Finite Group Databasebeta

← #30595754

Subgroups — #30595754

Order 15616.

572 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461605C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3#21460635C214yesmaximal, complemented
4#21454175C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×#14519832—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12C2×#14519764—21no—
13C2×#14519764—21no—
14#16839665—21no—
15#16839665—21no—
16#16839665C412yes—
17#16839665C2212yes—
18C42×Dic61C2211yescharacteristic
19C2×#127×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—24no—
23#14519832—42no—
24C4×#92420—24no—
25C22×Dic122—21no—
26#14519777—42no—
27#14519764—44no—
28#14519764—42no—
29#14519764—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C412yes—
32C2×C22⋊Dic61—22no—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42C22×D4×C61—21no—
43C22×D4×C61—21no—
44C22×D4×C61C2×C412yes—
45#127×C61—42no—
46C2×C42×C61C2×C411yescharacteristic
47C24×C61—22no—
48C2×D4×C61—24no—
49C2×D4×C61—42no—
50C2×D4×C61—42no—
51C2×D4×C61—42no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—42no—
56C2×D4×C61—42no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—22no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×Dic122—42no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×#92420—24no—
69C2×#92420—24no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C42×C61—22no—
75C22⋊Dic61—44no—
76C22⋊Dic61—44no—
77C22⋊Dic61—42no—
78C22⋊Dic61—42no—
79C22⋊Dic61—44no—
80C4⋊Dic61—42no—
81C4⋊Dic61—42no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—41no—
87C4×Dic61D812yes—
88C4×Dic61SD1612yes—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61—42no—
92C23×C61—42no—
93C23×C61—42no—
94C23×C61—42no—
95C23×C61—42no—
96C23×C61C2×C22⋊C411yescharacteristic
97D4×C61—84no—
98D4×C61—84no—
99D4×C61—84no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61#10012yes—
105C2×C4×C61#10212yes—
106C2×C4×C61#10412yes—
107C2×C4×C61#10412yes—
108C2×C4×C61#13112yes—
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—21no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61#10212yes—
122C2×Dic61C2×D811yescharacteristic
123C2×Dic61C2×SD1611yescharacteristic
124C2×Dic61AGL(1,ℤ/8)12yes—
125Dic122—84no—
126#92420—44no—
127#92420—44no—
128#7679—611nomaximal, Sylow
129C22×C61—82no—
130C22×C61—82no—
131C22×C61—82no—
132C22×C61—82no—
133C22×C61—82no—
134C22×C61—82no—
135C22×C61—82no—
136C22×C61#40811yescharacteristic
137C22×C61#41011yescharacteristic
138C22×C61C2×#10011yescharacteristic
139C22×C61C2×#10211yescharacteristic
140C22×C61#41811yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61C2×#10411yescharacteristic
143C4×C61—22no—
144C4×C61—22no—
145C4×C61#32914yes—
146Dic61—22no—
147Dic61—21no—
148Dic61—21no—
149Dic61—22no—
150Dic61—41no—
151Dic61—82no—
152#2858—611no—
153#1767—611no—
154#1744—611no—
155#1270—614no—
156C2×C61—162no—
157C2×C61#146911yescharacteristic
158C2×C61#148411yescharacteristic
159C2×C61#149211yescharacteristic
160C2×C61#150211yescharacteristic
161C2×C61#150511yescharacteristic
162C2×C61C2×#32911yescharacteristic
163C2×C61#154511yescharacteristic
164C2×C4⋊Q8—611no—
165C2×#127#692311yescharacteristic
166C2×#124—1221no—
167C2×#124—1221no—
168C2×C4⋊C8—1221no—
169C2×#97—1221no—
170C2×C4×C8—1221no—
171#390—612no—
172#390—612no—
173#390—1221no—
174#390—1221no—
175C43—611no—
176#336—612no—
177#336—612no—
178#336—1221no—
179C61#767911yescharacteristic, complemented, Sylow
180C22×Q8—1221no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4C2×#692312yes—
184C22×C8—1222no—
185C22×C8—1222no—
186C4⋊Q8—2442no—
187#127—42no—
188#124—2442no—
189#124—2442no—
190#124—2444no—
191C2×C4⋊C4—612no—
192C2×C4⋊C4—1221no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4—1222no—
196C2×C22⋊C4—1222no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42C2×#692311yescharacteristic
204C4⋊C8—1224no—
205#97—2442no—
206C4×C8—1224no—
207C24—22no—
208C2×Q8—2442no—
209C2×Q8—2442no—
210C2×Q8—2442no—
211C2×D4—24no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1222no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228C2×C8—1224no—
229C2×C8—1224no—
230C2×C8—2442no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8—2442no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C22⋊C4—2444no—
237C22⋊C4—2442no—
238C22⋊C4—2442no—
239C22⋊C4—2444no—
240C22⋊C4—2444no—
241C42—22no—
242C42—612no—
243C42—612no—
244C42—1222no—
245C42—1222no—
246C42—1222no—
247C42—1222no—
248C42—2441no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23C2×C22⋊#692311yescharacteristic
257Q8—4884no—
258D4—84no—
259D4—84no—
260D4—84no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—612no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—612no—
269C2×C4—1221no—
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—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4#1451983712yes—
282C2×C4#1451983912yes—
283C2×C4#1451984112yes—
284C2×C4#1451984112yes—
285C2×C4#1451986412yes—
286C8—2444no—
287C8—2444no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22#1684073611yescharacteristic
296C22#1684074211yescharacteristic
297C22C2×#1451983711yescharacteristic
298C22C2×#1451983911yescharacteristic
299C22#1684075411yescharacteristic
300C22C2×#1451984111yescharacteristic
301C22C2×#1451984111yescharacteristic
302C4—22no—
303C4—22no—
304C4—1222no—
305C4—1221no—
306C4—1221no—
307C4—1222no—
308C4—4882no—
309C4—2441no—
310C4#1684061714yes—
311C2—162no—
312C2#2146108911yescharacteristic
313C2#2146113911yescharacteristic
314C2#2146116511yescharacteristic
315C2#2146119911yescharacteristic
316C2#2146120811yescharacteristic
317C2C2×#1684061711yescharacteristic
318C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#127#6923
hypocenterC61#7679
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21461605C2semidirect
2. #21461534C2semidirect
3. #21460635C2semidirect
179. C61#7679semidirect

Maximal subgroups

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

subgroupindex
#214616052
#214615342
#214606352
#214541752
#767961