Finite Group Databasebeta

← #11895660

Subgroups — #11895660

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C3×C4×#216C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591579C212yesmaximal, complemented
6#10591539C212yesmaximal, complemented
7#10590483C212yesmaximal, complemented
8#10590435C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic
10#10590281C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#81041—31nomaximal
13#79701—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64156C2212yes—
16#64103—22no—
17#64102C2212yes—
18#64084—21no—
19#64083C2211yescharacteristic
20C4×C4⋊(C3⋊D3)—21no—
21C4×#634C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63872C2212yes—
26#63866—21no—
27#63846—22no—
28#63843C2212yes—
29Dic3×Dic6—21no—
30C2×#3717C2212yes—
31C3×#835C2211yescharacteristic
32C3×#835C2212yes—
33C3×#810C2211yescharacteristic
34C3×#808C2212yes—
35C3×#807C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63564C2212yes—
42#63553C2212yes—
43#5721—31no—
44#5585—31no—
45#5585—31no—
46#5585—61no—
47#5570—31no—
48C3×#475—31no—
49C3×C4×Q16—31no—
50#5185—32no—
51#5088—31no—
52C4×#216D311yescharacteristic, complemented
53#5027—31no—
54#5020D311yescharacteristic, complemented
55#4891—32no—
56#4871—32no—
57#4852—32no—
58#4848—31no—
59#4830—31no—
60#4800—32no—
61#4800—32no—
62#4798—32no—
63#4788—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3—22no—
71C2×#634D411yescharacteristic
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3752—22no—
79#3752—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C3×#216—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3717—24no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—21no—
102C3×C4×Q8—31no—
103C3×C4×Q8C2×D311yescharacteristic
104C3×C4×Q8C2×D311yescharacteristic
105#947—32no—
106#947—32no—
107#947—62no—
108Q8×Dic3—32no—
109Q8×Dic3—61no—
110#944—61no—
111C2×#216C2×D311yescharacteristic
112C2×#215—32no—
113C2×#204—32no—
114#894—62no—
115#894—62no—
116#894—64no—
117#893—32no—
118#893—32no—
119#893—62no—
120#890—32no—
121#890—32no—
122#890—62no—
123#889—62no—
124#887—32no—
125#875—61no—
126#875—61no—
127#875—62no—
128#874—31no—
129#874—31no—
130#874—61no—
131C4×D12—61no—
132C4×D12—61no—
133C4×D12—62no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#107—31no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×#103—32no—
145C3×#103—31no—
146C3×#103—31no—
147C3×C4×C8—31no—
148#835C2×D312yes—
149#835C2×D311yescharacteristic
150#821—32no—
151#821—32no—
152#821—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156C8×Dic3—32no—
157#810C2×D311yescharacteristic
158#809—32no—
159#809—32no—
160#809—32no—
161#808C2×D312yes—
162#807C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—22no—
166C32×Q8—21no—
167C32×Q8—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—42no—
178C4⋊(C3⋊D3)—81no—
179C4×C3⋊D3—82no—
180#634—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×Dic6—21no—
185C3×Dic6—42no—
186C3×Dic6#4112yes—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—91no—
191#557—91no—
192#488—92no—
193#486—91no—
194#478—92no—
195#475—31no—
196#464—92no—
197#460—91no—
198C8×Q8—91no—
199C4×Q16—31no—
200C4×SD16—92no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×Q8C22×D311yescharacteristic
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—62no—
213C2×D12—61no—
214C2×D12—61no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—64no—
218C2×Dic6—21no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6C22×D311yescharacteristic
223C3×Q16—62no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C42—22no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#216—22no—
245#215—64no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—21no—
265Dic3⋊C4—32no—
266Dic3⋊C4—32no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271C4×Dic3—21no—
272C4×Dic3—32no—
273C4×Dic3—32no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D312yes—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—22no—
292C3⋊Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C2×Q16—31no—
297C2×SD16—92no—
298C4⋊Q8—31no—
299C4⋊Q8—181no—
300#127—91no—
301#125—92no—
302#125—182no—
303#124—92no—
304#124—181no—
305#123—182no—
306C4×Q8—31no—
307C4×Q8—91no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×Q8D3211yescharacteristic
311C4×D4—92no—
312C4×D4—181no—
313#107—31no—
314#106—32no—
315C4⋊C8—31no—
316C4⋊C8—92no—
317#103—31no—
318#103—32no—
319#103—31no—
320#102—92no—
321#102—92no—
322#102—92no—
323C4×C8—31no—
324C4×C8—92no—
325C22×D3—64no—
326C22×D3—62no—
327C22×D3—62no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—32no—
333C3×Q8—41no—
334C3×Q8—41no—
335C3×Q8—61no—
336C3×Q8—122no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364D12—62no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—122no—
369D12—122no—
370D12—124no—
371D12—122no—
372D12—122no—
373D12—241no—
374D12—241no—
375D12—242no—
376C4×D3—242no—
377C4×D3—242no—
378C4×D3—244no—
379Dic6—21no—
380Dic6—42no—
381Dic6—62no—
382Dic6—62no—
383Dic6—122no—
384Dic6#23512yes—
385C3×C8—62no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—82no—
395C2×Q8—31no—
396C2×Q8—61no—
397C2×Q8—91no—
398C2×Q8C2×D3211yescharacteristic
399C2×D4—92no—
400C2×D4—181no—
401C2×D4—181no—
402C22×C4—182no—
403Q16—62no—
404SD16—184no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—32no—
408C4⋊C4—21no—
409C4⋊C4—32no—
410C4⋊C4—31no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—91no—
414C4⋊C4—92no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4C2×D3211yescharacteristic
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42—21no—
423C42—61no—
424C42—92no—
425C42—182no—
426C42C2×D3211yescharacteristic
427C22×C3—21no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—124no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4#91612yes—
455C3×C4#91912yes—
456C3×C4C2×#23511yescharacteristic
457C3×C4#100711yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4#101011yescharacteristic
460Dic3—22no—
461Dic3—42no—
462Dic3—41no—
463Dic3—62no—
464Dic3—62no—
465Dic3—62no—
466Dic3—62no—
467Dic3—122no—
468Dic3—122no—
469C32#336511yescharacteristic, complemented, Sylow
470C23—182no—
471Q8—21no—
472Q8—21no—
473Q8—32no—
474Q8—61no—
475Q8—122no—
476Q8—182no—
477D4—182no—
478D4—182no—
479D4—362no—
480D4—721no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—722no—
489C2×C4#381111yescharacteristic
490C2×C4#381111yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—62no—
494C8—61no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3#555211yescharacteristic
499C2×C3#563311yescharacteristic
500C2×C3C2×#91611yescharacteristic
501C2×C3C2×#91911yescharacteristic
502C2×C3#577011yescharacteristic
503C2×C3#577811yescharacteristic
504D3—244no—
505D3—242no—
506D3—242no—
507C22—362no—
508C22—362no—
509C22—362no—
510C22C2×#381111yescharacteristic
511C4—21no—
512C4—41no—
513C4—41no—
514C4—62no—
515C4—122no—
516C4—121no—
517C4—182no—
518C4—182no—
519C4#6395012yes—
520C4#6429711yescharacteristic
521C4D3×#23511yescharacteristic
522C3—21no—
523C3#7970111yescharacteristic, complemented
524C3#8104111yescharacteristic, complemented
525C2—722no—
526C2#1059491611yescharacteristic
527C2C2×#6395011yescharacteristic
528C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. C3×C4×#216C2semidirect
4. C3×#5020C2semidirect
5. #10591579C2semidirect
6. #10591539C2semidirect
7. #10590483C2semidirect
8. #10590435C2semidirect
11. #10590254C2semidirect
52. C4×#216D3semidirect
54. #5020D3semidirect
469. C32#3365semidirect
523. C3#79701semidirect
524. C3#81041semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105938612
C3×C4×#2162
C3×#50202
#105915792
#105915392
#105904832
#105904352
#105903672
#105902812
#105902542
#810413
#797013