D811yescharacteristic
121C2×Dic61C2×SD1611yescharacteristic
122C2×Dic61#13712yes—
123C4×D61—24no—
124C4×D61—24no—
125C4×D61—44no—
126C4×D61—44no—
127#92420—44no—
128#92420—44no—
129#7685—611nomaximal, Sylow
130C22×C61#40811yescharacteristic
131C22×C61C2×#9911yescharacteristic
132C22×C61C2×#10111yescharacteristic
133C22×C61C2×#10211yescharacteristic
134C22×C61#41911yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61C2×#10411yescharacteristic
137C2×D61—22no—
138C2×D61—22no—
139C2×D61—22no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—82no—
147C4×C61#32714yes—
148Dic61—22no—
149Dic61—21no—
150Dic61—21no—
151Dic61—22no—
152Dic61—82no—
153#2857—611no—
154C4×C22⋊C8—611no—
155#1728—611no—
156#1271—614no—
157C2×C61#147211yescharacteristic
158C2×C61#148511yescharacteristic
159C2×C61#149211yescharacteristic
160C2×C61C2×#32711yescharacteristic
161C2×C61#150811yescharacteristic
162C2×C61#152611yescharacteristic
163C2×C61#154611yescharacteristic
164D61—42no—
165C22×M16—1221no—
166C2×C4⋊Q8#692311yescharacteristic
167C2×C22⋊Q8—1221no—
168C22×C42—611no—
169C2×C22⋊C8—1221no—
170C2×C4×C8—1221no—
171#391—1221no—
172#389—612no—
173#389—1221no—
174#384—611no—
175#380—612no—
176#380—1221no—
177#336—612no—
178#336—612no—
179#336—1221no—
180C61#768511yescharacteristic, complemented, Sylow
181C22×Q8—21no—
182C23×C4—611no—
183C23×C4—611no—
184C23×C4—611no—
185C2×M16—1224no—
186C2×M16—2442no—
187C2×M16—2442no—
188C22×C8—1222no—
189C22×C8—1222no—
190C4⋊Q8—42no—
191C22⋊Q8—2442no—
192C22⋊Q8—2442no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—612no—
195C2×C4⋊C4—1222no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C2×#692312yes—
199C2×C22⋊C4—1222no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—2442no—
204C2×C42C2×#692311yescharacteristic
205C22⋊C8—1224no—
206C4×C8—2442no—
207#95—1222no—
208#95—1222no—
209C24—611no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—22no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—612no—
218C22×C4—612no—
219C22×C4—1222no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—1222no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—1222no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4C22⋊#692311yescharacteristic
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22×#692311yescharacteristic
231M16—2448no—
232C2×C8—1224no—
233C2×C8—1224no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—1224no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C22⋊C4—2444no—
246C42—22no—
247C42—1222no—
248C42—2441no—
249C42—2441no—
250C23—612no—
251C23—1221no—
252C23—1221no—
253C23—1221no—
254C23—1221no—
255C23—1221no—
256C23—1221no—
257C23C2×C22⋊#692311yescharacteristic
258Q8—84no—
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—1224no—
277C2×C4—1224no—
278C2×C4—2444no—
279C2×C4—2444no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4#1451983512yes—
284C2×C4#1451983912yes—
285C2×C4#1451984112yes—
286C2×C4#1451984212yes—
287C2×C4#1451986512yes—
288C8—2444no—
289C8—2444no—
290C22—1222no—
291C22—1222no—
292C22—1222no—
293C22—2441no—
294C22—2441no—
295C22—2441no—
296C22—2441no—
297C22#1684073711yescharacteristic
298C22C2×#1451983511yescharacteristic
299C22D61⋊#10111yescharacteristic
300C22C2×#1451983911yescharacteristic
301C22#1684075511yescharacteristic
302C22C2×#1451984111yescharacteristic
303C22C2×#1451984211yescharacteristic
304C4—22no—
305C4—22no—
306C4—82no—
307C4—1222no—
308C4—1221no—
309C4—1221no—
310C4—1222no—
311C4—4882no—
312C4#1684061314yes—
313C2—2442no—
314C2#2146109911yescharacteristic
315C2#2146114311yescharacteristic
316C2#2146116611yescharacteristic
317C2C2×#1684061311yescharacteristic
318C2#2146121911yescharacteristic
319C2#2146127711yescharacteristic
320C2#2146132911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7685
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
3. #21460638C2semidirect
180. C61#7685semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614832
#214606382
#214541662
#768561