Finite Group Databasebeta

← #29589577

Subgroups — #29589577

Order 15616.

398 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 83 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#21450300C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic
3#21443762C212yesmaximal, complemented
4#21443752C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7#16839726—21no—
8#16839700—21no—
9#16839700—21no—
10#16839667C411yescharacteristic
11#16839667C2211yescharacteristic
12#16839627C411yescharacteristic
13#16839627C2211yescharacteristic
14#16839625—21no—
15#16839625—21no—
16C4×C22⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C2×#11758194—41no—
25#14519756—41no—
26#14519756—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61C2×C411yescharacteristic
33C22⋊#92418—22no—
34C22⋊#92418—41no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—41no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—22no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×C8×C61—42no—
81C2×C8×C61—82no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—42no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93#11758194—82no—
94C2×#92418—42no—
95C23×C61—22no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61#9911yescharacteristic
100C23×C61#9911yescharacteristic
101C23×C61C2×C22⋊C411yescharacteristic
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—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61#13112yes—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—42no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133Dic122—82no—
134C8×C61—82no—
135#92418—82no—
136#11551—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—42no—
145C22×C61—42no—
146C22×C61#35412yes—
147C22×C61#40811yescharacteristic
148C22×C61C2×#9911yescharacteristic
149C22×C61#41311yescharacteristic
150C4×C61—22no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156Dic61—81no—
157Dic61—81no—
158Dic61—81no—
159Dic61—81no—
160#2503—611no—
161#1463—611no—
162C2×#324D6111yescharacteristic
163#1324—612no—
164#1319—612no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61—22no—
168C2×C61—41no—
169C2×C61#146811yescharacteristic
170C2×C61C2×#35411yescharacteristic
171C2×C61#213311yescharacteristic
172C2×C22⋊Q8—611no—
173C22×C4⋊C4C2×D6111yescharacteristic
174#407—1221no—
175C2×C22⋊C8—21no—
176#400—1221no—
177#400—1221no—
178#391—611no—
179#391—611no—
180#382—611no—
181#382—611no—
182#381—1221no—
183#381—1221no—
184C4×C22⋊C4—611no—
185#324—21no—
186#324—612no—
187#324—1221no—
188#324C2×D6112yes—
189C61#1155111yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C23×C4C4×D6111yescharacteristic
192C23×C4D24411yescharacteristic
193C23×C4C22⋊D6111yescharacteristic
194C2×M16—2441no—
195C22×C8—41no—
196C22⋊Q8—2441no—
197C22⋊Q8—2441no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C4×D6111yescharacteristic
203C2×C4⋊C4D24411yescharacteristic
204C2×C4⋊C4C22⋊D6111yescharacteristic
205C2×C4⋊C4C22×D6111yescharacteristic
206C2×C22⋊C4—1221no—
207C2×C22⋊C4—1221no—
208C2×C42—611no—
209C2×C42—611no—
210C22⋊C8—22no—
211C22⋊C8—41no—
212C22⋊C8—1222no—
213C22⋊C8—2441no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223C24#1175819811yescharacteristic
224C2×Q8—1222no—
225C2×Q8—2441no—
226C2×Q8—2441no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4#1175819811yescharacteristic
242C22×C4#1175819811yescharacteristic
243C22×C4#1175819811yescharacteristic
244C22×C4C2×C4×D6111yescharacteristic
245C22×C4C2×D24411yescharacteristic
246C22×C4C2×C22⋊D6111yescharacteristic
247M16—4882no—
248C2×C8—42no—
249C2×C8—82no—
250C2×C8—2442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—2441no—
256C4⋊C4—2442no—
257C22⋊C4—2442no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C42—1222no—
261C42—2441no—
262C23—21no—
263C23—21no—
264C23—22no—
265C23—41no—
266C23#1451969111yescharacteristic
267C23#1451969111yescharacteristic
268C23C2×#1175819811yescharacteristic
269Q8—4882no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2442no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451978312yes—
301C8—82no—
302C8—4882no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22#1683955612yes—
313C22#1683972811yescharacteristic
314C22C2×#1451969111yescharacteristic
315C22#1683974411yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—4881no—
323C4—4881no—
324C4—4881no—
325C4—4881no—
326C2—21no—
327C2—21no—
328C2—22no—
329C2—41no—
330C2#2144416511yescharacteristic
331C2C2×#1683955611yescharacteristic
332C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#324C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#324D61
hypocenterC61#11551
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #21443762C2semidirect
4. #21443752C2semidirect
189. C61#11551semidirect

Maximal subgroups

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

subgroupindex
#214503002
#214441492
#214437622
#214437522
C2×C61×#3242
#1155161