Finite Group Databasebeta

← #30601770

Subgroups — #30601770

Order 15616.

500 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461604C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3C2×#16840619C212yesmaximal
4C2×#16840619C212yesmaximal
5#21454181C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8C2×#14519832C2212yes—
9C2×#14519832C2212yes—
10C2×C4×#92420—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—
27#14519844—24no—
28#14519832—24no—
29#14519832—22no—
30#14519832—22no—
31#14519832—22no—
32#14519832D414yes—
33C4×#92420—24no—
34#14519768—22no—
35#14519768—22no—
36#14519768—22no—
37#14519768—22no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54#14519684—21no—
55#14519684—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×#92420—24no—
73C2×#92420—24no—
74C2×#92420—24no—
75C2×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—22no—
80C42×C61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83C4⋊Dic61—42no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90#11758196—42no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61C2×D412yes—
99C4×Dic61#4112yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
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#10112yes—
115C2×C4×C61C4×D412yes—
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#10412yes—
131C2×Dic61#10412yes—
132C2×Dic61#12112yes—
133C2×Dic61#12411yescharacteristic
134C2×Dic61#12711yescharacteristic
135#92420—28no—
136#92420—44no—
137#9686—611nomaximal, Sylow
138C22×C61#39011yescharacteristic
139C22×C61C2×#10111yescharacteristic
140C22×C61C2×#10111yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61C2×#10411yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—22no—
146C4×C61—22no—
147C4×C61—41no—
148C4×C61—81no—
149C4×C61—81no—
150Dic61—22no—
151Dic61—21no—
152Dic61—21no—
153Dic61—22no—
154Dic61—81no—
155Dic61—81no—
156Dic61#33014yescomplemented
157#2859—611no—
158#1767—611no—
159C4×#97—611no—
160C2×#330—612no—
161C2×#330—612no—
162C2×C61C2×#33011yescharacteristic
163C2×C61#152611yescharacteristic
164C2×C61#152811yescharacteristic
165C2×C61#153111yescharacteristic
166C2×C61#196211yescharacteristic
167C2×C61#196611yescharacteristic
168C2×C61#198011yescharacteristic
169C2×#125—611no—
170C2×#125—611no—
171C2×C4⋊C8—1221no—
172C2×#97—612no—
173C2×#97—612no—
174C2×#97—1221no—
175C2×C4×C8—1221no—
176#389—1221no—
177#389—1221no—
178#389—1221no—
179#389—1221no—
180#384—611no—
181#384—611no—
182#382—611no—
183#382#692311yescharacteristic
184C43—611no—
185#336—1221no—
186#330—1224no—
187#330—1224no—
188C61#968611yescharacteristic, complemented, Sylow
189C22×C8—1222no—
190C22×C8—1222no—
191#125—1222no—
192#125—1222no—
193#125—1222no—
194#125—1222no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
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⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C4⋊C4C2×#692311yescharacteristic
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42C2×#692311yescharacteristic
214C4⋊C8—1224no—
215#97—614no—
216#97—1222no—
217#97—1222no—
218#97—1222no—
219#97—1224no—
220C4×C8—1224no—
221#95—21no—
222#95—21no—
223#95—1221no—
224#95—1221no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22⋊#692311yescharacteristic
235C22×C4C22×#692311yescharacteristic
236C2×C8—1224no—
237C2×C8—1224no—
238C2×C8—1224no—
239C2×C8—1224no—
240C2×C8—2442no—
241C2×C8—2442no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—1222no—
245C4⋊C4—1222no—
246C4⋊C4—2442no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C4⋊C4—2442no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2442no—
256C42—22no—
257C42—612no—
258C42—612no—
259C42—1222no—
260C42—1222no—
261C42—1222no—
262C42—1222no—
263C42—2441no—
264C23C2×C22⋊#692311yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—612no—
279C2×C4—612no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—612no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4#1451983812yes—
298C2×C4D4×#692312yes—
299C8—1228no—
300C8—2444no—
301C22#1684071411yescharacteristic
302C22C2×#1451983811yescharacteristic
303C22D61⋊#10111yescharacteristic
304C22D61⋊#10411yescharacteristic
305C22D61⋊#10411yescharacteristic
306C22D61⋊#10411yescharacteristic
307C22#1684075911yescharacteristic
308C4—22no—
309C4—22no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—614no—
314C4—1222no—
315C4—1222no—
316C4—1221no—
317C4—1221no—
318C4—4881no—
319C4—4881no—
320C2D61⋊#33011yescharacteristic
321C2#2146127611yescharacteristic
322C2#2146128211yescharacteristic
323C2#2146129111yescharacteristic
324C2#2146195411yescharacteristic
325C2#2146196211yescharacteristic
326C2#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#9686
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
156. Dic61#330semidirect
188. C61#9686semidirect

Maximal subgroups

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

subgroupindex
#214616042
C4×#145198322
C2×#168406192
#214541812
#968661