Finite Group Databasebeta

← #30604536

Subgroups — #30604536

Order 15616.

368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462179C211yesmaximal, characteristic, complemented
2#21462178C211yesmaximal, characteristic, complemented
3#21460770C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5#21454528C211yesmaximal, characteristic
6#16840683—21no—
7C4⋊#11758187C2212yes—
8#16840657—21no—
9#16840657—21no—
10#16840648—21no—
11C4×#11758187C2212yes—
12C2×#14519785—21no—
13#16840309C411yescharacteristic
14#16839841C411yescharacteristic
15#16839838—21no—
16D4×#92418C2211yescharacteristic
17#16839827C2211yescharacteristic
18#16839825—21no—
19#16839784C411yescharacteristic
20#16839727—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C2×#11758222—21no—
26#14519785—44no—
27C2×#11758189—21no—
28C2×#11758189—21no—
29C22×#92418—21no—
30C2×C8×D61—21no—
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519776C811yescharacteristic
34#14519773C811yescharacteristic
35#14519763—21no—
36#14519752C811yescharacteristic
37#14519750—21no—
38#14519748C811yescharacteristic
39C4×D244C2×C411yescharacteristic
40C4×C22⋊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
55C2×D4×C61C2×C811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—21no—
58C2×C22⋊D61—21no—
59C2×C22⋊D61—21no—
60#11758222—42no—
61#11758222—42no—
62C2×D244—21no—
63C2×D244C2×C811yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C4×D61C2×C811yescharacteristic
67C2×C4×D61M1611yescharacteristic
68C2×Dic122—21no—
69M16×C61—42no—
70C2×C8×C61—21no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22⋊C411yescharacteristic
73C4⋊C4×C61C2×C811yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61C22×C411yescharacteristic
76C22⋊Dic61—21no—
77#11758198—21no—
78#11758198—21no—
79C4⋊Dic61C2×C811yescharacteristic
80#11758196—21no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61C2×C811yescharacteristic
83C4×Dic61M1611yescharacteristic
84C2×#92418—21no—
85C2×#92418—42no—
86C2×#92418C2×D411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88#11758189—42no—
89#11758189—42no—
90C8×D61—22no—
91C8×D61—41no—
92C8×D61—42no—
93#11758187—42no—
94#11758187—42no—
95C23×C61—21no—
96C22×D61—21no—
97C22×D61C22⋊C811yescharacteristic
98D4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C22×C811yescharacteristic
104C2×C4×C61C2×M1611yescharacteristic
105C22⋊D61—42no—
106C22⋊D61—42no—
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61C22⋊C811yescharacteristic
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112D244—22no—
113D244—42no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—22no—
117C4×D61—22no—
118C4×D61—41no—
119C4×D61—41no—
120Dic122—42no—
121C8×C61—21no—
122C8×C61—21no—
123C8×C61—41no—
124#92418—21no—
125#92418—41no—
126#92418AGL(1,ℤ/8)12yes—
127#11630—611nomaximal, Sylow
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61C2×C22⋊C811yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61#41811yescharacteristic
141C4×C61#42111yescharacteristic
142C4×C61#50412yes—
143Dic61—21no—
144Dic61—21no—
145Dic61—41no—
146Dic61#35012yes—
147#2931—611no—
148#2162—611no—
149#2162—611no—
150D4⋊C16—612no—
151D4⋊C16—612no—
152C2×C61—81no—
153C2×C61#147811yescharacteristic
154C2×C61#211311yescharacteristic
155C2×C61C2×#35011yescharacteristic
156D61—41no—
157D61—81no—
158C2×#131—1221no—
159#532—611no—
160#436—611no—
161#436—1221no—
162#436#692311yescharacteristic
163C8×D4—611no—
164C8×D4—611no—
165C8×D4—1221no—
166#423—611no—
167#408—1221no—
168C2×C4×C8—611no—
169C4⋊C16—612no—
170C4⋊C16—1221no—
171C22⋊C16—1221no—
172C22⋊C16—1221no—
173C4×C16—612no—
174C4×C16—1221no—
175C61#1163011yescharacteristic, complemented, Sylow
176C2×#41—1221no—
177#131—2444no—
178C2×M16—21no—
179C2×M16—1221no—
180C2×M16—1221no—
181C22×C8—611no—
182C22×C8—611no—
183C22×C8—1221no—
184C22×C8—1221no—
185C4⋊Q8—611no—
186#127—611no—
187#124—1221no—
188#121—611no—
189#121—611no—
190#121—1221no—
191C4×D4—611no—
192C4×D4—1221no—
193C4×D4C2×#692311yescharacteristic
194C2×C42—611no—
195C2×C16—1222no—
196C2×C16—1222no—
197C4⋊C8—611no—
198C4⋊C8—1221no—
199C4⋊C8C2×#692311yescharacteristic
200C22⋊C8—21no—
201C22⋊C8—1221no—
202C22⋊C8—1221no—
203C22⋊C8—1221no—
204C4×C8—611no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8C2×#692311yescharacteristic
208#41—2442no—
209#41—2442no—
210C2×Q8—1221no—
211C2×D4—611no—
212C2×D4—1221no—
213C2×D4—1221no—
214C2×D4—1221no—
215C2×D4—1221no—
216C2×D4D61⋊C811yescharacteristic
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222M16—42no—
223M16—2442no—
224M16—2442no—
225C2×C8—21no—
226C2×C8—611no—
227C2×C8—611no—
228C2×C8—1222no—
229C2×C8—1221no—
230C2×C8—2441no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8C22⋊#692311yescharacteristic
234C2×C8C22⋊#692311yescharacteristic
235C4⋊C4—611no—
236C4⋊C4—1221no—
237C4⋊C4D61⋊C811yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—1221no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C42—611no—
243C42—611no—
244C42—611no—
245C42C22×#692311yescharacteristic
246C16—2442no—
247C16—2442no—
248C23—21no—
249C23—611no—
250C23—1221no—
251Q8—2442no—
252D4—22no—
253D4—1222no—
254D4—2442no—
255D4—2442no—
256D4—2442no—
257D4—2442no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4C2×C22⋊#692311yescharacteristic
272C2×C4C2×D61⋊C811yescharacteristic
273C2×C4D61⋊M1611yescharacteristic
274C8—21no—
275C8—21no—
276C8—41no—
277C8—612no—
278C8—1221no—
279C8—2441no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22—2441no—
287C22—2441no—
288C22—2441no—
289C22D61⋊(C22⋊C8)11yescharacteristic
290C4—21no—
291C4—41no—
292C4—612no—
293C4—1221no—
294C4—1221no—
295C4—2441no—
296C4#1684075411yescharacteristic
297C4#1684075911yescharacteristic
298C4#1684082112yes—
299C2—81no—
300C2—4881no—
301C2—2441no—
302C2#2146111911yescharacteristic
303C2#2146205011yescharacteristic
304C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radical#16840309C4
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11630
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462179C2semidirect
2. #21462178C2semidirect
3. #21460770C2semidirect
4. D4⋊#11758187C2semidirect
175. C61#11630semidirect

Maximal subgroups

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

subgroupindex
#214621792
#214621782
#214607702
D4⋊#117581872
#214545282
#1163061