Finite Group Databasebeta

← #30604260

Subgroups — #30604260

Order 15616.

408 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461070C211yesmaximal, characteristic, complemented
2#21461050C211yesmaximal, characteristic, complemented
3#21460760C212yesmaximal, complemented
4#21460747C212yesmaximal, complemented
5#21450282C211yesmaximal, characteristic
6#16840782—21no—
7#16840778—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840605—21no—
11#16840605—21no—
12C2×#14519736C2211yescharacteristic
13#16839676—21no—
14#16839676—21no—
15#16839665C411yescharacteristic
16#16839665C2211yescharacteristic
17#16839650—21no—
18#16839650—21no—
19#16839631C411yescharacteristic
20#16839627C2211yescharacteristic
21C4×C22⋊Dic61C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29#14519736—41no—
30#14519736—41no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2311yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×C22⋊Dic61D411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52#121×C61—41no—
53#121×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C2×D4×C61—81no—
63C2×D4×C61—81no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C22⋊Dic61—42no—
87C22⋊Dic61—81no—
88C22⋊Dic61—81no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—81no—
92#11758196—81no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112D4×C61—82no—
113D4×C61—84no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#9911yescharacteristic
124C2×C4×C61#9911yescharacteristic
125C2×C4×C61#13112yes—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140#92420—82no—
141#92420—82no—
142#11550—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61#40811yescharacteristic
158C22×C61C2×#9911yescharacteristic
159C22×C61#41311yescharacteristic
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—81no—
164Dic61—42no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—81no—
170#2500—611no—
171#1464—611no—
172#1458—611no—
173#1324—612no—
174#1318—612no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61—81no—
178C2×C61—161no—
179C2×C61#146811yescharacteristic
180C2×C61#212611yescharacteristic
181C2×C61#213411yescharacteristic
182C2×#121#692311yescharacteristic
183C2×#117—611no—
184#432—1221no—
185#431—1221no—
186#394—1221no—
187#394—1221no—
188#390—611no—
189#390—611no—
190#388—1221no—
191#388—1221no—
192#384—611no—
193#382—611no—
194C4×C22⋊C4—611no—
195#324—612no—
196#324—612no—
197#323—1221no—
198#323—1221no—
199C61#1155011yescharacteristic, complemented, Sylow
200C22×D4—21no—
201C22×D4C2×#692311yescharacteristic
202C23×C4C2×#692311yescharacteristic
203#121—41no—
204#121—41no—
205#117—2441no—
206#117—2441no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C2×#692311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228#97—2441no—
229C4×C8—2441no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C24—21no—
234C24C22⋊#692311yescharacteristic
235C2×D4—22no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—42no—
239C2×D4—81no—
240C2×D4—81no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22×#692311yescharacteristic
254C2×C8—2442no—
255C2×C8—2442no—
256C4⋊C4—41no—
257C4⋊C4—4881no—
258C4⋊C4—4881no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—4881no—
264C22⋊C4—4881no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42—1222no—
275C42—2441no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C22⋊#692311yescharacteristic
289D4—82no—
290D4—84no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—1222no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4#1451983511yescharacteristic
315C2×C4#1451983511yescharacteristic
316C2×C4#1451986412yes—
317C8—4882no—
318C8—4882no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1684073511yescharacteristic
334C22C2×#1451983511yescharacteristic
335C22#1684074911yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—81no—
340C4—4881no—
341C4—2442no—
342C4—2441no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—161no—
350C2#2146108411yescharacteristic
351C2#2146209011yescharacteristic
352C2#2146211811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC22×C61C2×#99
cosocleC2×C4⋊Dic61C23
hypercenterC2×#121#6923
hypocenterC61#11550
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21461050C2semidirect
3. #21460760C2semidirect
4. #21460747C2semidirect
199. C61#11550semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214610502
#214607602
#214607472
#214502822
#1155061