Finite Group Databasebeta

← #11895304

Subgroups — #11895304

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic, complemented
2#10596014C211yesmaximal, characteristic, complemented
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4#10592864C212yesmaximal, complemented
5#10592720C211yesmaximal, characteristic, complemented
6#10592714C211yesmaximal, characteristic
7#10592570C212yesmaximal, complemented
8#10592499C212yesmaximal, complemented
9#10592455C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic, complemented
11C8×#634C211yesmaximal, characteristic, complemented
12#79621—34nomaximal
13C2×C32×SD16C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64156C2212yes—
17D4×C3⋊Dic3C2212yes—
18C2×#3753C2212yes—
19C2×C4⋊(C3⋊Dic3)—21no—
20#64133—21no—
21#64103—22no—
22#64102C2212yes—
23#64099C2212yes—
24#64087—22no—
25#64084—21no—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—21no—
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#106C2211yescharacteristic
31C32×#103C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63662C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5585—34no—
43#5543—34no—
44C3×C4×SD16D314yescomplemented
45#5165—38no—
46#5021—34no—
47#5015—34no—
48#4871—38no—
49#4800—38no—
50#4756—38no—
51#4694—34no—
52C8×Dic6—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C22×C3⋊Dic3—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×#634—21no—
62C2×#634D411yescharacteristic
63C32×SD16—22no—
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2311yescharacteristic
68C32×C4⋊C4C2311yescharacteristic
69C32×C22⋊C4—21no—
70C32×C42—21no—
71C32×C42C2311yescharacteristic
72#3757—22no—
73#3753—24no—
74#3752—22no—
75#3752—22no—
76#3752—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)C2312yes—
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3361—91noSylow
86C2×C3×SD16C2×D314yes—
87C3×C4×Q8C2×D314yes—
88C3×C4×D4C2×D314yes—
89#947—38no—
90D4×Dic3—38no—
91C2×#213—38no—
92C2×C4⋊Dic3—64no—
93#924—64no—
94#894—68no—
95#893—38no—
96#890—38no—
97#878—68no—
98#875—64no—
99#874—34no—
100C4×D12—64no—
101#869—34no—
102C4×Dic6—34no—
103C3×#106C2×D314yes—
104C3×#103C2×D314yes—
105C3×#102C2×D314yes—
106C3×C4×C8C2×D314yes—
107#835—38no—
108#821—38no—
109#821—38no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#809—38no—
113#807—38no—
114C4⋊(C3⋊C8)—34no—
115C23×C32—21no—
116C22×C3⋊D3—22no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×D4—21no—
120C32×D4#4112yes—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—82no—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3C2×D412yes—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—42no—
135C4⋊(C3⋊D3)—81no—
136C4×C3⋊D3—82no—
137#634—22no—
138#634—81no—
139C32×C8—21no—
140C32×C8—21no—
141C3⋊(C3⋊C8)—22no—
142#559—91no—
143#554—91no—
144#488—92no—
145#486—91no—
146#478—92no—
147#477—91no—
148#463—92no—
149#459—91no—
150C8×Q8—91no—
151C4×SD16C3⋊D311yescharacteristic, complemented
152C4×D8—92no—
153C2×C3×Q8C22×D314yes—
154C2×C3×D4C22×D314yes—
155C22×C3×C4—24no—
156C22×Dic3—68no—
157C2×D12—38no—
158C2×D12—64no—
159C2×D12—64no—
160C2×C4×D3—68no—
161C2×Dic6—34no—
162C2×Dic6—64no—
163C3×SD16—28no—
164C2×C3×C8C22×D314yes—
165C2×C3×C8C22×D314yes—
166C3×C4⋊C4—24no—
167C3×C4⋊C4C22×D314yes—
168C3×C4⋊C4C22×D314yes—
169C3×C22⋊C4—24no—
170C3×C42—24no—
171C3×C42C22×D314yes—
172#217—68no—
173#213—616no—
174(C2×D3)⋊C4—68no—
175(C2×D3)⋊C4—68no—
176(C2×D3)⋊C4—68no—
177C4⋊Dic3—34no—
178C4⋊Dic3—38no—
179C4⋊Dic3—68no—
180C4⋊Dic3—64no—
181Dic3⋊C4—38no—
182Dic3⋊C4—68no—
183C4×Dic3—38no—
184C2×C3⋊C8—38no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C32×C4—21no—
193C32×C4—41no—
194C32×C4—41no—
195C32×C4—41no—
196C32×C4#13512yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—42no—
202C2×SD16C2×C3⋊D311yescharacteristic
203C2×D8—92no—
204C4⋊Q8—91no—
205#127—91no—
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—182no—
211C22⋊Q8—181no—
212C4×Q8—91no—
213C4×Q8C2×C3⋊D311yescharacteristic
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—181no—
217C4×D4C2×C3⋊D311yescharacteristic
218C2×C4⋊C4—181no—
219#107—92no—
220#106C2×C3⋊D311yescharacteristic
221C4⋊C8—92no—
222C4⋊C8—91no—
223#103—92no—
224#103C2×C3⋊D311yescharacteristic
225#102—92no—
226#102—92no—
227#102—92no—
228#102C2×C3⋊D311yescharacteristic
229C4×C8—92no—
230C4×C8C2×C3⋊D311yescharacteristic
231C23×C3—24no—
232C22×D3—68no—
233C3×Q8—24no—
234C3×Q8—24no—
235C3×D4—24no—
236C3×D4#23518yes—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—48no—
241C2×C3×C4D3×D414yes—
242C2×C3×C4D3×D414yes—
243C2×C3×C4C23×D314yes—
244C2×Dic3—38no—
245C2×Dic3—38no—
246C2×Dic3—68no—
247C2×Dic3—248no—
248D12—68no—
249D12—68no—
250D12—128no—
251D12—244no—
252C4×D3—248no—
253Dic6—68no—
254Dic6—244no—
255C3×C8—24no—
256C3×C8—24no—
257C3⋊C8—68no—
258C2×C32—42no—
259C2×C32#54811yescharacteristic
260C2×C32C2×#13511yescharacteristic
261C2×C32#57611yescharacteristic
262C3⋊D3—82no—
263C2×Q8—91no—
264C2×Q8—181no—
265C2×Q8C22×C3⋊D311yescharacteristic
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—182no—
272C22×C4—182no—
273SD16—22no—
274D8—184no—
275C2×C8—92no—
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—91no—
280C4⋊C4—92no—
281C4⋊C4—92no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4C22×C3⋊D311yescharacteristic
286C4⋊C4C22×C3⋊D311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—21no—
293C42—92no—
294C42C22×C3⋊D311yescharacteristic
295C22×C3—28no—
296C22×C3—44no—
297C22×C3—44no—
298C22×C3C2×D3×D414yes—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—128no—
302C3×C4—24no—
303C3×C4—44no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4#91618yes—
307C3×C4C2×#23514yes—
308C3×C4#101014yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—128no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—21no—
314C23—182no—
315Q8—21no—
316Q8—21no—
317Q8—182no—
318Q8—721no—
319D4—21no—
320D4—182no—
321D4—182no—
322D4—362no—
323D4—721no—
324D4#382812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—182no—
332C2×C4—722no—
333C2×C4—722no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—182no—
340C2×C3—48no—
341C2×C3#555214yes—
342C2×C3C2×#91614yes—
343C2×C3#576914yes—
344D3—248no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—182no—
357C4—182no—
358C4—362no—
359C4#6412512yes—
360C4C2×#382811yescharacteristic
361C4#6436711yescharacteristic
362C3#7962114yescomplemented
363C2—42no—
364C2—722no—
365C2#1059602311yescharacteristic
366C2C2×#6412511yescharacteristic
367C2#1059624011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radical#10592714C2
hypercenterC4×SD16C3⋊D3
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10596056C2semidirect
2. #10596014C2semidirect
3. C32×C4×SD16C2semidirect
4. #10592864C2semidirect
5. #10592720C2semidirect
7. #10592570C2semidirect
8. #10592499C2semidirect
9. #10592455C2semidirect
10. #10592393C2semidirect
11. C8×#634C2semidirect
44. C3×C4×SD16D3semidirect
151. C4×SD16C3⋊D3semidirect
312. C32#3361semidirect
362. C3#79621semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960142
C32×C4×SD162
#105928642
#105927202
#105927142
#105925702
#105924992
#105924552
#105923932
C8×#6342
#796213