Finite Group Databasebeta

← #30601064

Subgroups — #30601064

Order 15616.

384 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462733C211yesmaximal, characteristic
2#21461353C211yesmaximal, characteristic
3#21461349C211yesmaximal, characteristic
4#21461311C211yesmaximal, characteristic
5#21460686C211yesmaximal, characteristic
6#21460686C211yesmaximal, characteristic
7#21456362C211yesmaximal, characteristic
8#16840814—22no—
9#16840813—22no—
10#16840787—22no—
11#16840785C2211yescharacteristic
12#16840785C2211yescharacteristic
13#16840785C2211yescharacteristic
14#16840785C2211yescharacteristic
15#16840622—22no—
16#16840621—22no—
17#16840619—22no—
18#16840317C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20#16840170—22no—
21#16840165C411yescharacteristic
22#16840160C411yescharacteristic
23#16840158C411yescharacteristic
24#16839803—22no—
25C4×#11758189C2211yescharacteristic
26C61×#500C411yescharacteristic
27#14519844—22no—
28#14519844—21no—
29#14519844—21no—
30#14519844D412yes—
31#14519844D412yes—
32C4⋊#92420—22no—
33#14519834—21no—
34#14519834—21no—
35#14519834—21no—
36#14519834—21no—
37#14519832—22no—
38#14519832—21no—
39#14519832—21no—
40#14519832—21no—
41#14519832—21no—
42C4×#92420—22no—
43C2×Q8×D61—21no—
44C2×#11758189—21no—
45#14519777C2×C411yescharacteristic
46#14519777C2×C411yescharacteristic
47#14519776—21no—
48#14519776—21no—
49#14519775—21no—
50#14519768D412yes—
51#14519757—21no—
52#14519753—21no—
53Q8×Dic61—21no—
54#14519742—21no—
55#14519735D412yes—
56C4⋊C4×D61—21no—
57C4⋊C4×D61—21no—
58C42×D61C2311yescharacteristic
59#14519710—22no—
60#14519709—22no—
61#14519708—22no—
62#14519687—21no—
63C4×#92418C2×C411yescharacteristic
64C4⋊Q8×C61C2×C411yescharacteristic
65C4⋊Q8×C61C2×C411yescharacteristic
66#107×C61—22no—
67C4×C8×C61C2×C411yescharacteristic
68C2×Q8×C61—21no—
69C2×Q8×C61—21no—
70Q8×D61—82no—
71C2×C4×D61—41no—
72C2×C4×D61C2×D411yescharacteristic
73C2×C4×D61#4111yescharacteristic
74C2×C4×D61#4111yescharacteristic
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—41no—
78C2×#92420—22no—
79C2×#92420—22no—
80C2×#92420—41no—
81C2×#92420—41no—
82C2×C8×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61C22⋊C412yes—
87C42×C61C22×C411yescharacteristic
88#11758198—22no—
89C4⋊Dic61—21no—
90C4⋊Dic61—22no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C22⋊C412yes—
94#11758196—22no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—22no—
98C4×Dic61C2×D411yescharacteristic
99C4×Dic61C2×D411yescharacteristic
100C4×Dic61C2×D411yescharacteristic
101C2×#92418—21no—
102#11758189—24no—
103C22×D61#12311yescharacteristic
104Q8×C61—81no—
105Q8×C61—81no—
106C2×C4×C61—22no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61C4×D411yescharacteristic
110C2×C4×C61C4×D411yescharacteristic
111C2×Dic61—22no—
112C2×Dic61—41no—
113C2×Dic61#12011yescharacteristic
114C2×Dic61#12111yescharacteristic
115C2×Dic61#12111yescharacteristic
116C4×D61—22no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—82no—
120Dic122—82no—
121Dic122—81no—
122Dic122—81no—
123#92420—42no—
124#92420—42no—
125#92420—81no—
126#92420—81no—
127C8×C61—22no—
128#92418—22no—
129#9420—611nomaximal, Sylow
130C22×C61#38611yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—42no—
138C4×C61—81no—
139Dic61—21no—
140Dic61—21no—
141Dic61—42no—
142Dic61—81no—
143Dic61#45612yes—
144#3165—611no—
145#2987—611no—
146#1558—611no—
147#1556—611no—
148#1537—611no—
149#1291—611no—
150#1291—611no—
151C2×C61#188611yescharacteristic
152C2×C61#190211yescharacteristic
153C2×C61#190311yescharacteristic
154D61—41no—
155#533—611no—
156C2×C4⋊Q8—611no—
157#501—1222no—
158#500—611no—
159#500#692311yescharacteristic
160#498—611no—
161#498—611no—
162#446—1222no—
163#446—1222no—
164#433—1222no—
165#432—611no—
166#432—611no—
167#432—611no—
168#432—611no—
169#428—1222no—
170C4×M16—611no—
171#333—1222no—
172#332—1222no—
173#330—1222no—
174C61#942011yescharacteristic, complemented, Sylow
175C22×Q8—1221no—
176C2×M16—1221no—
177C4⋊Q8—611no—
178C4⋊Q8—611no—
179C4⋊Q8—1221no—
180C4⋊Q8—1221no—
181C4⋊Q8—1221no—
182C4⋊Q8C2×#692311yescharacteristic
183C4⋊Q8C2×#692311yescharacteristic
184#125—612no—
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187C4×Q8—1221no—
188C4×Q8—1221no—
189#117—612no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C42—611no—
193#107—22no—
194#107—1222no—
195#106—1222no—
196#106—1222no—
197C4⋊C8—612no—
198C4⋊C8—612no—
199C4⋊C8—1221no—
200C4⋊C8—1221no—
201C4⋊C8—1222no—
202C4⋊C8—1222no—
203C22⋊C8—1221no—
204C22⋊C8—1221no—
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207#97—1221no—
208#97—1221no—
209#97—1221no—
210#97—1221no—
211#97—1221no—
212#97—1222no—
213C4×C8—611no—
214C4×C8—1222no—
215C4×C8C2×#692311yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—1221no—
219C2×Q8—1221no—
220C2×Q8—4882no—
221C2×Q8—2441no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—2441no—
226M16—1224no—
227C2×C8—21no—
228C2×C8—1221no—
229C2×C8—1222no—
230C2×C8—1222no—
231C2×C8—2441no—
232C2×C8—2441no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—612no—
237C4⋊C4—1222no—
238C4⋊C4—1222no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4C22⋊#692312yes—
245C22⋊C4—1222no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42—1222no—
250C42C22×#692311yescharacteristic
251C23—611no—
252Q8—81no—
253Q8—81no—
254Q8—4881no—
255Q8—4881no—
256Q8—4882no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—4882no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4C2×C22⋊#692311yescharacteristic
269C2×C4D4×#692311yescharacteristic
270C2×C4D4×#692311yescharacteristic
271C8—22no—
272C8—1222no—
273C8—4881no—
274C8—4881no—
275C8—2442no—
276C8—2442no—
277C22—1221no—
278C22—1221no—
279C22—1221no—
280C22#1684071011yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—42no—
285C4—81no—
286C4—612no—
287C4—1221no—
288C4—1221no—
289C4—4881no—
290C4—2442no—
291C2—2441no—
292C2#2146182511yescharacteristic
293C2#2146184911yescharacteristic
294C2#2146185011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#386
prime radicalC22×D61#123
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9420
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
174. C61#9420semidirect

Maximal subgroups

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

subgroupindex
#214627332
#214613532
#214613492
#214613112
#214606862
#214563622
#942061