Finite Group Databasebeta

← #30604548

Subgroups — #30604548

Order 15616.

386 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 88 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#21462182C211yesmaximal, characteristic, complemented
2#21462179C211yesmaximal, characteristic, complemented
3#21460772C212yesmaximal, complemented
4#21460771C212yesmaximal, complemented
5#436×D61C211yesmaximal, characteristic
6#16840683—21no—
7C4⋊#11758187C2212yescomplemented
8#16840657—21no—
9#16840657—21no—
10#16840650C2212yescomplemented
11#16840648—21no—
12C2×M16×D61—21no—
13C4×D4×D61C411yescharacteristic
14#16839841C411yescharacteristic
15#16839840C2211yescharacteristic
16#16839839C2211yescharacteristic
17#16839838—21no—
18#16839837—21no—
19C4⋊C8×D61C411yescharacteristic
20C22⋊C8×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C2×D4×D61C811yescharacteristic
26C22×C4×D61—21no—
27C2×#11758194—21no—
28C2×#11758189—21no—
29C2×#11758189—21no—
30M16×D61—44no—
31C2×C8×D61—21no—
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34C4×D244C2×C411yescharacteristic
35D4×Dic61C811yescharacteristic
36#14519739C811yescharacteristic
37C4×C22⋊D61—21no—
38#14519737—21no—
39C4⋊C4×D61C811yescharacteristic
40C22⋊C4×D61—21no—
41C42×D61C2×C411yescharacteristic
42C4⋊#92418C2×C411yescharacteristic
43#14519706—21no—
44C22⋊#92418—21no—
45#14519689—21no—
46#14519689—21no—
47C4×#92418C2311yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×M16×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C23×D61—21no—
56C2×D4×C61C2×C811yescharacteristic
57C22×C4×C61—21no—
58C2×C22⋊D61—21no—
59C22×Dic61—21no—
60D4×D61—42no—
61C2×D244C2×C811yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—42no—
66C2×C4×D61—42no—
67C2×C4×D61C22⋊C411yescharacteristic
68C2×C4×D61C2×C811yescharacteristic
69C2×C4×D61M1611yescharacteristic
70M16×C61—42no—
71C2×C8×C61—21no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22⋊C411yescharacteristic
74C4⋊C4×C61C2×C811yescharacteristic
75C22⋊C4×C61—21no—
76C42×C61C22×C411yescharacteristic
77C22⋊Dic61—21no—
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61C2×C811yescharacteristic
81#11758196—21no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61C2×C811yescharacteristic
84C4×Dic61M1611yescharacteristic
85#11758194—42no—
86C2×#92418—21no—
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89#11758189—42no—
90#11758189—42no—
91C8×D61—22no—
92C8×D61—41no—
93C8×D61—42no—
94#11758187—42no—
95#11758187—42no—
96C23×C61—21no—
97C22×D61—21no—
98C22×D61—42no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61C22⋊C811yescharacteristic
102D4×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C22×C811yescharacteristic
108C2×C4×C61C2×M1611yescharacteristic
109C22⋊D61—42no—
110C2×Dic61—21no—
111C2×Dic61—42no—
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C2×Dic61C22⋊C811yescharacteristic
115D244—41no—
116C4×D61—22no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—22no—
120C4×D61—42no—
121C4×D61—42no—
122C4×D61—41no—
123C4×D61—41no—
124C8×C61—21no—
125C8×C61—21no—
126C8×C61—41no—
127#92418—21no—
128#92418—41no—
129#92418AGL(1,ℤ/8)12yes—
130#11634—611nomaximal, Sylow
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61C2×C22⋊C811yescharacteristic
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—84no—
141C2×D61#35012yes—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61#41811yescharacteristic
146C4×C61#42111yescharacteristic
147Dic61—21no—
148Dic61—21no—
149Dic61—41no—
150Dic61#34912yes—
151C2×#436—611no—
152#2163—611no—
153#2162—611no—
154#1330—612no—
155#1330—612no—
156C2×C61—81no—
157C2×C61#147811yescharacteristic
158C2×C61C2×#34911yescharacteristic
159C2×C61C2×#35011yescharacteristic
160D61—22no—
161D61—81no—
162C22×M16—1221no—
163C2×C4×D4—611no—
164#436—611no—
165#436—611no—
166#436—611no—
167#436—1221no—
168#436—1221no—
169#436#692311yescharacteristic
170C2×C4⋊C8—611no—
171C2×C22⋊C8—1221no—
172C2×C4×C8—611no—
173C4⋊C16—612no—
174C4⋊C16—1221no—
175C22⋊C16—1221no—
176C22⋊C16—1221no—
177#346—612no—
178C4×C16—1221no—
179C61#1163411yescharacteristic, complemented, Sylow
180C22×D4—611no—
181C23×C4—1221no—
182C2×M16—21no—
183C2×M16—1221no—
184C2×M16—1221no—
185C2×M16—1221no—
186C2×M16—2444no—
187C22×C8—611no—
188C22×C8—611no—
189C22×C8—1221no—
190C4×D4—611no—
191C4×D4—611no—
192C4×D4—611no—
193C4×D4—1221no—
194C4×D4—1221no—
195C4×D4C2×#692311yescharacteristic
196C2×C4⋊C4—611no—
197C2×C22⋊C4—1221no—
198C2×C42—611no—
199C2×C16—1222no—
200C2×C16—1222no—
201C4⋊C8—611no—
202C4⋊C8—1221no—
203C4⋊C8C2×#692311yescharacteristic
204C22⋊C8—21no—
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8C2×#692311yescharacteristic
212C24—1221no—
213C2×D4—611no—
214C2×D4—1221no—
215C2×D4—2442no—
216C2×D4D61⋊C811yescharacteristic
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—2442no—
226C22×C4—2442no—
227M16—42no—
228M16—2442no—
229M16—2442no—
230M16—2442no—
231C2×C8—21no—
232C2×C8—611no—
233C2×C8—611no—
234C2×C8—1222no—
235C2×C8—1221no—
236C2×C8—2441no—
237C2×C8—2442no—
238C2×C8C22⋊#692311yescharacteristic
239C2×C8C22⋊#692311yescharacteristic
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4D61⋊C811yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C22⋊C4—1221no—
247C42—611no—
248C42—611no—
249C42—611no—
250C42C22×#692311yescharacteristic
251C16—2442no—
252C16—2442no—
253C23—21no—
254C23—611no—
255C23—1221no—
256C23—2442no—
257C23—2442no—
258C23—2442no—
259D4—41no—
260D4—2441no—
261D4—2442no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—611no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4C2×C22⋊#692311yescharacteristic
279C2×C4C2×D61⋊C811yescharacteristic
280C2×C4D61⋊M1611yescharacteristic
281C8—21no—
282C8—21no—
283C8—41no—
284C8—612no—
285C8—1221no—
286C8—2441no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—612no—
291C22—1221no—
292C22—1221no—
293C22—4884no—
294C22—2441no—
295C22—2441no—
296C22—2441no—
297C22D61⋊(C22⋊C8)11yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—612no—
302C4—1221no—
303C4—1221no—
304C4—2441no—
305C4#1684075411yescharacteristic
306C4#1684075911yescharacteristic
307C2—81no—
308C2—1222no—
309C2—4881no—
310C2#2146111911yescharacteristic
311C2D61⋊#34911yescharacteristic
312C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11634
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462182C2semidirect
2. #21462179C2semidirect
3. #21460772C2semidirect
4. #21460771C2semidirect
7. C4⋊#11758187C22semidirect
10. #16840650C22semidirect
179. C61#11634semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214621792
#214607722
#214607712
#436×D612
#1163461