Finite Group Databasebeta

← #29590536

Subgroups — #29590536

Order 15616.

420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451512C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic
3#21444152C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443845C211yesmaximal, characteristic, complemented
6#21443825C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519768C411yescharacteristic
10C2×#14519735C2211yescharacteristic
11#16839816—21no—
12#16839701C2211yescharacteristic
13#16839699C411yescharacteristic
14#16839688C411yescharacteristic
15#16839661—21no—
16#16839654—21no—
17#16839645—21no—
18#16839633—21no—
19#16839607C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758194—21no—
29C2×#11758189—41no—
30M16×D61—24no—
31M16×D61—42no—
32C2×C8×D61—41no—
33#14519768—41no—
34#14519768—41no—
35#14519735—41no—
36#14519735—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51#14519687—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80M16×C61—22no—
81M16×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—42no—
92C4⋊Dic61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—42no—
103#11758194—22no—
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107#11758189—44no—
108C8×D61—44no—
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61#10412yes—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
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×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#9911yescharacteristic
142C2×Dic61#9911yescharacteristic
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C8×C61—42no—
148C8×C61—81no—
149#92418—42no—
150#92418—81no—
151#11767—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C2×#9911yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C2×D61—22no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—42no—
161C2×D61—81no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—81no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—81no—
173Dic61—81no—
174#2611—611no—
175#1742—611no—
176#1464—611no—
177#1353—611no—
178#1353—611no—
179#1346—611no—
180#1346D6111yescharacteristic, complemented
181C2×C61—21no—
182C2×C61—21no—
183C2×C61#150411yescharacteristic
184C2×C61#212311yescharacteristic
185C2×C61#213211yescharacteristic
186D61—42no—
187C22×M16—1221no—
188C2×#125—611no—
189C2×#117—611no—
190#432—1221no—
191#400—611no—
192#399—611no—
193#398C2×D6111yescharacteristic
194#397—611no—
195#389—1221no—
196#388—1221no—
197#387—1221no—
198#385—1221no—
199#376—611no—
200#343—611no—
201#343—1221no—
202#343C2×D6111yescharacteristic
203#324—611no—
204#324C2×D6111yescharacteristic
205#323—1221no—
206C61#1176711yescharacteristic, complemented, Sylow
207C23×C4—611no—
208C2×M16—21no—
209C2×M16—1224no—
210C2×M16—1221no—
211C2×M16—2441no—
212C2×M16—2442no—
213C22×C8—2441no—
214#125—2441no—
215#125—2441no—
216#117—2441no—
217#117—2441no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C4×D6111yescharacteristic
225C2×C4⋊C4C22×D6111yescharacteristic
226C2×C22⋊C4—611no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—1221no—
233C4⋊C8—2441no—
234C22⋊C8—21no—
235C22⋊C8—1221no—
236#97—2441no—
237#95—21no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95C4×D6111yescharacteristic
244C24—611no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1222no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C2×C4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260M16—22no—
261M16—41no—
262M16—1222no—
263M16—2444no—
264M16—2441no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—2444no—
268C2×C8—2441no—
269C2×C8—2441no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C42—1221no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42—2442no—
289C23—612no—
290C23—1221no—
291C23—1221no—
292C23—2441no—
293C23—2441no—
294C23C22⋊C4×D6111yescharacteristic
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451980111yescharacteristic
326C2×C4#1451980611yescharacteristic
327C8—42no—
328C8—81no—
329C8—4881no—
330C8—2442no—
331C22—21no—
332C22—21no—
333C22—1222no—
334C22—4881no—
335C22—2442no—
336C22—2441no—
337C22—2441no—
338C22#99×D6111yescharacteristic
339C22#1683976011yescharacteristic
340C22#104×D6111yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—1221no—
348C4—1221no—
349C4—4881no—
350C4—4881no—
351C4—2441no—
352C4—2441no—
353C2—21no—
354C2—21no—
355C2—2442no—
356C2#2144432011yescharacteristic
357C2#2144747111yescharacteristic
358C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11767
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443847C2semidirect
5. #21443845C2semidirect
6. #21443825C2semidirect
7. C61×#1346C2semidirect
180. #1346D61semidirect
206. C61#11767semidirect

Maximal subgroups

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

subgroupindex
#214515122
#214455562
#214441522
#214438472
#214438452
#214438252
C61×#13462
#1176761