Finite Group Databasebeta

← #30599135

Subgroups — #30599135

Order 15616.

386 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C4×#14519848C211yesmaximal, characteristic, complemented
2#21461374C211yesmaximal, characteristic, complemented
3#21461155C212yesmaximal
4#21460705C212yesmaximal, complemented
5#21454782C211yesmaximal, characteristic
6C2×#14519848—21no—
7#16840766C2212yes—
8C4×#11758213C2212yes—
9#16840638—21no—
10#16840623—21no—
11#16840623—21no—
12#16840612—22no—
13D4⋊#92420—22no—
14C4×#11758224C2211yescharacteristic
15#16839892C411yescharacteristic
16#16839889C411yescharacteristic
17#16839840C411yescharacteristic
18#16839836—21no—
19#16839831—21no—
20#16839814C2211yescharacteristic
21#16839812—21no—
22M16×Dic61—21no—
23C4×C8×D61C2211yescharacteristic
24C61×#436C411yescharacteristic
25C2×#11758213—22no—
26C2×#11758213—22no—
27#14519848—24no—
28C4⋊#92420—22no—
29C4⋊#92420—22no—
30#14519832—22no—
31C4×#92420—22no—
32C2×#11758224Q811yescharacteristic
33C2×#11758194—21no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C4×Dic122C2×C411yescharacteristic
37#14519742D411yescharacteristic
38D4×Dic61D411yescharacteristic
39C4×C22⋊D61—21no—
40#14519737—21no—
41#14519735Q811yescharacteristic
42#14519733—21no—
43C2×C4×Dic61—21no—
44C42×D61C2311yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47#14519706—21no—
48C22⋊#92418—21no—
49#14519689—21no—
50#14519687—21no—
51#14519687—21no—
52C4×#92418C2×C411yescharacteristic
53C8×Dic61—21no—
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C2×M16×C61—21no—
57C4×D4×C61C2×C411yescharacteristic
58C4⋊C8×C61C2×C411yescharacteristic
59C22⋊C8×C61—21no—
60C4×C8×C61C2×C411yescharacteristic
61C2×D4×C61C4⋊C411yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66#11758224—42no—
67C2×C4×D61C2×D411yescharacteristic
68C2×C4×D61C2×Q811yescharacteristic
69C2×C4×D61#4111yescharacteristic
70C2×Dic122C4⋊C411yescharacteristic
71C2×#92420—42no—
72C2×#92420—42no—
73#11758213—24no—
74#11758213—42no—
75#11758213—82no—
76M16×C61—42no—
77C2×C8×C61—21no—
78C2×C8×C61C22⋊C411yescharacteristic
79C2×C8×C61C22⋊C411yescharacteristic
80C4⋊C4×C61C4⋊C411yescharacteristic
81C22⋊C4×C61—21no—
82C42×C61C22×C411yescharacteristic
83C22⋊Dic61—21no—
84#11758198—21no—
85C4⋊Dic61C4⋊C411yescharacteristic
86#11758196—21no—
87#11758196—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61C2×D411yescharacteristic
92C4×Dic61C2×D411yescharacteristic
93C4×Dic61#4111yescharacteristic
94#11758194—42no—
95C2×#92418—21no—
96C2×#92418C22⋊C411yescharacteristic
97C2×#92418C22⋊C411yescharacteristic
98C8×D61—22no—
99C8×D61—41no—
100C23×C61—21no—
101C22×D61C22⋊Q811yescharacteristic
102D4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C2×C4⋊C411yescharacteristic
108C2×C4×C61#11711yescharacteristic
109C22⋊D61—42no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61#12111yescharacteristic
115C2×Dic61#12111yescharacteristic
116C2×Dic61C22⋊Q811yescharacteristic
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—22no—
120C4×D61—22no—
121Dic122—22no—
122#92420—44no—
123#92420—82no—
124C8×C61—21no—
125C8×C61—41no—
126C8×C61#10412yes—
127#92418—21no—
128#92418—21no—
129#92418—41no—
130#8672—611nomaximal, Sylow
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61#38011yescharacteristic
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—21no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61C2×#10411yescharacteristic
141C4×C61#42111yescharacteristic
142C4×C61#43012yes—
143Dic61—21no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61#47112yes—
148#2965—611no—
149C4×#108—611no—
150#1566—611no—
151#1489—612no—
152#1299—612no—
153C2×C61—81no—
154C2×C61#180611yescharacteristic
155C2×C61#181111yescharacteristic
156C2×C61#181511yescharacteristic
157D61—41no—
158C4×#41—611no—
159#446—611no—
160#446—611no—
161#436—611no—
162#436#692311yescharacteristic
163#435—1221no—
164#435—1221no—
165#431—611no—
166#431—1221no—
167C2×#108—1221no—
168#423—612no—
169C4×M16—612no—
170C4×M16—1221no—
171C2×C4×C8—611no—
172#341—1221no—
173#334—1221no—
174#334—1221no—
175Q8⋊C8—1222no—
176D4⋊C8—1222no—
177C61#867211yescharacteristic, complemented, Sylow
178C2×#41—611no—
179C2×M16—21no—
180C2×M16—1221no—
181C2×M16—1222no—
182C2×M16—1222no—
183C22×C8—611no—
184C22×C8—611no—
185C4×Q8—611no—
186C4×Q8—611no—
187C4×D4—611no—
188C4×D4—1221no—
189C4×D4—1221no—
190C4×D4C2×#692311yescharacteristic
191#117—611no—
192#117—1221no—
193C2×C42—611no—
194C2×C42—1221no—
195#108—1224no—
196C4⋊C8—611no—
197C4⋊C8—1222no—
198C4⋊C8—1222no—
199C4⋊C8—1221no—
200C4⋊C8—1221no—
201C4⋊C8C2×#692311yescharacteristic
202C22⋊C8—21no—
203C22⋊C8—1221no—
204C22⋊C8—1221no—
205#97—1222no—
206#97—1221no—
207#97—1221no—
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8—1221no—
212C4×C8—1222no—
213C4×C8C2×#692311yescharacteristic
214#41—2442no—
215C2×Q8—611no—
216C2×D4—1221no—
217C2×D4C4⋊#692311yescharacteristic
218C22×C4—21no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—1221no—
223C22×C4—1221no—
224M16—42no—
225M16—1224no—
226M16—4882no—
227M16—2442no—
228M16—2442no—
229C2×C8—21no—
230C2×C8—611no—
231C2×C8—611no—
232C2×C8—1222no—
233C2×C8—1221no—
234C2×C8—2441no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8C22⋊#692311yescharacteristic
238C2×C8C22⋊#692311yescharacteristic
239C4⋊C4—611no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4C4⋊#692311yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42C22×#692311yescharacteristic
253C23—21no—
254C23—611no—
255Q8—1222no—
256D4—22no—
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—1221no—
270C2×C4—2442no—
271C2×C4—2442no—
272C2×C4C2×C22⋊#692311yescharacteristic
273C2×C4C2×C4⋊#692311yescharacteristic
274C2×C4#1451985611yescharacteristic
275C8—21no—
276C8—41no—
277C8—1221no—
278C8—1221no—
279C8—4882no—
280C8—2444no—
281C8—2441no—
282C8#1451984112yes—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—1221no—
287C22—1221no—
288C22—1221no—
289C22#1684070411yescharacteristic
290C4—21no—
291C4—41no—
292C4—612no—
293C4—1221no—
294C4—1221no—
295C4—2441no—
296C4—2441no—
297C4C2×#1451984111yescharacteristic
298C4#1684075911yescharacteristic
299C4#1684077712yes—
300C2—81no—
301C2—2441no—
302C2#2146169111yescharacteristic
303C2#2146170011yescharacteristic
304C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61#380
prime radicalC2×#11758224Q8
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8672
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C4×#14519848C2semidirect
2. #21461374C2semidirect
4. #21460705C2semidirect
177. C61#8672semidirect

Maximal subgroups

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

subgroupindex
C4×#145198482
#214613742
#214611552
#214607052
#214547822
#867261