Finite Group Databasebeta

← #30605195

Subgroups — #30605195

Order 15616.

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

normal subgroups only

This group has 434 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#21461682C211yesmaximal, characteristic
2#21461080C211yesmaximal, characteristic
3#21460816C212yesmaximal, complemented
4#21460800C212yesmaximal, complemented
5#21449085C211yesmaximal, characteristic
6#16840782—21no—
7C2×#14519836—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C2×#14519739C2211yescharacteristic
13C2×#14519735C411yescharacteristic, complemented
14#16839697C2211yescharacteristic
15#16839692C411yescharacteristic, complemented
16#16839691—21no—
17#16839689C2211yescharacteristic
18#16839680—21no—
19#16839613—21no—
20#16839609—21no—
21#16839609C411yescharacteristic, complemented
22C61×#400C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25#14519844—41no—
26#14519836—42no—
27C22⋊#92420—22no—
28#14519832—41no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519739—41no—
34#14519739—41no—
35#14519735—41no—
36#14519735—41no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×#11758198C2311yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C23×D61C2×D411yescharacteristic
59C22×#6923—42no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C22⋊#6923—42no—
80C22⋊#6923—42no—
81C2×#92420—42no—
82C4⋊#6923—82no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—42no—
88#11758198—42no—
89#11758198—42no—
90#11758198—41no—
91#11758198—41no—
92C4⋊Dic61—41no—
93#11758196—42no—
94#11758196—42no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—42no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C23×C61C2×C22⋊C411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61AGL(1,ℤ/8)11yescharacteristic
111C22×D61#13711yescharacteristic
112C2×#6923—82no—
113C2×#6923—82no—
114C2×#6923—82no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61#9911yescharacteristic
138C2×Dic61#9911yescharacteristic
139D244—42no—
140D244—42no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—81no—
145#92420—82no—
146#11822—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61C2×#9911yescharacteristic
150C22×C61#41711yescharacteristic
151C22×C61#42111yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164#6923—162no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—21no—
171Dic61—42no—
172Dic61—41no—
173Dic61—81no—
174Dic61#35212yes—
175#2395—611no—
176#1799—611no—
177#1466—611no—
178#1352—612no—
179#1344—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61#151311yescharacteristic
183C2×C61C2×#35211yescharacteristic
184C2×C61#212611yescharacteristic
185D61—41no—
186D61—41no—
187D61—81no—
188C2×C4×D4—611no—
189C2×#117—611no—
190#432—1221no—
191C2×#99—1221no—
192#400#692311yescharacteristic, complemented
193#399—611no—
194#398—611no—
195#397—611no—
196#397—1221no—
197#394—1221no—
198#380—1221no—
199C4×C4⋊C4—1221no—
200C4×C22⋊C4—611no—
201C4×C22⋊C4—1221no—
202#342—612no—
203#323—612no—
204#323—1221no—
205C61#1182211yescharacteristic, complemented, Sylow
206C22×D4—611no—
207C23×C4—611no—
208C23×C4—611no—
209C4×D4—2441no—
210C4×D4—2441no—
211#117—2441no—
212#117—2441no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—2441no—
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C4⋊C4C2×#692311yescharacteristic
219C2×C22⋊C4—611no—
220C2×C22⋊C4—611no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1222no—
226C2×C42—611no—
227C2×C42—1221no—
228C2×C42—1221no—
229C4⋊C8—2441no—
230#99—2442no—
231C22⋊C8—1222no—
232#97—2441no—
233#95—21no—
234#95—21no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—2441no—
239#95C2×#692311yescharacteristic
240C24—611no—
241C24—611no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—2441no—
245C2×D4—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22×#692311yescharacteristic
262C2×C8—2442no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—4882no—
266C4⋊C4—2441no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C42—1221no—
279C42—1221no—
280C42—2441no—
281C42—2441no—
282C42—2442no—
283C23—611no—
284C23—611no—
285C23—1221no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—2441no—
291C23—2441no—
292C23—2441no—
293C23—2441no—
294C23C2×C22⋊#692311yescharacteristic
295D4—2442no—
296D4—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1222no—
313C2×C4—1222no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4882no—
317C2×C4—4882no—
318C2×C4—4882no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C8—4882no—
329C22—21no—
330C22—21no—
331C22—1221no—
332C22—1221no—
333C22—4881no—
334C22—4881no—
335C22—4881no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22D61⋊#9911yescharacteristic
344C22#1684075311yescharacteristic
345C22#1684076111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—612no—
352C4—1221no—
353C4—9762no—
354C4—4881no—
355C4—2442no—
356C4—2441no—
357C2—21no—
358C2—21no—
359C2—4881no—
360C2—2441no—
361C2—2441no—
362C2#2146123711yescharacteristic
363C2D61⋊#35211yescharacteristic
364C2#2146209111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×#11758198C23
hypercenter#400#6923
hypocenterC61#11822
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #21460816C2semidirect
4. #21460800C2semidirect
13. C2×#14519735C4semidirect
15. #16839692C4semidirect
21. #16839609C4semidirect
22. C61×#400C4semidirect
192. #400#6923semidirect
205. C61#11822semidirect

Maximal subgroups

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

subgroupindex
#214616822
#214610802
#214608162
#214608002
#214490852
#1182261