Finite Group Databasebeta

← #30600540

Subgroups — #30600540

Order 15616.

458 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462501C211yesmaximal, characteristic
2#21461334C212yesmaximal, complemented
3#21461053C211yesmaximal, characteristic
4#21460672C212yesmaximal, complemented
5#21451647C211yesmaximal, characteristic
6#16840787—24no—
7#16840779C2212yes—
8#16840765C2212yes—
9#16840734—21no—
10C4×#11758217—21no—
11#16840621—24no—
12#16840607—21no—
13#16840606—21no—
14C2×#14519776C2211yescharacteristic
15C2×#14519735C2211yescharacteristic
16#16839701C411yescharacteristic
17#16839699C411yescharacteristic
18#16839697C411yescharacteristic
19#16839683—21no—
20#16839675—21no—
21#16839659—21no—
22#16839626C2211yescharacteristic
23#16839621—21no—
24C61×#400C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27#14519844D414yes—
28C4⋊#92420—22no—
29#14519834—24no—
30C22⋊#92420—22no—
31#14519832—22no—
32C4×#92420—22no—
33C4×#92420—22no—
34C22×Dic122—21no—
35C22×C4×D61D411yescharacteristic
36#14519776—22no—
37#14519776—22no—
38#14519735—22no—
39#14519735—22no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60#95×C61C2×C411yescharacteristic
61C23×D61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×Dic122—42no—
77C2×Dic122—81no—
78C2×Dic122—81no—
79#11758217—42no—
80#11758217—42no—
81C2×#92420—24no—
82C2×#92420—42no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—81no—
88#11758198—81no—
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91C4⋊Dic61—81no—
92#11758196—41no—
93#11758196—41no—
94#11758196—42no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61C2×D412yes—
99C4×Dic61#4112yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—41no—
105C22×D61—41no—
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×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61C4×D412yes—
119C2×Dic61—21no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61#12011yescharacteristic
129C2×Dic61#12112yes—
130C2×Dic61#12311yescharacteristic
131C2×Dic61#13512yes—
132C2×Dic61#13712yes—
133C4×D61—42no—
134C4×D61—42no—
135Dic122—84no—
136#92420—44no—
137#92420—82no—
138#9194—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61#38611yescharacteristic
142C22×C61#41611yescharacteristic
143C22×C61#41911yescharacteristic
144C2×D61—42no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—81no—
149C4×C61—22no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153C4×C61—81no—
154Dic61—22no—
155Dic61—41no—
156Dic61—81no—
157Dic61—81no—
158Dic61#45212yes—
159Dic61#48512yes—
160#2921—611no—
161#2628—611no—
162#1549—612no—
163#1458—611no—
164#1286—612no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61#187311yescharacteristic
168C2×C61#191011yescharacteristic
169C2×C61#191511yescharacteristic
170D61—81no—
171C2×C4⋊Q8—611no—
172C2×#117—611no—
173#433—1224no—
174#431—612no—
175#423—612no—
176#407—1221no—
177C4×M16—1221no—
178#400—611no—
179#400#692311yescharacteristic
180#399—611no—
181#399—611no—
182#395—1221no—
183#393—1221no—
184#389—1221no—
185#382—611no—
186#380—1221no—
187#332—1224no—
188#324—1221no—
189#323—1221no—
190C61#919411yescharacteristic, complemented, Sylow
191C22×Q8—1221no—
192C23×C4—611no—
193C2×M16—1222no—
194C4⋊Q8—1222no—
195C4⋊Q8—1222no—
196#117—1222no—
197#117—1222no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C22⋊C4—611no—
207C2×C22⋊C4—611no—
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C42—611no—
211C2×C42—611no—
212C4⋊C8—614no—
213C4⋊C8—1222no—
214C4⋊C8—1222no—
215C22⋊C8—1224no—
216C22⋊C8—1222no—
217#97—1222no—
218C4×C8—1222no—
219C4×C8—1222no—
220#95—21no—
221#95—21no—
222#95—611no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95C2×#692311yescharacteristic
227C24—611no—
228C2×Q8—4881no—
229C2×Q8—4881no—
230C2×Q8—2442no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4C22⋊#692311yescharacteristic
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22×#692311yescharacteristic
245M16—2442no—
246M16—2442no—
247C2×C8—1224no—
248C2×C8—2442no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—4881no—
254C4⋊C4—4881no—
255C4⋊C4—2442no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C22⋊C4—1222no—
259C22⋊C4—1222no—
260C22⋊C4—4881no—
261C22⋊C4—4881no—
262C42—612no—
263C42—612no—
264C42—1221no—
265C42—1221no—
266C23—1221no—
267C23—1221no—
268C23—1221no—
269C23—2441no—
270C23—2441no—
271C23C2×C22⋊#692311yescharacteristic
272Q8—4884no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—612no—
290C2×C4—1221no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4D4×#692312yes—
302C8—4882no—
303C8—2444no—
304C22—21no—
305C22—21no—
306C22—4881no—
307C22—2442no—
308C22—2441no—
309C22—2441no—
310C22—2441no—
311C22#1684071011yescharacteristic
312C22#1684075211yescharacteristic
313C22#1684075511yescharacteristic
314C4—22no—
315C4—41no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—612no—
320C4—612no—
321C4—1222no—
322C4—4881no—
323C4—4881no—
324C4—2441no—
325C2—21no—
326C2—21no—
327C2—4881no—
328C2#2146180511yescharacteristic
329C2#2146186311yescharacteristic
330C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#400#6923
hypocenterC61#9194
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #21461334C2semidirect
4. #21460672C2semidirect
190. C61#9194semidirect

Maximal subgroups

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

subgroupindex
#214625012
#214613342
#214610532
#214606722
#214516472
#919461