Finite Group Databasebeta

← #30600271

Subgroups — #30600271

Order 15616.

630 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 116 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#21462666C211yesmaximal, characteristic, complemented
2#21461120C212yesmaximal, complemented
3#21461059C211yesmaximal, characteristic, complemented
4#21460643C212yesmaximal, complemented
5#21448543C211yesmaximal, characteristic
6D4×#92420—24no—
7#16840778C2212yes—
8#16840778C2212yes—
9C2×C22⋊#92420—22no—
10#16840610—24no—
11#16840605—22no—
12C2×#14519773C411yescharacteristic
13C2×D4×Dic61C2211yescharacteristic
14C2×#14519739C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839639—22no—
17#16839638—22no—
18#16839627C411yescharacteristic
19#16839608C2211yescharacteristic
20C61×#390C411yescharacteristic
21C22×#92420—24no—
22C4⋊#92420—22no—
23C4⋊#92420—22no—
24C22⋊#92420—24no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C4×#92420—22no—
28C4×#92420D414yescomplemented
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—22no—
31C23×Dic61D412yes—
32C22×C4×D61—21no—
33#14519773—22no—
34#14519773C814yescomplemented
35D4×Dic61—22no—
36D4×Dic61—22no—
37#14519739—22no—
38#14519739—22no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61D412yes—
41C2×#11758198—21no—
42C2×#11758198—22no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—22no—
46#14519684—21no—
47#14519684—21no—
48C22×D4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61—22no—
51C2×C42×C61C2×C411yescharacteristic
52C24×C61C22⋊C412yes—
53C23×D61—21no—
54C2×D4×C61—22no—
55C2×D4×C61—22no—
56C2×D4×C61C2×C812yes—
57C2×D4×C61M1612yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C2×C22⋊D61—28no—
62C2×C22⋊D61—82no—
63C2×C22⋊D61—82no—
64C22×Dic61—21no—
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—82no—
68C22×Dic61C22⋊C412yes—
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—21no—
74C2×D244C2×C812yescomplemented
75C2×C4×D61—42no—
76C2×C4×D61—82no—
77C2×#92420—24no—
78C2×#92420—42no—
79C2×#92420—84no—
80C4⋊C4×C61—22no—
81C22⋊C4×C61—82no—
82C42×C61—22no—
83C22⋊Dic61—24no—
84#11758198—41no—
85#11758198—41no—
86#11758198—82no—
87C4⋊Dic61—22no—
88C4×Dic61—21no—
89C4×Dic61C2×C812yescomplemented
90C4×Dic61C2×D412yes—
91C4×Dic61#4112yes—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—42no—
95C23×C61—42no—
96C23×C61C22⋊C814yes—
97C23×C61C2×C22⋊C411yescharacteristic
98C22×D61—22no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—41no—
102C22×D61—41no—
103D4×C61—24no—
104D4×C61—24no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61C4×D412yes—
111C2×C4×C61C22×C811yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C2×C4×C61#13112yes—
114C22⋊D61—88no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—44no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—42no—
123C2×Dic61—82no—
124C2×Dic61#12011yescharacteristic
125C2×Dic61#12112yes—
126C2×Dic61#12311yescharacteristic
127D244—24no—
128D244—42no—
129C4×D61—84no—
130#92420—44no—
131#92420—82no—
132#9101—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—24no—
136C22×C61—44no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61—82no—
140C22×C61#38611yescharacteristic
141C22×C61C2×C22⋊C811yescharacteristic
142C22×C61#40811yescharacteristic
143C2×D61—44no—
144C2×D61—42no—
145C2×D61—82no—
146C2×D61—81no—
147C2×D61—81no—
148C4×C61—81no—
149C4×C61—81no—
150C4×C61C8×D412yes—
151C4×C61#43512yes—
152Dic61—22no—
153Dic61—21no—
154Dic61—21no—
155Dic61—42no—
156Dic61—42no—
157#2972—611no—
158#2328—611no—
159#1478—612no—
160#1460—611no—
161#1274—612no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—44no—
165C2×C61#186911yescharacteristic
166C2×C61#191011yescharacteristic
167C2×C61#191111yescharacteristic
168D61—82no—
169C2×#127—611no—
170C2×C4×D4—611no—
171C2×C4×D4—611no—
172C8×D4—1224no—
173#431—612no—
174#431—612no—
175C2×C22⋊C8—1222no—
176#390—611no—
177#390#692311yescharacteristic
178#386—1222no—
179#386—1222no—
180#382—611no—
181#376—611no—
182D4⋊C8—1224no—
183#323—1222no—
184C61#910111yescharacteristic, complemented, Sylow
185C22×D4—611no—
186C22×D4—1222no—
187C22×D4C2×#692311yescharacteristic
188C23×C4—612no—
189C23×C4—1221no—
190C22×C8—1224no—
191#127—614no—
192#127—1222no—
193C4×D4—1222no—
194C4×D4—1222no—
195C4×D4—1222no—
196C4×D4—1222no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4C2×#692311yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—612no—
201C2×C22⋊C4—1222no—
202C2×C22⋊C4—1221no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42C2×#692311yescharacteristic
206C4⋊C8—1222no—
207C4⋊C8—1222no—
208C22⋊C8—1222no—
209C22⋊C8—1224no—
210C22⋊C8—1222no—
211C4×C8—614no—
212C4×C8—1222no—
213#95—1221no—
214#95—1221no—
215#95—1222no—
216C24—1221no—
217C24C22⋊#692312yes—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—612no—
221C2×D4—1228no—
222C2×D4—1222no—
223C2×D4—1221no—
224C2×D4—1222no—
225C2×D4—4882no—
226C2×D4—4882no—
227C2×D4D61⋊C812yes—
228C2×D4#1175821312yes—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—612no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—1221no—
237C22×C4—4882no—
238C22×C4—4882no—
239C22×C4—2442no—
240C22×C4C22×#692311yescharacteristic
241C2×C8—1224no—
242C2×C8—4884no—
243C2×C8—2442no—
244C4⋊C4—22no—
245C4⋊C4—1222no—
246C22⋊C4—82no—
247C22⋊C4—1224no—
248C22⋊C4—4882no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C42—22no—
252C42—612no—
253C42—612no—
254C42—612no—
255C42—1221no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—1222no—
261C23—2442no—
262C23—2442no—
263C23—2441no—
264C23—2441no—
265C23#1451983414yes—
266C23C2×C22⋊#692311yescharacteristic
267D4—24no—
268D4—24no—
269D4—1224no—
270D4—4888no—
271D4—2442no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—611no—
278C2×C4—612no—
279C2×C4—611no—
280C2×C4—1222no—
281C2×C4—1222no—
282C2×C4—4884no—
283C2×C4—4882no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2444no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2442no—
290C2×C4D4×#692312yes—
291C2×C4C2×D61⋊C811yescharacteristic
292C2×C4C2×#1175821311yescharacteristic
293C2×C4#1451986412yes—
294C8—4882no—
295C8—2444no—
296C22—21no—
297C22—21no—
298C22—24no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22—82no—
303C22—4882no—
304C22—4881no—
305C22—4881no—
306C22—2444no—
307C22—2442no—
308C22#1684071011yescharacteristic
309C22C2×#1451983411yescharacteristic
310C22#1684073511yescharacteristic
311C4—81no—
312C4—81no—
313C4—1222no—
314C4—1221no—
315C4—1221no—
316C4—2442no—
317C4—2442no—
318C4#1684078912yes—
319C4#1684079112yes—
320C2—21no—
321C2—21no—
322C2—44no—
323C2—4882no—
324C2#2146179411yescharacteristic
325C2#2146186211yescharacteristic
326C2#2146186411yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61#386
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9101
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21462666C2semidirect
2. #21461120C2semidirect
3. #21461059C2semidirect
4. #21460643C2semidirect
28. C4×#92420D4semidirect
34. #14519773C8semidirect
74. C2×D244C2×C8semidirect
89. C4×Dic61C2×C8semidirect
184. C61#9101semidirect

Maximal subgroups

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

subgroupindex
#214626662
#214611202
#214610592
#214606432
#214485432
#910161