Finite Group Databasebeta

← #30595452

Subgroups — #30595452

Order 15616.

482 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461747C211yesmaximal, characteristic, complemented
2#21461735C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21448281C211yesmaximal, characteristic
6C2×#14519844—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×D4×Dic61C411yescharacteristic
13C2×#14519733—21no—
14#16839665C2211yescharacteristic
15#16839660C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839656—21no—
18#16839650—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C22⋊C4×Dic61—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C23×Dic61—21no—
27D4×Dic61—22no—
28D4×Dic61C814yescomplemented
29#14519733—44no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×D4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52C24×C61—21no—
53C2×D4×C61—21no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61C2×C812yes—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—24no—
63C22×Dic61—21no—
64C22×Dic61—42no—
65C22×Dic61—42no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—42no—
79C42×C61—41no—
80C22⋊Dic61—24no—
81C22⋊Dic61—41no—
82C22⋊Dic61—42no—
83C22⋊Dic61—41no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61C2×C812yes—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—21no—
90C4×Dic61—22no—
91C4×Dic61—21no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—42no—
96C4×Dic61C2×C812yes—
97C4×Dic61M1612yes—
98C23×C61—22no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106D4×C61—42no—
107D4×C61—42no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61C22×C811yescharacteristic
120C2×C4×C61C2×M1611yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—22no—
130C2×Dic61—48no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61C22⋊C812yes—
137C2×Dic61C22⋊C812yes—
138C2×Dic61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61AGL(1,ℤ/8)12yes—
140C2×Dic61#13711yescharacteristic
141#92420—82no—
142#92420—82no—
143#7594—611nomaximal, Sylow
144C22×C61—42no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61C2×C22⋊C811yescharacteristic
152C22×C61#41011yescharacteristic
153C22×C61#41311yescharacteristic
154C22×C61#41711yescharacteristic
155C22×C61#41811yescharacteristic
156C22×C61#42111yescharacteristic
157C22×C61#42111yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163Dic61—22no—
164Dic61—22no—
165Dic61—21no—
166Dic61—21no—
167Dic61—22no—
168Dic61—42no—
169Dic61—81no—
170#2293—611no—
171#1839—611no—
172#1831—611no—
173#1271—612no—
174#1270—612no—
175C2×C61—82no—
176C2×C61#145811yescharacteristic
177C2×C61#147711yescharacteristic
178C2×C61#147811yescharacteristic
179C2×C61#151211yescharacteristic
180C2×C61#151411yescharacteristic
181C2×C61#153511yescharacteristic
182C2×C61#155711yescharacteristic
183C2×C4×D4—611no—
184C2×#117—1221no—
185C2×C4⋊C8—1221no—
186#390—611no—
187#390#692311yescharacteristic
188#389—611no—
189#389—611no—
190#388—1221no—
191#388—1221no—
192C4×C4⋊C4—611no—
193C4×C22⋊C4—1221no—
194C43—611no—
195#336—612no—
196#336—612no—
197#336—1221no—
198#336—1221no—
199#336—1221no—
200C61#759411yescharacteristic, complemented, Sylow
201C22×D4C2×#692311yescharacteristic
202C23×C4—1221no—
203C22×C8—1222no—
204C22×C8—1222no—
205C4×D4—614no—
206C4×D4—1222no—
207#117—2444no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—1221no—
225C2×C42C2×#692311yescharacteristic
226C4⋊C8—2442no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C24—21no—
231C2×D4—21no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4D61⋊C812yes—
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1224no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C2×C8—2442no—
253C2×C8—2442no—
254C4⋊C4—41no—
255C4⋊C4—612no—
256C4⋊C4—1221no—
257C4⋊C4—2441no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—1224no—
263C22⋊C4—2442no—
264C22⋊C4—2441no—
265C22⋊C4—2441no—
266C42—41no—
267C42—612no—
268C42—612no—
269C42—1221no—
270C42—1221no—
271C42—1222no—
272C42—2441no—
273C42—2441no—
274C42—2441no—
275C42—2442no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊#692311yescharacteristic
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—612no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1222no—
311C2×C4—2448no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4C2×D61⋊C811yescharacteristic
318C2×C4D61⋊M1611yescharacteristic
319C8—4882no—
320C8—4882no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22D61⋊(C22⋊C8)11yescharacteristic
329C22#1684074211yescharacteristic
330C22#1684074911yescharacteristic
331C22#1684075311yescharacteristic
332C22#1684075411yescharacteristic
333C22#1684075911yescharacteristic
334C22#1684076011yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—1222no—
341C4—1222no—
342C4—1221no—
343C4—1221no—
344C4—1222no—
345C4—4881no—
346C4—2442no—
347C2—82no—
348C2#2146105111yescharacteristic
349C2#2146111511yescharacteristic
350C2#2146111911yescharacteristic
351C2#2146123111yescharacteristic
352C2#2146123911yescharacteristic
353C2#2146130411yescharacteristic
354C2#2146135111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7594
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21461735C2semidirect
3. #21460638C2semidirect
28. D4×Dic61C8semidirect
200. C61#7594semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617352
#214606382
#214606352
#214482812
#759461