Finite Group Databasebeta

← #29580082

Subgroups — #29580082

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454171C211yesmaximal, characteristic
2#21444049C211yesmaximal, characteristic
3#21443699C214yesmaximal
4C4×C22⋊C8×C61C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519756—21no—
7C22×C4⋊Dic61—21no—
8#16839668—21no—
9#16839660—21no—
10#16839660C412yescomplemented
11#16839632C411yescharacteristic, complemented
12#16839622—21no—
13#16839622C2212yes—
14C2×#14519684—21no—
15C2×#14519684C2212yes—
16C22×C42×C61C2211yescharacteristic
17C2×C22⋊C8×C61C2212yes—
18C2×C4×C8×C61—21no—
19C61×#336—21no—
20C22×Dic122—21no—
21C23×Dic61—22no—
22#14519777—42no—
23#14519756—42no—
24#14519756—42no—
25C2×C4⋊Dic61—24no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—42no—
30C2×C4⋊Dic61—42no—
31C2×C4⋊Dic61C2×C412yes—
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758196—22no—
34C2×C22⋊Dic61—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684—24no—
38#14519684—42no—
39C23×C4×C61D411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C22×C8×C61—22no—
43C2×C42×C61—42no—
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C22⋊C8×C61—22no—
49C22⋊C8×C61Q814yescomplemented
50C4×C8×C61—42no—
51C24×C61C2×D411yescharacteristic
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61D812yes—
63C22×C4×C61SD1612yes—
64C22×C4×C61SD1612yes—
65C22×C4×C61Q1612yes—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×Q812yes—
69C22×C4×C61#4112yes—
70C22×Dic61—24no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—42no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×C8×C61—24no—
83C2×C8×C61—42no—
84C2×C8×C61—42no—
85C42×C61—22no—
86C42×C61—22no—
87C42×C61—41no—
88C42×C61—41no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C4⋊Dic61—42no—
92C4⋊Dic61—48no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—42no—
97#11758196—44no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61C2×C22⋊C411yescharacteristic
103C23×C61#12411yescharacteristic
104C23×C61C4⋊Q811yescharacteristic
105C23×C61C2×D811yescharacteristic
106C23×C61C2×SD1611yescharacteristic
107C23×C61C2×SD1611yescharacteristic
108C23×C61C2×Q1611yescharacteristic
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—24no—
120C2×C4×C61—24no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61#9912yes—
126C2×C4×C61#10212yes—
127C2×C4×C61#10212yes—
128C2×C4×C61#10312yes—
129C2×C4×C61#10312yes—
130C2×C4×C61#10412yes—
131C2×C4×C61C4×Q812yes—
132C2×C4×C61C22⋊Q812yes—
133C2×Dic61—44no—
134C2×Dic61—44no—
135C2×Dic61—44no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—82no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C2×Dic61—82no—
146Dic122—84no—
147C8×C61—44no—
148#9885—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#39111yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61#41011yescharacteristic
164C22×C61C2×#10211yescharacteristic
165C22×C61C2×#10311yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C22×C61#42111yescharacteristic
168C22×C61#48611yescharacteristic
169C22×C61#48711yescharacteristic
170C22×C61#49811yescharacteristic
171C22×C61#50011yescharacteristic
172C4×C61—22no—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—22no—
176C4×C61—22no—
177C4×C61#32714yes—
178Dic61—84no—
179Dic61—82no—
180Dic61—82no—
181#2857—611no—
182C4×C22⋊C8D6111yescharacteristic
183C4⋊#95—611no—
184#1294—614no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61C2×#32711yescharacteristic
190C2×C61#150311yescharacteristic
191C2×C61#151711yescharacteristic
192C2×C61#152011yescharacteristic
193C2×C61#198611yescharacteristic
194C2×C61#199011yescharacteristic
195C2×C61#199611yescharacteristic
196C2×C4⋊Q8—611no—
197C2×C22⋊Q8—1221no—
198C22×C4⋊C4—1221no—
199C22×C42C2×D6111yescharacteristic
200C2×C22⋊C8C2×D6112yes—
201C2×C4×C8—21no—
202#391—1221no—
203#389—612no—
204#389—1221no—
205#384—611no—
206#380—612no—
207#380—1221no—
208C2×#95—612no—
209C2×#95—1221no—
210#336—21no—
211C61#988511yescharacteristic, complemented, Sylow
212C22×Q8—1221no—
213C23×C4—1222no—
214C23×C4D24411yescharacteristic
215C23×C4D24411yescharacteristic
216C23×C4C22×D6111yescharacteristic
217C22×C8—22no—
218C4⋊Q8—2442no—
219C22⋊Q8—2442no—
220C22⋊Q8—2442no—
221C2×C4⋊C4—612no—
222C2×C4⋊C4—612no—
223C2×C4⋊C4—1224no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1222no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—2442no—
229C2×C4⋊C4—2442no—
230C2×C22⋊C4—1222no—
231C2×C42—42no—
232C2×C42C4×D6111yescharacteristic
233C2×C42C4×D6111yescharacteristic
234C2×C42C22⋊D6111yescharacteristic
235C2×C42C22⋊D6111yescharacteristic
236C22⋊C8—22no—
237C22⋊C8Dic12214yescomplemented
238C4×C8—42no—
239#95—1222no—
240#95—1222no—
241#95—1224no—
242#95—2442no—
243C24C2×D24411yescharacteristic
244C2×Q8—2442no—
245C2×Q8—2442no—
246C2×Q8—2442no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1224no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4#1175819012yes—
263C22×C4#1175819012yes—
264C22×C4D48812yes—
265C22×C4Dic24412yes—
266C22×C4#1175819811yescharacteristic
267C22×C4#1175819811yescharacteristic
268C22×C4#1175819811yescharacteristic
269C22×C4#1175819811yescharacteristic
270C22×C4C2×Dic12212yes—
271C22×C4C2×C4×D6111yescharacteristic
272C22×C4#1175822212yes—
273C22×C4C2×C22⋊D6111yescharacteristic
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4—2448no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2444no—
283C4⋊C4—2442no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—22no—
287C42—22no—
288C42—41no—
289C42—41no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C2×#1175819811yescharacteristic
295C23#1451976511yescharacteristic
296C23#1451977711yescharacteristic
297C23C2×D48811yescharacteristic
298C23C2×#1175819011yescharacteristic
299C23C2×#1175819011yescharacteristic
300C23C2×Dic24411yescharacteristic
301Q8—4884no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—4882no—
319C2×C4—4882no—
320C2×C4—4882no—
321C2×C4—4882no—
322C2×C4—2444no—
323C2×C4—2444no—
324C2×C4—2444no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4#1451969112yes—
332C2×C4#1451969912yes—
333C2×C4#1451969912yes—
334C2×C4#1451970212yes—
335C2×C4#1451970212yes—
336C2×C4#1451970312yes—
337C2×C4C4×Dic12212yes—
338C2×C4#1451975612yes—
339C8—44no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22#1683966811yescharacteristic
353C22C2×#1451969111yescharacteristic
354C22#1683973511yescharacteristic
355C22C2×#1451969911yescharacteristic
356C22C2×#1451970211yescharacteristic
357C22C2×#1451970311yescharacteristic
358C22#1683977811yescharacteristic
359C22#1684010911yescharacteristic
360C22#1684011311yescharacteristic
361C22#1684016011yescharacteristic
362C22#1684016711yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—4884no—
369C4—4882no—
370C4—4882no—
371C4#1683949714yes—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C2×#1683949711yescharacteristic
377C2#2144431911yescharacteristic
378C2#2144438011yescharacteristic
379C2#2144439211yescharacteristic
380C2#2144676311yescharacteristic
381C2#2144678011yescharacteristic
382C2#2144680411yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC4×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC4×C22⋊C8D61
hypocenterC61#9885
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
10. #16839660C4semidirect
11. #16839632C4semidirect
49. C22⋊C8×C61Q8semidirect
211. C61#9885semidirect
237. C22⋊C8Dic122semidirect

Maximal subgroups

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

subgroupindex
#214541712
#214440492
#214436992
C4×C22⋊C8×C612
#988561