Finite Group Databasebeta

← #30603838

Subgroups — #30603838

Order 15616.

602 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461050C212yesmaximal, complemented
2#21460750C212yesmaximal, complemented
3#21460748C212yesmaximal, complemented
4#21448309C211yesmaximal, characteristic
5#16840778—22no—
6#16840607C2214yes—
7#16840605—22no—
8C22×#11758222C411yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16839668C411yescharacteristic
11#16839668C2211yescharacteristic
12#16839664C411yescharacteristic
13#16839664C2211yescharacteristic
14#16839641—22no—
15C4×#11758198—22no—
16C22×C42×C61C411yescharacteristic
17C4⋊#92420—42no—
18C22⋊#92420—24no—
19C4×#92420—42no—
20C2×#11758222—22no—
21C2×#11758222—41no—
22C2×#11758222—41no—
23C2×#11758222—42no—
24C2×#11758222C814yescomplemented
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C22×C22⋊D61—21no—
28C22×C4×D61—21no—
29#14519736—41no—
30#14519736—41no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2311yescharacteristic
33C2×C22⋊Dic61D412yes—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×C4×Dic61D412yes—
37#14519684—22no—
38#14519684—22no—
39C23×C4×C61—21no—
40C23×C4×C61C2×C411yescharacteristic
41C2×C42×C61—21no—
42C2×C42×C61—42no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C24×C61C22⋊C411yescharacteristic
46C23×D61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—42no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C2×C812yes—
57C22×C4×C61M1612yes—
58C22×C4×C61C22×C411yescharacteristic
59C2×C22⋊D61—24no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61—42no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C412yes—
64C22×Dic61C2×D412yes—
65#11758222—44no—
66#11758222—44no—
67#11758222—44no—
68#11758222—44no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244—41no—
72C2×D244C2×C812yes—
73C2×C4×D61—24no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—42no—
77C2×Dic122—21no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122C2×C812yes—
81C2×#92420—44no—
82C42×C61—41no—
83C42×C61—41no—
84C42×C61—42no—
85C22⋊Dic61—42no—
86#11758198—44no—
87#11758198—44no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—41no—
95C23×C61—41no—
96C23×C61C22⋊C812yes—
97C23×C61C2×C22⋊C411yescharacteristic
98C22×D61—22no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—41no—
102C22×D61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—48no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61C22⋊C812yes—
117C2×C4×C61#9911yescharacteristic
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#10012yes—
120C2×C4×C61C22×C811yescharacteristic
121C2×C4×C61C2×M1611yescharacteristic
122C22⋊D61—48no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130D244—42no—
131D244—42no—
132C4×D61—44no—
133C4×D61—44no—
134Dic122—42no—
135Dic122—42no—
136#92420—84no—
137#11431—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—22no—
141C22×C61—42no—
142C22×C61—42no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61C2×C22⋊C811yescharacteristic
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#10011yescharacteristic
148C2×D61—44no—
149C2×D61—42no—
150C2×D61—82no—
151C2×D61—81no—
152C2×D61—81no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—42no—
157C4×C61#32312yes—
158C4×C61#32312yes—
159Dic61—42no—
160Dic61—42no—
161Dic61—42no—
162#2297—611no—
163#1458—612no—
164#1319—612no—
165#1318—612no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61—42no—
169C2×C61C2×#32311yescharacteristic
170C2×C61#212611yescharacteristic
171C2×C61#213211yescharacteristic
172D61—82no—
173C22×#41—611no—
174C2×#117—611no—
175C22×C42#692311yescharacteristic
176#431—1222no—
177#391—611no—
178#391—611no—
179#390—611no—
180#390—611no—
181#386—1222no—
182C4×C22⋊C4—1222no—
183#324—614no—
184#323—1222no—
185C61#1143111yescharacteristic, complemented, Sylow
186C2×#41—614no—
187C2×#41—1222no—
188C2×#41—2441no—
189C2×#41—2441no—
190C2×#41—2442no—
191C22×Q8—611no—
192C22×D4—611no—
193C22×D4—1221no—
194C23×C4—21no—
195C23×C4—1221no—
196C23×C4C2×#692311yescharacteristic
197#117—2441no—
198#117—2441no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C22⋊C4—612no—
202C2×C22⋊C4—1222no—
203C2×C22⋊C4—1222no—
204C2×C42—21no—
205C2×C42—42no—
206C2×C42—612no—
207C2×C42C2×#692311yescharacteristic
208C2×C42C2×#692311yescharacteristic
209C4⋊C8—2442no—
210C22⋊C8—1224no—
211C4×C8—2442no—
212#95—1222no—
213#95—1222no—
214C24—1221no—
215C24C22⋊#692311yescharacteristic
216#41—2444no—
217#41—2444no—
218#41—2444no—
219#41—2444no—
220C2×Q8—612no—
221C2×Q8—1221no—
222C2×Q8—2441no—
223C2×Q8—2441no—
224C2×D4—612no—
225C2×D4—1224no—
226C2×D4—1221no—
227C2×D4—2441no—
228C2×D4—2441no—
229C2×D4—2442no—
230C2×D4—2442no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—612no—
240C22×C4—612no—
241C22×C4—1221no—
242C22×C4—1224no—
243C22×C4—2441no—
244C22×C4—2441no—
245C22×C4—2442no—
246C22×C4D61⋊C812yes—
247C22×C4#1175821312yes—
248C22×C4C22⋊#692311yescharacteristic
249C22×C4C22×#692311yescharacteristic
250C2×C8—2444no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C22⋊C4—2444no—
254C22⋊C4—2444no—
255C22⋊C4—2442no—
256C42—41no—
257C42—41no—
258C42—42no—
259C42—1222no—
260C42—1222no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—1222no—
266C23—2442no—
267C23—2442no—
268C23—2441no—
269C23—2441no—
270C23#1451983412yes—
271C23C2×C22⋊#692311yescharacteristic
272Q8—2442no—
273Q8—2442no—
274D4—2442no—
275D4—2442no—
276D4—2448no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—48no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—1222no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2444no—
296C2×C4—2444no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4#1451983412yes—
300C2×C4#1451983611yescharacteristic
301C2×C4#1451983611yescharacteristic
302C2×C4#1451983712yes—
303C2×C4C2×D61⋊C811yescharacteristic
304C2×C4C2×#1175821311yescharacteristic
305C8—4884no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—4882no—
314C22—4881no—
315C22—4881no—
316C22—2444no—
317C22—2442no—
318C22C2×#1451983411yescharacteristic
319C22C2×#1451983611yescharacteristic
320C22C2×#1451983711yescharacteristic
321C4—21no—
322C4—21no—
323C4—42no—
324C4—42no—
325C4—2442no—
326C4—2442no—
327C4—2442no—
328C4#1684060612yes—
329C4#1684060612yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—4882no—
334C2C2×#1684060611yescharacteristic
335C2#2146209211yescharacteristic
336C2#2146211211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C42#6923
hypocenterC61#11431
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #21461050C2semidirect
2. #21460750C2semidirect
3. #21460748C2semidirect
24. C2×#11758222C8semidirect
185. C61#11431semidirect

Maximal subgroups

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

subgroupindex
#214610502
#214607502
#214607482
#214483092
#1143161