Finite Group Databasebeta

← #30594506

Subgroups — #30594506

Order 15616.

372 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461683C211yesmaximal, characteristic
2#21461679C211yesmaximal, characteristic
3#21446109C211yesmaximal, characteristic
4#16840765—21no—
5C2×#14519837—21no—
6C2×#14519835—21no—
7#16840704—21no—
8#16840642C412yescomplemented
9#16840640C412yes—
10C23×#92418C411yescharacteristic, complemented
11C2×C4×C22⋊D61C2211yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C2×C22⋊C8×C61C411yescharacteristic, complemented
15C2×#11758217—22no—
16C2×C4⋊#6923—41no—
17C2×C22⋊#6923—22no—
18#14519844—41no—
19C4⋊#92420—41no—
20#14519837—41no—
21#14519837—41no—
22#14519835—41no—
23#14519835—41no—
24(C2×#6923)⋊C4—41no—
25C22×C22⋊D61D411yescharacteristic
26C22×C4×D61D411yescharacteristic
27C22×#92418—21no—
28C22×#92418—42no—
29C22×#92418—41no—
30C4×C22⋊D61—41no—
31C4×C22⋊D61—41no—
32C2×#11758196C2×C411yescharacteristic
33C2×C22⋊Dic61Q811yescharacteristic
34C2×#11758198C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36#14519689—42no—
37C23×C4×C61C2×C411yescharacteristic
38C22×C8×C61—21no—
39C22⋊C8×C61—41no—
40C24×C61C4⋊C411yescharacteristic
41C23×D61C22⋊C411yescharacteristic
42C22×#6923—42no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61C4211yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C2×C22⋊D61—41no—
50C2×C22⋊D61—41no—
51C2×C22⋊D61D811yescharacteristic
52C2×C22⋊D61SD1611yescharacteristic
53C2×C22⋊D61SD1611yescharacteristic
54C2×C22⋊D61Q1611yescharacteristic
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C4⋊C411yescharacteristic
57C22×Dic61C4⋊C411yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—41no—
61C2×C4×D61—41no—
62C22⋊#6923—42no—
63C22⋊#6923—42no—
64#11758217—42no—
65#11758217—42no—
66C2×#92420—42no—
67C4⋊#6923—81no—
68C4⋊#6923—81no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C22⋊Dic61—41no—
73#11758198—41no—
74#11758196—41no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C2×#92418—22no—
78C2×#92418—41no—
79C2×#92418—42no—
80C2×#92418—41no—
81C2×#92418—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—41no—
85C23×C61—41no—
86C23×C61#9511yescharacteristic
87C23×C61#10611yescharacteristic
88C23×C61#10711yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61#10211yescharacteristic
94C22×D61#10311yescharacteristic
95C2×#6923—82no—
96C2×#6923—82no—
97C2×#6923—82no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—42no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#9911yescharacteristic
107C22⋊D61—41no—
108C22⋊D61—41no—
109C22⋊D61—41no—
110C22⋊D61—41no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61#10211yescharacteristic
118C2×Dic61#10311yescharacteristic
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—81no—
122#92420—82no—
123C8×C61—81no—
124#92418—42no—
125#7236—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—41no—
131C22×C61—41no—
132C22×C61—42no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61H(3,ℤ/4)11yescharacteristic
136C22×C61#34011yescharacteristic
137C22×C61#34211yescharacteristic
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—81no—
145#6923—162no—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61AΣL(1,𝔽16)11yescharacteristic
149C4×C61#35211yescharacteristic
150Dic61—21no—
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154#1869—611no—
155#1800—611no—
156#1799—611no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—41no—
160C2×C61—41no—
161C2×C61#128911yescharacteristic
162C2×C61#139011yescharacteristic
163C2×C61#139511yescharacteristic
164D61—41no—
165D61—41no—
166C23×C8—611no—
167C2×C4×D4—611no—
168#423—1221no—
169C2×#100—1221no—
170C2×#99—1221no—
171C2×C22⋊C8—1221no—
172C2×C22⋊C8#692311yescharacteristic, complemented
173#380—1221no—
174#343—612no—
175#342—612no—
176#336—1221no—
177C61#723611yescharacteristic, complemented, Sylow
178C22×D4—611no—
179C23×C4—611no—
180C23×C4C2×#692311yescharacteristic
181C2×M16—1222no—
182C22×C8—21no—
183C22×C8—1221no—
184C22×C8—2442no—
185C22×C8—2441no—
186C4×D4—2441no—
187C4×D4—2441no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—2441no—
190C2×C22⋊C4—611no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—1222no—
193C2×C42—611no—
194C4⋊C8—2441no—
195C4⋊C8—2441no—
196#100—2441no—
197#100—2441no—
198#99—2441no—
199#99—2441no—
200C22⋊C8—41no—
201C22⋊C8—2442no—
202#95—2441no—
203C24—611no—
204C24C4⋊#692311yescharacteristic
205C2×D4—611no—
206C2×D4—611no—
207C2×D4—611no—
208C2×D4—611no—
209C2×D4—2441no—
210C2×D4—2441no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—2441no—
221C22×C4—2441no—
222C22×C4—2442no—
223C22×C4C4×#692311yescharacteristic
224C22×C4C22⋊#692311yescharacteristic
225M16—2442no—
226M16—2442no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—1222no—
231C2×C8—2442no—
232C2×C8—2441no—
233C2×C8—2442no—
234C2×C8—2441no—
235C2×C8—2442no—
236C4⋊C4—4881no—
237C4⋊C4—4881no—
238C4⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2442no—
242C22⋊C4—2442no—
243C42—1221no—
244C42—1221no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—611no—
250C23—611no—
251C23—1221no—
252C23—1221no—
253C23—2441no—
254C23—2441no—
255C23(C2×#6923)⋊C411yescharacteristic
256C23#1451984511yescharacteristic
257C23#1451984611yescharacteristic
258D4—2441no—
259D4—2441no—
260D4—2441no—
261D4—2441no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—4881no—
276C2×C4—4882no—
277C2×C4—4882no—
278C2×C4—4882no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4#1451983511yescharacteristic
284C2×C4#1451983611yescharacteristic
285C8—81no—
286C8—4882no—
287C8—2442no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—1221no—
298C22—1221no—
299C22—4881no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22—2441no—
304C22#1684063011yescharacteristic
305C22#1684063611yescharacteristic
306C22#1684064011yescharacteristic
307C4—21no—
308C4—41no—
309C4—1221no—
310C4—1221no—
311C4—9762no—
312C4—2441no—
313C4—2441no—
314C4#1684066311yescharacteristic
315C4#1684066511yescharacteristic
316C2—21no—
317C2—21no—
318C2—41no—
319C2—41no—
320C2—2441no—
321C2—2441no—
322C2#2146068211yescharacteristic
323C2#2146090411yescharacteristic
324C2#2146092011yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#342
prime radicalC22×C22⋊D61D4
cosocleC2×C4×C22⋊D61C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7236
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
8. #16840642C4semidirect
10. C23×#92418C4semidirect
14. C2×C22⋊C8×C61C4semidirect
172. C2×C22⋊C8#6923semidirect
177. C61#7236semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214616792
#214461092
#723661