Finite Group Databasebeta

← #30595740

Subgroups — #30595740

Order 15616.

488 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461546C211yesmaximal, characteristic
2C4×#14519834C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21454157C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519757C411yescharacteristic
13C2×C42×D61C2211yescharacteristic
14#16839668C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839649—21no—
18#16839648—21no—
19#16839633—21no—
20#16839624—21no—
21#16839619C411yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—24no—
27#14519832—42no—
28C4×#92420—42no—
29C22×Dic122C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519757—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42C42×D61—42no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C23×D61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×Dic122—22no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×#92420—24no—
78C2×#92420—24no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—42no—
86C42×C61—41no—
87#11758198—42no—
88#11758198—42no—
89C4⋊Dic61—22no—
90C4⋊Dic61—42no—
91#11758196—42no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61#10412yes—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
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×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61#10412yes—
117C2×C4×C61#13112yes—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#9912yes—
131C2×Dic61#13512yes—
132C2×Dic61#13712yes—
133C4×D61—44no—
134C4×D61—44no—
135C4×D61—44no—
136Dic122—82no—
137#92420—44no—
138#92420—44no—
139#7675—611nomaximal, Sylow
140C22×C61#40811yescharacteristic
141C22×C61C2×#9911yescharacteristic
142C22×C61#41311yescharacteristic
143C22×C61#41611yescharacteristic
144C22×C61#41911yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C22×C61C2×#10411yescharacteristic
147C2×D61—22no—
148C2×D61—22no—
149C2×D61—22no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—41no—
157C4×C61—81no—
158C4×C61—81no—
159Dic61—22no—
160Dic61—22no—
161Dic61—22no—
162Dic61—81no—
163Dic61—81no—
164#2855—611no—
165#1749—611no—
166C4×C22⋊C8—611no—
167#1272—612no—
168#1271—612no—
169C2×C61#146811yescharacteristic
170C2×C61#148511yescharacteristic
171C2×C61#149411yescharacteristic
172C2×C61#150111yescharacteristic
173C2×C61#150811yescharacteristic
174C2×C61#152411yescharacteristic
175C2×C61#155411yescharacteristic
176D61—42no—
177C2×C22⋊Q8—611no—
178C22×C42—611no—
179C2×C22⋊C8—1221no—
180C2×C22⋊C8—1221no—
181C2×#97—1221no—
182C2×C4×C8—1221no—
183#391—611no—
184#391—611no—
185#389—611no—
186#389#692311yescharacteristic
187#387—1221no—
188#387—1221no—
189#385—1221no—
190#381—1221no—
191#380—611no—
192#336—612no—
193#336—612no—
194C61#767511yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C23×C4—611no—
197C23×C4—611no—
198C23×C4—611no—
199C22×C8—1222no—
200C22×C8—1222no—
201C22⋊Q8—2442no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4C2×#692311yescharacteristic
207C2×C4⋊C4C2×#692311yescharacteristic
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—2442no—
214C2×C42C2×#692311yescharacteristic
215C22⋊C8—1224no—
216C22⋊C8—1224no—
217#97—2442no—
218C4×C8—2442no—
219#95—21no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226C24—611no—
227C2×Q8—1222no—
228C2×Q8—2441no—
229C2×Q8—2441no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1222no—
236C22×C4—1222no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1222no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—2441no—
244C22×C4—2441no—
245C22×C4—2441no—
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22⋊#692311yescharacteristic
248C22×C4C22×#692311yescharacteristic
249C2×C8—1224no—
250C2×C8—1224no—
251C2×C8—2442no—
252C2×C8—2442no—
253C2×C8—2442no—
254C2×C8—2442no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—1222no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C22⋊C4—2442no—
262C22⋊C4—2442no—
263C42—41no—
264C42—1222no—
265C42—1222no—
266C42—2441no—
267C23—612no—
268C23—1221no—
269C23—1221no—
270C23—1221no—
271C23—1221no—
272C23—1221no—
273C23—1221no—
274C23C2×C22⋊#692311yescharacteristic
275Q8—4882no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—612no—
290C2×C4—612no—
291C2×C4—612no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—2444no—
299C2×C4—2444no—
300C2×C4—2444no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4#1451984112yes—
308C2×C4#1451986512yes—
309C8—2444no—
310C8—2444no—
311C22—1222no—
312C22—1222no—
313C22—1222no—
314C22—2441no—
315C22—2441no—
316C22—2441no—
317C22—2441no—
318C22#1684073711yescharacteristic
319C22D61⋊#9911yescharacteristic
320C22#1684074811yescharacteristic
321C22#1684075211yescharacteristic
322C22#1684075511yescharacteristic
323C22C2×#1451984111yescharacteristic
324C22D61⋊#10411yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—1222no—
331C4—1222no—
332C4—1222no—
333C4—4881no—
334C4—4881no—
335C2—2442no—
336C2#2146108711yescharacteristic
337C2#2146114311yescharacteristic
338C2#2146117311yescharacteristic
339C2#2146119511yescharacteristic
340C2#2146121711yescharacteristic
341C2#2146126911yescharacteristic
342C2#2146134411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7675
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460638C2semidirect
194. C61#7675semidirect

Maximal subgroups

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

subgroupindex
#214615462
C4×#145198342
#214606402
#214606382
#214541572
#767561