Finite Group Databasebeta

← #29589415

Subgroups — #29589415

Order 15616.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448222C211yesmaximal, characteristic
2#21444153C211yesmaximal, characteristic
3#21443764C212yesmaximal, complemented
4#21443762C212yesmaximal, complemented
5C61×#1464C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic
7C22×C4×Dic61C411yescharacteristic
8#16839819—21no—
9#16839631C411yescharacteristic
10#16839631C2211yescharacteristic
11#16839627C411yescharacteristic
12#16839627C2211yescharacteristic
13#16839620—21no—
14#16839620—21no—
15C4×#11758196—21no—
16C4×#11758196—21no—
17#16839488C2212yes—
18#16839486—21no—
19C2×#117×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#324C2212yes—
22C61×#323—21no—
23C23×Dic61—21no—
24#14519736—41no—
25#14519736—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×C22⋊Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61—22no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C4⋊#92418—41no—
40C22⋊#92418—22no—
41#14519688—41no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C23×C4×C61C2×C411yescharacteristic
47#117×C61—41no—
48#117×C61—41no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C4⋊C8×C61—41no—
56C22⋊C8×C61—22no—
57#97×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—24no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C2×C8×C61—42no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—42no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—42no—
90#11758196—42no—
91#11758196—42no—
92#11758196—42no—
93C4×Dic61—24no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61M1612yes—
99C4×Dic61M1612yes—
100C2×#92418—42no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61#10112yes—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#9911yescharacteristic
124C2×C4×C61#9911yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×C4×C61C2×M1611yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—48no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C8×C61—82no—
141#92418—82no—
142#11513—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—42no—
147C22×C61—42no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61#40711yescharacteristic
151C22×C61C2×#9911yescharacteristic
152C22×C61C2×#10111yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161Dic61—24no—
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165#2285—611no—
166#1464—611no—
167#1464D6111yescharacteristic
168#1325—612no—
169#1324—612no—
170C2×C61—21no—
171C2×C61—21no—
172C2×C61—42no—
173C2×C61#146311yescharacteristic
174C2×C61#212611yescharacteristic
175C2×C61#213211yescharacteristic
176C2×#117—611no—
177C2×#117C2×D6111yescharacteristic
178C22×C42—611no—
179#432—21no—
180#432—1221no—
181#384—611no—
182#384—611no—
183#382—611no—
184#382—611no—
185#380—1221no—
186#380—1221no—
187C4×C4⋊C4—1221no—
188C4×C4⋊C4—1221no—
189#324—612no—
190#324C2×D6112yes—
191#323—21no—
192#323—1221no—
193C61#1151311yescharacteristic, complemented, Sylow
194C23×C4—1221no—
195C23×C4C4×D6111yescharacteristic
196#117—41no—
197#117—41no—
198#117—2441no—
199#117—2441no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4C4×D6111yescharacteristic
207C2×C4⋊C4C22×D6111yescharacteristic
208C2×C22⋊C4—1221no—
209C2×C22⋊C4D24411yescharacteristic
210C2×C22⋊C4C22⋊D6111yescharacteristic
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—1222no—
214C2×C42—1222no—
215C2×C42—1221no—
216C2×C42—1221no—
217C2×C42D24411yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—2441no—
221C22⋊C8—22no—
222C22⋊C8—1222no—
223#97—41no—
224#97—2441no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229C24#1175819811yescharacteristic
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—1221no—
236C22×C4—1224no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—2442no—
241C22×C4—2442no—
242C22×C4#1175819811yescharacteristic
243C22×C4#1175819811yescharacteristic
244C22×C4#1175819811yescharacteristic
245C22×C4C2×C4×D6111yescharacteristic
246C22×C4C2×D24411yescharacteristic
247C22×C4C2×C22⋊D6111yescharacteristic
248C2×C8—42no—
249C2×C8—2442no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—2442no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—612no—
266C42—612no—
267C42—1224no—
268C42—1221no—
269C42—1221no—
270C42—2441no—
271C42—2441no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1451969512yes—
277C23C2×#1175819811yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—2448no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4#1451969111yescharacteristic
308C2×C4#1451969111yescharacteristic
309C2×C4M16×D6111yescharacteristic
310C2×C4M16×D6111yescharacteristic
311C8—82no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22#1683972511yescharacteristic
321C22C2×#1451969111yescharacteristic
322C22C2×#1451969511yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1224no—
332C4—4881no—
333C4—4881no—
334C4—2442no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#2144414811yescharacteristic
339C2#2144748211yescharacteristic
340C2#2144750211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11513
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #21443764C2semidirect
4. #21443762C2semidirect
193. C61#11513semidirect

Maximal subgroups

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

subgroupindex
#214482222
#214441532
#214437642
#214437622
C61×#14642
#1151361