Finite Group Databasebeta

← #29583787

Subgroups — #29583787

Order 15616.

366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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#21455620C211yesmaximal, characteristic
2#21445835C211yesmaximal, characteristic
3#21444589C211yesmaximal, characteristic
4#21444383C211yesmaximal, characteristic
5#21444142C211yesmaximal, characteristic
6#21443678C211yesmaximal, characteristic
7C61×#1542C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840066—22no—
10#16840054—21no—
11#16840044—21no—
12#16839815C2211yescharacteristic
13#16839805—21no—
14#16839786C2211yescharacteristic
15#16839770—21no—
16C2×#14519702—21no—
17#16839628C2211yescharacteristic
18#16839525—21no—
19#16839512—22no—
20#16839499—22no—
21#16839487—22no—
22C61×#533C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#333—21no—
26C61×#332—21no—
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31C4×Dic122—21no—
32C4×Dic122—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37#14519710—22no—
38#14519708—22no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418D412yes—
42#14519702—42no—
43#14519700—22no—
44#14519700—22no—
45C22⋊#92418D412yes—
46C4×#92418—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C4⋊Q8×C61D411yescharacteristic
51C4⋊Q8×C61D411yescharacteristic
52#125×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57#117×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C4×C8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122SD1612yes—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61—41no—
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102#11758194—41no—
103#11758194—41no—
104C2×#92418—22no—
105C2×#92418—22no—
106C23×C61#12111yescharacteristic
107Q8×C61—81no—
108Q8×C61—81no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12111yescharacteristic
116C2×C4×C61#12311yescharacteristic
117C2×C4×C61#12311yescharacteristic
118C2×C4×C61#12411yescharacteristic
119C2×C4×C61C2×SD1611yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×Dic61—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129C2×Dic61—81no—
130C2×Dic61—81no—
131Dic122—22no—
132Dic122—22no—
133Dic122—41no—
134Dic122—41no—
135C8×C61—81no—
136C8×C61—81no—
137#92418—42no—
138#92418—42no—
139#10470—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#39411yescharacteristic
143C22×C61#46511yescharacteristic
144C22×C61#47011yescharacteristic
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—81no—
150C4×C61—81no—
151C4×C61#44811yescharacteristic
152C4×C61#45211yescharacteristic
153C4×C61#48311yescharacteristic
154C4×C61#48511yescharacteristic
155Dic61—42no—
156Dic61—81no—
157Dic61—161no—
158#3078—611no—
159#1805—611no—
160#1570—611no—
161#1542D6111yescharacteristic
162#1518—611no—
163#1461—611no—
164#1286—611no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61#203511yescharacteristic
168C2×C61#204911yescharacteristic
169C2×C61#205311yescharacteristic
170#533C2×D6111yescharacteristic
171C2×C4×Q8—611no—
172#479—1222no—
173#477—1221no—
174#475—1221no—
175#431—611no—
176#431C2×D6111yescharacteristic
177#428—1221no—
178#423—611no—
179C2×C4⋊C8C2×D6111yescharacteristic
180#419—1221no—
181C2×#103—1221no—
182#382—611no—
183#340—1221no—
184#334—1222no—
185#333—21no—
186#332—21no—
187#328—1222no—
188#324—1222no—
189C61#1047011yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C2×M16—1221no—
192C22×C8—21no—
193C4⋊Q8C22⋊D6111yescharacteristic
194C4⋊Q8C22⋊D6111yescharacteristic
195#125—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—1221no—
201C4×Q8—1221no—
202C4×Q8—1221no—
203C4×Q8—1221no—
204#117—21no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C42—1221no—
209C2×C42C22×D6111yescharacteristic
210#107—1222no—
211#106—1222no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—612no—
216C4⋊C8—1221no—
217C4⋊C8—1221no—
218#103—1222no—
219#103—1222no—
220#103—2442no—
221C22⋊C8—21no—
222C22⋊C8—612no—
223C4×C8—21no—
224C4×C8—1221no—
225#95—1221no—
226#95—1221no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—612no—
230C2×Q8—1221no—
231C2×Q8—1221no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—2441no—
238C22×C4#1175822211yescharacteristic
239C22×C4D4×D6111yescharacteristic
240C22×C4D4×D6111yescharacteristic
241M16—2441no—
242M16—2441no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—1222no—
248C2×C8—1222no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C22⋊C4—41no—
262C42—41no—
263C42—2441no—
264C42—2441no—
265C42#1175822211yescharacteristic
266C42D4×D6111yescharacteristic
267C42#1175822411yescharacteristic
268C42C2×C22⋊D6111yescharacteristic
269C23#1451975011yescharacteristic
270Q8—81no—
271Q8—81no—
272Q8—1222no—
273Q8—1222no—
274Q8—2441no—
275Q8—2441no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—1222no—
281C2×C4—4881no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4#1451974511yescharacteristic
289C2×C4#1451974911yescharacteristic
290C2×C4#1451975011yescharacteristic
291C2×C4#1451975911yescharacteristic
292C2×C4#1451976011yescharacteristic
293C2×C4#1451976311yescharacteristic
294C2×C4SD16×D6111yescharacteristic
295C2×C4#1451980011yescharacteristic
296C2×C4#1451980611yescharacteristic
297C2×C4#1451980911yescharacteristic
298C8—81no—
299C8—81no—
300C8—2442no—
301C8—2442no—
302C22—21no—
303C22—21no—
304C22#1683967711yescharacteristic
305C22#1683999411yescharacteristic
306C22#1684001911yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—9761no—
314C4—4881no—
315C4—2442no—
316C4#1683989911yescharacteristic
317C4#1683992311yescharacteristic
318C4#1684009111yescharacteristic
319C4#1684010211yescharacteristic
320C2—21no—
321C2—21no—
322C2#2144701311yescharacteristic
323C2#2144709911yescharacteristic
324C2#2144712311yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1542C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1542D61
hypocenterC61#10470
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
189. C61#10470semidirect

Maximal subgroups

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

subgroupindex
#214556202
#214458352
#214445892
#214443832
#214441422
#214436782
C61×#15422
#1047061