Finite Group Databasebeta

← #11870837

Subgroups — #11870837

Order 1152.

1362 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
1C32×#529C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#10592765C212yesmaximal, complemented
4#10592756C212yesmaximal, complemented
5#10592745C211yesmaximal, characteristic, complemented
6#10592743C211yesmaximal, characteristic, complemented
7#10592735C211yesmaximal, characteristic
8#10592733C211yesmaximal, characteristic, complemented
9C4×#3755C212yesmaximal, complemented
10C4×#3753C212yesmaximal, complemented
11#10592624C211yesmaximal, characteristic, complemented
12#83141—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C32×#126—21no—
16C32×#125C2211yescharacteristic, complemented
17C32×#124C2211yescharacteristic, complemented
18C32×#123—21no—
19C32×C22⋊Q8C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4—21no—
23C32×C4×D4C2211yescharacteristic, complemented
24C32×#117—21no—
25C2×C32×C42C2211yescharacteristic
26C2×#3755C2212yes—
27C2×#3753C2212yes—
28C2×#3752—21no—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C4×C4⋊(C3⋊D3)—21no—
31C4×C4⋊(C3⋊D3)—21no—
32C4×C4⋊(C3⋊D3)C2212yes—
33C4×C4⋊(C3⋊D3)C2212yes—
34#63662C2212yescomplemented
35#63659C2212yescomplemented
36#63657C2211yescharacteristic
37#63657C2211yescharacteristic
38#63636C2212yes—
39#63636C2212yes—
40#63635C2212yescomplemented
41#63634C2212yescomplemented
42C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
43C4×C3⋊(C3⋊C8)C2212yescomplemented
44C3×#529D314yescomplemented
45C2×C4×D12—34no—
46#5066—38no—
47#5057—38no—
48#5046—34no—
49#5044—34no—
50#5036—34no—
51#5034—34no—
52C4×#215—38no—
53C4×#213—38no—
54#4925—34no—
55C23×C3⋊D3—21no—
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4D411yescharacteristic
61C22×C32×C4D411yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—24no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—44no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77C32×C22⋊C4—21no—
78C32×C22⋊C4—21no—
79C32×C22⋊C4—21no—
80C32×C22⋊C4—21no—
81C32×C42—21no—
82C32×C42D411yescharacteristic
83C32×C42D411yescharacteristic
84C32×C42C2311yescharacteristic
85C32×C42C2311yescharacteristic
86#3755—24no—
87#3753—24no—
88#3752—22no—
89#3752—22no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2312yes—
92C2×C3⋊(C3⋊C8)C2312yes—
93C2×C3⋊(C3⋊C8)C2312yes—
94#3105—91noSylow
95C22×D12—34no—
96C22×C4×D3—64no—
97C3×#126—24no—
98C3×#125C2×D314yescomplemented
99C3×#124C2×D314yescomplemented
100C3×#123—24no—
101C3×C22⋊Q8C2×D314yes—
102C3×#121C2×D314yes—
103C3×C4×Q8C2×D314yescomplemented
104C3×C4×D4—24no—
105C3×C4×D4C2×D314yescomplemented
106C3×#117—24no—
107C2×C3×C42C2×D314yes—
108C2×#215—38no—
109C2×#213—38no—
110C2×(C2×D3)⋊C4—64no—
111C2×C4⋊Dic3—34no—
112C4×D12—38no—
113C4×D12—38no—
114C4×D12—64no—
115C4×D12—64no—
116#835—38no—
117#832—38no—
118#830—34no—
119#830—34no—
120#809—38no—
121#809—38no—
122#808—38no—
123#807—38no—
124C4⋊(C3⋊C8)—38no—
125C4×C3⋊C8—38no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—24no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C32×Q8—22no—
133C32×D4—22no—
134C32×D4—42no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C4⋊(C3⋊D3)—24no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)#4114yes—
153C4×C3⋊D3—44no—
154C4×C3⋊D3—44no—
155C3⋊(C3⋊C8)—22no—
156C3⋊(C3⋊C8)—22no—
157#529C3⋊D311yescharacteristic, complemented
158C2×C4×D4—91no—
159#484—91no—
160#481—91no—
161#478—92no—
162#463—92no—
163#450—91no—
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431—91no—
168C23×D3—64no—
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4#6714yes—
174C22×C3×C4#6714yes—
175C22×C3×C4C22×D314yes—
176C22×Dic3—64no—
177C2×D12—38no—
178C2×D12—616no—
179C2×D12—64no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C2×C4×D3—1216no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4—24no—
187C3×C4⋊C4C22×D314yes—
188C3×C4⋊C4C22×D314yes—
189C3×C22⋊C4—24no—
190C3×C22⋊C4—24no—
191C3×C22⋊C4—24no—
192C3×C22⋊C4—24no—
193C3×C22⋊C4—24no—
194C3×C42—24no—
195C3×C42#6714yes—
196C3×C42#6714yes—
197C3×C42C22×D314yes—
198C3×C42C22×D314yes—
199#215—616no—
200#213—616no—
201(C2×D3)⋊C4—68no—
202(C2×D3)⋊C4—68no—
203C4⋊Dic3—38no—
204C4⋊Dic3—64no—
205C2×C3⋊C8—38no—
206C2×C3⋊C8—38no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—41no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32#13512yes—
213C22×C32C22×D411yescharacteristic
214C2×C3⋊D3—24no—
215C2×C3⋊D3—48no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—42no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4—41no—
225C32×C4AGL(1,ℤ/8)12yes—
226C32×C4C2×#4112yes—
227C3⋊Dic3—42no—
228C22×D4—91no—
229C23×C4—181no—
230C2×SD16—92no—
231C2×D8—92no—
232#126—21no—
233#125C2×C3⋊D311yescharacteristic, complemented
234#124C2×C3⋊D311yescharacteristic, complemented
235#123—21no—
236C22⋊Q8C2×C3⋊D311yescharacteristic
237#121C2×C3⋊D311yescharacteristic
238C4×Q8C2×C3⋊D311yescharacteristic, complemented
239C4×D4—21no—
240C4×D4—92no—
241C4×D4—92no—
242C4×D4—181no—
243C4×D4—181no—
244C4×D4C2×C3⋊D311yescharacteristic, complemented
245#117—21no—
246C2×C4⋊C4—91no—
247C2×C22⋊C4—181no—
248C2×C42C2×C3⋊D311yescharacteristic
249#107—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—92no—
253#102—92no—
254#102—92no—
255#102—92no—
256C22⋊C8—91no—
257C22⋊C8—91no—
258C4×C8—92no—
259C23×C3—24no—
260C23×C3C2×#6714yes—
261C22×D3—616no—
262C22×D3—68no—
263C22×D3—128no—
264C22×D3—128no—
265C3×Q8—28no—
266C3×D4—28no—
267C3×D4—48no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—28no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—48no—
275C2×C3×C4C2×#6714yes—
276C2×C3×C4C2×#6714yes—
277C2×C3×C4C2×#6714yes—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×C3×C4C23×D314yes—
281C2×Dic3—68no—
282C2×Dic3—128no—
283D12—316no—
284D12—616no—
285D12—68no—
286C4×D3—1216no—
287C4×D3—1216no—
288C3⋊C8—68no—
289C3⋊C8—68no—
290C2×C32—22no—
291C2×C32—81no—
292C2×C32#52511yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
295C3⋊D3—44no—
296C24—181no—
297C2×Q8C22×C3⋊D311yescharacteristic
298C2×D4—21no—
299C2×D4—92no—
300C2×D4—184no—
301C2×D4—181no—
302C2×D4C22×C3⋊D311yescharacteristic
303C22×C4—21no—
304C22×C4—181no—
305C22×C4—182no—
306C22×C4—182no—
307C22×C4—364no—
308C22×C4#63811yescharacteristic
309C22×C4#63811yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311SD16—184no—
312D8—184no—
313C2×C8—92no—
314C2×C8—92no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—92no—
320C4⋊C4—181no—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C4⋊C4C22×C3⋊D311yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—182no—
329C22⋊C4—182no—
330C42—21no—
331C42#63811yescharacteristic
332C42#63811yescharacteristic
333C42C22×C3⋊D311yescharacteristic
334C42C22×C3⋊D311yescharacteristic
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—44no—
338C22×C3—44no—
339C22×C3—44no—
340C22×C3#95018yes—
341C22×C3C22×#6714yes—
342C2×D3—616no—
343C2×D3—1232no—
344C2×D3—128no—
345C2×D3—128no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—24no—
350C3×C4—44no—
351C3×C4—44no—
352C3×C4—44no—
353C3×C4#94918yes—
354C3×C4D3×#4118yes—
355Dic3—128no—
356C32#310511yescharacteristic, complemented, Sylow
357C23—21no—
358C23—184no—
359C23—182no—
360C23—362no—
361C23—362no—
362C23C2×#63811yescharacteristic
363Q8—22no—
364D4—22no—
365D4—42no—
366D4—94no—
367D4—184no—
368D4—182no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—182no—
377C2×C4—364no—
378C2×C4—362no—
379C2×C4—364no—
380C2×C4C2×#63811yescharacteristic
381C2×C4C2×#63811yescharacteristic
382C2×C4C2×#63811yescharacteristic
383C2×C4C2×#63811yescharacteristic
384C2×C4C2×#63811yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—182no—
387C8—182no—
388C2×C3—28no—
389C2×C3—84no—
390C2×C3C2×#94914yes—
391C2×C3C2×#95014yes—
392C2×C3#582814yes—
393D3—1216no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—184no—
400C22—368no—
401C22—362no—
402C22—362no—
403C22#6415912yes—
404C22C22×#63811yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—362no—
413C4#6415812yes—
414C4#41×C3⋊D312yes—
415C3#8314114yescomplemented
416C2—22no—
417C2—81no—
418C2—364no—
419C2C2×#6415811yescharacteristic
420C2C2×#6415911yescharacteristic
421C2#1059629911yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#529C2
socleC22×C32C22×D4
prime radical#10592735C2
hypercenter#529C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C32×#529C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. #10592765C2semidirect
4. #10592756C2semidirect
5. #10592745C2semidirect
6. #10592743C2semidirect
8. #10592733C2semidirect
9. C4×#3755C2semidirect
10. C4×#3753C2semidirect
11. #10592624C2semidirect
16. C32×#125C22semidirect
17. C32×#124C22semidirect
21. C32×C4×Q8C22semidirect
23. C32×C4×D4C22semidirect
34. #63662C22semidirect
35. #63659C22semidirect
40. #63635C22semidirect
41. #63634C22semidirect
42. C4⋊(C3⋊(C3⋊C8))C22semidirect
43. C4×C3⋊(C3⋊C8)C22semidirect
44. C3×#529D3semidirect
98. C3×#125C2×D3semidirect
99. C3×#124C2×D3semidirect
103. C3×C4×Q8C2×D3semidirect
105. C3×C4×D4C2×D3semidirect
157. #529C3⋊D3semidirect
233. #125C2×C3⋊D3semidirect
234. #124C2×C3⋊D3semidirect
238. C4×Q8C2×C3⋊D3semidirect
244. C4×D4C2×C3⋊D3semidirect
356. C32#3105semidirect
415. C3#83141semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C2×C4×C4⋊(C3⋊D3)2
#105927652
#105927562
#105927452
#105927432
#105927352
#105927332
C4×#37552
C4×#37532
#105926242
#831413