Finite Group Databasebeta

← #30601014

Subgroups — #30601014

Order 15616.

486 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462714C211yesmaximal, characteristic
2#21461686C211yesmaximal, characteristic
3#21461332C212yesmaximal
4#21460717C212yesmaximal
5#21451023C211yesmaximal, characteristic
6#16840811—24no—
7#16840779—21no—
8#16840779C2212yes—
9#16840778—21no—
10#16840765C2212yes—
11C2×#14519838—21no—
12#16840642—21no—
13#16840622—24no—
14C2×#14519775C2211yescharacteristic
15C2×#14519742C2211yescharacteristic
16#16839683C411yescharacteristic
17#16839682C411yescharacteristic
18#16839681C411yescharacteristic
19#16839666—21no—
20#16839659—21no—
21#16839657—21no—
22#16839631—21no—
23#16839613C2211yescharacteristic
24C61×#395C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844D414yes—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C4×#92420—22no—
35C4×#92420—22no—
36C22×Dic122C2×C411yescharacteristic
37C22×Dic122D411yescharacteristic
38#14519775—22no—
39#14519775—22no—
40#14519742—22no—
41#14519742—22no—
42C2×C4⋊Dic61—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×#11758196D411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×Q8×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—22no—
64C2×Q8×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—22no—
77C2×Dic122—22no—
78C2×Dic122—22no—
79C2×Dic122—81no—
80C2×Dic122SD1612yes—
81C2×Dic122Q1612yes—
82#11758217—42no—
83#11758217—42no—
84C2×#92420—24no—
85C2×#92420—42no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—81no—
88C4⋊Dic61—81no—
89#11758196—24no—
90#11758196—22no—
91#11758196—22no—
92#11758196—41no—
93#11758196—42no—
94#11758196—41no—
95#11758196—81no—
96#11758196—81no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C4×Dic61C2×D412yes—
103C4×Dic61#4112yes—
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—82no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
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#10312yes—
118C2×C4×C61C4×D412yes—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#10312yes—
131C2×Dic61#12011yescharacteristic
132C2×Dic61#12112yes—
133C2×Dic61#12311yescharacteristic
134C2×Dic61C2×SD1611yescharacteristic
135C2×Dic61C2×Q1611yescharacteristic
136C2×Dic61#13512yes—
137Dic122—24no—
138Dic122—24no—
139Dic122—82no—
140#92420—44no—
141#92420—82no—
142#9392—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61#38611yescharacteristic
146C22×C61C2×#10311yescharacteristic
147C22×C61#41611yescharacteristic
148C4×C61—22no—
149C4×C61—22no—
150C4×C61—42no—
151C4×C61—41no—
152C4×C61—81no—
153Dic61—21no—
154Dic61—22no—
155Dic61—42no—
156Dic61—41no—
157Dic61—81no—
158Dic61#45612yes—
159Dic61#46512yes—
160Dic61#46712yes—
161#2982—611no—
162#2567—611no—
163#1801—611no—
164#1548—612no—
165#1303—612no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#188611yescharacteristic
169C2×C61#189211yescharacteristic
170C2×C61#191411yescharacteristic
171C2×C4⋊Q8—611no—
172C2×C4×Q8—611no—
173C8×Q8—1224no—
174#431—612no—
175#431—1221no—
176#431—1221no—
177#423—612no—
178C2×#101—1221no—
179#395—611no—
180#395—611no—
181#395—611no—
182#395#692311yescharacteristic
183#391—1221no—
184#389—1221no—
185#389—1221no—
186#384—1221no—
187C4×C4⋊C4—611no—
188#343—1221no—
189#333—1224no—
190C61#939211yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×Q8—611no—
193C22×Q8C2×#692311yescharacteristic
194C2×M16—1222no—
195C4⋊Q8—1222no—
196C4⋊Q8—1222no—
197C4×Q8—1222no—
198C4×Q8—1222no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4C2×#692311yescharacteristic
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—1221no—
213C4⋊C8—614no—
214C4⋊C8—1222no—
215C4⋊C8—1222no—
216C4⋊C8—1222no—
217C4⋊C8—1222no—
218#101—2442no—
219C22⋊C8—1222no—
220C4×C8—1222no—
221C4×C8—1222no—
222C4×C8—1222no—
223#95—21no—
224#95—611no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95C2×#692311yescharacteristic
229C2×Q8—22no—
230C2×Q8—81no—
231C2×Q8—612no—
232C2×Q8—612no—
233C2×Q8—1222no—
234C2×Q8—1222no—
235C2×Q8—1222no—
236C2×Q8—4881no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248M16—2442no—
249M16—2442no—
250C2×C8—1224no—
251C2×C8—2442no—
252C4⋊C4—22no—
253C4⋊C4—81no—
254C4⋊C4—1222no—
255C4⋊C4—1224no—
256C4⋊C4—1222no—
257C4⋊C4—4881no—
258C4⋊C4—4881no—
259C4⋊C4—4881no—
260C4⋊C4—2441no—
261C4⋊C4—2442no—
262C4⋊C4—2441no—
263C42—612no—
264C42—612no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—1221no—
269C42—2442no—
270C23C2×C22⋊#692311yescharacteristic
271Q8—82no—
272Q8—1224no—
273Q8—1224no—
274Q8—4882no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—612no—
291C2×C4—611no—
292C2×C4—612no—
293C2×C4—1222no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1222no—
297C2×C4—1221no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4#1451984012yes—
305C2×C4D4×#692312yes—
306C8—4882no—
307C8—2444no—
308C22—21no—
309C22—21no—
310C22#1684071011yescharacteristic
311C22C2×#1451984011yescharacteristic
312C22#1684075211yescharacteristic
313C4—22no—
314C4—22no—
315C4—42no—
316C4—41no—
317C4—81no—
318C4—612no—
319C4—612no—
320C4—612no—
321C4—1221no—
322C4—1222no—
323C4—4881no—
324C4—2442no—
325C4—2441no—
326C2—21no—
327C2—21no—
328C2#2146182511yescharacteristic
329C2#2146183211yescharacteristic
330C2#2146187011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#395#6923
hypocenterC61#9392
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
190. C61#9392semidirect

Maximal subgroups

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

subgroupindex
#214627142
#214616862
#214613322
#214607172
#214510232
#939261