Finite Group Databasebeta

← #30601784

Subgroups — #30601784

Order 15616.

456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461605C211yesmaximal, characteristic
2#21461536C211yesmaximal, characteristic
3C2×#16840619C212yesmaximal
4C2×#16840619C212yesmaximal
5#21454181C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13#16840619—24no—
14C2×#14519768C2211yescharacteristic
15C2×#14519768C2211yescharacteristic
16#16839659—21no—
17#16839659—21no—
18#16839659—21no—
19#16839659—21no—
20#16839631C411yescharacteristic
21#16839631C411yescharacteristic
22#16839628C411yescharacteristic
23C42×Dic61C2211yescharacteristic
24C61×#382C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—24no—
28#14519832—22no—
29#14519832—22no—
30#14519832—22no—
31#14519832D414yes—
32#14519768—22no—
33#14519768—22no—
34#14519768—22no—
35#14519768—22no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
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×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—22no—
77C4⋊C4×C61—22no—
78C42×C61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C4⋊Dic61—42no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758196—42no—
85#11758196—42no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61C2×D412yes—
97C4×Dic61#4112yes—
98C23×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#10112yes—
113C2×C4×C61C4×D412yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
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#10112yes—
129C2×Dic61#10412yes—
130C2×Dic61#12112yes—
131C2×Dic61#12411yescharacteristic
132C2×Dic61#12711yescharacteristic
133#92420—44no—
134#92420—44no—
135#9690—611nomaximal, Sylow
136C22×C61#39011yescharacteristic
137C22×C61C2×#10111yescharacteristic
138C22×C61C2×#10111yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C22×C61#42111yescharacteristic
141C22×C61#42111yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61—81no—
148Dic61—22no—
149Dic61—21no—
150Dic61—21no—
151Dic61—22no—
152Dic61—22no—
153Dic61—81no—
154Dic61—81no—
155#2859—611no—
156#1767—611no—
157#1745—611no—
158C2×#330—612no—
159C2×#330—612no—
160C2×C61#152811yescharacteristic
161C2×C61#153111yescharacteristic
162C2×C61#153411yescharacteristic
163C2×C61#153711yescharacteristic
164C2×C61#196311yescharacteristic
165C2×C61#196611yescharacteristic
166C2×C61#198011yescharacteristic
167C2×#125—611no—
168C2×#125—611no—
169C2×C4⋊C8—1221no—
170C2×#97—612no—
171C2×#97—612no—
172#389—1221no—
173#389—1221no—
174#389—1221no—
175#389—1221no—
176#384—611no—
177#384—611no—
178#382—611no—
179#382#692311yescharacteristic
180C43—611no—
181#336—1221no—
182#336—1221no—
183#336—1221no—
184#330—1224no—
185#330—1224no—
186C61#969011yescharacteristic, complemented, Sylow
187C22×C8—1222no—
188C22×C8—1222no—
189#125—1222no—
190#125—1222no—
191#125—1222no—
192#125—1222no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42C2×#692311yescharacteristic
212C4⋊C8—1224no—
213#97—614no—
214#97—1222no—
215#97—1222no—
216#97—1222no—
217#95—21no—
218#95—21no—
219#95—1221no—
220#95—1221no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22×#692311yescharacteristic
232C2×C8—1224no—
233C2×C8—1224no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—1222no—
241C4⋊C4—1222no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2442no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2442no—
250C4⋊C4—2442no—
251C4⋊C4—2442no—
252C42—22no—
253C42—612no—
254C42—612no—
255C42—1222no—
256C42—1222no—
257C42—2441no—
258C42—2441no—
259C42—2441no—
260C23C2×C22⋊#692311yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—612no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4#1451983812yes—
294C2×C4D4×#692312yes—
295C8—2444no—
296C8—2444no—
297C22#1684071411yescharacteristic
298C22C2×#1451983811yescharacteristic
299C22D61⋊#10111yescharacteristic
300C22D61⋊#10411yescharacteristic
301C22#1684075911yescharacteristic
302C22#1684075911yescharacteristic
303C22#1684075911yescharacteristic
304C4—22no—
305C4—22no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—1222no—
310C4—1222no—
311C4—1222no—
312C4—1221no—
313C4—1221no—
314C4—4881no—
315C4—4881no—
316C2#2146128211yescharacteristic
317C2#2146129111yescharacteristic
318C2#2146130211yescharacteristic
319C2#2146131011yescharacteristic
320C2#2146195611yescharacteristic
321C2#2146196211yescharacteristic
322C2#2146198411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#9690
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
186. C61#9690semidirect

Maximal subgroups

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

subgroupindex
#214616052
#214615362
C2×#168406192
#214541812
#969061