Finite Group Databasebeta

← #29574149

Subgroups — #29574149

Order 15616.

364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 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#21454756C211yesmaximal, characteristic
2#21446540C211yesmaximal, characteristic
3#21444319C211yesmaximal, characteristic
4#21444221C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic
6#21443663C211yesmaximal, characteristic
7C61×#1571C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839891—22no—
10#16839891—22no—
11#16839815C2211yescharacteristic
12#16839790—21no—
13C2×#14519706—21no—
14#16839720—21no—
15C2×#14519688C2211yescharacteristic
16C4×C4⋊Dic61C2211yescharacteristic
17#16839516—21no—
18#16839500C412yes—
19#16839500C412yes—
20#16839492—22no—
21C61×#431C2211yescharacteristic
22C61×#423C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C61×#335—22no—
25C22×#92418D411yescharacteristic
26C22×#92418D411yescharacteristic
27#14519777Q811yescharacteristic
28#14519777Q811yescharacteristic
29#14519769—21no—
30#14519756—21no—
31#14519756C2×C412yes—
32C4×Dic122—21no—
33C4×Dic122D412yes—
34#14519736—21no—
35C2×C4⋊Dic61—21no—
36C2×C4×Dic61—21no—
37C4⋊#92418—21no—
38#14519706—24no—
39#14519706—42no—
40C22⋊#92418—21no—
41#14519688—21no—
42#14519688—21no—
43#14519687—22no—
44C4×#92418—21no—
45C8×Dic61—22no—
46#14519684C2×C411yescharacteristic
47#14519684C2×C411yescharacteristic
48C2×M16×C61—21no—
49C22×C8×C61—21no—
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61D412yes—
56C22⋊C8×C61C2×C412yes—
57C4×C8×C61—21no—
58C22×C4×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C2×Dic122—21no—
64C2×Dic122C4⋊C412yes—
65M16×C61—41no—
66M16×C61—41no—
67C2×C8×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C42×C61C2×D411yescharacteristic
73C42×C61C2×D411yescharacteristic
74C42×C61C2×Q811yescharacteristic
75C42×C61#4111yescharacteristic
76C22⋊Dic61—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—42no—
81C4⋊Dic61C4⋊C412yes—
82#11758196—22no—
83#11758196—22no—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88C2×#92418—21no—
89C2×#92418—21no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418Q1612yes—
94C23×C61C4×D411yescharacteristic
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61C2×C4⋊C411yescharacteristic
98C2×C4×C61C4×D411yescharacteristic
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C22⋊Q811yescharacteristic
101C2×C4×C61C22⋊Q811yescharacteristic
102C2×C4×C61#12311yescharacteristic
103C2×C4×C61C2×Q1611yescharacteristic
104C2×C4×C61#13511yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C61#13711yescharacteristic
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115Dic122—42no—
116Dic122—81no—
117C8×C61—42no—
118C8×C61—42no—
119C8×C61—81no—
120#92418—22no—
121#92418—41no—
122#92418—81no—
123#8879—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61#38511yescharacteristic
127C22×C61C4×Q1611yescharacteristic
128C22×C61#44011yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61#44911yescharacteristic
134C4×C61#45111yescharacteristic
135C4×C61#47711yescharacteristic
136C4×C61#47911yescharacteristic
137Dic61—42no—
138Dic61—42no—
139Dic61—42no—
140Dic61—81no—
141#2961—611no—
142#1940—611no—
143#1571D6111yescharacteristic
144#1503—611no—
145#1481—611no—
146#1303—611no—
147#1281—611no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61#186111yescharacteristic
151C2×C61#186311yescharacteristic
152C2×C61#186811yescharacteristic
153#533—611no—
154#446—1222no—
155#446—1222no—
156#431—611no—
157#431C2×D6111yescharacteristic
158#424—1221no—
159#423C2×D6111yescharacteristic
160C2×C4⋊C8—1221no—
161C2×C4⋊C8C2×D6111yescharacteristic
162#405—1221no—
163C2×#97—611no—
164C4×C4⋊C4—611no—
165#336—1221no—
166#335—22no—
167#328—612no—
168#328—612no—
169Q8⋊C8—1222no—
170C61#887911yescharacteristic, complemented, Sylow
171C2×M16—21no—
172C22×C8—21no—
173C22×C8—611no—
174C22×C8—611no—
175C4⋊Q8—611no—
176C4⋊Q8—611no—
177#125—1221no—
178C22⋊Q8—612no—
179C22⋊Q8—1221no—
180C4×Q8—612no—
181C4×Q8—1221no—
182#117—1221no—
183C2×C4⋊C4—1221no—
184C2×C42—1221no—
185C2×C42C22×D6111yescharacteristic
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—1224no—
191C4⋊C8—1221no—
192C4⋊C8—2442no—
193C4⋊C8C22⋊D6112yes—
194C22⋊C8—1221no—
195C22⋊C8C4×D6112yes—
196#97—1222no—
197#97—1221no—
198#97—1221no—
199C4×C8—21no—
200C4×C8—1222no—
201C4×C8—1221no—
202#95—611no—
203#95—611no—
204C2×Q8—612no—
205C2×Q8—1221no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4C2×C4×D6111yescharacteristic
209C22×C4D4×D6111yescharacteristic
210C22×C4#1175822611yescharacteristic
211M16—41no—
212M16—41no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—612no—
219C2×C8—1221no—
220C2×C8—1221no—
221C2×C8—1221no—
222C2×C8—1221no—
223C2×C8—1221no—
224C2×C8—2441no—
225C4⋊C4—612no—
226C4⋊C4—1222no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1222no—
231C4⋊C4—2442no—
232C22⋊C4—1222no—
233C42—1222no—
234C42—2441no—
235C42—2441no—
236C42#1175822211yescharacteristic
237C42D4×D6111yescharacteristic
238C42Q8×D6111yescharacteristic
239C42C2×C22⋊D6111yescharacteristic
240C23#1451973911yescharacteristic
241Q8—4881no—
242Q8—2442no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4C4⋊C4×D6111yescharacteristic
254C2×C4C4×C22⋊D6111yescharacteristic
255C2×C4#1451974511yescharacteristic
256C2×C4#1451975311yescharacteristic
257C2×C4#1451975511yescharacteristic
258C2×C4#1451976211yescharacteristic
259C2×C4Q16×D6111yescharacteristic
260C2×C4#1451979611yescharacteristic
261C2×C4#1451980111yescharacteristic
262C2×C4#1451980911yescharacteristic
263C8—42no—
264C8—42no—
265C8—81no—
266C8—1222no—
267C8—4881no—
268C8—2441no—
269C22—21no—
270C22—21no—
271C22#1683963311yescharacteristic
272C22#1683985611yescharacteristic
273C22#1683986111yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—4881no—
279C4—2442no—
280C4—2442no—
281C4—2442no—
282C4#1683990411yescharacteristic
283C4#1683991611yescharacteristic
284C4#1684005611yescharacteristic
285C4#1684006811yescharacteristic
286C2—21no—
287C2—21no—
288C2#2144605611yescharacteristic
289C2#2144607011yescharacteristic
290C2#2144610311yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1571C2
socleC22×C61#385
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1571D61
hypocenterC61#8879
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
170. C61#8879semidirect

Maximal subgroups

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

subgroupindex
#214547562
#214465402
#214443192
#214442212
#214437202
#214436632
C61×#15712
#887961