Finite Group Databasebeta

← #29658193

Subgroups — #29658193

Order 15616.

928 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 179 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#21456967C212yesmaximal, complemented
2#21456279C211yesmaximal, characteristic
3#21444959C214yesmaximal, complemented
4#21444940C214yesmaximal, complemented
5#21444481C211yesmaximal, characteristic
6#21444240C212yesmaximal, complemented
7C61×#3550C211yesmaximal, characteristic
8C2×#14519807—22no—
9C2×#14519777C2211yescharacteristic
10#16840165—22no—
11#16840157—22no—
12#16840141C2212yes—
13#16840134C2212yes—
14#16840112—22no—
15#16840095—24no—
16#16840057C2218yes—
17#16839815C2212yes—
18C4×#11758194C2211yescharacteristic
19#16839511C2212yes—
20#16839506C2212yes—
21Q8⋊#92418C2218yes—
22C61×#563—22no—
23C61×#559C2212yes—
24Q82×C61C2212yes—
25C61×#556—22no—
26D4×Q8×C61—22no—
27C61×#542—24no—
28C61×#536—22no—
29C61×#533C2212yes—
30C61×#532C2211yescharacteristic
31C22×Dic122—21no—
32#14519807—48no—
33C2×#11758202—24no—
34C2×#11758200—24no—
35C2×#11758194—21no—
36#14519777—22no—
37#14519777—21no—
38#14519777C2312yes—
39C2×C4⋊Dic61—22no—
40#14519710—28no—
41C4⋊#92418C2314yes—
42#14519701—28no—
43C22⋊#92418—22no—
44#14519688—21no—
45C4×#92418—22no—
46C4×#92418C2312yes—
47C2×#41×C61D412yes—
48C22×Q8×C61—22no—
49C4⋊Q8×C61—24no—
50C4⋊Q8×C61—24no—
51C4⋊Q8×C61D412yes—
52C4⋊Q8×C61D412yes—
53C4⋊Q8×C61C2311yescharacteristic
54#127×C61C2311yescharacteristic
55#126×C61—28no—
56#125×C61—22no—
57#124×C61—24no—
58#124×C61—24no—
59#124×C61D412yes—
60#123×C61—24no—
61#123×C61—24no—
62C22⋊Q8×C61—24no—
63C22⋊Q8×C61—28no—
64C22⋊Q8×C61—22no—
65C22⋊Q8×C61D414yes—
66#121×C61—22no—
67C4×Q8×C61—24no—
68C4×Q8×C61—22no—
69C4×Q8×C61C2314yes—
70C4×D4×C61—24no—
71C4×D4×C61—22no—
72#117×C61—22no—
73#117×C61—22no—
74C2×C42×C61C2311yescharacteristic
75#41×C61—44no—
76C2×Q8×C61—24no—
77C2×Q8×C61—22no—
78C2×Q8×C61—84no—
79C2×Q8×C61C2×D414yes—
80C2×Q8×C61C2×D412yes—
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61C2×D412yes—
84C22×C4×C61—24no—
85C22×C4×C61—22no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D412yes—
88C22×Dic61—41no—
89C2×Dic122—22no—
90C2×Dic122—44no—
91C2×Dic122—41no—
92C4⋊C4×C61—28no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—24no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—24no—
99C4⋊C4×C61C2×D414yes—
100C22⋊C4×C61—24no—
101C22⋊C4×C61—28no—
102C22⋊C4×C61—24no—
103C22⋊C4×C61—24no—
104C42×C61—24no—
105C42×C61—24no—
106C42×C61C2×D412yes—
107C42×C61C2×D411yescharacteristic
108C42×C61C2411yescharacteristic
109#11758202—48no—
110#11758200—48no—
111C4⋊Dic61—24no—
112C4⋊Dic61—42no—
113#11758194—24no—
114C2×#92418—22no—
115C2×#92418—24no—
116C23×C61—22no—
117C23×C61#12011yescharacteristic
118Q8×C61—28no—
119Q8×C61—42no—
120Q8×C61—44no—
121Q8×C61—84no—
122D4×C61—42no—
123D4×C61—44no—
124D4×C61—82no—
125C2×C4×C61—24no—
126C2×C4×C61—22no—
127C2×C4×C61—24no—
128C2×C4×C61—22no—
129C2×C4×C61—24no—
130C2×C4×C61—44no—
131C2×C4×C61—84no—
132C2×C4×C61#12012yes—
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61C22×D411yescharacteristic
135C2×C4×C61C22×D412yes—
136C2×Dic61—42no—
137C2×Dic61—82no—
138Dic122—44no—
139Dic122—82no—
140#92418—24no—
141#92418—44no—
142#18719—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—21no—
145C22×C61—44no—
146C22×C61—42no—
147C22×C61C2×#12011yescharacteristic
148C4×C61—22no—
149C4×C61—21no—
150C4×C61—44no—
151C4×C61—42no—
152C4×C61—44no—
153C4×C61#45312yes—
154C4×C61#57814yes—
155Dic61—82no—
156#3550D6111yescharacteristic
157#3230—612no—
158#3152—611no—
159#1633—614no—
160#1630—614no—
161#1543—611no—
162#1485—612no—
163C2×C61—41no—
164C2×C61—82no—
165C2×C61#301112yes—
166C2×C61C2×#45311yescharacteristic
167C2×#137—1222no—
168#563—22no—
169#559C2×D6112yes—
170Q82C2×D6112yes—
171#556—22no—
172D4×Q8—22no—
173#542—24no—
174#536—22no—
175#533C2×D6112yes—
176#532C2×D6111yescharacteristic
177C2×C4⋊Q8—611no—
178#500—1222no—
179#497—1222no—
180#494—612no—
181#492—612no—
182#487—1222no—
183#484—1224no—
184#477—618no—
185#431—612no—
186C4×M16—611no—
187#333—612no—
188#331—612no—
189Q8⋊C8—618no—
190C61#1871911yescharacteristic, complemented, Sylow
191C2×#41C22⋊D6112yes—
192C22×Q8—22no—
193C22×Q8—1221no—
194#137—2448no—
195C2×Q16—1224no—
196C2×SD16—1224no—
197C2×M16—1221no—
198C4⋊Q8—24no—
199C4⋊Q8—24no—
200C4⋊Q8—612no—
201C4⋊Q8—1222no—
202C4⋊Q8—1221no—
203C4⋊Q8C22⋊D6112yes—
204C4⋊Q8C22⋊D6112yes—
205C4⋊Q8C22×D6111yescharacteristic
206#127C22×D6111yescharacteristic
207#126—28no—
208#125—22no—
209#124—24no—
210#124—24no—
211#124C22⋊D6112yes—
212#123—24no—
213#123—24no—
214C22⋊Q8—24no—
215C22⋊Q8—28no—
216C22⋊Q8—22no—
217C22⋊Q8C22⋊D6114yes—
218#121—22no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8C22×D6114yes—
222C4×D4—24no—
223C4×D4—22no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—1222no—
227C2×C42C22×D6111yescharacteristic
228#107—1228no—
229C4⋊C8—614no—
230#103—1228no—
231C22⋊C8—1222no—
232#97—1221no—
233C4×C8—612no—
234C4×C8—1222no—
235#41—44no—
236C2×Q8—24no—
237C2×Q8—22no—
238C2×Q8—84no—
239C2×Q8—1222no—
240C2×Q8—2444no—
241C2×Q8—2441no—
242C2×Q8C2×C22⋊D6114yes—
243C2×Q8C2×C22⋊D6112yes—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4C2×C22⋊D6112yes—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—2441no—
250C22×C4C2×C22⋊D6112yes—
251C22×C4C2×C22⋊D6111yescharacteristic
252Q16—2448no—
253SD16—2448no—
254M16—1224no—
255C2×C8—1222no—
256C2×C8—1224no—
257C4⋊C4—28no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—1224no—
265C4⋊C4—2442no—
266C4⋊C4C2×C22⋊D6114yes—
267C22⋊C4—24no—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C42—24no—
272C42—24no—
273C42C2×C22⋊D6112yes—
274C42C2×C22⋊D6111yescharacteristic
275C42C23×D6111yescharacteristic
276C23—22no—
277C23#1451974611yescharacteristic
278Q8—28no—
279Q8—42no—
280Q8—44no—
281Q8—84no—
282Q8—4882no—
283Q8—2444no—
284D4—42no—
285D4—44no—
286D4—82no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—44no—
293C2×C4—84no—
294C2×C4—4882no—
295C2×C4—2442no—
296C2×C4#1451974612yes—
297C2×C4#1451974611yescharacteristic
298C2×C4C22×C22⋊D6111yescharacteristic
299C2×C4C22×C22⋊D6112yes—
300C8—1224no—
301C8—2444no—
302C22—22no—
303C22—21no—
304C22—44no—
305C22—42no—
306C22C2×#1451974611yescharacteristic
307C4—22no—
308C4—21no—
309C4—44no—
310C4—42no—
311C4—44no—
312C4—4882no—
313C4#1683993012yes—
314C4#1684057714yes—
315C2—41no—
316C2—82no—
317C2#2145511412yes—
318C2C2×#1683993011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3550C2
socleC22×C61C2×#120
prime radicalC61×#532C22
hypercenter#3550D61
hypocenterC61#18719
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #21456967C2semidirect
3. #21444959C2semidirect
4. #21444940C2semidirect
6. #21444240C2semidirect
190. C61#18719semidirect

Maximal subgroups

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

subgroupindex
#214569672
#214562792
#214449592
#214449402
#214444812
#214442402
C61×#35502
#1871961