Finite Group Databasebeta

← #30606507

Subgroups — #30606507

Order 15616.

548 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 102 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×#16840664C212yesmaximal
2C4×#14519837C211yesmaximal, characteristic
3C4×#14519835C211yesmaximal, characteristic
4#21460903C212yesmaximal
5#21448488C211yesmaximal, characteristic
6C2×#14519837C2212yes—
7C2×#14519835C2212yes—
8C4×#11758217—21no—
9C4×C22⋊#6923—21no—
10#16840664C418yescomplemented
11#16840642—21no—
12#16840640—21no—
13C2×#14519760C2211yescharacteristic
14C2×C4×C22⋊D61C2211yescharacteristic
15#16839657—21no—
16#16839652—21no—
17#16839643—21no—
18#16839641C2211yescharacteristic
19#16839635C411yescharacteristic, complemented
20#16839633—21no—
21#16839625C411yescharacteristic, complemented
22C4×C22⋊Dic61C411yescharacteristic, complemented
23C22×C4⋊C4×C61C411yescharacteristic, complemented
24C2×#11758217—22no—
25C2×C22⋊#6923—22no—
26C2×C4×#6923—41no—
27#14519837—22no—
28#14519837C2×C414yes—
29#14519835—22no—
30#14519835C2×C414yes—
31#14519832—41no—
32C4×#92420—41no—
33(C2×#6923)⋊C4—41no—
34C22×C22⋊D61C2311yescharacteristic
35C22×C4×D61D411yescharacteristic
36#14519760—22no—
37#14519760C2×C414yes—
38C4×C22⋊D61—41no—
39C4×C22⋊D61—41no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61—21no—
50C2×C4×Dic61D411yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C23×C4×C61C2×C411yescharacteristic
57C23×C4×C61C2×C411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—41no—
62C2×C4⋊C4×C61—41no—
63C24×C61C22×C411yescharacteristic
64C23×D61C2×D411yescharacteristic
65C22×#6923—42no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61—81no—
76C22×C4×C61C4212yescomplemented
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61C22×C412yes—
82C2×C22⋊D61#4112yes—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—81no—
91C22⋊#6923—24no—
92C22⋊#6923—42no—
93#11758217—24no—
94#11758217—42no—
95C2×#92420—42no—
96C4×#6923—82no—
97C4⋊C4×C61—42no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C22⋊Dic61—21no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61C4212yescomplemented
104#11758198—24no—
105#11758198—41no—
106#11758198—81no—
107#11758196—24no—
108#11758196—41no—
109#11758196—81no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—81no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C4211yescharacteristic
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61#11711yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61C4×D412yes—
125C2×#6923—44no—
126C2×#6923—82no—
127C2×#6923—82no—
128C2×C4×C61—22no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—82no—
142C2×C4×C61#9911yescharacteristic
143C2×C4×C61#9911yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—42no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61C4×D412yes—
159C4×D61—42no—
160C4×D61—81no—
161#92420—44no—
162#12621—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—42no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61C4×C22⋊C411yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61#41011yescharacteristic
175C2×D61—22no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—42no—
179C2×D61—81no—
180#6923—84no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—42no—
185C4×C61—81no—
186Dic61—22no—
187Dic61—42no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191#2322—611no—
192C2×#352—612no—
193C4×#100—611no—
194C4×#99—611no—
195#1390—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—41no—
199C2×C61—41no—
200C2×C61C4×#9911yescharacteristic
201C2×C61#212111yescharacteristic
202C2×C61#212311yescharacteristic
203D61—42no—
204C2×#123—611no—
205C2×C4×D4—611no—
206C22×C4⋊C4#692311yescharacteristic, complemented
207C2×#100—612no—
208C2×#99—612no—
209C4×M16—1221no—
210#389—1221no—
211#388—1221no—
212#387—1221no—
213#386—611no—
214#385—611no—
215#385—1221no—
216#381—611no—
217C4×C22⋊C4—611no—
218C4×C22⋊C4—1221no—
219#352—618no—
220#343—1221no—
221#342—1221no—
222C61#1262111yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C23×C4—611no—
225C23×C4C2×#692311yescharacteristic
226C23×C4C2×#692311yescharacteristic
227C23×C4C2×#692311yescharacteristic
228C2×M16—1222no—
229#123—614no—
230#123—1222no—
231C4×D4—2441no—
232C4×D4—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1222no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—1221no—
249C2×C42—2441no—
250#100—614no—
251#100—1222no—
252#99—614no—
253#99—1222no—
254#97—2441no—
255C4×C8—2441no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—2441no—
262C24—611no—
263C24C22×#692311yescharacteristic
264C2×D4—612no—
265C2×D4—612no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—4881no—
286C22×C4—2442no—
287C22×C4C4×#692312yescomplemented
288C22×C4C22⋊#692311yescharacteristic
289C22×C4C22⋊#692311yescharacteristic
290M16—1224no—
291M16—2442no—
292C2×C8—2442no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—1224no—
297C4⋊C4—4881no—
298C4⋊C4—2441no—
299C22⋊C4—612no—
300C22⋊C4—1224no—
301C22⋊C4—1221no—
302C22⋊C4—1224no—
303C22⋊C4—4881no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2442no—
307C22⋊C4—2441no—
308C42—1221no—
309C42—1221no—
310C42—4881no—
311C42—4882no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—612no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23C2×C4×#692311yescharacteristic
322C23C2×C22⋊#692311yescharacteristic
323C23#1451985611yescharacteristic
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1222no—
346C2×C4—4881no—
347C2×C4—4882no—
348C2×C4—4882no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2444no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4#1451983511yescharacteristic
359C2×C4#1451983511yescharacteristic
360C8—2444no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—1222no—
371C22—4881no—
372C22—2442no—
373C22—2441no—
374C22—2441no—
375C22C4×C22⋊#692311yescharacteristic
376C22C2×#1451983511yescharacteristic
377C22#1684074111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—42no—
382C4—81no—
383C4—1222no—
384C4—4881no—
385C4—4884no—
386C4—2442no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—2442no—
394C2C4×#1451983511yescharacteristic
395C2#2146207411yescharacteristic
396C2#2146208111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radical, cosocleC22×C22⋊D61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#12621
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #16840664C4semidirect
19. #16839635C4semidirect
21. #16839625C4semidirect
22. C4×C22⋊Dic61C4semidirect
23. C22×C4⋊C4×C61C4semidirect
76. C22×C4×C61C42semidirect
103. C22⋊Dic61C42semidirect
206. C22×C4⋊C4#6923semidirect
222. C61#12621semidirect
287. C22×C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168406642
C4×#145198372
C4×#145198352
#214609032
#214484882
#1262161