Finite Group Databasebeta

← #30606579

Subgroups — #30606579

Order 15616.

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

normal subgroups only

This group has 452 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
1#21462545C211yesmaximal, characteristic
2#21462113C211yesmaximal, characteristic
3#21461577C212yesmaximal, complemented
4#21460918C212yesmaximal, complemented
5#21447483C211yesmaximal, characteristic
6C2×#14519865C411yescharacteristic, complemented
7C2×#14519864C2211yescharacteristic
8#16840794—22no—
9#16840791—22no—
10#16840766C411yescharacteristic, complemented
11#16840749C2212yes—
12#16840737C411yescharacteristic, complemented
13#16840736C2211yescharacteristic
14#16840726—22no—
15#16840721C411yescharacteristic, complemented
16#16840672C412yescomplemented
17#16840671C412yescomplemented
18#16840643—22no—
19#16840311C2211yescharacteristic
20#16839734C2212yes—
21#16839557C411yescharacteristic
22#16839554C412yes—
23C61×#354C411yescharacteristic
24#14519865—42no—
25#14519864—42no—
26C2×#11758213—21no—
27C2×#11758213C2×C411yescharacteristic
28C2×#11758213C2×C411yescharacteristic
29C2×#11758217—22no—
30C2×#11758217D412yes—
31C2×D61⋊C8—21no—
32C2×D61⋊C8C2×C411yescharacteristic
33C2×D61⋊C8C2×C411yescharacteristic
34C22×#92420D412yes—
35C4⋊#92420—22no—
36#14519838C2×C414yes—
37#14519837—22no—
38#14519834—22no—
39C22⋊#92420—22no—
40#14519832—21no—
41#14519832—21no—
42#14519832—42no—
43C4×#92420—42no—
44C2×#11758226C2×C411yescharacteristic
45C2×#11758224C2311yescharacteristic
46#14519775C2×C411yescharacteristic
47#14519773C2×C411yescharacteristic
48#14519765C2×C411yescharacteristic
49#14519750—22no—
50#14519737—22no—
51#14519733—22no—
52C42×D61C2×C411yescharacteristic
53#14519692C2×C412yes—
54#14519691—22no—
55#124×C61C2×C411yescharacteristic
56#99×C61C2×C412yes—
57C2×Q8×C61C4211yescharacteristic
58C2×D4×C61C22×C411yescharacteristic
59C2×C22⋊D61—22no—
60C2×C22⋊D61#4112yes—
61C22×Dic61C2×D412yes—
62#11758226—41no—
63#11758226—41no—
64#11758224—41no—
65#11758224—41no—
66C2×D244—21no—
67C2×D244C4211yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C22×C411yescharacteristic
71C2×Dic122C22×C411yescharacteristic
72#11758217—24no—
73#11758217—42no—
74#11758217—42no—
75C2×#92420—22no—
76C2×#92420—22no—
77C2×#92420—21no—
78C2×#92420—21no—
79C2×#92420—42no—
80C2×#92420C22⋊C411yescharacteristic
81C2×#92420C22⋊C412yes—
82C2×#92420C22⋊C411yescharacteristic
83#11758213—41no—
84#11758213—42no—
85#11758213—41no—
86D61⋊C8—22no—
87D61⋊C8—42no—
88D61⋊C8—41no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—22no—
91C42×C61C4211yescharacteristic
92C22⋊Dic61—22no—
93#11758198—22no—
94#11758196—22no—
95#11758196—42no—
96C4×Dic61—21no—
97C4×Dic61—42no—
98C4×Dic61C4211yescharacteristic
99C23×C61C4×D412yes—
100C22×D61—21no—
101C22×D61#11711yescharacteristic
102Q8×C61—41no—
103D4×C61—41no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61C2×C4211yescharacteristic
108C22⋊D61—42no—
109C22⋊D61—82no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—21no—
113C2×Dic61—42no—
114C2×Dic61C2×C22⋊C411yescharacteristic
115C2×Dic61C4×D412yes—
116D244—41no—
117D244—42no—
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—81no—
123Dic122—41no—
124#92420—21no—
125#92420—22no—
126#92420—44no—
127#92420—41no—
128#92420—41no—
129#92420#9912yes—
130#12634—611nomaximal, Sylow
131C22×C61—22no—
132C22×C61—42no—
133C22×C61C4×C22⋊C411yescharacteristic
134C2×D61—21no—
135C2×D61—41no—
136C2×D61—42no—
137C2×D61—41no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—82no—
142Dic61—22no—
143Dic61—41no—
144Dic61—82no—
145Dic61C2×#9911yescharacteristic
146Dic61#41011yescharacteristic
147#2932—611no—
148#2132—611no—
149#2126—611no—
150#1757—612no—
151#1395—612no—
152C2×C61—21no—
153C2×C61—42no—
154C2×C61C4×#9911yescharacteristic
155D61—41no—
156D61—81no—
157C2×#131—611no—
158C2×#131—611no—
159#532—611no—
160#435—1222no—
161#435—1222no—
162#423—611no—
163#413—612no—
164#410—612no—
165#408—611no—
166#408—611no—
167#405—1222no—
168C2×#97—611no—
169#356—612no—
170#355—612no—
171#354—611no—
172#354#692311yescharacteristic
173#353—612no—
174#344—1222no—
175C61#1263411yescharacteristic, complemented, Sylow
176C2×#41—611no—
177C2×#41—611no—
178#131—2442no—
179#131—2442no—
180C2×M16—612no—
181C2×M16—611no—
182C2×M16—611no—
183C2×M16—1221no—
184C2×M16—1222no—
185C22×C8—612no—
186C22×C8—611no—
187C22×C8—611no—
188C22×C8—1221no—
189C4⋊Q8—611no—
190#127—611no—
191#124—611no—
192#124C2×#692311yescharacteristic
193#121—1222no—
194C4×D4—1222no—
195#117—1222no—
196C2×C42—611no—
197C4⋊C8—1222no—
198#101—614no—
199#100—1222no—
200#99—612no—
201#99—1222no—
202#99C2×#692312yes—
203C22⋊C8—1222no—
204C22⋊C8—1222no—
205#97—1221no—
206#97—1221no—
207#97—2442no—
208C4×C8—2442no—
209#41—2441no—
210#41—2441no—
211#41—2441no—
212#41—2441no—
213C2×Q8—611no—
214C2×Q8C4×#692311yescharacteristic
215C2×D4—612no—
216C2×D4—611no—
217C2×D4—1221no—
218C2×D4—1222no—
219C2×D4C22×#692311yescharacteristic
220C22×C4—612no—
221C22×C4—611no—
222C22×C4—1221no—
223C22×C4—1221no—
224M16—1224no—
225M16—2442no—
226M16—2441no—
227M16—2442no—
228M16—2442no—
229M16—2441no—
230C2×C8—611no—
231C2×C8—611no—
232C2×C8—612no—
233C2×C8—1222no—
234C2×C8—1222no—
235C2×C8—1222no—
236C2×C8—1221no—
237C2×C8—1221no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2441no—
241C4⋊C4—1222no—
242C4⋊C4—2442no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—1222no—
246C22⋊C4—1222no—
247C42—611no—
248C42—1221no—
249C42—2442no—
250C42C4×#692311yescharacteristic
251C23—611no—
252C23—1221no—
253C23D4×#692312yes—
254Q8—41no—
255Q8—2441no—
256D4—41no—
257D4—4882no—
258D4—2441no—
259D4—2442no—
260D4—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—611no—
265C2×C4—612no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4—4881no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2442no—
275C2×C4C2×C4×#692311yescharacteristic
276C8—612no—
277C8—1221no—
278C8—1222no—
279C8—2441no—
280C8—2441no—
281C8—2444no—
282C22—22no—
283C22—42no—
284C22—1221no—
285C22—2442no—
286C22—2441no—
287C22—2441no—
288C22C22⋊C4×#692311yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—611no—
294C4—611no—
295C4—1222no—
296C4—4882no—
297C4—2441no—
298C2—21no—
299C2—42no—
300C2—4881no—
301C2—2441no—
302C2#99×#692311yescharacteristic
subgroupG/H
centerC2#99×#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC61×#354C4
socleC2×C61C4×#99
prime radical#16840311C22
cosocleC2×#11758224C23
hypercenter#354#6923
hypocenterC61#12634
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #21461577C2semidirect
4. #21460918C2semidirect
6. C2×#14519865C4semidirect
10. #16840766C4semidirect
12. #16840737C4semidirect
15. #16840721C4semidirect
16. #16840672C4semidirect
17. #16840671C4semidirect
175. C61#12634semidirect

Maximal subgroups

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

subgroupindex
#214625452
#214621132
#214615772
#214609182
#214474832
#1263461