Finite Group Databasebeta

← #11874444

Subgroups — #11874444

Order 1152.

1283 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1283 conjugacy classes of subgroups — too many to draw. Only its 180 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#10596196C211yesmaximal, characteristic, complemented
2C2×#63950C214yesmaximal, complemented
3#10593971C211yesmaximal, characteristic, complemented
4C3×#5086C212yesmaximal, complemented
5#10591629C212yesmaximal, complemented
6#10591621C212yesmaximal, complemented
7#10590351C212yesmaximal, complemented
8#10590322C211yesmaximal, characteristic, complemented
9#81869—32nomaximal
10C2×#3832C2212yes—
11C2×#3796C2212yes—
12C32×C4⋊Q8C2211yescharacteristic
13#64156C2212yes—
14#64104—22no—
15#64102—22no—
16#64083C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×#216C2214yes—
19C2×C3×#215C2214yes—
20C3×#875C2212yes—
21#63950—216no—
22#63914C2211yescharacteristic
23#63912—22no—
24#63902—22no—
25#63873C2211yescharacteristic
26C2×#3717C2214yes—
27C2×#3714C2214yes—
28C2×#3710C2212yes—
29C3×#803C2212yes—
30#63555C2212yes—
31C2×#919—34no—
32C2×#916—34no—
33#5725—32no—
34#5725—61no—
35#5668—32no—
36C3×#497—32no—
37#5190—34no—
38#5176—34no—
39#5086D312yescomplemented
40#5058—32no—
41#4712—32no—
42D3×#97—32no—
43C2×C32×Q8C2312yes—
44#3832—28no—
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4⋊(C3⋊D3)C2312yes—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3D412yes—
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×C3×D12C2312yes—
52C2×C3×Dic6C2312yes—
53C2×#626—22no—
54C2×#625—22no—
55C2×D3×Dic3—22no—
56#3796—28no—
57C32×C4⋊C4—22no—
58C32×C42C2311yescharacteristic
59#3752—24no—
60C4×C3⋊Dic3D412yes—
61C4×C3⋊Dic3C2311yescharacteristic
62C3×#216—28no—
63C3×#215—28no—
64C3×(C2×D3)⋊C4—24no—
65C2×C3×C3⋊C8C2314yes—
66#3724—22no—
67#3717—28no—
68#3714—28no—
69#3710D418yescomplemented
70#3150—91noSylow
71C2×#239—34no—
72C2×#239—32no—
73C2×#239—62no—
74C2×#237—32no—
75C2×C3×Q16—34no—
76C2×C3×SD16—34no—
77C3×C4⋊Q8—21no—
78C3×C4⋊Q8C2×D312yes—
79C3×#124—32no—
80#947—34no—
81#947—62no—
82#944—32no—
83C2×#216C2×D314yes—
84C2×#215—34no—
85C2×#215C2×D314yes—
86#940—32no—
87C2×#213—34no—
88#919—616no—
89#916—616no—
90C2×D24—34no—
91C2×#204—34no—
92C2×D3×C8—34no—
93#895—64no—
94#895—64no—
95#893—64no—
96#893—64no—
97#884—64no—
98#67⋊C4—64no—
99#875C2×D312yes—
100#874—32no—
101#874—61no—
102C42×D3—32no—
103C42×D3—61no—
104C3×#97—32no—
105#815—34no—
106#803C2×D312yes—
107C22×C3⋊D3—22no—
108C22×C3⋊D3C2×D411yescharacteristic
109C22×C3×D3—22no—
110C32×Q8—24no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D412yes—
113C2×C32×C4C2411yescharacteristic
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×D411yescharacteristic
116C4⋊(C3⋊D3)—24no—
117C4⋊(C3⋊D3)—44no—
118C4⋊(C3⋊D3)—44no—
119C4×C3⋊D3—42no—
120C4×C3⋊D3—44no—
121C4×C3⋊D3C2×D414yes—
122C2×C3×Dic3—22no—
123C3×D12—24no—
124C3×Dic6—24no—
125#626—44no—
126#625—44no—
127D3×Dic3—44no—
128C3×C3⋊C8C2×D418yes—
129C2×#135—94no—
130#532—91no—
131#532—91no—
132#497—32no—
133#497—92no—
134#496—92no—
135#496—92no—
136C2×#97—91no—
137C2×C3×Q8—22no—
138C2×C3×Q8—32no—
139C2×C3×Q8C22×D314yes—
140C2×C3×D4—32no—
141C2×#67—62no—
142C2×#67—64no—
143C22×Dic3—62no—
144#239—68no—
145#239—68no—
146#239—68no—
147#239—128no—
148#237—68no—
149C2×D12—34no—
150C2×D12—62no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×D12—62no—
155C2×D12—64no—
156C2×D12C22×D312yes—
157C2×C4×D3—32no—
158C2×C4×D3—34no—
159C2×C4×D3—61no—
160C2×C4×D3—62no—
161C2×C4×D3—64no—
162C2×C4×D3—62no—
163C2×C4×D3—64no—
164C2×Dic6C22×D312yes—
165C3×Q16—68no—
166C3×SD16—68no—
167C2×C3×C8—34no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170C3×C22⋊C4—64no—
171C3×C42—21no—
172C3×C42C22×D312yes—
173#216—28no—
174#215—28no—
175#215—68no—
176#213—68no—
177(C2×D3)⋊C4—24no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—68no—
180Dic3⋊C4—64no—
181C4×Dic3—34no—
182C4×Dic3—32no—
183C4×Dic3—62no—
184C4×Dic3—61no—
185C2×C3⋊C8C22×D314yes—
186D24—68no—
187#204—68no—
188D3×C8—316no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—22no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—44no—
193C2×C3⋊D3#12712yes—
194C2×C3×D3—42no—
195C2×C3×D3—44no—
196C32×C4—22no—
197C32×C4—42no—
198C32×C4C22×D412yes—
199C3⋊Dic3—22no—
200C3⋊Dic3#12712yes—
201C3×Dic3—42no—
202C2×#41—92no—
203C2×#41—92no—
204#135—1816no—
205C2×Q16—34no—
206C2×SD16—34no—
207C2×SD16—94no—
208C2×D8—94no—
209C22×C8—92no—
210C4⋊Q8—91no—
211C4⋊Q8D3211yescharacteristic
212#127—91no—
213#127—91no—
214#124—32no—
215#124—92no—
216#121—182no—
217#121—182no—
218C4×D4—182no—
219C4×D4—182no—
220C2×C42—91no—
221#97—32no—
222#97—92no—
223C23×C3—62no—
224C22×D3—22no—
225C22×D3—32no—
226C22×D3—61no—
227C22×D3—64no—
228C22×D3—64no—
229C3×Q8—24no—
230C3×Q8—24no—
231C3×Q8—44no—
232C3×Q8—64no—
233C3×D4—64no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—62no—
239C2×C3×C4D3×D414yes—
240C2×C3×C4C23×D312yes—
241#67—124no—
242#67—128no—
243C2×Dic3—22no—
244C2×Dic3—32no—
245C2×Dic3—34no—
246C2×Dic3—61no—
247C2×Dic3—62no—
248C2×Dic3—124no—
249D12—24no—
250D12—64no—
251D12—64no—
252D12—124no—
253D12—128no—
254D12—128no—
255D12—128no—
256D12—128no—
257D12—124no—
258C4×D3—38no—
259C4×D3—64no—
260C4×D3—128no—
261C4×D3—124no—
262C4×D3—124no—
263C4×D3—128no—
264C4×D3—124no—
265Dic6—24no—
266C3×C8—38no—
267C3⋊C8D3×D418yes—
268C2×C32C2×#12711yescharacteristic
269C2×C32#57512yes—
270C3⋊D3—22no—
271C3⋊D3—82no—
272C3×D3—82no—
273#41—188no—
274#41—188no—
275C2×Q8—32no—
276C2×Q8C2×D3212yes—
277C2×D4—32no—
278C2×D4—92no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—182no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4—182no—
286C22×C4—182no—
287Q16—68no—
288SD16—68no—
289SD16—188no—
290D8—188no—
291C2×C8—34no—
292C2×C8—98no—
293C4⋊C4—22no—
294C4⋊C4—182no—
295C22⋊C4—64no—
296C22⋊C4—184no—
297C42—91no—
298C42—92no—
299C42C2×D3211yescharacteristic
300C22×C3—21no—
301C22×C3—122no—
302C22×C3—124no—
303C22×C3C2×D3×D412yes—
304C2×D3—34no—
305C2×D3—42no—
306C2×D3—44no—
307C2×D3—62no—
308C2×D3—64no—
309C2×D3—122no—
310C2×D3—124no—
311C2×D3—128no—
312C2×D3—124no—
313C2×D3—128no—
314C3×C4—24no—
315C3×C4—24no—
316C3×C4—22no—
317C3×C4—44no—
318C3×C4—44no—
319C3×C4—122no—
320C3×C4C2×D3×D414yes—
321Dic3—34no—
322Dic3—42no—
323Dic3—62no—
324Dic3—64no—
325Dic3—122no—
326C32#315011yescharacteristic, complemented, Sylow
327C23—62no—
328C23—91no—
329C23—182no—
330Q8—24no—
331Q8—64no—
332D4—64no—
333D4—184no—
334D4—364no—
335D4—364no—
336D4—364no—
337D4—364no—
338C2×C4—22no—
339C2×C4—62no—
340C2×C4—91no—
341C2×C4—94no—
342C2×C4—92no—
343C2×C4—362no—
344C2×C4—364no—
345C2×C4—364no—
346C2×C4#381112yes—
347C2×C4C22×D3211yescharacteristic
348C8—38no—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3—242no—
352C2×C3D3×#12712yes—
353C2×C3#577714yes—
354D3—64no—
355D3—82no—
356D3—122no—
357D3—244no—
358D3—244no—
359C22—92no—
360C22—122no—
361C22—124no—
362C22—182no—
363C22—362no—
364C22—364no—
365C22C2×#381111yescharacteristic
366C4—22no—
367C4—42no—
368C4—92no—
369C4—122no—
370C4—182no—
371C4D32×D412yes—
372C3—21no—
373C3#8186912yescomplemented
374C2—182no—
375C2—242no—
376C2—722no—
377C2#1059530011yescharacteristic
378C2#1059532312yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3150
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. C2×#63950C2semidirect
3. #10593971C2semidirect
4. C3×#5086C2semidirect
5. #10591629C2semidirect
6. #10591621C2semidirect
7. #10590351C2semidirect
8. #10590322C2semidirect
39. #5086D3semidirect
69. #3710D4semidirect
326. C32#3150semidirect
373. C3#81869semidirect

Maximal subgroups

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

subgroupindex
#105961962
C2×#639502
#105939712
C3×#50862
#105916292
#105916212
#105903512
#105903222
#818693