Finite Group Databasebeta

← #11878725

Subgroups — #11878725

Order 1152.

1011 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591174C214yesmaximal, complemented
5#10590379C214yesmaximal, complemented
6#10590373C212yesmaximal, complemented
7#10590287C212yesmaximal, complemented
8#83213—31nomaximal
9#79312—31nomaximal
10C2×#3828—21no—
11C22×C3×Dic6C2212yes—
12C2×C32×C42C2211yescharacteristic
13#64139—21no—
14#64139C2212yes—
15#64084—21no—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C2212yes—
19#64078C2211yescharacteristic
20C2×C3×C4⋊Dic3—21no—
21C2×C3×C4⋊Dic3—21no—
22C3×#869—21no—
23C3×#869—21no—
24C3×#869C2212yes—
25C3×#869C2212yes—
26C2×#3717C2218yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yes—
29C3×C4×C3⋊C8C2212yes—
30#63566C2218yes—
31C2×C3×C4⋊Q8—31no—
32#5477—31no—
33#5477—31no—
34#5477—61no—
35C2×#869D311yescharacteristic, complemented
36C3×#431—31no—
37#5227—34no—
38#5085—32no—
39#5083—34no—
40#5079—32no—
41#4925D311yescharacteristic, complemented
42#4841—34no—
43#4738—34no—
44#4693—32no—
45#4681—32no—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C2×#638—22no—
50#3828—44no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)C2312yes—
54C2×C4×C3⋊D3—22no—
55C2×#634—21no—
56C22×C3×Dic3—22no—
57C2×C3×Dic6—22no—
58C2×C3×Dic6—44no—
59C2×C3×Dic6C2314yes—
60C32×C42D411yescharacteristic
61C32×C42D411yescharacteristic
62C32×C42C2311yescharacteristic
63C32×C42C2311yescharacteristic
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C3×C4⋊Dic3—22no—
69C3×C4⋊Dic3—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3—22no—
72C2×C3×C3⋊C8C2314yes—
73#3717—48no—
74#3206—91noSylow
75C22×C3×Q8—32no—
76C2×#235—62no—
77C2×#235—61no—
78C2×#235—61no—
79C22×Dic6C2×D312yes—
80C3×C4⋊Q8—32no—
81C3×C4⋊Q8—32no—
82C3×C4⋊Q8—61no—
83C3×C4⋊Q8—61no—
84C2×C3×C4⋊C4—61no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C42—21no—
87C2×C3×C42C2×D311yescharacteristic
88C2×C3×C42C2×D311yescharacteristic
89C2×#215—38no—
90#930—32no—
91#930—32no—
92#930—62no—
93#930—62no—
94#930—61no—
95#930—61no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—21no—
98C2×#204—38no—
99#875—62no—
100#875—61no—
101#875—61no—
102#874—31no—
103#874—31no—
104#874—61no—
105C4×D12—32no—
106C4×D12—32no—
107C4×D12—62no—
108C4×D12—62no—
109C4×D12—61no—
110C4×D12—61no—
111#869—21no—
112#869—21no—
113#869—31no—
114#869—31no—
115#869—61no—
116#869C2×D312yes—
117#869C2×D312yes—
118C3×C4⋊C8—32no—
119C3×C22⋊C8—32no—
120C3×C4×C8—32no—
121#835—38no—
122#830C2×D312yes—
123#816—38no—
124C4⋊(C3⋊C8)C2×D312yes—
125C4×C3⋊C8C2×D312yes—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4SD1614yescomplemented
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—44no—
138C2×C3⋊Dic3—22no—
139C4⋊(C3⋊D3)—24no—
140C4⋊(C3⋊D3)—42no—
141C4⋊(C3⋊D3)—42no—
142C4×C3⋊D3—44no—
143#634—42no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—44no—
146C3×Dic6—28no—
147C3×Dic6—44no—
148C3×C3⋊C8—24no—
149#532—91no—
150C2×C4⋊Q8—31no—
151#492—92no—
152#487—92no—
153#461—94no—
154#448—94no—
155#431—31no—
156C2×C3×Q8—34no—
157C2×C3×Q8—62no—
158C2×C3×Q8—124no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—62no—
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—64no—
170C2×#67—62no—
171C2×#67—62no—
172C22×Dic3—22no—
173#235—128no—
174#235—124no—
175#235—124no—
176C2×D12—32no—
177C2×D12—32no—
178C2×D12—62no—
179C2×D12—62no—
180C2×D12—62no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×C4×D3—64no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×Dic6—22no—
189C2×Dic6—44no—
190C2×Dic6—62no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×Dic6C22×D314yes—
194C2×C3×C8—34no—
195C3×C4⋊C4—62no—
196C3×C4⋊C4—62no—
197C3×C4⋊C4—62no—
198C3×C4⋊C4—62no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42D1211yescharacteristic
204C3×C42D1211yescharacteristic
205C3×C42#6711yescharacteristic
206C3×C42#6711yescharacteristic
207C3×C42C22×D311yescharacteristic
208C3×C42C22×D311yescharacteristic
209C3×C42C22×D311yescharacteristic
210C3×C42C22×D311yescharacteristic
211#215—128no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218C4⋊Dic3—22no—
219C4⋊Dic3—22no—
220C4⋊Dic3—22no—
221C4⋊Dic3—22no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C2×C3⋊C8C22×D314yes—
229#204—128no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C2×SD1612yes—
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—42no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4C2×SD1612yes—
240C32×C4C2×SD1612yes—
241C32×C4#13712yes—
242C32×C4H(5,𝔽2)12yes—
243C3⋊Dic3—42no—
244C3×Dic3—44no—
245C2×#41—181no—
246C22×Q8—32no—
247C2×SD16—98no—
248C4⋊Q8—32no—
249C4⋊Q8—32no—
250C4⋊Q8—61no—
251C4⋊Q8—61no—
252C4⋊Q8—91no—
253#127—91no—
254#124—181no—
255#121—92no—
256#121—181no—
257C4×D4—92no—
258C4×D4—181no—
259C2×C4⋊C4—61no—
260C2×C4⋊C4—61no—
261C2×C42D3211yescharacteristic
262C4⋊C8—32no—
263#103—98no—
264C22⋊C8—32no—
265C4×C8—32no—
266C23×C3—21no—
267C23×C3C2×D1211yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—64no—
270C22×D3—62no—
271C22×D3—62no—
272C3×Q8—68no—
273C3×Q8—124no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—24no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—64no—
288C2×C3×C4—124no—
289C2×C3×C4#20414yescomplemented
290C2×C3×C4#21514yescomplemented
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303#67—128no—
304#67—124no—
305#67—124no—
306C2×Dic3—24no—
307C2×Dic3—44no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311D12—64no—
312D12—64no—
313D12—124no—
314D12—124no—
315D12—124no—
316D12—122no—
317D12—122no—
318D12—122no—
319D12—122no—
320C4×D3—128no—
321C4×D3—124no—
322C4×D3—124no—
323Dic6—28no—
324Dic6—44no—
325Dic6—124no—
326Dic6—122no—
327Dic6—122no—
328C3×C8—64no—
329C3⋊C8—24no—
330C2×C32—22no—
331C2×C32#53511yescharacteristic
332C2×C32C22×SD1611yescharacteristic
333C2×C32C2×#13711yescharacteristic
334C3⋊D3—82no—
335#41—364no—
336C2×Q8—34no—
337C2×Q8—62no—
338C2×Q8—124no—
339C2×Q8—181no—
340C2×D4—92no—
341C2×D4—182no—
342C2×D4—181no—
343C2×D4—181no—
344C22×C4—62no—
345C22×C4—182no—
346C22×C4#62611yescharacteristic
347C22×C4#62611yescharacteristic
348C22×C4C2×D3211yescharacteristic
349SD16—368no—
350C2×C8—34no—
351C4⋊C4—62no—
352C4⋊C4—62no—
353C4⋊C4—62no—
354C4⋊C4—62no—
355C4⋊C4—92no—
356C4⋊C4—181no—
357C22⋊C4—182no—
358C22⋊C4—182no—
359C42#62611yescharacteristic
360C42#62611yescharacteristic
361C42C2×D3211yescharacteristic
362C42C2×D3211yescharacteristic
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3C2×#20412yes—
372C22×C3C2×#21512yes—
373C22×C3C22×D1211yescharacteristic
374C22×C3C22×#6711yescharacteristic
375C2×D3—124no—
376C2×D3—124no—
377C2×D3—124no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—122no—
382C2×D3—122no—
383C2×D3—122no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—124no—
395C3×C4C2×#20412yes—
396C3×C4C2×#20412yes—
397C3×C4#90912yes—
398C3×C4C2×#21512yes—
399C3×C4C2×#21512yes—
400C3×C4#94212yes—
401C3×C4#100412yes—
402C3×C4#100912yes—
403Dic3—44no—
404Dic3—124no—
405Dic3—122no—
406Dic3—122no—
407C32#320611yescharacteristic, complemented, Sylow
408C23—182no—
409C23C2×#62611yescharacteristic
410Q8—68no—
411Q8—124no—
412Q8—362no—
413D4—184no—
414D4—364no—
415D4—362no—
416D4—362no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—64no—
420C2×C4—124no—
421C2×C4—182no—
422C2×C4—364no—
423C2×C4#371714yescomplemented
424C2×C4C2×#62611yescharacteristic
425C2×C4C2×#62611yescharacteristic
426C2×C4C2×#62611yescharacteristic
427C2×C4C2×#62611yescharacteristic
428C2×C4C2×#62611yescharacteristic
429C2×C4C22×D3211yescharacteristic
430C8—64no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—42no—
437C2×C3#552511yescharacteristic
438C2×C3C22×#20411yescharacteristic
439C2×C3C2×#90911yescharacteristic
440C2×C3#580511yescharacteristic
441C2×C3C22×#21511yescharacteristic
442C2×C3C2×#94211yescharacteristic
443D3—244no—
444D3—242no—
445D3—242no—
446C22—21no—
447C22—21no—
448C22—362no—
449C22—362no—
450C22—362no—
451C22C2×#371712yes—
452C22C22×#62611yescharacteristic
453C4—21no—
454C4—21no—
455C4—124no—
456C4—362no—
457C4C2×#371712yes—
458C4C2×#371712yes—
459C4#6383312yes—
460C4#6430712yes—
461C3—21no—
462C3#7931211yescharacteristic, complemented
463C3#8321311yescharacteristic, complemented
464C2—22no—
465C2—722no—
466C2C22×#371711yescharacteristic
467C2C2×#6383311yescharacteristic
468C2#1059504211yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10595948C2
hypercenterC2×C42D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#869C2semidirect
3. C3×#4925C2semidirect
4. #10591174C2semidirect
5. #10590379C2semidirect
6. #10590373C2semidirect
7. #10590287C2semidirect
35. C2×#869D3semidirect
41. #4925D3semidirect
130. C2×C32×C4SD16semidirect
289. C2×C3×C4#204semidirect
290. C2×C3×C4#215semidirect
407. C32#3206semidirect
423. C2×C4#3717semidirect
462. C3#79312semidirect
463. C3#83213semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×#8692
C3×#49252
#105911742
#105903792
#105903732
#105902872
#832133
#793123