Finite Group Databasebeta

← #11787758

Subgroups — #11787758

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#10596303C211yesmaximal, characteristic
2#10596216C211yesmaximal, characteristic, complemented
3C32×#421C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10592705C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#70417—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64156C411yescharacteristic, complemented
14#64153C411yescharacteristic, complemented
15#64149C411yescharacteristic, complemented
16#64148—22no—
17#64145C411yescharacteristic, complemented
18C4×#638—22no—
19#64135C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#64116—22no—
23M16×C3⋊D3—22no—
24#64110—22no—
25C32×#104—22no—
26#63664—22no—
27#63633—22no—
28#5832—34no—
29#5745—34no—
30C3×#421D314yescomplemented
31#5236—34no—
32#5006—34no—
33#4555—34no—
34#4532—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—22no—
45C2×#638D412yes—
46C22×C3⋊Dic3—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
52C2×C4×C3⋊D3D412yes—
53C2×#634C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16D412yescomplemented
56C2×C32×C8—21no—
57C32×C4⋊C4—21no—
58C32×C22⋊C4—21no—
59C32×C42—21no—
60#3757—22no—
61#3757—21no—
62#3752—22no—
63C4⋊(C3⋊Dic3)—21no—
64#3750—22no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69#3748—21no—
70#3748D412yescomplemented
71C2×C3⋊(C3⋊C8)—21no—
72#3743—24no—
73C8×C3⋊D3—24no—
74#1884—91noSylow
75C2×C3×#41C2×D314yes—
76C2×#235—34no—
77C2×C3×M16C2×D314yes—
78C3×#117C2×D314yes—
79#947—34no—
80#944—34no—
81#940—34no—
82#939—68no—
83#936—34no—
84C4×#67—68no—
85#926—34no—
86C2×C4×Dic3—34no—
87C2×#208—34no—
88#907—68no—
89D3×M16—68no—
90#901—68no—
91C3×#104—28no—
92#837—68no—
93#806—68no—
94C23×C32—21no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3C22⋊C412yes—
97C32×Q8—21no—
98C32×Q8—21no—
99C32×D4—21no—
100C32×D4—21no—
101C32×D4—41no—
102C32×D4—41no—
103C2×C32×C4—21no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
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—44no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—42no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C22⋊C412yes—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125#634—21no—
126#634—21no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—22no—
129#568—91no—
130#532—91no—
131#421—91no—
132#421C3⋊D311yescharacteristic, complemented
133#410—91no—
134#339—91no—
135#339—91no—
136C3×#41—24no—
137C3×#41—24no—
138C3×#41—24no—
139C3×#41—24no—
140C2×C3×Q8C4×D314yes—
141C2×C3×D4—24no—
142C2×C3×D4C4×D314yes—
143C22×C3×C4—24no—
144C22×C3×C4C22×D314yes—
145C2×#67—38no—
146C2×#67—68no—
147C22×Dic3—64no—
148#235—64no—
149#235—64no—
150#235—64no—
151#235—64no—
152C2×D12—34no—
153C2×C4×D3—38no—
154C2×Dic6—34no—
155C3×M16—24no—
156C3×M16#6718yescomplemented
157C2×C3×C8—24no—
158C3×C4⋊C4—24no—
159C3×C22⋊C4—24no—
160C3×C42—24no—
161#217—68no—
162#217—64no—
163(C2×D3)⋊C4—68no—
164C4⋊Dic3—64no—
165Dic3⋊C4—68no—
166C4×Dic3—34no—
167C4×Dic3—34no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170#208—38no—
171#208—64no—
172C2×C3⋊C8—64no—
173ΓL(1,𝔽25)—616no—
174D3×C8—616no—
175C22×C32—41no—
176C22×C32—42no—
177C22×C32—41no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12111yescharacteristic
180C22×C32#12111yescharacteristic
181C2×C3⋊D3—22no—
182C2×C3⋊D3—42no—
183C32×C4—41no—
184C32×C4—81no—
185C32×C4C4×D411yescharacteristic
186C32×C4C4×D411yescharacteristic
187C32×C4#12011yescharacteristic
188C32×C4#12311yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C3⋊Dic3—81no—
193C2×#41—91no—
194C2×#41C2×C3⋊D311yescharacteristic
195#131—182no—
196#131—182no—
197C2×M16—91no—
198C2×M16—182no—
199C2×M16C2×C3⋊D311yescharacteristic
200C4⋊Q8—91no—
201#127—91no—
202#124—91no—
203#124—91no—
204#121—182no—
205C4×D4—182no—
206#117—91no—
207#117C2×C3⋊D311yescharacteristic
208C2×C42—91no—
209#104—22no—
210#104—182no—
211#99—182no—
212C23×C3—24no—
213C23×C3D3×D414yes—
214C22×D3—38no—
215C3×Q8—24no—
216C3×Q8—24no—
217C3×D4—24no—
218C3×D4—24no—
219C3×D4—44no—
220C3×D4—44no—
221C2×C3×C4—24no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4C2×C4×D314yes—
226C2×C3×C4#23514yes—
227C2×C3×C4D3×D414yes—
228C2×C3×C4D3×D414yes—
229C2×C3×C4#23714yes—
230C2×C3×C4C2×#6714yes—
231#67—68no—
232#67—68no—
233#67—1216no—
234C2×Dic3—38no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—128no—
238C2×Dic3—124no—
239D12—64no—
240D12—64no—
241C4×D3—68no—
242C4×D3—68no—
243Dic6—64no—
244Dic6—64no—
245C3×C8—28no—
246C3⋊C8—68no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32—81no—
251C2×C32#38611yescharacteristic
252C3⋊D3—42no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—181no—
258#41—181no—
259#41—181no—
260#41—181no—
261C2×Q8—91no—
262C2×Q8C4×C3⋊D311yescharacteristic
263C2×D4—21no—
264C2×D4—92no—
265C2×D4—91no—
266C2×D4—182no—
267C2×D4C4×C3⋊D311yescharacteristic
268C22×C4—21no—
269C22×C4—92no—
270C22×C4—181no—
271C22×C4C22×C3⋊D311yescharacteristic
272M16—21no—
273M16—92no—
274M16—184no—
275M16—181no—
276M16#63812yescomplemented
277C2×C8—21no—
278C2×C8—184no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—182no—
282C4⋊C4—181no—
283C22⋊C4—21no—
284C22⋊C4—182no—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C42—21no—
288C42—91no—
289C42—91no—
290C42—181no—
291C42—181no—
292C22×C3—44no—
293C22×C3—48no—
294C22×C3—44no—
295C22×C3D3×C22⋊C414yes—
296C22×C3#88414yes—
297C22×C3#93814yes—
298C2×D3—68no—
299C2×D3—128no—
300C3×C4—44no—
301C3×C4—84no—
302C3×C4#67⋊C414yes—
303C3×C4#88314yes—
304C3×C4C4×#6714yes—
305C3×C4#93714yes—
306Dic3—68no—
307Dic3—68no—
308Dic3—124no—
309Dic3—244no—
310C32#188411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—92no—
313C23D4×C3⋊D311yescharacteristic
314Q8—21no—
315Q8—21no—
316Q8—181no—
317Q8—181no—
318D4—21no—
319D4—21no—
320D4—41no—
321D4—41no—
322D4—182no—
323D4—182no—
324D4—181no—
325D4—181no—
326D4—364no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—92no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—181no—
336C2×C4—362no—
337C2×C4—361no—
338C2×C4C2×C4×C3⋊D311yescharacteristic
339C2×C4#382811yescharacteristic
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4#383011yescharacteristic
343C2×C4C2×#63811yescharacteristic
344C8—22no—
345C8—182no—
346C2×C3—24no—
347C2×C3—24no—
348C2×C3—24no—
349C2×C3—84no—
350C2×C3#495614yes—
351D3—128no—
352C22—41no—
353C22—42no—
354C22—41no—
355C22—182no—
356C22—362no—
357C22C22⋊C4×C3⋊D311yescharacteristic
358C22#6409311yescharacteristic
359C22#6414711yescharacteristic
360C4—41no—
361C4—81no—
362C4—182no—
363C4—182no—
364C4—361no—
365C4—721no—
366C4#6409011yescharacteristic
367C4#6409211yescharacteristic
368C4C4×#63811yescharacteristic
369C4#6414611yescharacteristic
370C3#7041714yescomplemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—81no—
375C2—362no—
376C2#1059265511yescharacteristic
subgroupG/H
centerC4#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#421C2
socleC2×C32#386
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenter#421C3⋊D3
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #10596216C2semidirect
3. C32×#421C2semidirect
4. #10592935C2semidirect
5. #10592705C2semidirect
6. #10589421C2semidirect
7. #10589398C2semidirect
13. #64156C4semidirect
14. #64153C4semidirect
15. #64149C4semidirect
17. #64145C4semidirect
30. C3×#421D3semidirect
55. C32×M16D4semidirect
70. #3748D4semidirect
132. #421C3⋊D3semidirect
156. C3×M16#67semidirect
276. M16#638semidirect
310. C32#1884semidirect
370. C3#70417semidirect

Maximal subgroups

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

subgroupindex
#105963032
#105962162
C32×#4212
#105929352
#105927052
#105894212
#105893982
#704173