Finite Group Databasebeta

← #29583791

Subgroups — #29583791

Order 15616.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#21455626C211yesmaximal, characteristic
2#21445835C211yesmaximal, characteristic
3#21444477C211yesmaximal, characteristic
4#21444384C211yesmaximal, characteristic
5#21444142C211yesmaximal, characteristic
6#21443679C211yesmaximal, characteristic
7C61×#1570C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840070—22no—
11#16840058—21no—
12#16840048—21no—
13#16839815C2211yescharacteristic
14#16839804—21no—
15#16839772—21no—
16C2×#14519702—21no—
17#16839628C2211yescharacteristic
18#16839525—21no—
19#16839510—21no—
20#16839507—21no—
21#16839500—22no—
22#16839487—22no—
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#334—22no—
27C22×Dic122D411yescharacteristic
28#14519777D411yescharacteristic
29#14519777D411yescharacteristic
30#14519769—21no—
31#14519756—21no—
32#14519756—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39#14519736—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519711—22no—
45#14519709—22no—
46C4⋊#92418—21no—
47#14519702—22no—
48#14519702—22no—
49#14519702—42no—
50C22⋊#92418—21no—
51C4×#92418—21no—
52#14519684—21no—
53#14519684—21no—
54C2×M16×C61—21no—
55C22×C8×C61—21no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61D412yes—
62C22⋊C8×C61D412yes—
63C4×C8×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—41no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122SD1612yes—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—22no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C42×C61C2×D411yescharacteristic
86C42×C61C2×D411yescharacteristic
87C42×C61#4111yescharacteristic
88C42×C61#4111yescharacteristic
89C22⋊Dic61—41no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C2×#92418—41no—
106C23×C61#12111yescharacteristic
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61#12111yescharacteristic
111C2×C4×C61#12111yescharacteristic
112C2×C4×C61#12311yescharacteristic
113C2×C4×C61#12311yescharacteristic
114C2×C4×C61#12411yescharacteristic
115C2×C4×C61C2×SD1611yescharacteristic
116C2×C4×C61#13511yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—81no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129Dic122—22no—
130Dic122—22no—
131Dic122—41no—
132Dic122—41no—
133Dic122—81no—
134Dic122—81no—
135C8×C61—42no—
136C8×C61—42no—
137C8×C61—81no—
138#92418—81no—
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#44811yescharacteristic
150C4×C61#45211yescharacteristic
151C4×C61#48311yescharacteristic
152C4×C61#48511yescharacteristic
153Dic61—42no—
154Dic61—81no—
155Dic61—81no—
156Dic61—81no—
157Dic61—161no—
158#3078—611no—
159#1805—611no—
160#1570D6111yescharacteristic
161#1542—611no—
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#533—611no—
171C2×C4×Q8—611no—
172#479—1222no—
173#477—1221no—
174#475—1221no—
175#431—611no—
176#431C2×D6111yescharacteristic
177#428—1221no—
178#423C2×D6111yescharacteristic
179C2×C4⋊C8C2×D6111yescharacteristic
180#419—1221no—
181C2×#103—1221no—
182#382—611no—
183#340—1221no—
184#334—22no—
185#333—1221no—
186#332—1221no—
187#328—1222no—
188#324—1222no—
189C61#1047011yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C2×M16—21no—
192C22×C8—21no—
193C4⋊Q8—611no—
194C4⋊Q8—611no—
195#125—1221no—
196C22⋊Q8—1221no—
197C22⋊Q8—1221no—
198C4×Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C4×Q8—1221no—
202C4×Q8—1221no—
203C4×Q8—1221no—
204#117—1221no—
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—21no—
216C4⋊C8—1221no—
217C4⋊C8C22⋊D6112yes—
218#103—1222no—
219#103—1222no—
220#103—2442no—
221C22⋊C8—1221no—
222C22⋊C8D24412yes—
223C4×C8—21no—
224C4×C8—1221no—
225#95—1221no—
226#95—1221no—
227C2×Q8—612no—
228C2×Q8—1221no—
229C2×Q8—1221no—
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×C4C2×D24411yescharacteristic
239C22×C4D4×D6111yescharacteristic
240C22×C4#1175822611yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—2441no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C22⋊C4—2441no—
262C42—2441no—
263C42—2441no—
264C42—2441no—
265C42#1175822211yescharacteristic
266C42D4×D6111yescharacteristic
267C42#1175822611yescharacteristic
268C42C2×C22⋊D6111yescharacteristic
269C23#1451975211yescharacteristic
270Q8—1222no—
271Q8—1222no—
272Q8—4881no—
273Q8—4881no—
274Q8—2441no—
275Q8—2441no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—1222no—
279C2×C4—4881no—
280C2×C4—4881no—
281C2×C4—4881no—
282C2×C4—4881no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4#1451974511yescharacteristic
289C2×C4#1451975111yescharacteristic
290C2×C4#1451975211yescharacteristic
291C2×C4#1451976211yescharacteristic
292C2×C4#1451976211yescharacteristic
293C2×C4#1451976611yescharacteristic
294C2×C4SD16×D6111yescharacteristic
295C2×C4#1451979811yescharacteristic
296C2×C4#1451980611yescharacteristic
297C2×C4#1451980611yescharacteristic
298C8—42no—
299C8—42no—
300C8—81no—
301C8—4881no—
302C22—21no—
303C22—21no—
304C22#1683967911yescharacteristic
305C22#1683999211yescharacteristic
306C22#1684002111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—9761no—
312C4—4881no—
313C4—4881no—
314C4—4881no—
315C4—2442no—
316C4#1683989911yescharacteristic
317C4#1683992111yescharacteristic
318C4#1684009411yescharacteristic
319C4#1684010611yescharacteristic
320C2—21no—
321C2—21no—
322C2#2144701711yescharacteristic
323C2#2144710111yescharacteristic
324C2#2144712511yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1570C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1570D61
hypocenterC61#10470
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

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
#214556262
#214458352
#214444772
#214443842
#214441422
#214436792
C61×#15702
#1047061