Finite Group Databasebeta

← #29589676

Subgroups — #29589676

Order 15616.

358 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 73 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#21451032C211yesmaximal, characteristic
2#21444161C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443763C211yesmaximal, characteristic
5#21443762C211yesmaximal, characteristic
6#21443762C211yesmaximal, characteristic
7C61×#1324C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839703—21no—
13#16839703—21no—
14#16839668C411yescharacteristic
15#16839667C411yescharacteristic
16#16839666—21no—
17#16839666—21no—
18#16839627C2211yescharacteristic
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#382C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122C2×C411yescharacteristic
29#14519776—41no—
30#14519776—41no—
31#14519742—41no—
32#14519742—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42#14519706—41no—
43#14519706—41no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46#14519687—41no—
47C8×Dic61—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—44no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C42×C61—21no—
85C42×C61—21no—
86C4⋊Dic61—41no—
87#11758196—41no—
88#11758196—41no—
89#11758196—42no—
90#11758196—42no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#13111yescharacteristic
114C2×C4×C61#13111yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61#9911yescharacteristic
129C2×Dic61#9911yescharacteristic
130C2×Dic61#10112yes—
131Dic122—42no—
132Dic122—42no—
133Dic122—82no—
134Dic122—82no—
135C8×C61—81no—
136C8×C61—81no—
137#92418—81no—
138#92418—81no—
139#11573—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#40811yescharacteristic
143C22×C61C2×#9911yescharacteristic
144C22×C61C2×#10111yescharacteristic
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—81no—
150C4×C61—81no—
151Dic61—21no—
152Dic61—22no—
153Dic61—41no—
154Dic61—41no—
155Dic61—81no—
156Dic61—81no—
157Dic61#35512yes—
158#2568—611no—
159#1467—611no—
160#1461—611no—
161#1324—611no—
162#1324—611no—
163#1324—611no—
164#1324D6111yescharacteristic
165C2×C61—21no—
166C2×C61—21no—
167C2×C61#147211yescharacteristic
168C2×C61#212911yescharacteristic
169C2×C61C2×#35511yescharacteristic
170C2×C4⋊Q8—611no—
171C2×C4×Q8—611no—
172#432—1221no—
173#431—1221no—
174#400—1221no—
175#400—1221no—
176#391—611no—
177#391—611no—
178#391—1221no—
179#391—1221no—
180#382—611no—
181#382C2×D6111yescharacteristic
182C4×C4⋊C4—611no—
183#324—611no—
184#324—611no—
185#324—1221no—
186#324—1221no—
187#324C2×D6111yescharacteristic
188#324C2×D6111yescharacteristic
189C61#1157311yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C22×Q8—1221no—
192C4⋊Q8—2441no—
193C4⋊Q8—2441no—
194C4×Q8—2441no—
195C4×Q8—2441no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C4×D6111yescharacteristic
202C2×C4⋊C4C22×D6111yescharacteristic
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42C4×D6111yescharacteristic
208C4⋊C8—2441no—
209C4⋊C8—2441no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C22⋊C8—1221no—
213C22⋊C8—1221no—
214#97—2441no—
215C4×C8—2441no—
216#95—21no—
217#95—21no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225C2×Q8—1222no—
226C2×Q8—1221no—
227C2×Q8—1221no—
228C2×Q8—2441no—
229C2×Q8—2441no—
230C2×Q8—2441no—
231C2×Q8—2444no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4C2×C4×D6111yescharacteristic
241C22×C4D4×D6111yescharacteristic
242C22×C4D4×D6111yescharacteristic
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—2441no—
246C2×C8—2441no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C42—21no—
255C42—21no—
256C42—1221no—
257C42—1221no—
258C42—1221no—
259C42—1221no—
260C42—1221no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C23C22⋊C4×D6111yescharacteristic
265Q8—4882no—
266Q8—4882no—
267Q8—2442no—
268Q8—2442no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—612no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4#1451978311yescharacteristic
297C2×C4#1451978511yescharacteristic
298C8—81no—
299C8—81no—
300C8—4881no—
301C8—4881no—
302C22—21no—
303C22—21no—
304C22#1683972711yescharacteristic
305C22#99×D6111yescharacteristic
306C22#101×D6111yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—612no—
314C4—1221no—
315C4—1222no—
316C4—4881no—
317C4—4881no—
318C4—2441no—
319C4—2441no—
320C2—21no—
321C2—21no—
322C2#2144418111yescharacteristic
323C2#2144749211yescharacteristic
324C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11573
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
189. C61#11573semidirect

Maximal subgroups

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

subgroupindex
#214510322
#214441612
#214441412
#214437632
#214437622
C61×#13242
#1157361