Finite Group Databasebeta

← #11865747

Subgroups — #11865747

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C2×#64159C212yesmaximal, complemented
3#10595948C211yesmaximal, characteristic, complemented
4#10592730C211yesmaximal, characteristic, complemented
5#10592727C212yesmaximal, complemented
6#10592726C211yesmaximal, characteristic, complemented
7#10592718C211yesmaximal, characteristic, complemented
8#10592715C212yesmaximal, complemented
9#10592714C211yesmaximal, characteristic, complemented
10#10592701C212yesmaximal, complemented
11C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
12#82525—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2212yes—
15C32×C4×Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×D4—21no—
18C32×C4×D4—21no—
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×#117—21no—
22C32×#117C2211yescharacteristic
23C2×C32×C42—21no—
24C2×C32×C42C2211yescharacteristic
25#64159—28no—
26C2×#3756C2212yes—
27C2×#3755C2212yes—
28C2×#3754C2212yes—
29C2×#3753C2212yes—
30#64139—21no—
31#64139—21no—
32C22×C3⋊(C3⋊C8)C2212yes—
33#64084C2212yes—
34#64083C2211yescharacteristic
35C4×C4⋊(C3⋊D3)—21no—
36C4×C4⋊(C3⋊D3)—21no—
37#64078C2211yescharacteristic
38#63637C2212yes—
39#63637C2212yes—
40#63636C2212yes—
41#63636C2212yes—
42C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
43C4⋊(C3⋊(C3⋊C8))C2212yes—
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×C4×#41D314yescomplemented
46C2×#950—38no—
47#5477—34no—
48#5031—34no—
49#5028—38no—
50#5027—34no—
51#5019—34no—
52#5016—38no—
53#5015—34no—
54#5002—38no—
55C2×C4⋊(C3⋊C8)—34no—
56C32×#41—22no—
57C32×#41D414yescomplemented
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4C2311yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4D411yescharacteristic
65C22×C32×C4D411yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—22no—
68#3828—24no—
69#3828—24no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4×C3⋊D3—22no—
74C2×#634C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C22⋊C4—21no—
81C32×C22⋊C4—21no—
82C32×C42—21no—
83C32×C42—21no—
84C32×C42—21no—
85C32×C42D411yescharacteristic
86C32×C42D411yescharacteristic
87C32×C42C2311yescharacteristic
88C32×C42C2311yescharacteristic
89#3756—24no—
90#3755—24no—
91#3754—24no—
92#3753—24no—
93#3752—22no—
94#3752—22no—
95C4⋊(C3⋊Dic3)—21no—
96C4⋊(C3⋊Dic3)—21no—
97C2×C3⋊(C3⋊C8)—24no—
98C2×C3⋊(C3⋊C8)C2312yes—
99C2×C3⋊(C3⋊C8)C2312yes—
100#3035—91noSylow
101C2×C3×#41C2×D314yes—
102C2×#235—38no—
103C3×C4×Q8C2×D314yes—
104C3×C4×Q8C2×D314yes—
105C3×C4×D4—24no—
106C3×C4×D4—24no—
107C3×C4×D4C2×D314yes—
108C3×C4×D4C2×D314yes—
109C3×#117—24no—
110C3×#117C2×D314yes—
111C2×C3×C42—24no—
112C2×C3×C42C2×D314yes—
113#950—632no—
114C2×#216—38no—
115C2×#215—38no—
116C2×#214—38no—
117C2×#213—38no—
118#930—64no—
119#930—64no—
120C22×C3⋊C8—38no—
121#875—38no—
122#874—34no—
123C4×D12—64no—
124C4×D12—64no—
125#869—34no—
126#810—38no—
127#810—38no—
128#809—38no—
129#809—38no—
130C4⋊(C3⋊C8)—34no—
131C4⋊(C3⋊C8)—38no—
132C4⋊(C3⋊C8)—34no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C32×Q8—21no—
137C32×Q8C2×D412yes—
138C32×D4—24no—
139C32×D4—21no—
140C32×D4C2×D412yes—
141C2×C32×C4—21no—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—41no—
147C2×C32×C4—42no—
148C2×C32×C4—42no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157#638—44no—
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—42no—
162C4⋊(C3⋊D3)—42no—
163C4×C3⋊D3—44no—
164#634—22no—
165#634—22no—
166C3⋊(C3⋊C8)—22no—
167C3⋊(C3⋊C8)—22no—
168C2×#135—92no—
169#532—91no—
170C4×#41C3⋊D311yescharacteristic, complemented
171#464—92no—
172#463—92no—
173#462—91no—
174#461—91no—
175#460—91no—
176#459—91no—
177C2×C4⋊C8—91no—
178#416—92no—
179C3×#41—28no—
180C3×#41D12116yescomplemented
181C2×C3×Q8C22×D314yes—
182C2×C3×D4—24no—
183C2×C3×D4C22×D314yes—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4#6714yes—
188C22×C3×C4#6714yes—
189C22×C3×C4C22×D314yes—
190C2×#67—68no—
191#235—616no—
192#235—616no—
193C2×D12—38no—
194C2×D12—64no—
195C2×D12—64no—
196C2×C4×D3—68no—
197C2×Dic6—38no—
198C3×C4⋊C4—24no—
199C3×C4⋊C4—24no—
200C3×C4⋊C4C22×D314yes—
201C3×C4⋊C4C22×D314yes—
202C3×C22⋊C4—24no—
203C3×C22⋊C4—24no—
204C3×C22⋊C4—24no—
205C3×C42—24no—
206C3×C42—24no—
207C3×C42—24no—
208C3×C42#6714yes—
209C3×C42#6714yes—
210C3×C42C22×D314yes—
211C3×C42C22×D314yes—
212#216—616no—
213#215—616no—
214#214—616no—
215#213—616no—
216(C2×D3)⋊C4—68no—
217(C2×D3)⋊C4—68no—
218C4⋊Dic3—64no—
219C4⋊Dic3—64no—
220C2×C3⋊C8—38no—
221C2×C3⋊C8—38no—
222C2×C3⋊C8—616no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—22no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32#12112yes—
229C22×C32C22×D411yescharacteristic
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C32×C4—22no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—41no—
238C32×C4—41no—
239C32×C4#12112yes—
240C32×C4#13512yescomplemented
241C32×C4C22×D411yescharacteristic
242C32×C4C2×#4111yescharacteristic
243C3⋊Dic3—42no—
244C2×#41—92no—
245C2×#41C2×C3⋊D311yescharacteristic
246#135—188no—
247C2×Q16—92no—
248C2×SD16—92no—
249C2×SD16—92no—
250C2×D8—92no—
251C22×C8—92no—
252C4⋊Q8—91no—
253#127—91no—
254#124—92no—
255#121—181no—
256#121—181no—
257C4×Q8C2×C3⋊D311yescharacteristic
258C4×Q8C2×C3⋊D311yescharacteristic
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4C2×C3⋊D311yescharacteristic
264C4×D4C2×C3⋊D311yescharacteristic
265#117—21no—
266#117C2×C3⋊D311yescharacteristic
267C2×C42—21no—
268C2×C42C2×C3⋊D311yescharacteristic
269C4⋊C8—91no—
270C4⋊C8—91no—
271C4⋊C8—92no—
272#103—92no—
273#103—92no—
274#102—92no—
275#102—92no—
276C23×C3—24no—
277C23×C3C2×#6714yes—
278C22×D3—68no—
279C3×Q8—24no—
280C3×Q8C2×D1218yes—
281C3×D4—216no—
282C3×D4—24no—
283C3×D4C2×D1218yes—
284C2×C3×C4—24no—
285C2×C3×C4—216no—
286C2×C3×C4—28no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—44no—
290C2×C3×C4—48no—
291C2×C3×C4—48no—
292C2×C3×C4C2×D1218yes—
293C2×C3×C4#23518yes—
294C2×C3×C4C2×#6714yes—
295C2×C3×C4C2×#6714yes—
296C2×C3×C4C2×#6714yes—
297C2×C3×C4C2×#6714yes—
298C2×C3×C4C2×#6714yes—
299C2×C3×C4C23×D314yes—
300#67—1216no—
301C2×Dic3—68no—
302D12—68no—
303D12—68no—
304D12—128no—
305D12—128no—
306C4×D3—1216no—
307Dic6—68no—
308Dic6—68no—
309C3⋊C8—68no—
310C3⋊C8—68no—
311C2×C32—22no—
312C2×C32—42no—
313C2×C32C2×#12111yescharacteristic
314C2×C32C2×#13511yescharacteristic
315C2×C32#57511yescharacteristic
316C3⋊D3—82no—
317#41—22no—
318#41—184no—
319#41—184no—
320#41C4⋊(C3⋊D3)14yescomplemented
321C2×Q8—92no—
322C2×Q8C22×C3⋊D311yescharacteristic
323C2×D4—21no—
324C2×D4—92no—
325C2×D4—182no—
326C2×D4—181no—
327C2×D4—181no—
328C2×D4C22×C3⋊D311yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—182no—
333C22×C4#63811yescharacteristic
334C22×C4#63811yescharacteristic
335C22×C4C22×C3⋊D311yescharacteristic
336Q16—184no—
337SD16—184no—
338SD16—184no—
339D8—184no—
340C2×C8—92no—
341C2×C8—92no—
342C2×C8—184no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4C22×C3⋊D311yescharacteristic
348C4⋊C4C22×C3⋊D311yescharacteristic
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—182no—
353C22⋊C4—182no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42#63811yescharacteristic
358C42#63811yescharacteristic
359C42C22×C3⋊D311yescharacteristic
360C42C22×C3⋊D311yescharacteristic
361C22×C3—24no—
362C22×C3—24no—
363C22×C3—28no—
364C22×C3—44no—
365C22×C3—44no—
366C22×C3#93018yes—
367C22×C3C22×#6714yes—
368C2×D3—128no—
369C2×D3—128no—
370C2×D3—128no—
371C3×C4—28no—
372C3×C4—24no—
373C3×C4—24no—
374C3×C4—24no—
375C3×C4—44no—
376C3×C4—44no—
377C3×C4#93018yes—
378C3×C4#95018yescomplemented
379C3×C4C22×D1214yes—
380C3×C4C2×#23514yes—
381Dic3—128no—
382C32#303511yescharacteristic, complemented, Sylow
383C23—21no—
384C23—182no—
385C23C2×#63811yescharacteristic
386Q8—21no—
387Q8—182no—
388Q8—182no—
389Q8C2×C4⋊(C3⋊D3)12yes—
390D4—24no—
391D4—21no—
392D4—182no—
393D4—182no—
394D4—362no—
395D4—364no—
396D4—362no—
397D4C2×C4⋊(C3⋊D3)12yes—
398C2×C4—21no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—182no—
407C2×C4—364no—
408C2×C4C2×C4⋊(C3⋊D3)12yes—
409C2×C4#382812yes—
410C2×C4C2×#63811yescharacteristic
411C2×C4C2×#63811yescharacteristic
412C2×C4C2×#63811yescharacteristic
413C2×C4C2×#63811yescharacteristic
414C2×C4C2×#63811yescharacteristic
415C2×C4C23×C3⋊D311yescharacteristic
416C8—182no—
417C8—182no—
418C2×C3—28no—
419C2×C3—48no—
420C2×C3C2×#93014yes—
421C2×C3C2×#95014yes—
422C2×C3#582214yes—
423D3—248no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—362no—
430C22—362no—
431C22—362no—
432C22#6413912yes—
433C22C22×#63811yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—362no—
441C4#6413912yes—
442C4#6415912yescomplemented
443C4C22×C4⋊(C3⋊D3)11yescharacteristic
444C4C2×#382811yescharacteristic
445C3#8252514yescomplemented
446C2—22no—
447C2—42no—
448C2—722no—
449C2C2×#6413911yescharacteristic
450C2C2×#6415911yescharacteristic
451C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
hypercenterC4×#41C3⋊D3
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. C2×#64159C2semidirect
3. #10595948C2semidirect
4. #10592730C2semidirect
5. #10592727C2semidirect
6. #10592726C2semidirect
7. #10592718C2semidirect
8. #10592715C2semidirect
9. #10592714C2semidirect
10. #10592701C2semidirect
11. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
45. C3×C4×#41D3semidirect
57. C32×#41D4semidirect
170. C4×#41C3⋊D3semidirect
180. C3×#41D12semidirect
240. C32×C4#135semidirect
320. #41C4⋊(C3⋊D3)semidirect
378. C3×C4#950semidirect
382. C32#3035semidirect
442. C4#64159semidirect
445. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×#641592
#105959482
#105927302
#105927272
#105927262
#105927182
#105927152
#105927142
#105927012
C2×C4⋊(C3⋊(C3⋊C8))2
#825253