Finite Group Databasebeta

← #11870701

Subgroups — #11870701

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596067C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic, complemented
3C32×#481C211yesmaximal, characteristic, complemented
4#10592739C211yesmaximal, characteristic, complemented
5#10592667C211yesmaximal, characteristic, complemented
6#10592553C212yesmaximal, complemented
7#10592551C212yesmaximal, complemented
8#10592461C212yesmaximal, complemented
9#10592457C212yesmaximal, complemented
10#10592437C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#81308—34nomaximal
13C2×#3830—21no—
14C22×#634C2211yescharacteristic
15C32×#121C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64149C2211yescharacteristic
18#64148—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3754C2212yes—
21#64139C2211yescharacteristic
22C2×#3750—21no—
23C2×C4×C3⋊Dic3—21no—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×#3744C2212yes—
26#64102C2211yescharacteristic
27#64097C2211yescharacteristic
28#64096—21no—
29#64096—21no—
30#64096C2212yes—
31#64096C2212yes—
32#64094—21no—
33#64090—21no—
34C32×#106C2212yes—
35C32×#102C2212yes—
36C32×C22⋊C8C2211yescharacteristic
37#63657C2211yescharacteristic
38#63643C2212yes—
39#63641C2212yes—
40C8×C3⋊Dic3C2212yes—
41#63637C2212yes—
42#63636C2212yes—
43#63635C2212yes—
44#5596—34no—
45C2×#887—34no—
46C3×#481D314yescomplemented
47#5040—34no—
48#4968—34no—
49#4854—38no—
50#4852—38no—
51#4762—38no—
52#4758—38no—
53#4738—34no—
54#4718—34no—
55C2×C32×D4—21no—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60C2×#638—21no—
61C2×#638—21no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3D411yescharacteristic
65C22×C3⋊Dic3D411yescharacteristic
66#3830—44no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634—21no—
70C2×#634—24no—
71C2×#634—21no—
72C2×#634C2312yes—
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78#3757—21no—
79#3754—24no—
80#3752—21no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84#3750—22no—
85#3750—22no—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93#3744—24no—
94#3103—91noSylow
95C2×#237—64no—
96C22×Dic6—34no—
97C3×#121C2×D314yes—
98C2×C3×C4⋊C4C2×D314yes—
99#940—34no—
100#939—64no—
101D4×Dic3—34no—
102C2×#214—38no—
103#930—34no—
104C2×Dic3⋊C4—64no—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—64no—
107C2×#204—38no—
108#893—34no—
109#888—34no—
110#887—38no—
111#887—38no—
112#887—64no—
113#887—64no—
114#885—64no—
115#67⋊C4—64no—
116C3×#106C2×D318yes—
117C3×#102C2×D318yes—
118C3×C22⋊C8C2×D314yes—
119#830—34no—
120#816—38no—
121Dic3⋊C8—38no—
122C8×Dic3—38no—
123#810—38no—
124#809—38no—
125#808—38no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—21no—
129C32×D4—22no—
130C32×D4—42no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—21no—
134C2×C32×C4—42no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—42no—
138#638—42no—
139#638—42no—
140C2×C3⋊Dic3—24no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3SD1614yescomplemented
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C4⋊(C3⋊D3)—22no—
151C4×C3⋊D3—42no—
152#634—24no—
153#634—22no—
154#634—42no—
155#634#4114yescomplemented
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158#532—91no—
159C2×C4×Q8—91no—
160#481—91no—
161#481C3⋊D311yescharacteristic, complemented
162#475—92no—
163#460—92no—
164#448—91no—
165#448—91no—
166C4×SD16—92no—
167C4×SD16—92no—
168#431—91no—
169C2×C3×D4—24no—
170C2×C3×D4C22×D314yes—
171C22×C3×C4—24no—
172C22×C3×C4C22×D314yes—
173C2×#67—64no—
174C2×#67—64no—
175C2×#67—64no—
176C22×Dic3—34no—
177C22×Dic3—34no—
178C22×Dic3—64no—
179C22×Dic3—64no—
180#237—1216no—
181C2×D12—34no—
182C2×C4×D3—64no—
183C2×Dic6—38no—
184C2×Dic6—616no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C2×C3×C8C22×D318yes—
188C3×C4⋊C4—24no—
189C3×C4⋊C4C22×D318yes—
190C3×C4⋊C4C22×D314yes—
191C3×C22⋊C4—24no—
192#217—64no—
193#214—616no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—64no—
196C4⋊Dic3—34no—
197Dic3⋊C4—64no—
198Dic3⋊C4—68no—
199Dic3⋊C4—68no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—68no—
205C4×Dic3—68no—
206C2×C3⋊C8—38no—
207#204—616no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32C2×SD1612yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—42no—
221C32×C4C2×#4112yes—
222C3⋊Dic3—24no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—41no—
226C3⋊Dic3C2×SD1612yes—
227C3⋊Dic3C2×SD1612yes—
228C2×#41—181no—
229C22×Q8—91no—
230C2×SD16—92no—
231C2×SD16—92no—
232C4⋊Q8—91no—
233#127—91no—
234#124—181no—
235#121—91no—
236#121—181no—
237#121C2×C3⋊D311yescharacteristic
238C4×Q8—92no—
239C4×Q8—92no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—91no—
243C4×D4—91no—
244C4×D4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4C2×C3⋊D311yescharacteristic
247C2×C42—91no—
248C2×C42—181no—
249#106—92no—
250#106C2×C3⋊D312yes—
251C4⋊C8—92no—
252#103—92no—
253#103—92no—
254#102—92no—
255#102C2×C3⋊D312yes—
256C22⋊C8—91no—
257C22⋊C8C2×C3⋊D311yescharacteristic
258C4×C8—92no—
259C23×C3—24no—
260C23×C3D3×D414yes—
261C22×D3—64no—
262C3×D4—28no—
263C3×D4—48no—
264C2×C3×C4—28no—
265C2×C3×C4—28no—
266C2×C3×C4—24no—
267C2×C3×C4—48no—
268C2×C3×C4D3×D414yes—
269C2×C3×C4C23×D314yes—
270#67—128no—
271#67—128no—
272#67—128no—
273C2×Dic3—316no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—616no—
279C2×Dic3—68no—
280C2×Dic3—64no—
281C2×Dic3—128no—
282C2×Dic3—124no—
283D12—68no—
284C4×D3—128no—
285Dic6—316no—
286Dic6—616no—
287Dic6—68no—
288Dic6—128no—
289C3×C8—28no—
290C3⋊C8—68no—
291C2×C32—22no—
292C2×C32—81no—
293C2×C32#52511yescharacteristic
294C2×C32C22×SD1611yescharacteristic
295C2×C32#57511yescharacteristic
296C3⋊D3—81no—
297#41—364no—
298C2×Q8—92no—
299C2×Q8—181no—
300C2×Q8—184no—
301C2×Q8—181no—
302C2×D4—21no—
303C2×D4—91no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4C22×C3⋊D311yescharacteristic
308C22×C4—21no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—181no—
312C22×C4—181no—
313C22×C4—181no—
314C22×C4C22×C3⋊D311yescharacteristic
315SD16—184no—
316SD16—184no—
317C2×C8—92no—
318C2×C8C22×C3⋊D312yes—
319C4⋊C4—21no—
320C4⋊C4—91no—
321C4⋊C4—182no—
322C4⋊C4—182no—
323C4⋊C4—181no—
324C4⋊C4C22×C3⋊D312yes—
325C4⋊C4C22×C3⋊D311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—91no—
334C42—182no—
335C42—182no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—44no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3D3×SD1618yes—
342C22×C3C2×D3×D414yes—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—24no—
347C3×C4—44no—
348C3×C4—48no—
349C3×C4D3×#4118yes—
350Dic3—38no—
351Dic3—38no—
352Dic3—616no—
353Dic3—64no—
354Dic3—64no—
355Dic3—124no—
356C32#310311yescharacteristic, complemented, Sylow
357C23—21no—
358C23—181no—
359C23D4×C3⋊D311yescharacteristic
360Q8—94no—
361Q8—184no—
362Q8—182no—
363Q8—362no—
364D4—22no—
365D4—42no—
366D4—182no—
367D4—362no—
368D4—362no—
369D4—362no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—91no—
379C2×C4—184no—
380C2×C4—182no—
381C2×C4—181no—
382C2×C4—362no—
383C2×C4—362no—
384C2×C4—361no—
385C2×C4D4×C3⋊D311yescharacteristic
386C2×C4C23×C3⋊D311yescharacteristic
387C8—22no—
388C8—182no—
389C2×C3—28no—
390C2×C3—84no—
391C2×C3#565614yes—
392C2×C3C2×D3×SD1614yes—
393C2×C3#577314yes—
394D3—244no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22SD16×C3⋊D312yes—
404C22C2×D4×C3⋊D311yescharacteristic
405C4—21no—
406C4—41no—
407C4—42no—
408C4—92no—
409C4—92no—
410C4—184no—
411C4—181no—
412C4—181no—
413C4—361no—
414C4#41×C3⋊D312yes—
415C3#8130814yescomplemented
416C2—22no—
417C2—81no—
418C2—721no—
419C2#1059612711yescharacteristic
420C2C2×SD16×C3⋊D311yescharacteristic
421C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#481C2
socleC22×C32C22×D4
prime radical#10596067C2
hypercenter#481C3⋊D3
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#64096C2semidirect
3. C32×#481C2semidirect
4. #10592739C2semidirect
5. #10592667C2semidirect
6. #10592553C2semidirect
7. #10592551C2semidirect
8. #10592461C2semidirect
9. #10592457C2semidirect
10. #10592437C2semidirect
11. #10592417C2semidirect
46. C3×#481D3semidirect
145. C2×C3⋊Dic3SD16semidirect
155. #634#41semidirect
161. #481C3⋊D3semidirect
356. C32#3103semidirect
415. C3#81308semidirect

Maximal subgroups

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

subgroupindex
#105960672
C2×#640962
C32×#4812
#105927392
#105926672
#105925532
#105925512
#105924612
#105924572
#105924372
#105924172
#813083