Finite Group Databasebeta

← #11787672

Subgroups — #11787672

Order 1152.

1002 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64118C211yesmaximal, characteristic
2#10595994C211yesmaximal, characteristic
3#10592703C211yesmaximal, characteristic, complemented
4#10592628C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic
6C32×#339C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#68775—34nomaximal
9C2×#3828C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16#64118—22no—
17#64118C414yescomplemented
18C2×#3746—21no—
19C2×#3744—21no—
20#64101—21no—
21C4⋊C4×C3⋊D3—21no—
22#64090—22no—
23C4×C4⋊(C3⋊D3)—21no—
24C4×#634—21no—
25#63658—22no—
26#63637—21no—
27#63637—21no—
28#63632—22no—
29C2×#909—34no—
30#5523—34no—
31#5004—34no—
32#4929—34no—
33C2×#805—34no—
34C3×#339D314yescomplemented
35#4554—34no—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D412yes—
41#3828—21no—
42#3828—21no—
43#3828C2×C412yes—
44#3828D412yes—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—22no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634C2×C412yescomplemented
54C2×#634D411yescharacteristic
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58C32×C4⋊C4D411yescharacteristic
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61C32×C42—21no—
62C32×C42—21no—
63C32×C42—21no—
64#3752—22no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67#3750—22no—
68C4×C3⋊Dic3—22no—
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72#3746—24no—
73#3744—24no—
74#1882—91noSylow
75C2×#235—34no—
76C22×Dic6—34no—
77C2×C3×M16C2×D314yes—
78C3×#117C2×D314yes—
79C2×C3×C42C2×D314yes—
80C2×C4⋊Dic3—34no—
81C2×#208—34no—
82#909—316no—
83#909—68no—
84C2×Dic12—64no—
85C2×#204—64no—
86#892—64no—
87D3×C4⋊C4—64no—
88#67⋊C4—68no—
89C4×D12—64no—
90C4×Dic6—64no—
91C3⋊#95—68no—
92#810—64no—
93#810—64no—
94#805—68no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—21no—
97C2×C32×C4—22no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108#638—22no—
109#638—22no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—42no—
116C4⋊(C3⋊D3)—21no—
117C4⋊(C3⋊D3)C22⋊C412yes—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—82no—
121#634—21no—
122#634—22no—
123#634—22no—
124#634—41no—
125#634—41no—
126#634C22⋊C412yes—
127C32×C8—22no—
128C3⋊(C3⋊C8)—41no—
129C2×#137—91no—
130#520—91no—
131C2×#104—91no—
132#419—91no—
133#391—91no—
134#343—91no—
135#339C3⋊D311yescharacteristic, complemented
136C22×C3×C4—24no—
137C22×C3×C4C22×D314yes—
138C2×#67—64no—
139C22×Dic3—38no—
140C22×Dic3—64no—
141#235—38no—
142#235—38no—
143#235—64no—
144#235—64no—
145C2×D12—34no—
146C2×C4×D3—64no—
147C2×C4×D3—68no—
148C2×Dic6—34no—
149C2×Dic6—38no—
150C2×Dic6—64no—
151C2×Dic6—64no—
152C2×Dic6—64no—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C3×M16—24no—
156C3×M16C4×D318yescomplemented
157C2×C3×C8—24no—
158C3×C4⋊C4D1214yes—
159C3×C4⋊C4D1214yes—
160C3×C22⋊C4—24no—
161C3×C42—24no—
162C3×C42—24no—
163C3×C42—24no—
164(C2×D3)⋊C4—68no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
167Dic3⋊C4—68no—
168C4×Dic3—68no—
169#208—64no—
170#208—64no—
171C2×C3⋊C8—64no—
172Dic12—616no—
173#204—616no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32C4×D411yescharacteristic
177C22×C32#12011yescharacteristic
178C22×C32#12111yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3—41no—
181C2×C3⋊D3—41no—
182C32×C4—42no—
183C32×C4—41no—
184C32×C4—41no—
185C32×C4C2×C22⋊C411yescharacteristic
186C32×C4C4×D411yescharacteristic
187C32×C4#12111yescharacteristic
188C32×C4#12311yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—42no—
191C3⋊Dic3—42no—
192C2×#41—91no—
193C22×Q8—91no—
194#137—94no—
195#137—182no—
196C2×Q16—181no—
197C2×SD16—181no—
198C2×M16—91no—
199C2×M16C2×C3⋊D311yescharacteristic
200C4×Q8—181no—
201C4×D4—181no—
202C4×D4—182no—
203#117—181no—
204#117C2×C3⋊D311yescharacteristic
205C2×C4⋊C4—91no—
206C2×C4⋊C4—181no—
207C2×C42C2×C3⋊D311yescharacteristic
208#104—182no—
209#103—181no—
210#103—181no—
211#95—182no—
212C23×C3D3×D414yes—
213C22×D3—64no—
214C2×C3×C4—28no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×D1214yes—
221C2×C3×C4#23514yes—
222C2×C3×C4D3×D414yes—
223C2×C3×C4D3×D414yes—
224C2×C3×C4#23914yes—
225#67—68no—
226#67—68no—
227C2×Dic3—64no—
228C2×Dic3—68no—
229C2×Dic3—68no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232C2×Dic3—128no—
233D12—38no—
234D12—64no—
235C4×D3—68no—
236C4×D3—68no—
237C4×D3—248no—
238Dic6—38no—
239Dic6—64no—
240Dic6—68no—
241Dic6—68no—
242Dic6—124no—
243Dic6—124no—
244C3×C8—28no—
245C3⋊C8—124no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32#38611yescharacteristic
249C2×C32#45511yescharacteristic
250C2×C32#45611yescharacteristic
251C3⋊D3—42no—
252#41—92no—
253#41—92no—
254#41—181no—
255#41—181no—
256C2×Q8—92no—
257C2×Q8—91no—
258C2×Q8—181no—
259C2×Q8—181no—
260C2×Q8—181no—
261C2×Q8—181no—
262C2×Q8—181no—
263C2×D4—91no—
264C2×D4—181no—
265C22×C4—21no—
266C22×C4—92no—
267C22×C4—182no—
268C22×C4—181no—
269C22×C4—181no—
270C22×C4C22×C3⋊D311yescharacteristic
271Q16—184no—
272SD16—184no—
273M16—21no—
274M16—181no—
275M16—181no—
276M16C4×C3⋊D312yescomplemented
277C2×C8—21no—
278C2×C8—181no—
279C4⋊C4—182no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
283C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—182no—
286C42—21no—
287C42—21no—
288C42—21no—
289C42—182no—
290C22×C3—24no—
291C22×C3—24no—
292C22×C3#88214yes—
293C22×C3#88414yes—
294C22×C3#89314yes—
295C2×D3—68no—
296C2×D3—124no—
297C2×D3—124no—
298C3×C4—48no—
299C3×C4—44no—
300C3×C4—44no—
301C3×C4C4×D1214yes—
302C3×C4D3×C22⋊C414yes—
303C3×C4#89414yes—
304C3×C4#89514yes—
305Dic3—68no—
306Dic3—128no—
307Dic3—128no—
308C32#188211yescharacteristic, complemented, Sylow
309C23—181no—
310C23D4×C3⋊D311yescharacteristic
311Q8—92no—
312Q8—181no—
313Q8—182no—
314Q8—182no—
315Q8—361no—
316Q8—361no—
317D4—92no—
318D4—182no—
319D4—182no—
320D4—181no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—181no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—361no—
332C2×C4—361no—
333C2×C4—362no—
334C2×C4—722no—
335C2×C4C2×C4×C3⋊D311yescharacteristic
336C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
337C2×C4#382811yescharacteristic
338C2×C4D4×C3⋊D311yescharacteristic
339C2×C4D4×C3⋊D311yescharacteristic
340C2×C4#383211yescharacteristic
341C8—22no—
342C8—361no—
343C2×C3—24no—
344C2×C3—24no—
345C2×C3#466514yes—
346C2×C3#482514yes—
347C2×C3#482614yes—
348D3—128no—
349C22—21no—
350C22—21no—
351C22—182no—
352C22—361no—
353C22—361no—
354C22#6409111yescharacteristic
355C22#6409311yescharacteristic
356C22#6410211yescharacteristic
357C4—42no—
358C4—41no—
359C4—41no—
360C4—182no—
361C4—362no—
362C4—362no—
363C4C4×C4⋊(C3⋊D3)11yescharacteristic
364C4C22⋊C4×C3⋊D311yescharacteristic
365C4#6410311yescharacteristic
366C4#6410411yescharacteristic
367C3#6877514yescomplemented
368C2—21no—
369C2—21no—
370C2—362no—
371C2#1059236411yescharacteristic
372C2#1059252411yescharacteristic
373C2#1059252511yescharacteristic
subgroupG/H
centerC22#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #10592703C2semidirect
4. #10592628C2semidirect
6. C32×#339C2semidirect
7. #10589420C2semidirect
17. #64118C4semidirect
34. C3×#339D3semidirect
53. C2×#634C2×C4semidirect
56. C32×M16C2×C4semidirect
135. #339C3⋊D3semidirect
156. C3×M16C4×D3semidirect
276. M16C4×C3⋊D3semidirect
308. C32#1882semidirect
367. C3#68775semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959942
#105927032
#105926282
C2×#636322
C32×#3392
#105894202
#687753