Finite Group Databasebeta

← #29591174

Subgroups — #29591174

Order 15616.

372 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451030C211yesmaximal, characteristic
2#21445814C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic
5#21443846C211yesmaximal, characteristic
6#21443845C211yesmaximal, characteristic
7C61×#1353C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11#16839785—21no—
12C2×#14519695—21no—
13#16839702C411yescharacteristic
14#16839701C2211yescharacteristic
15#16839700C411yescharacteristic
16#16839666—21no—
17#16839666—21no—
18#16839666—21no—
19#16839626—21no—
20#16839613C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C2×#11758194—21no—
30#14519776—41no—
31#14519776—41no—
32#14519742—41no—
33#14519742—41no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196C2×C411yescharacteristic
38C2×#11758196D411yescharacteristic
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519706—41no—
44#14519706—41no—
45#14519706—41no—
46#14519695—42no—
47C22⋊#92418—21no—
48C8×Dic61—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—44no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122SD1612yes—
80C2×Dic122Q1612yes—
81M16×C61—41no—
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊Dic61—41no—
88#11758196—41no—
89#11758196—41no—
90#11758196—42no—
91#11758196—42no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61C2×SD1611yescharacteristic
116C2×C4×C61C2×Q1611yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—22no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#9911yescharacteristic
130C2×Dic61#9911yescharacteristic
131C2×Dic61#10312yes—
132C2×Dic61#10312yes—
133Dic122—42no—
134Dic122—42no—
135Dic122—82no—
136Dic122—82no—
137C8×C61—81no—
138C8×C61—81no—
139#92418—81no—
140#92418—81no—
141#11907—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61C2×#9911yescharacteristic
145C22×C61C2×#10311yescharacteristic
146C22×C61#42111yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—81no—
152C4×C61—81no—
153Dic61—21no—
154Dic61—22no—
155Dic61—22no—
156Dic61—41no—
157Dic61—81no—
158Dic61—81no—
159Dic61#35512yes—
160#2568—611no—
161#1801—611no—
162#1461—611no—
163#1353—611no—
164#1353—611no—
165#1353—611no—
166#1353D6111yescharacteristic
167C2×C61—21no—
168C2×C61—21no—
169C2×C61#152011yescharacteristic
170C2×C61#212311yescharacteristic
171C2×C61C2×#35511yescharacteristic
172C2×C4⋊Q8—611no—
173C2×C4×Q8—611no—
174#431—1221no—
175#423—1221no—
176C2×#101—1221no—
177#400—611no—
178#400—611no—
179#400—611no—
180#400C2×D6111yescharacteristic
181#391—1221no—
182#391—1221no—
183#391—1221no—
184#382—1221no—
185C4×C4⋊C4—611no—
186#343—611no—
187#343C2×D6111yescharacteristic
188#324—611no—
189#324—1221no—
190#324C2×D6111yescharacteristic
191C61#1190711yescharacteristic, complemented, Sylow
192C22×Q8—611no—
193C22×Q8—1221no—
194C2×M16—21no—
195C2×M16—1221no—
196C4⋊Q8—2441no—
197C4⋊Q8—2441no—
198C4×Q8—2441no—
199C4×Q8—2441no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C4×D6111yescharacteristic
206C2×C4⋊C4C22×D6111yescharacteristic
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—1221no—
211C4⋊C8—2441no—
212C4⋊C8—2441no—
213C4⋊C8—2441no—
214#101—2442no—
215C22⋊C8—21no—
216C22⋊C8—1221no—
217C4×C8—2441no—
218#95—21no—
219#95—21no—
220#95—611no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95C4×D6111yescharacteristic
228C2×Q8—612no—
229C2×Q8—612no—
230C2×Q8—2441no—
231C2×Q8—2441no—
232C2×Q8—2441no—
233C2×Q8—2441no—
234C2×Q8—2444no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4C2×C4×D6111yescharacteristic
244C22×C4D4×D6111yescharacteristic
245C22×C4D4×D6111yescharacteristic
246M16—41no—
247M16—41no—
248M16—2441no—
249M16—2441no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—2441no—
253C2×C8—2441no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42—2442no—
268C23C22⋊C4×D6111yescharacteristic
269Q8—4882no—
270Q8—4882no—
271Q8—2442no—
272Q8—2442no—
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—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—1222no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2442no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4SD16×D6111yescharacteristic
301C2×C4Q16×D6111yescharacteristic
302C8—81no—
303C8—81no—
304C8—4881no—
305C8—4881no—
306C22—21no—
307C22—21no—
308C22#99×D6111yescharacteristic
309C22#103×D6111yescharacteristic
310C22#1683977711yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—612no—
318C4—1222no—
319C4—1222no—
320C4—1221no—
321C4—4881no—
322C4—4881no—
323C4—2441no—
324C2—21no—
325C2—21no—
326C2#2144438911yescharacteristic
327C2#2144747111yescharacteristic
328C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11907
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
191. C61#11907semidirect

Maximal subgroups

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

subgroupindex
#214510302
#214458142
#214441412
#214438472
#214438462
#214438452
C61×#13532
#1190761