Finite Group Databasebeta

← #30594647

Subgroups — #30594647

Order 15616.

388 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 56 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#21461797C211yesmaximal, characteristic
2#21461569C211yesmaximal, characteristic
3#21445606C211yesmaximal, characteristic
4C22×#11758213C411yescharacteristic, complemented
5C2×#14519837—21no—
6C2×#14519834C411yescharacteristic, complemented
7C2×C22⋊#92420—21no—
8C4×#11758217—21no—
9#16840642C412yescomplemented
10#16840628—21no—
11C2×#14519737C2211yescharacteristic
12C2×#14519691—21no—
13C22⋊C4×Dic61—21no—
14#16839529C411yescharacteristic
15C61×#342C411yescharacteristic
16C2×#11758213—41no—
17C2×#11758213—42no—
18C2×#11758217—22no—
19C22×#92420—21no—
20C22×#92420—21no—
21#14519837—22no—
22#14519837—22no—
23#14519834—41no—
24C22⋊#92420—42no—
25#14519832—41no—
26C4×#92420—41no—
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30#14519737—41no—
31#14519737—41no—
32C2×#11758196C2×C411yescharacteristic
33C2×C22⋊Dic61—21no—
34C2×#11758198Q811yescharacteristic
35C2×C4×Dic61—41no—
36C2×C4×Dic61D411yescharacteristic
37#14519691—24no—
38#14519684—41no—
39C2×C22⋊C4×C61—21no—
40C2×C22⋊C4×C61C2×C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C23×D61C4⋊C411yescharacteristic
43C22×C4×C61—41no—
44C22×C4×C61C4211yescharacteristic
45C22×C4×C61C4⋊C411yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—41no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C4⋊C411yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—41no—
61C2×C4×D61—41no—
62#11758217—24no—
63#11758217—42no—
64C2×#92420—22no—
65C2×#92420—42no—
66C2×#92420—41no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70C2×#92420—41no—
71#11758213—42no—
72#11758213—42no—
73C22⋊C4×C61—22no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C22⋊Dic61—22no—
77C22⋊Dic61—41no—
78#11758198—41no—
79#11758196—41no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61—81no—
83C4×Dic61—81no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—41no—
87C23×C61—41no—
88C23×C61#9511yescharacteristic
89C23×C61#10411yescharacteristic
90C23×C61#10411yescharacteristic
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—41no—
95C22×D61—41no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—81no—
102C2×C4×C61—81no—
103C22⋊D61—42no—
104C22⋊D61—42no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—81no—
115C2×Dic61—81no—
116C2×Dic61—81no—
117C2×Dic61#9911yescharacteristic
118C2×Dic61#9911yescharacteristic
119C2×Dic61#10412yes—
120C4×D61—42no—
121C4×D61—41no—
122C4×D61—41no—
123#92420—44no—
124#92420—42no—
125#92420—81no—
126#7282—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—81no—
136C22×C61#33911yescharacteristic
137C22×C61#33911yescharacteristic
138C22×C61#34211yescharacteristic
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—81no—
143C2×D61—81no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—82no—
147Dic61—22no—
148Dic61—21no—
149Dic61—41no—
150Dic61—82no—
151Dic61AΣL(1,𝔽16)11yescharacteristic
152Dic61#35211yescharacteristic
153#1870—611no—
154C4×#100—611no—
155C4×#99—611no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61—41no—
159C2×C61—41no—
160C2×C61#129711yescharacteristic
161C2×C61#139011yescharacteristic
162C2×C61#139511yescharacteristic
163D61—81no—
164C22×M16—611no—
165C2×C4×D4—611no—
166C2×#100—1221no—
167C2×#99—1221no—
168C2×C22⋊C8—611no—
169C2×C22⋊C8—1221no—
170C4×M16—1221no—
171C4×C22⋊C4—1221no—
172#343—612no—
173#342—611no—
174#342#692311yescharacteristic
175#336—1221no—
176C61#728211yescharacteristic, complemented, Sylow
177C22×D4—611no—
178C23×C4—611no—
179C23×C4—611no—
180C2×M16—1222no—
181C2×M16—2442no—
182C2×M16—2441no—
183C22×C8—1221no—
184C22×C8—1221no—
185C4×D4—2441no—
186C4×D4—2441no—
187C2×C4⋊C4—611no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—1221no—
191C2×C22⋊C4C2×#692311yescharacteristic
192C2×C42—611no—
193C2×C42—2441no—
194#100—1222no—
195#100—1222no—
196#99—1224no—
197C22⋊C8—2442no—
198C22⋊C8—2441no—
199#97—2441no—
200C4×C8—2441no—
201#95—2441no—
202C24—611no—
203C24C22⋊#692311yescharacteristic
204C2×D4—1222no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4—2441no—
208C22×C4—41no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4—2441no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4C4×#692311yescharacteristic
222C22×C4C4⋊#692311yescharacteristic
223M16—1224no—
224M16—2442no—
225M16—2442no—
226M16—2442no—
227C2×C8—1222no—
228C2×C8—2441no—
229C2×C8—2441no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8—2442no—
233C2×C8—2441no—
234C4⋊C4—2441no—
235C22⋊C4—22no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—1222no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C42—1221no—
242C42—1221no—
243C42—4881no—
244C42—4881no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—1221no—
250C23—1221no—
251C23—1221no—
252C23—2441no—
253C23—2441no—
254C23(C2×#6923)⋊C411yescharacteristic
255C23#1451984111yescharacteristic
256C23#1451984211yescharacteristic
257D4—2442no—
258D4—2442no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—611no—
267C2×C4—612no—
268C2×C4—611no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—4881no—
275C2×C4—4881no—
276C2×C4—4881no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2442no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2441no—
284C8—4881no—
285C8—2442no—
286C8—2444no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—4881no—
297C22—4881no—
298C22—2441no—
299C22—2441no—
300C22—2441no—
301C22#1684063211yescharacteristic
302C22#1684063311yescharacteristic
303C22#1684063911yescharacteristic
304C4—41no—
305C4—41no—
306C4—82no—
307C4—611no—
308C4—611no—
309C4—1221no—
310C4—1222no—
311C4—4882no—
312C4—2441no—
313C2—21no—
314C2—21no—
315C2—41no—
316C2—41no—
317C2—4881no—
318C2#2146070011yescharacteristic
319C2#2146090211yescharacteristic
320C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#342C4
socleC22×C61#342
prime radicalC22×C22⋊D61D4
cosocleC2×#14519737C22
hypercenter#342#6923
hypocenterC61#7282
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C22×#11758213C4semidirect
6. C2×#14519834C4semidirect
9. #16840642C4semidirect
176. C61#7282semidirect

Maximal subgroups

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

subgroupindex
#214617972
#214615692
#214456062
#728261