Finite Group Databasebeta

← #30599141

Subgroups — #30599141

Order 15616.

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

normal subgroups only

This group has 386 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
1C4×#14519848C211yesmaximal, characteristic, complemented
2#21461378C211yesmaximal, characteristic, complemented
3#21461155C212yesmaximal
4#21460705C212yesmaximal, complemented
5#21454782C211yesmaximal, characteristic
6C2×#14519848—21no—
7#16840766C2212yes—
8C4×#11758213C2212yes—
9#16840638—21no—
10#16840626—21no—
11#16840626—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—41no—
114C2×Dic61—41no—
115C2×Dic61#12111yescharacteristic
116C2×Dic61#12111yescharacteristic
117C2×Dic61C22⋊Q811yescharacteristic
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—22no—
121C4×D61—21no—
122C4×D61—21no—
123Dic122—22no—
124#92420—44no—
125#92420—82no—
126C8×C61—21no—
127C8×C61—21no—
128C8×C61—41no—
129#92418—21no—
130#92418—41no—
131#92418#10412yes—
132#8673—611nomaximal, Sylow
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61#38011yescharacteristic
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61C2×#10411yescharacteristic
143C4×C61#42111yescharacteristic
144C4×C61#43012yes—
145Dic61—21no—
146Dic61—21no—
147Dic61—41no—
148Dic61—41no—
149Dic61#47211yescharacteristic
150Dic61#47311yescharacteristic
151#2965—611no—
152C4×#108—611no—
153#1567—611no—
154#1489—612no—
155#1299—612no—
156C2×C61—81no—
157C2×C61#180611yescharacteristic
158C2×C61#181111yescharacteristic
159C2×C61#181611yescharacteristic
160D61—41no—
161C4×#41—611no—
162#446—611no—
163#446—611no—
164#436—611no—
165#436#692311yescharacteristic
166#435—1221no—
167#435—1221no—
168#431—611no—
169#431—1221no—
170C2×#108—1221no—
171#423—612no—
172C4×M16—612no—
173C4×M16—1221no—
174C2×C4×C8—611no—
175#341—1221no—
176#335—1221no—
177#335—1221no—
178Q8⋊C8—1222no—
179D4⋊C8—1222no—
180C61#867311yescharacteristic, complemented, Sylow
181C2×#41—611no—
182C2×M16—21no—
183C2×M16—1221no—
184C2×M16—1222no—
185C2×M16—1222no—
186C22×C8—611no—
187C22×C8—611no—
188C4×Q8—611no—
189C4×Q8—611no—
190C4×D4—611no—
191C4×D4—1221no—
192C4×D4—1221no—
193C4×D4C2×#692311yescharacteristic
194#117—611no—
195#117—1221no—
196C2×C42—611no—
197C2×C42—1221no—
198#108—1224no—
199C4⋊C8—611no—
200C4⋊C8—1222no—
201C4⋊C8—1222no—
202C4⋊C8—1221no—
203C4⋊C8—1221no—
204C4⋊C8C2×#692311yescharacteristic
205C22⋊C8—21no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208#97—1222no—
209#97—1221no—
210#97—1221no—
211C4×C8—611no—
212C4×C8—611no—
213C4×C8—611no—
214C4×C8—1221no—
215C4×C8—1222no—
216C4×C8C2×#692311yescharacteristic
217#41—2442no—
218C2×Q8—611no—
219C2×D4—1221no—
220C2×D4C4⋊#692311yescharacteristic
221C22×C4—21no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—1221no—
226C22×C4—1221no—
227M16—42no—
228M16—1224no—
229M16—4882no—
230M16—2442no—
231M16—2442no—
232C2×C8—21no—
233C2×C8—611no—
234C2×C8—611no—
235C2×C8—1222no—
236C2×C8—1221no—
237C2×C8—2441no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8C22⋊#692311yescharacteristic
241C2×C8C22⋊#692311yescharacteristic
242C4⋊C4—611no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4C4⋊#692311yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C42—611no—
250C42—611no—
251C42—611no—
252C42—1221no—
253C42—1221no—
254C42—1221no—
255C42C22×#692311yescharacteristic
256C23—21no—
257C23—611no—
258Q8—1222no—
259D4—22no—
260D4—2442no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2442no—
277C2×C4C2×C22⋊#692311yescharacteristic
278C2×C4C2×C4⋊#692311yescharacteristic
279C2×C4#1451985611yescharacteristic
280C8—21no—
281C8—21no—
282C8—41no—
283C8—612no—
284C8—1221no—
285C8—4882no—
286C8—2444no—
287C8—2441no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—1221no—
292C22—1221no—
293C22—1221no—
294C22#1684070411yescharacteristic
295C4—21no—
296C4—41no—
297C4—611no—
298C4—611no—
299C4—1221no—
300C4—1221no—
301C4—2441no—
302C4—2441no—
303C4D61⋊#10411yescharacteristic
304C4#1684076011yescharacteristic
305C4#1684077712yes—
306C2—81no—
307C2—2441no—
308C2#2146169311yescharacteristic
309C2#2146170011yescharacteristic
310C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61#380
prime radicalC2×#11758224Q8
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8673
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. #21461378C2semidirect
4. #21460705C2semidirect
180. C61#8673semidirect

Maximal subgroups

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

subgroupindex
C4×#145198482
#214613782
#214611552
#214607052
#214547822
#867361