Finite Group Databasebeta

← #30594770

Subgroups — #30594770

Order 15616.

374 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461068C211yesmaximal, characteristic
2#21461008C211yesmaximal, characteristic
3#21444147C211yesmaximal, characteristic
4#16840733—21no—
5C2×(C2×#6923)⋊C4—21no—
6C2×(C2×#6923)⋊C4—21no—
7C2×(C2×#6923)⋊C4C411yescharacteristic
8C2×(C2×#6923)⋊C4C411yescharacteristic
9#16840608—21no—
10#16840607C412yescomplemented
11C2×C4⋊C4×D61C2211yescharacteristic
12#16839724—21no—
13#16839488C411yescharacteristic, complemented
14#16839487—21no—
15C61×#324C411yescharacteristic, complemented
16C23×#6923—21no—
17C23×#6923—21no—
18C2×#11758213—41no—
19#14519834—41no—
20C22⋊#92420—22no—
21(C2×#6923)⋊C4—41no—
22(C2×#6923)⋊C4—41no—
23(C2×#6923)⋊C4—42no—
24(C2×#6923)⋊C4—42no—
25C22×C4×D61C2×C411yescharacteristic
26C22×C4×D61D411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758189—41no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196D411yescharacteristic
31C2×#11758196Q811yescharacteristic
32C4⋊C4×D61—41no—
33C4⋊C4×D61—41no—
34C22⋊#92418—21no—
35#14519689—41no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C23×D61C22⋊C411yescharacteristic
39C22×#6923—22no—
40C22×#6923—22no—
41C22×#6923—41no—
42C22×#6923—41no—
43C22×#6923—41no—
44C22×#6923—41no—
45C22×#6923—41no—
46C22×#6923—41no—
47C22×#6923—41no—
48C22×#6923—41no—
49C22×#6923—41no—
50C22×#6923—41no—
51C22×#6923—41no—
52C22×#6923—41no—
53C22×C4×C61C4211yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C4⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C4⋊C411yescharacteristic
58C22×Dic61C4⋊C411yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×#92420—42no—
72#11758213—81no—
73#11758213—81no—
74C2×C8×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79C2×#92418—41no—
80#11758189—81no—
81#11758189—81no—
82C23×C61#9511yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61#9911yescharacteristic
90C22×D61#9911yescharacteristic
91C2×#6923—42no—
92C2×#6923—42no—
93C2×#6923—42no—
94C2×#6923—42no—
95C2×#6923—42no—
96C2×#6923—42no—
97C2×#6923—81no—
98C2×#6923—81no—
99C2×#6923—81no—
100C2×#6923—81no—
101C2×#6923—81no—
102C2×#6923—81no—
103C2×#6923—81no—
104C2×#6923—81no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C4×D61—42no—
120C4×D61—42no—
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—41no—
124C4×D61—41no—
125C4×D61—81no—
126C4×D61—81no—
127#92420—82no—
128C8×C61—81no—
129#92418—81no—
130#7326—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#34211yescharacteristic
134C22×C61#34411yescharacteristic
135C22×C61#34411yescharacteristic
136C2×D61—21no—
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61#35311yescharacteristic
149C2×D61#35411yescharacteristic
150C2×D61#35511yescharacteristic
151C2×D61#35611yescharacteristic
152#6923—82no—
153#6923—82no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160#1463—611no—
161#1463—611no—
162#1445—611no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#130611yescharacteristic
166C2×C61#139311yescharacteristic
167C2×C61#139411yescharacteristic
168D61—21no—
169D61—21no—
170D61—21no—
171D61—21no—
172C22×C4⋊C4—611no—
173#407—1221no—
174#407—1221no—
175C2×#95—611no—
176C2×#95—611no—
177C2×#95—1221no—
178C2×#95—1221no—
179#324—612no—
180#324—611no—
181#324—1221no—
182#324—1221no—
183#324#692311yescharacteristic, complemented
184C61#732611yescharacteristic, complemented, Sylow
185C23×C4—611no—
186C23×C4—611no—
187C23×C4—611no—
188C23×C4—1221no—
189C23×C4—1221no—
190C2×M16—2441no—
191C2×M16—2441no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—2441no—
196C2×C4⋊C4—2441no—
197C2×C4⋊C4C2×#692311yescharacteristic
198C22⋊C8—21no—
199C22⋊C8—1222no—
200C22⋊C8—1221no—
201C22⋊C8—2441no—
202C22⋊C8—2441no—
203#95—2441no—
204#95—2441no—
205#95—2442no—
206#95—2442no—
207C24—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4—2441no—
222C22×C4—2441no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4—2441no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4—2441no—
234C22×C4—2441no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4C4×#692311yescharacteristic
238C22×C4C4⋊#692311yescharacteristic
239C22×C4C22⋊#692311yescharacteristic
240M16—4881no—
241M16—4881no—
242M16—4881no—
243M16—4881no—
244C2×C8—41no—
245C2×C8—2441no—
246C2×C8—2442no—
247C4⋊C4—41no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C23—611no—
252C23—611no—
253C23—1221no—
254C23—1221no—
255C23—1221no—
256C23—1221no—
257C23—1221no—
258C23—1221no—
259C23(C2×#6923)⋊C411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—4881no—
273C2×C4—4881no—
274C2×C4—4881no—
275C2×C4—4881no—
276C2×C4—4881no—
277C2×C4—4881no—
278C2×C4—4881no—
279C2×C4—4881no—
280C2×C4—4881no—
281C2×C4—4881no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2441no—
295C2×C4—2441no—
296C8—81no—
297C8—4881no—
298C8—4882no—
299C22—21no—
300C22—21no—
301C22—611no—
302C22—611no—
303C22—611no—
304C22—611no—
305C22—1221no—
306C22—1221no—
307C22—1221no—
308C22—1221no—
309C22—1221no—
310C22—1221no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—1221no—
316C22—1221no—
317C22#1684063911yescharacteristic
318C22#1684064411yescharacteristic
319C22#1684064511yescharacteristic
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4882no—
324C4—4882no—
325C4—2441no—
326C4—2441no—
327C4—2441no—
328C2—21no—
329C2—21no—
330C2—1221no—
331C2—1221no—
332C2—1221no—
333C2—1221no—
334C2#2146072311yescharacteristic
335C2#2146091211yescharacteristic
336C2#2146091511yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×D61C22
hypercenter#324#6923
hypocenterC61#7326
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
10. #16840607C4semidirect
13. #16839488C4semidirect
15. C61×#324C4semidirect
183. #324#6923semidirect
184. C61#7326semidirect

Maximal subgroups

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

subgroupindex
#214610682
#214610082
#214441472
#732661