Finite Group Databasebeta

← #11788559

Subgroups — #11788559

Order 1152.

996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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#10596219C211yesmaximal, characteristic
2C4×#3828C211yesmaximal, characteristic, complemented
3#10592705C211yesmaximal, characteristic, complemented
4#10592704C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589425C211yesmaximal, characteristic, complemented
8#68778—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C4×#638—22no—
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64118—21no—
18#64118C412yescomplemented
19#64117—21no—
20#64117C412yescomplemented
21#64113—22no—
22C4×C4⋊(C3⋊D3)—21no—
23#64081—21no—
24C42×C3⋊D3—21no—
25C4×#634—21no—
26#63633—22no—
27#63632—22no—
28#63632—21no—
29#63632—21no—
30#5748—34no—
31C4×#235—34no—
32#5006—34no—
33#5005—34no—
34C2×#805—34no—
35C3×#339D314yescomplemented
36#4559—34no—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C2×#638—21no—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47#3828C2×C412yes—
48#3828D412yes—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic, complemented
55C2×#634D411yescharacteristic
56C32×M16—21no—
57C32×M16C2×C412yescomplemented
58C2×C32×C8—21no—
59C32×C4⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C42—21no—
62C32×C42—21no—
63C32×C42D411yescharacteristic
64C32×C42D411yescharacteristic
65#3757D412yes—
66#3752—22no—
67C4⋊(C3⋊Dic3)—21no—
68#3750—22no—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—21no—
71#3748—21no—
72#3748—21no—
73C2×C3⋊(C3⋊C8)—21no—
74#3746—22no—
75#3745—22no—
76#3744—22no—
77#3744—22no—
78#1906—91noSylow
79C2×#235—34no—
80C2×#235—34no—
81C2×C3×M16C2×D314yes—
82C3×#117C2×D314yes—
83C2×C3×C42C2×D314yes—
84C4×#67—68no—
85#926—34no—
86C2×#208—34no—
87#909—38no—
88#909—64no—
89#908—38no—
90#908—64no—
91#904—68no—
92C4×D12—64no—
93#872—64no—
94C42×D3—64no—
95C4×Dic6—64no—
96#806—68no—
97#805—68no—
98#805—64no—
99#805—64no—
100C23×C32C2×D411yescharacteristic
101C22×C3⋊D3—21no—
102C22×C3⋊D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—42no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113#638—22no—
114#638—22no—
115#638—41no—
116#638—41no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)C22⋊C412yes—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—44no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—41no—
129#634—21no—
130#634—21no—
131#634—21no—
132#634C22⋊C412yes—
133C32×C8—22no—
134C3⋊(C3⋊C8)—41no—
135#575—91no—
136C4×#41—91no—
137#421—91no—
138C2×#104—91no—
139#410—91no—
140#344—91no—
141#339C3⋊D311yescharacteristic, complemented
142C22×C3×C4—24no—
143C22×C3×C4C22×D314yes—
144C2×#67—64no—
145C2×#67—64no—
146#235—38no—
147#235—38no—
148#235—64no—
149#235—64no—
150#235—64no—
151#235—64no—
152#235—64no—
153#235—64no—
154C2×D12—34no—
155C2×D12—34no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×C4×D3—64no—
159C2×Dic6—34no—
160C2×Dic6—34no—
161C3×M16—24no—
162C3×M16C4×D318yescomplemented
163C2×C3×C8—24no—
164C3×C4⋊C4—24no—
165C3×C22⋊C4—24no—
166C3×C42—24no—
167C3×C42—24no—
168C3×C42D1214yes—
169C3×C42D1214yes—
170#217—38no—
171(C2×D3)⋊C4—68no—
172C4⋊Dic3—64no—
173Dic3⋊C4—68no—
174C4×Dic3—68no—
175C4×Dic3—64no—
176#208—64no—
177#208—64no—
178C2×C3⋊C8—64no—
179Dic12—68no—
180D24—68no—
181#204—68no—
182#204—68no—
183C22×C32—41no—
184C22×C32C4×D411yescharacteristic
185C22×C32#12011yescharacteristic
186C22×C32#12111yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—81no—
191C32×C4—22no—
192C32×C4—41no—
193C32×C4—81no—
194C32×C4C2×C22⋊C411yescharacteristic
195C32×C4C4×D411yescharacteristic
196C32×C4#12111yescharacteristic
197C32×C4#12311yescharacteristic
198C3⋊Dic3—22no—
199C3⋊Dic3—42no—
200C3⋊Dic3—41no—
201C2×#41—91no—
202C2×#41—91no—
203#137—92no—
204#137—181no—
205AGL(1,ℤ/8)—92no—
206AGL(1,ℤ/8)—181no—
207#135—182no—
208C2×M16—91no—
209C2×M16C2×C3⋊D311yescharacteristic
210C4×Q8—181no—
211C4×D4—181no—
212C4×D4—182no—
213#117—91no—
214#117—181no—
215#117C2×C3⋊D311yescharacteristic
216C2×C42—181no—
217C2×C42C2×C3⋊D311yescharacteristic
218#104—182no—
219#104—181no—
220#104—181no—
221#99—182no—
222C23×C3D3×D414yes—
223C22×D3—64no—
224C22×D3—64no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—48no—
228C2×C3×C4—44no—
229C2×C3×C4C2×C4×D314yes—
230C2×C3×C4C2×D1214yes—
231C2×C3×C4#23514yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4D3×D414yes—
234C2×C3×C4#23914yes—
235#67—68no—
236#67—68no—
237#67—124no—
238#67—124no—
239C2×Dic3—64no—
240C2×Dic3—68no—
241C2×Dic3—64no—
242D12—38no—
243D12—64no—
244D12—64no—
245D12—64no—
246C4×D3—68no—
247C4×D3—68no—
248C4×D3—1216no—
249C4×D3—124no—
250C4×D3—124no—
251Dic6—38no—
252Dic6—64no—
253Dic6—64no—
254Dic6—64no—
255C3×C8—28no—
256C3⋊C8—124no—
257C2×C32—21no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32#38611yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—81no—
263#41—92no—
264#41—92no—
265#41—181no—
266#41—181no—
267#41—181no—
268#41—181no—
269#41—181no—
270#41—181no—
271C2×Q8—91no—
272C2×Q8—91no—
273C2×D4—91no—
274C2×D4—91no—
275C2×D4—181no—
276C2×D4—181no—
277C22×C4—21no—
278C22×C4—182no—
279C22×C4—181no—
280C22×C4—181no—
281C22×C4C22×C3⋊D311yescharacteristic
282Q16—182no—
283SD16—182no—
284SD16—182no—
285D8—182no—
286M16—21no—
287M16—181no—
288M16—181no—
289M16C4×C3⋊D312yescomplemented
290C2×C8—21no—
291C2×C8—181no—
292C4⋊C4—21no—
293C4⋊C4—182no—
294C4⋊C4—181no—
295C22⋊C4—21no—
296C22⋊C4—92no—
297C22⋊C4—182no—
298C42—21no—
299C42—21no—
300C42—182no—
301C42—181no—
302C42C4⋊(C3⋊D3)11yescharacteristic
303C42C4⋊(C3⋊D3)11yescharacteristic
304C22×C3—44no—
305C22×C3#88214yes—
306C22×C3#88414yes—
307C22×C3#89314yes—
308C2×D3—68no—
309C2×D3—128no—
310C2×D3—124no—
311C2×D3—244no—
312C3×C4—28no—
313C3×C4—44no—
314C3×C4—84no—
315C3×C4C4×D1214yes—
316C3×C4D3×C22⋊C414yes—
317C3×C4#89414yes—
318C3×C4#89514yes—
319Dic3—68no—
320Dic3—128no—
321Dic3—124no—
322C32#190611yescharacteristic, complemented, Sylow
323C23—181no—
324C23—181no—
325C23D4×C3⋊D311yescharacteristic
326Q8—92no—
327Q8—181no—
328Q8—181no—
329Q8—181no—
330D4—92no—
331D4—182no—
332D4—182no—
333D4—181no—
334D4—181no—
335D4—181no—
336D4—361no—
337D4—361no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—181no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—181no—
347C2×C4—364no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4C2×C4×C3⋊D311yescharacteristic
351C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
352C2×C4#382811yescharacteristic
353C2×C4D4×C3⋊D311yescharacteristic
354C2×C4D4×C3⋊D311yescharacteristic
355C2×C4#383211yescharacteristic
356C8—22no—
357C8—361no—
358C2×C3—24no—
359C2×C3—24no—
360C2×C3—24no—
361C2×C3#466514yes—
362D3—128no—
363D3—244no—
364C22—41no—
365C22—182no—
366C22—362no—
367C22—361no—
368C22—721no—
369C22#6409111yescharacteristic
370C22#6409311yescharacteristic
371C22#6410211yescharacteristic
372C4—22no—
373C4—41no—
374C4—81no—
375C4—182no—
376C4—362no—
377C4—361no—
378C4C4×C4⋊(C3⋊D3)11yescharacteristic
379C4C22⋊C4×C3⋊D311yescharacteristic
380C4#6410311yescharacteristic
381C4#6410411yescharacteristic
382C3#6877814yescomplemented
383C2—21no—
384C2—21no—
385C2—21no—
386C2—362no—
387C2—721no—
388C2#1059236411yescharacteristic
subgroupG/H
centerC4#64104
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC2×C32#386
prime radical#10596219C2
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1906
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C4×#3828C2semidirect
3. #10592705C2semidirect
4. #10592704C2semidirect
5. C2×#63632C2semidirect
6. C32×#339C2semidirect
7. #10589425C2semidirect
18. #64118C4semidirect
20. #64117C4semidirect
35. C3×#339D3semidirect
49. C2×C4⋊(C3⋊D3)C2×C4semidirect
54. C2×#634C2×C4semidirect
57. C32×M16C2×C4semidirect
141. #339C3⋊D3semidirect
162. C3×M16C4×D3semidirect
289. M16C4×C3⋊D3semidirect
322. C32#1906semidirect
382. C3#68778semidirect

Maximal subgroups

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

subgroupindex
#105962192
C4×#38282
#105927052
#105927042
C2×#636322
C32×#3392
#105894252
#687783