Finite Group Databasebeta

← #11870707

Subgroups — #11870707

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#10596187C211yesmaximal, characteristic
2C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4#10592869C212yesmaximal, complemented
5SD16×C3⋊Dic3C212yesmaximal, complemented
6#10592774C211yesmaximal, characteristic, complemented
7#10592719C211yesmaximal, characteristic, complemented
8#10592550C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic, complemented
10#10592476C212yesmaximal, complemented
11#10592457C212yesmaximal, complemented
12#80360—34nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3830—21no—
15C2×C32×SD16C2212yes—
16C32×#127C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2211yescharacteristic
19#64147—21no—
20#64147C2212yes—
21#64145—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2212yes—
24C2×#3754C2212yes—
25C4⋊C4×C3⋊D3—21no—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#64096—21no—
28#64096C2211yescharacteristic
29C42×C3⋊D3—21no—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C4×#634—21no—
33C4×#634C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35C32×#102C2212yes—
36#63662C2212yes—
37#63659C2212yes—
38#63647C2212yes—
39#63644C2212yes—
40#63643C2212yes—
41C8×C3⋊Dic3C2212yes—
42#63635C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5716—34no—
45C4×D3×Q8—34no—
46C3×#460D314yescomplemented
47#5170—38no—
48Dic3×SD16—38no—
49#5075—34no—
50#5020—34no—
51#4851—34no—
52#4833—34no—
53#4777—38no—
54#4758—38no—
55C2×C32×Q8C2311yescharacteristic
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×#638—22no—
60C22×C3⋊Dic3—22no—
61Q8×C3⋊D3—22no—
62Q8×C3⋊D3—22no—
63#3830—44no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×#634—21no—
70C2×#634—21no—
71C2×#634C2311yescharacteristic
72C32×SD16—24no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3757—22no—
79#3757—22no—
80#3754—24no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—21no—
86#3750—21no—
87#3750—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3103—91noSylow
96C2×D3×Q8—34no—
97C2×#237—64no—
98C2×C3×SD16C2×D318yes—
99C3×#127C2×D314yes—
100C3×C4×Q8C2×D314yes—
101Q8×Dic3—34no—
102#938—38no—
103#938—64no—
104#936—64no—
105D4×Dic3—38no—
106D4×Dic3—64no—
107C2×#214—38no—
108D3×C4⋊C4—34no—
109D3×C4⋊C4—64no—
110#887—34no—
111#887—64no—
112C42×D3—34no—
113C42×D3—64no—
114#869—34no—
115C4×Dic6—34no—
116C4×Dic6—64no—
117C3×C4⋊C8C2×D314yes—
118C3×#102C2×D318yes—
119#835—38no—
120#832—38no—
121(C2×D3)⋊C8—38no—
122#817—38no—
123#816—38no—
124C8×Dic3—38no—
125#808—38no—
126C4⋊(C3⋊C8)—34no—
127C23×C32—22no—
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—21no—
130C32×Q8#4112yescomplemented
131C32×D4—22no—
132C32×D4—22no—
133C32×D4—42no—
134C32×D4—42no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—44no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—44no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C4×C3⋊D3—24no—
149C4×C3⋊D3—21no—
150C4×C3⋊D3—21no—
151C4×C3⋊D3—41no—
152C4×C3⋊D3—42no—
153C4×C3⋊D3SD1614yescomplemented
154#634—24no—
155#634—21no—
156#634—42no—
157#634#4112yescomplemented
158C32×C8—22no—
159C3⋊(C3⋊C8)—22no—
160#532—91no—
161C2×C4×Q8—91no—
162#481—92no—
163#475—91no—
164#475—91no—
165#460—91no—
166#460C3⋊D311yescharacteristic, complemented
167#448—92no—
168C4×SD16—92no—
169C4×SD16—92no—
170#431—91no—
171C2×C3×Q8C22×D314yes—
172C2×C3×D4—24no—
173C2×C3×D4—24no—
174C2×C3×D4C22×D318yes—
175C2×#67—68no—
176C22×Dic3—68no—
177D3×Q8—68no—
178D3×Q8—68no—
179#237—1216no—
180C2×C4×D3—34no—
181C2×C4×D3—34no—
182C2×C4×D3—34no—
183C2×C4×D3—64no—
184C2×C4×D3—64no—
185C2×Dic6—34no—
186C2×Dic6—64no—
187C2×Dic6—64no—
188C3×SD16—216no—
189C2×C3×C8C22×D318yes—
190C3×C4⋊C4—24no—
191C3×C4⋊C4C22×D314yes—
192C3×C42—24no—
193C3×C42C22×D314yes—
194#217—68no—
195#217—68no—
196#214—616no—
197C4⋊Dic3—38no—
198C4⋊Dic3—34no—
199C4⋊Dic3—64no—
200C4⋊Dic3—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C4×Dic3—34no—
207C4×Dic3—64no—
208C4×Dic3—64no—
209C4×Dic3—64no—
210C2×C3⋊C8—38no—
211C22×C32—42no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—21no—
216C2×C3⋊D3—21no—
217C2×C3⋊D3C2×SD1612yes—
218C32×C4—22no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4C2×SD1612yes—
222C32×C4C2×#4111yescharacteristic
223C32×C4C2×#4111yescharacteristic
224C3⋊Dic3—21no—
225C3⋊Dic3—22no—
226C3⋊Dic3—21no—
227C3⋊Dic3—42no—
228C3⋊Dic3—41no—
229C3⋊Dic3C2×SD1612yes—
230C2×#41—181no—
231C22×Q8—91no—
232C2×SD16—92no—
233C2×SD16C2×C3⋊D312yes—
234C4⋊Q8—91no—
235#127C2×C3⋊D311yescharacteristic
236#124—181no—
237#121—92no—
238#121—181no—
239C4×Q8—91no—
240C4×Q8—91no—
241C4×Q8—91no—
242C4×Q8—181no—
243C4×Q8—181no—
244C4×Q8C2×C3⋊D311yescharacteristic
245C4×D4—92no—
246C4×D4—181no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—181no—
249C2×C42—91no—
250C2×C42—181no—
251#106—92no—
252#106—92no—
253C4⋊C8—91no—
254C4⋊C8C2×C3⋊D311yescharacteristic
255#103—92no—
256#103—92no—
257#102—92no—
258#102C2×C3⋊D312yes—
259C22⋊C8—92no—
260C4×C8—92no—
261C23×C3—28no—
262C22×D3—34no—
263C3×Q8—24no—
264C3×Q8#23718yescomplemented
265C3×D4—28no—
266C3×D4—28no—
267C3×D4—48no—
268C3×D4—48no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4D3×D414yes—
273C2×C3×C4C23×D314yes—
274#67—1216no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—68no—
281C2×Dic3—1216no—
282C4×D3—316no—
283C4×D3—616no—
284C4×D3—64no—
285C4×D3—64no—
286C4×D3—124no—
287C4×D3—128no—
288Dic6—38no—
289Dic6—616no—
290Dic6—64no—
291Dic6—128no—
292C3×C8—28no—
293C3⋊C8—68no—
294C2×C32—82no—
295C2×C32#52511yescharacteristic
296C2×C32C22×SD1611yescharacteristic
297C2×C32#57511yescharacteristic
298C3⋊D3—22no—
299#41—364no—
300C2×Q8—91no—
301C2×Q8—181no—
302C2×Q8—182no—
303C2×Q8—182no—
304C2×Q8—181no—
305C2×Q8C22×C3⋊D311yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—182no—
309C2×D4C22×C3⋊D312yes—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—181no—
314C22×C4—181no—
315C22×C4—182no—
316SD16—24no—
317SD16—184no—
318C2×C8—92no—
319C2×C8C22×C3⋊D312yes—
320C4⋊C4—21no—
321C4⋊C4—91no—
322C4⋊C4—92no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4C22×C3⋊D311yescharacteristic
329C22⋊C4—182no—
330C22⋊C4—182no—
331C42—21no—
332C42—91no—
333C42—91no—
334C42—91no—
335C42—181no—
336C42—181no—
337C42—181no—
338C42C22×C3⋊D311yescharacteristic
339C22×C3—48no—
340C22×C3—48no—
341C22×C3—48no—
342C22×C3C2×D3×D414yes—
343C2×D3—38no—
344C2×D3—64no—
345C2×D3—64no—
346C3×C4—24no—
347C3×C4—28no—
348C3×C4—44no—
349C3×C4D3×SD1618yes—
350C3×C4C2×#23714yes—
351C3×C4D3×#4114yes—
352Dic3—38no—
353Dic3—64no—
354Dic3—68no—
355Dic3—64no—
356Dic3—128no—
357Dic3—124no—
358C32#310311yescharacteristic, complemented, Sylow
359C23—22no—
360C23—91no—
361Q8—21no—
362Q8—92no—
363Q8—184no—
364Q8—181no—
365Q8—362no—
366Q8#383012yescomplemented
367D4—22no—
368D4—22no—
369D4—42no—
370D4—42no—
371D4—364no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—91no—
375C2×C4—94no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—184no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—182no—
384C2×C4—361no—
385C2×C4—362no—
386C2×C4—364no—
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4C23×C3⋊D311yescharacteristic
390C8—22no—
391C8—182no—
392C2×C3—88no—
393C2×C3#560614yes—
394C2×C3C2×D3×SD1614yes—
395C2×C3#577314yes—
396D3—68no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—92no—
401C22—181no—
402C22—181no—
403C22C2×D4×C3⋊D311yescharacteristic
404C4—21no—
405C4—22no—
406C4—41no—
407C4—92no—
408C4—181no—
409C4—181no—
410C4—182no—
411C4—362no—
412C4—361no—
413C4SD16×C3⋊D312yes—
414C4C2×#383011yescharacteristic
415C4#41×C3⋊D311yescharacteristic
416C3#8036014yescomplemented
417C2—82no—
418C2—182no—
419C2#1059607711yescharacteristic
420C2C2×SD16×C3⋊D311yescharacteristic
421C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radical#10596187C2
hypercenter#460C3⋊D3
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C3⋊D3C2semidirect
3. C32×#460C2semidirect
4. #10592869C2semidirect
5. SD16×C3⋊Dic3C2semidirect
6. #10592774C2semidirect
7. #10592719C2semidirect
8. #10592550C2semidirect
9. #10592532C2semidirect
10. #10592476C2semidirect
11. #10592457C2semidirect
46. C3×#460D3semidirect
130. C32×Q8#41semidirect
153. C4×C3⋊D3SD16semidirect
157. #634#41semidirect
166. #460C3⋊D3semidirect
264. C3×Q8#237semidirect
358. C32#3103semidirect
366. Q8#3830semidirect
416. C3#80360semidirect

Maximal subgroups

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

subgroupindex
#105961872
C4×Q8×C3⋊D32
C32×#4602
#105928692
SD16×C3⋊Dic32
#105927742
#105927192
#105925502
#105925322
#105924762
#105924572
#803603