Finite Group Databasebeta

← #11895164

Subgroups — #11895164

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic6×D12C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590890C212yesmaximal, complemented
7#10590803C212yesmaximal, complemented
8Dic3×#204C212yesmaximal
9#10590752C212yesmaximal
10C4×#3716C211yesmaximal, characteristic
11#10590287C211yesmaximal, characteristic, complemented
12#80414—31nomaximal
13#79925—31nomaximal
14C2×D3×Dic6—21no—
15#64078C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63893—22no—
23Dic3×D12C2212yes—
24#63872—21no—
25#63866C2212yes—
26#63857—21no—
27#63846—22no—
28#63843—21no—
29Dic3×Dic6C2212yes—
30C2×#3716C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63644C2212yes—
33#63643C2212yes—
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2212yes—
41#63566C2212yes—
42#63563C2211yescharacteristic
43#5721—31no—
44Q8×D12—31no—
45#5570—31no—
46D4×Dic6—31no—
47C3×#461—31no—
48C3×C8×Q8—31no—
49#5162—32no—
50Dic3×SD16—32no—
51#5079—31no—
52C4×#214—31no—
53#4851—31no—
54#4851—31no—
55#4851—32no—
56#4851—61no—
57#4841—32no—
58#4841D311yescharacteristic
59#4830D311yescharacteristic, complemented
60#4792—32no—
61#4791—32no—
62C4×#204—32no—
63C4×#204—31no—
64#4681—31no—
65#4681—32no—
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C2×C32×C8C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×#204—24no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3716—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4×Q8—31no—
105C3×C4×D4—31no—
106Q8×Dic3—32no—
107Q8×Dic3—61no—
108#944—32no—
109D4×Dic3—32no—
110C2×#214—31no—
111#924—61no—
112C2×#204—31no—
113C2×#204C2×D312yes—
114#897—62no—
115#897—61no—
116#890—62no—
117#890—61no—
118#890—61no—
119#889—62no—
120#888—32no—
121#887—61no—
122#878—62no—
123C4×D12—32no—
124C4×D12C2×D311yescharacteristic
125#869—31no—
126#869—31no—
127#869—32no—
128#869—32no—
129#869—61no—
130#869C2×D311yescharacteristic
131C4×Dic6—32no—
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—21no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8C2×D311yescharacteristic
139C3×C4⋊C8C2×D311yescharacteristic
140C3×#103—32no—
141C3×C4×C8—32no—
142C3×C4×C8—31no—
143#835—32no—
144#835—32no—
145#832—31no—
146#821—31no—
147#817—32no—
148#817—32no—
149#817—31no—
150#817—62no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#816—31no—
156#816—62no—
157#816C2×D312yes—
158Dic3⋊C8C2×D312yes—
159C8×Dic3C2×D312yes—
160#810—31no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170#634—21no—
171#634—21no—
172#634—42no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6SD1614yescomplemented
183#627—44no—
184D3×Dic3—44no—
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—91no—
189D4×Q8—91no—
190#487—92no—
191#487—91no—
192#475—92no—
193#475—91no—
194#461—31no—
195#461—92no—
196C8×Q8—31no—
197C4×SD16—91no—
198C4×SD16—92no—
199C2×C3×Q8—31no—
200C2×C3×Q8—32no—
201C2×C3×D4—31no—
202C22×C3×C4—61no—
203C22×Dic3—62no—
204D3×Q8—124no—
205C2×D12C22×D311yescharacteristic
206C2×C4×D3—21no—
207C2×C4×D3—62no—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—121no—
216C2×Dic6—124no—
217C2×Dic6D1211yescharacteristic
218C2×Dic6C22×D312yes—
219C3×SD16—64no—
220C2×C3×C8—22no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C42—21no—
232C3×C42—32no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—62no—
236#214—62no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—31no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—31no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3—121no—
254C4⋊Dic3D1211yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256Dic3⋊C4—62no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—121no—
263Dic3⋊C4D1212yes—
264C4×Dic3—62no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—62no—
268C4×Dic3—121no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272#204—24no—
273#204—62no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4C2×SD1612yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3⋊Dic3—41no—
283C3⋊Dic3—42no—
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—181no—
290C2×SD16—32no—
291C2×SD16—91no—
292C4⋊Q8—31no—
293C4⋊Q8—92no—
294C4⋊Q8—92no—
295C4⋊Q8—91no—
296#125—182no—
297#125—181no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—92no—
302C4×Q8—91no—
303C4×Q8—181no—
304C4×D4—31no—
305C4×D4—92no—
306#106—91no—
307#106—92no—
308C4⋊C8—32no—
309C4⋊C8D3211yescharacteristic
310#103—32no—
311#103—91no—
312#103—92no—
313#103—92no—
314#103—92no—
315#102—91no—
316C4×C8—32no—
317C4×C8—31no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—34no—
321C3×Q8—62no—
322C3×Q8—62no—
323C3×D4—32no—
324C3×D4—61no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—62no—
331C2×C3×C4—61no—
332C2×C3×C4—122no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—21no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—62no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—62no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—122no—
350C2×Dic3—124no—
351C2×Dic3C2×D1212yes—
352C2×Dic3C2×D1212yes—
353D12—21no—
354D12#23712yes—
355C4×D3—42no—
356C4×D3—124no—
357Dic6—22no—
358Dic6—22no—
359Dic6—62no—
360Dic6—61no—
361Dic6—61no—
362Dic6—61no—
363Dic6—61no—
364Dic6—121no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368Dic6—124no—
369Dic6—242no—
370Dic6#20414yescomplemented
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—42no—
374C3×C8—61no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—31no—
383C2×Q8—32no—
384C2×Q8—91no—
385C2×Q8—182no—
386C2×Q8—181no—
387C2×Q8—364no—
388C2×D4—31no—
389C22×C4—61no—
390C22×C4—182no—
391SD16—64no—
392SD16—182no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C2×D3212yes—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—91no—
402C4⋊C4—92no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22⋊C4—61no—
410C22⋊C4—182no—
411C42—32no—
412C42—182no—
413C42—181no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—34no—
430C3×C4—41no—
431C3×C4—62no—
432C3×C4—121no—
433C3×C4—122no—
434C3×C4C2×#20412yes—
435C3×C4D3×SD1612yes—
436C3×C4C2×#23711yescharacteristic
437C3×C4#100711yescharacteristic
438C3×C4D3×#4111yescharacteristic
439C3×C4#101011yescharacteristic
440Dic3—22no—
441Dic3—41no—
442Dic3—42no—
443Dic3—122no—
444Dic3—122no—
445Dic3—121no—
446Dic3—122no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—242no—
451Dic3—241no—
452Dic3C2×#20414yes—
453C32#335911yescharacteristic, complemented, Sylow
454C23—61no—
455Q8—34no—
456Q8—62no—
457Q8—62no—
458Q8—181no—
459Q8—181no—
460Q8—364no—
461Q8—362no—
462D4—32no—
463D4—61no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—62no—
467C2×C4—61no—
468C2×C4—122no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—182no—
472C2×C4—364no—
473C2×C4D3×D1211yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—22no—
477C8—61no—
478C8—61no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3#557611yescharacteristic
484C2×C3#559811yescharacteristic
485C2×C3C22×#20411yescharacteristic
486C2×C3#575311yescharacteristic
487C2×C3C2×D3×SD1611yescharacteristic
488C2×C3#577911yescharacteristic
489D3—42no—
490C22—62no—
491C22—121no—
492C22—121no—
493C22C2×D3×D1211yescharacteristic
494C4—21no—
495C4—34no—
496C4—62no—
497C4—122no—
498C4—121no—
499C4—361no—
500C4—362no—
501C4—361no—
502C4D3×#20412yes—
503C4D3×#23711yescharacteristic
504C4#6431511yescharacteristic
505C3—21no—
506C3#7992511yescharacteristic, complemented
507C3#8041411yescharacteristic, complemented
508C2—122no—
509C2#1059438211yescharacteristic
510C2C2×D3×#20411yescharacteristic
511C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. #10592550C2semidirect
5. C3×#4830C2semidirect
6. #10590890C2semidirect
7. #10590803C2semidirect
11. #10590287C2semidirect
59. #4830D3semidirect
182. C3×Dic6SD16semidirect
370. Dic6#204semidirect
453. C32#3359semidirect
506. C3#79925semidirect
507. C3#80414semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105938612
#105925502
C3×#48412
C3×#48302
#105908902
#105908032
Dic3×#2042
#105907522
C4×#37162
#105902872
#804143
#799253