Finite Group Databasebeta

← #30605172

Subgroups — #30605172

Order 15616.

388 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461720C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21460820C212yesmaximal, complemented
4#21460818C212yesmaximal, complemented
5#21449089C211yesmaximal, characteristic
6#16840782—21no—
7#16840734—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519734C2211yescharacteristic
13#16839700C2211yescharacteristic
14#16839697C411yescharacteristic
15#16839695—21no—
16#16839684—21no—
17#16839681C2211yescharacteristic
18#16839673C411yescharacteristic
19C4×#11758196—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C4×#11758198—21no—
22C2×C4×Q8×C61C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28#14519832—41no—
29C22×C4×D61D411yescharacteristic
30#14519734—41no—
31#14519734—41no—
32C2×C4⋊Dic61—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196D411yescharacteristic
36C2×#11758196C2311yescharacteristic
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198C2×C411yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61D411yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684C2×C411yescharacteristic
48#14519684C2×C411yescharacteristic
49C22×Q8×C61C2×C411yescharacteristic
50C4×Q8×C61—41no—
51C4×Q8×C61—41no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C2×Q8×C61—42no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—22no—
72C2×C4×D61—41no—
73#11758217—42no—
74#11758217—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—41no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—41no—
82C42×C61—41no—
83#11758198—41no—
84#11758198—41no—
85#11758198—42no—
86#11758198—42no—
87C4⋊Dic61—42no—
88#11758196—41no—
89#11758196—41no—
90#11758196—42no—
91#11758196—42no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—42no—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—41no—
100C22×D61—41no—
101Q8×C61—42no—
102Q8×C61—42no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#9911yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#13712yes—
130C4×D61—42no—
131C4×D61—42no—
132#92420—82no—
133#92420—82no—
134#11816—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61C2×#9911yescharacteristic
138C22×C61#41911yescharacteristic
139C22×C61#42111yescharacteristic
140C2×D61—42no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—81no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—42no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—81no—
151Dic61—22no—
152Dic61—42no—
153Dic61—41no—
154Dic61—41no—
155Dic61—81no—
156#2396—611no—
157#1822—611no—
158#1464—611no—
159#1354—612no—
160#1353—612no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#151111yescharacteristic
164C2×C61#212011yescharacteristic
165C2×C61#213211yescharacteristic
166D61—81no—
167C2×C4×Q8#692311yescharacteristic
168C2×#117—611no—
169#432—1221no—
170#407—1221no—
171#400—611no—
172#399—611no—
173#398—1221no—
174#396—1221no—
175#395—611no—
176#393—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4—1221no—
179C4×C22⋊C4—1221no—
180#343—612no—
181#343—1221no—
182#324—612no—
183#323—1221no—
184C61#1181611yescharacteristic, complemented, Sylow
185C22×Q8C2×#692311yescharacteristic
186C23×C4—611no—
187C2×M16—1222no—
188C4×Q8—41no—
189C4×Q8—41no—
190#117—2441no—
191#117—2441no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C2×#692311yescharacteristic
199C2×C22⋊C4—611no—
200C2×C22⋊C4—611no—
201C2×C22⋊C4—1221no—
202C2×C22⋊C4—1221no—
203C2×C42—21no—
204C2×C42—611no—
205C2×C42—1221no—
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—2441no—
208C22⋊C8—1222no—
209C22⋊C8—2441no—
210C22⋊C8—2441no—
211#97—2441no—
212#95—611no—
213#95—611no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218C24—611no—
219C2×Q8—42no—
220C2×Q8—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—1222no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—2441no—
232C22×C4C22⋊#692311yescharacteristic
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22×#692311yescharacteristic
235M16—2442no—
236M16—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C22⋊C4—2442no—
249C22⋊C4—2442no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—41no—
254C42—1221no—
255C42—1221no—
256C42—2442no—
257C23—1221no—
258C23—1221no—
259C23—1221no—
260C23—2441no—
261C23—2441no—
262C23C2×C22⋊#692311yescharacteristic
263Q8—42no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—612no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4#1451983511yescharacteristic
293C2×C4#1451983511yescharacteristic
294C8—4882no—
295C8—4882no—
296C22—21no—
297C22—21no—
298C22—4881no—
299C22—2442no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22C2×#1451983511yescharacteristic
304C22#1684075511yescharacteristic
305C22#1684076111yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—1222no—
313C4—4881no—
314C4—2442no—
315C4—2441no—
316C4—2441no—
317C2—21no—
318C2—21no—
319C2—4881no—
320C2#2146122911yescharacteristic
321C2#2146207011yescharacteristic
322C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×C4×Q8#6923
hypocenterC61#11816
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
4. #21460818C2semidirect
184. C61#11816semidirect

Maximal subgroups

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

subgroupindex
#214617202
#214610722
#214608202
#214608182
#214490892
#1181661