Finite Group Databasebeta

← #30606282

Subgroups — #30606282

Order 15616.

768 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C2×#16840741C212yesmaximal
2#21460908C214yesmaximal, complemented
3#21454263C211yesmaximal, characteristic
4C2×#14519856—22no—
5#16840741—22no—
6#16840741—22no—
7#16840741C414yescomplemented
8#16840741C2214yes—
9C2×#14519836—22no—
10C2×#14519835C414yescomplemented
11C22×#11758222C2211yescharacteristic
12C22×#11758194C411yescharacteristic, complemented
13#16839730C412yescomplemented
14#16839730C2212yes—
15#16839728—22no—
16#16839725—22no—
17C22×M16×C61C411yescharacteristic, complemented
18#14519856—24no—
19#14519856—24no—
20#14519856—42no—
21#14519856—42no—
22C2×C4⋊#6923—42no—
23C2×C22⋊#6923—24no—
24C2×C4×#6923—42no—
25#14519836—24no—
26#14519836—24no—
27#14519835—24no—
28#14519835C2×C418yescomplemented
29C2×#11758222—42no—
30C2×#11758222—42no—
31C2×#11758222C2×C411yescharacteristic
32C2×#11758222C2×C412yes—
33C2×#11758222D411yescharacteristic
34C2×#11758222D412yes—
35C2×#11758222Q811yescharacteristic
36C2×#11758222C2311yescharacteristic
37C22×Dic122Q811yescharacteristic
38C22×D244D411yescharacteristic
39C22×C22⋊D61C2×C412yes—
40C22×C4×D61D412yes—
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194—42no—
44C22×#92418C2×C412yescomplemented
45#14519689—24no—
46#14519689—24no—
47C23×C4×C61C2×C411yescharacteristic
48C2×M16×C61—21no—
49C2×M16×C61—42no—
50C2×M16×C61C2×C412yescomplemented
51C22×C8×C61—21no—
52C24×C61C4211yescharacteristic
53C23×D61C22⋊C412yes—
54C22×#6923—44no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61C4211yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C4⋊C411yescharacteristic
61C22×C4×C61C4⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—42no—
64C2×C22⋊D61—42no—
65C2×C22⋊D61C4212yes—
66C2×C22⋊D61C22⋊C412yes—
67C2×C22⋊D61C4⋊C412yes—
68C2×C22⋊D61C22×C412yes—
69C22×Dic61C4⋊C412yes—
70#11758222—42no—
71#11758222—42no—
72#11758222—41no—
73#11758222—41no—
74#11758222—42no—
75#11758222—42no—
76#11758222—42no—
77#11758222—42no—
78#11758222—41no—
79#11758222—41no—
80C2×D244—42no—
81C2×D244C22⋊C412yes—
82C2×D244C4⋊C411yescharacteristic
83C2×D244C2×D411yescharacteristic
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61C22⋊C412yes—
89C2×C4×D61C22⋊C412yes—
90C2×C4×D61C4⋊C412yes—
91C2×C4×D61C2×D412yes—
92C2×Dic122—42no—
93C2×Dic122C4⋊C411yescharacteristic
94C2×Dic122C4⋊C412yes—
95C2×Dic122C2×Q811yescharacteristic
96C22⋊#6923—28no—
97C22⋊#6923—44no—
98C4⋊#6923—44no—
99C4⋊#6923—44no—
100C4×#6923—44no—
101C4×#6923—44no—
102M16×C61—42no—
103M16×C61—42no—
104C2×C8×C61—22no—
105C2×C8×C61—42no—
106#11758194—42no—
107#11758194—42no—
108C2×#92418—22no—
109C2×#92418—42no—
110C23×C61—22no—
111C23×C61—81no—
112C23×C61#9511yescharacteristic
113C23×C61#9511yescharacteristic
114C23×C61C2×C4211yescharacteristic
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—82no—
118C22×D61#9512yes—
119C22×D61C2×C22⋊C412yes—
120C2×#6923—48no—
121C2×#6923—88no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61#9511yescharacteristic
130C2×C4×C61#9511yescharacteristic
131C2×C4×C61#9912yes—
132C2×C4×C61#9912yes—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C2×C4⋊C411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61#9512yes—
142C2×Dic61C2×C4⋊C412yes—
143D244—42no—
144D244—41no—
145D244—41no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154Dic122—41no—
155Dic122—42no—
156Dic122—41no—
157C8×C61—42no—
158#92418—42no—
159#12577—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—82no—
166C22×C61#34212yes—
167C22×C61C2×#9511yescharacteristic
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—44no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—82no—
174#6923—88no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61#34212yes—
178C4×C61C2×#9911yescharacteristic
179C4×C61C2×#9911yescharacteristic
180Dic61—22no—
181Dic61—22no—
182C2×#410—612no—
183#2879—611no—
184#1391—614no—
185C2×C61—21no—
186C2×C61—22no—
187C2×C61—41no—
188C2×C61—41no—
189C2×C61C2×#34211yescharacteristic
190D61—42no—
191D61—42no—
192C22×#41—611no—
193C22×M16—611no—
194C22×M16#692311yescharacteristic, complemented
195C2×#117—1222no—
196#410—614no—
197#410—614no—
198#410—1222no—
199#410—1222no—
200C2×#99—614no—
201C2×#99—1222no—
202#408—612no—
203#408—612no—
204#408—1222no—
205#407—1222no—
206C61#1257711yescharacteristic, complemented, Sylow
207C2×#41—612no—
208C2×#41—611no—
209C2×#41—611no—
210C2×#41—612no—
211C2×#41—611no—
212C2×#41—611no—
213C2×#41—2442no—
214C2×#41—2442no—
215C22×Q8—611no—
216C22×D4—612no—
217C22×D4—611no—
218C23×C4—612no—
219C23×C4C2×#692311yescharacteristic
220C2×M16—21no—
221C2×M16—42no—
222C2×M16—1221no—
223C2×M16—1221no—
224C2×M16—2442no—
225C2×M16C2×#692312yescomplemented
226C22×C8—21no—
227C22×C8—612no—
228#117—1224no—
229#117—1224no—
230#117—2442no—
231#117—2442no—
232C2×C4⋊C4—2442no—
233C2×C22⋊C4—1224no—
234C2×C42—2442no—
235#99—618no—
236#99—1224no—
237#99—1224no—
238#99—1224no—
239C22⋊C8—1224no—
240C22⋊C8—1224no—
241C24—612no—
242C24C4×#692311yescharacteristic
243#41—2442no—
244#41—2441no—
245#41—2441no—
246#41—2441no—
247#41—2441no—
248#41—2442no—
249#41—2442no—
250#41—2442no—
251#41—2442no—
252#41—2442no—
253C2×Q8—612no—
254C2×Q8—611no—
255C2×Q8—611no—
256C2×Q8—2442no—
257C2×D4—612no—
258C2×D4—612no—
259C2×D4—612no—
260C2×D4—612no—
261C2×D4—612no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—2442no—
265C2×D4—2442no—
266C2×D4—2442no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—2444no—
279C22×C4C4×#692311yescharacteristic
280C22×C4C4⋊#692311yescharacteristic
281C22×C4C4⋊#692311yescharacteristic
282C22×C4C22⋊#692311yescharacteristic
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22×#692311yescharacteristic
285M16—42no—
286M16—42no—
287M16—2442no—
288M16—2442no—
289C2×C8—22no—
290C2×C8—42no—
291C2×C8—1222no—
292C2×C8—2442no—
293C4⋊C4—2444no—
294C4⋊C4—2444no—
295C22⋊C4—1228no—
296C22⋊C4—2444no—
297C42—2444no—
298C42—2444no—
299C23—22no—
300C23—81no—
301C23—612no—
302C23—612no—
303C23—1222no—
304C23—1222no—
305C23—4882no—
306C23(C2×#6923)⋊C411yescharacteristic
307C23(C2×#6923)⋊C411yescharacteristic
308C23C2×C4×#692311yescharacteristic
309Q8—2442no—
310Q8—2441no—
311Q8—2441no—
312D4—2442no—
313D4—2441no—
314D4—2441no—
315D4—2442no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—4888no—
339C2×C4—2448no—
340C2×C4(C2×#6923)⋊C411yescharacteristic
341C2×C4(C2×#6923)⋊C411yescharacteristic
342C2×C4#1451983512yes—
343C2×C4#1451983612yes—
344C2×C4C2×C22⋊#692311yescharacteristic
345C2×C4C2×C4⋊#692311yescharacteristic
346C8—42no—
347C8—2442no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—82no—
354C22—1222no—
355C22—1222no—
356C22—4882no—
357C22—2442no—
358C22—2442no—
359C22—2444no—
360C22#1684064012yes—
361C22C2×(C2×#6923)⋊C411yescharacteristic
362C4—21no—
363C4—21no—
364C4—1222no—
365C4—1222no—
366C4—4888no—
367C4#1684064012yes—
368C4C2×#1451983511yescharacteristic
369C4C2×#1451983611yescharacteristic
370C2—21no—
371C2—22no—
372C2—41no—
373C2—41no—
374C2—2442no—
375C2—2442no—
376C2C2×#1684064011yescharacteristic
subgroupG/H
centerC4C2×#14519836
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC2×C61C2×#342
prime radicalC22×#11758222C22
cosocleC2×#11758222C23
hypercenterC22×M16#6923
hypocenterC61#12577
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. #21460908C2semidirect
7. #16840741C4semidirect
10. C2×#14519835C4semidirect
12. C22×#11758194C4semidirect
13. #16839730C4semidirect
17. C22×M16×C61C4semidirect
28. #14519835C2×C4semidirect
44. C22×#92418C2×C4semidirect
50. C2×M16×C61C2×C4semidirect
194. C22×M16#6923semidirect
206. C61#12577semidirect
225. C2×M16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407412
#214609082
#214542632
#1257761