Finite Group Databasebeta

← #11867044

Subgroups — #11867044

Order 1152.

1500 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
1C2×#64121C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596077C212yesmaximal, complemented
4C32×#469C211yesmaximal, characteristic, complemented
5#10592858C211yesmaximal, characteristic, complemented
6#10592836C211yesmaximal, characteristic, complemented
7#10592741C212yesmaximal, complemented
8#10592566C211yesmaximal, characteristic, complemented
9#10592559C211yesmaximal, characteristic, complemented
10#10592479C212yesmaximal, complemented
11#10592471C212yesmaximal, complemented
12#80863—34nomaximal
13C2×#3830C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×D8C2211yescharacteristic, complemented
16C2×C32×M16C2211yescharacteristic
17C32×#121C2212yes—
18#64147C2212yes—
19#64146—22no—
20D4×C3⋊Dic3—22no—
21C2×#3754C2212yescomplemented
22#64133C2212yes—
23C2×#3748C2211yescharacteristic
24#64121—24no—
25M16×C3⋊D3—24no—
26C2×#3746C2211yescharacteristic, complemented
27C2×#3743C2211yescharacteristic
28C2×#3743C2211yescharacteristic
29C2×C8×C3⋊D3C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31#64106C2212yes—
32#64101C2212yes—
33#64092—22no—
34#64090—22no—
35C32×#106C2211yescharacteristic, complemented
36C32×#102C2212yescomplemented
37#63659C2212yescomplemented
38#63644C2211yescharacteristic, complemented
39#63643C2212yescomplemented
40#63637C2212yescomplemented
41#63634C2212yescomplemented
42C2×#912—34no—
43C2×D3×M16—34no—
44#5606—38no—
45C3×#469D314yescomplemented
46#5159—34no—
47#5137—34no—
48#5042—38no—
49#4867—34no—
50#4860—34no—
51#4780—38no—
52#4772—38no—
53C23×C3⋊D3D411yescharacteristic
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58C2×#638—22no—
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3D411yescharacteristic
61#3830—24no—
62#3830—24no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×#634C2312yes—
70C32×D8—22no—
71C32×M16—22no—
72C2×C32×C8C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76#3757—22no—
77#3757—22no—
78#3754—24no—
79#3752—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—22no—
84C4×C3⋊Dic3—22no—
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3746—22no—
89#3743—22no—
90#3743—22no—
91C8×C3⋊D3—22no—
92C8×C3⋊D3D414yescomplemented
93#3054—91noSylow
94C2×#237—38no—
95C22×C4×D3—34no—
96C2×C3×D8C2×D314yescomplemented
97C2×C3×M16C2×D314yes—
98C3×#121C2×D318yes—
99#938—38no—
100#937—68no—
101D4×Dic3—68no—
102C2×#214—38no—
103#924—38no—
104C2×#208—34no—
105#912—616no—
106D3×M16—616no—
107C2×Dic12—34no—
108C2×ΓL(1,𝔽25)—34no—
109C2×ΓL(1,𝔽25)—34no—
110C2×D3×C8—34no—
111C2×D3×C8—34no—
112#897—38no—
113#892—38no—
114#883—68no—
115#67⋊C4—68no—
116C3×#106C2×D314yescomplemented
117C3×#102C2×D318yescomplemented
118#832—38no—
119#817—34no—
120#816—38no—
121#810—38no—
122#807—38no—
123C23×C32—22no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3C2×D411yescharacteristic
128C22×C3⋊D3C2×D411yescharacteristic
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—44no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—44no—
138#638—44no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—44no—
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C4×C3⋊D3—22no—
146C4×C3⋊D3—21no—
147C4×C3⋊D3—21no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3C2×D412yes—
150C4×C3⋊D3#4112yes—
151#634—22no—
152#634—22no—
153C32×C8—21no—
154C32×C8C2×D412yes—
155C3⋊(C3⋊C8)—21no—
156C3⋊(C3⋊C8)C2×D412yes—
157C2×#135—91no—
158C22×M16—91no—
159#525—92no—
160#470—91no—
161#470—91no—
162#469—91no—
163#469C3⋊D311yescharacteristic, complemented
164#468—92no—
165#468—92no—
166#427—91no—
167#416—92no—
168C23×D3—34no—
169C2×C3×D4—28no—
170C2×C3×D4C22×D318yes—
171C22×C3×C4C22×D314yes—
172C2×#67—68no—
173C2×#67—68no—
174C22×Dic3—34no—
175C22×Dic3—68no—
176#237—616no—
177#237—616no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—34no—
181C2×C4×D3—34no—
182C2×C4×D3—68no—
183C2×C4×D3—68no—
184C2×Dic6—38no—
185C3×D8—28no—
186C3×M16—28no—
187C2×C3×C8C22×D314yes—
188C2×C3×C8C22×D314yes—
189C3×C4⋊C4C22×D318yes—
190C3×C22⋊C4—28no—
191#217—68no—
192#217—68no—
193#214—616no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196C4⋊Dic3—38no—
197C4⋊Dic3—68no—
198Dic3⋊C4—68no—
199C4×Dic3—68no—
200#208—68no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—34no—
203Dic12—68no—
204ΓL(1,𝔽25)—68no—
205ΓL(1,𝔽25)—68no—
206D3×C8—316no—
207D3×C8—68no—
208C22×C32—21no—
209C22×C32—22no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—42no—
213C22×C32C22×D411yescharacteristic
214C2×C3⋊D3—22no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3—22no—
217C2×C3⋊D3—44no—
218C2×C3⋊D3#12112yes—
219C32×C4—21no—
220C32×C4—42no—
221C32×C4C22×D411yescharacteristic
222C32×C4C2×#4111yescharacteristic
223C3⋊Dic3—21no—
224C3⋊Dic3—42no—
225C3⋊Dic3—42no—
226C3⋊Dic3#12112yes—
227C2×#41—92no—
228C23×C4—91no—
229#135—184no—
230C2×Q16—91no—
231C2×SD16—92no—
232C2×D8C2×C3⋊D311yescharacteristic, complemented
233C2×M16—91no—
234C2×M16—91no—
235C2×M16—91no—
236C2×M16—184no—
237C2×M16C2×C3⋊D311yescharacteristic
238C22×C8—91no—
239C22×C8—91no—
240#123—182no—
241C22⋊Q8—92no—
242C22⋊Q8—92no—
243#121—92no—
244#121C2×C3⋊D312yes—
245#120—182no—
246C4×D4—182no—
247C4×D4—182no—
248#117—92no—
249#107—92no—
250#106—91no—
251#106C2×C3⋊D311yescharacteristic, complemented
252#103—92no—
253#103—92no—
254#102—92no—
255#102C2×C3⋊D312yescomplemented
256C23×C3—28no—
257C23×C3D3×D414yes—
258C22×D3—34no—
259C22×D3—34no—
260C22×D3—68no—
261C22×D3—128no—
262C3×D4—28no—
263C3×D4—28no—
264C3×D4—416no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—28no—
268C2×C3×C4D3×D414yes—
269C2×C3×C4C23×D314yes—
270#67—1216no—
271#67—1216no—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—68no—
275C2×Dic3—68no—
276C2×Dic3—68no—
277C2×Dic3—1216no—
278C4×D3—38no—
279C4×D3—38no—
280C4×D3—68no—
281C4×D3—68no—
282C4×D3—64no—
283C4×D3—64no—
284Dic6—68no—
285Dic6—68no—
286C3×C8—24no—
287C3×C8D3×D418yes—
288C3⋊C8—38no—
289C3⋊C8—64no—
290C2×C32—41no—
291C2×C32—82no—
292C2×C32C2×#12111yescharacteristic
293C2×C32#57512yes—
294C3⋊D3—22no—
295C3⋊D3—41no—
296C24—91no—
297#41—184no—
298#41—184no—
299C2×Q8—92no—
300C2×D4—22no—
301C2×D4—182no—
302C2×D4—182no—
303C2×D4C22×C3⋊D312yes—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—182no—
310C22×C4—182no—
311C22×C4—182no—
312C22×C4C22×C3⋊D311yescharacteristic
313Q16—182no—
314SD16—184no—
315D8—22no—
316M16—22no—
317M16—182no—
318M16—182no—
319M16—182no—
320C2×C8—91no—
321C2×C8—94no—
322C2×C8—91no—
323C2×C8—182no—
324C2×C8C22×C3⋊D311yescharacteristic
325C2×C8C22×C3⋊D311yescharacteristic
326C4⋊C4—92no—
327C4⋊C4—182no—
328C4⋊C4—182no—
329C4⋊C4C22×C3⋊D312yes—
330C22⋊C4—22no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C22⋊C4—182no—
334C22⋊C4—182no—
335C42—182no—
336C22×C3—28no—
337C22×C3—24no—
338C22×C3—48no—
339C22×C3—48no—
340C22×C3—48no—
341C22×C3C2×D3×D414yes—
342C2×D3—38no—
343C2×D3—68no—
344C2×D3—68no—
345C2×D3—64no—
346C2×D3—1216no—
347C3×C4—24no—
348C3×C4—48no—
349C3×C4C2×D3×D414yes—
350C3×C4D3×#4114yes—
351Dic3—38no—
352Dic3—64no—
353Dic3—128no—
354Dic3—128no—
355C32#305411yescharacteristic, complemented, Sylow
356C23—22no—
357C23—91no—
358C23—91no—
359C23—182no—
360C23—362no—
361C23D4×C3⋊D311yescharacteristic
362Q8—182no—
363Q8—182no—
364D4—22no—
365D4—22no—
366D4—44no—
367D4—364no—
368D4—364no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—91no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—91no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—364no—
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—21no—
387C8—92no—
388C8—181no—
389C8D4×C3⋊D312yes—
390C2×C3—44no—
391C2×C3—88no—
392C2×C3D3×#12114yes—
393C2×C3#577318yes—
394D3—68no—
395D3—124no—
396C22—22no—
397C22—21no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—92no—
402C22—182no—
403C22—182no—
404C22—181no—
405C22—364no—
406C22C2×D4×C3⋊D311yescharacteristic
407C4—21no—
408C4—42no—
409C4—92no—
410C4—181no—
411C4—362no—
412C4—362no—
413C4C2×D4×C3⋊D311yescharacteristic
414C4#41×C3⋊D311yescharacteristic
415C3#8086314yescomplemented
416C2—41no—
417C2—82no—
418C2—182no—
419C2—361no—
420C2C3⋊D3×#12111yescharacteristic
421C2#1059624412yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#469C2
socleC22×C32C22×D4
hypercenter#469C3⋊D3
hypocenterC32#3054
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#64121C2semidirect
2. C2×M16×C3⋊D3C2semidirect
3. #10596077C2semidirect
4. C32×#469C2semidirect
5. #10592858C2semidirect
6. #10592836C2semidirect
7. #10592741C2semidirect
8. #10592566C2semidirect
9. #10592559C2semidirect
10. #10592479C2semidirect
11. #10592471C2semidirect
15. C2×C32×D8C22semidirect
21. C2×#3754C22semidirect
26. C2×#3746C22semidirect
35. C32×#106C22semidirect
36. C32×#102C22semidirect
37. #63659C22semidirect
38. #63644C22semidirect
39. #63643C22semidirect
40. #63637C22semidirect
41. #63634C22semidirect
45. C3×#469D3semidirect
92. C8×C3⋊D3D4semidirect
96. C2×C3×D8C2×D3semidirect
116. C3×#106C2×D3semidirect
117. C3×#102C2×D3semidirect
163. #469C3⋊D3semidirect
232. C2×D8C2×C3⋊D3semidirect
251. #106C2×C3⋊D3semidirect
255. #102C2×C3⋊D3semidirect
355. C32#3054semidirect
415. C3#80863semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
C2×M16×C3⋊D32
#105960772
C32×#4692
#105928582
#105928362
#105927412
#105925662
#105925592
#105924792
#105924712
#808633