Finite Group Databasebeta

← #11895363

Subgroups — #11895363

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593963C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590769C212yesmaximal, complemented
8#10590754C212yesmaximal, complemented
9#10590745C212yesmaximal, complemented
10#10590349C211yesmaximal, characteristic
11#10590283C211yesmaximal, characteristic, complemented
12#79927—31nomaximal
13#79621—31nomaximal
14#64083C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×#204C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63897—22no—
21#63896—22no—
22#63894—21no—
23#63894C2212yes—
24Dic3×D12C2212yes—
25D3×C4⋊Dic3—21no—
26#63869C2212yes—
27#63864—21no—
28#63864C2212yes—
29#63856—21no—
30C2×#3714C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63648C2212yes—
34C3×#821C2211yescharacteristic
35C3×#817C2211yescharacteristic
36C3×#816C2211yescharacteristic
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#5585—31no—
44#5585—31no—
45#5579—31no—
46#5543—31no—
47C3×C8×Q8—31no—
48C3×C4×SD16—31no—
49#5165—32no—
50#5021—31no—
51#5015—31no—
52#4871—32no—
53#4850—31no—
54#4847—32no—
55#4844—32no—
56#4843—31no—
57#4800—32no—
58#4756—32no—
59#4697—32no—
60#4694—31no—
61#4694—31no—
62#4694—61no—
63C4×D24—32no—
64C4×#204D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634—21no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#624—22no—
75C2×D3×Dic3—22no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3D411yescharacteristic
83C3×C4⋊Dic3C2311yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4—21no—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3—21no—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90C3×#204—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96(C2×D3)⋊Dic3—22no—
97#3714—24no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C3×C4×Q8—31no—
101C3×C4×Q8—31no—
102C3×C4×D4—31no—
103#947—32no—
104#947—61no—
105#946—61no—
106D4×Dic3—32no—
107C2×#213—32no—
108C2×C4⋊Dic3—61no—
109#924—61no—
110C2×D24—32no—
111C2×#204C2×D311yescharacteristic
112#896—62no—
113#894—62no—
114#894—62no—
115#893—32no—
116#893—61no—
117D3×C4⋊C4—61no—
118#890—32no—
119#878—62no—
120#875—32no—
121#875—61no—
122#874—31no—
123#874—31no—
124#874—61no—
125C4×D12—32no—
126C4×D12—32no—
127C4×D12—61no—
128C4×D12C2×D311yescharacteristic
129#870—32no—
130#869—31no—
131#869—31no—
132#869—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#106—31no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#103—31no—
139C3×#102—31no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—62no—
151#821—62no—
152#821C2×D311yescharacteristic
153#818—32no—
154#817C2×D311yescharacteristic
155#816—32no—
156#816C2×D311yescharacteristic
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#809—32no—
160#807—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C22×C3⋊D3—22no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)—42no—
171C4⋊(C3⋊D3)—81no—
172#634—81no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184#624—82no—
185D3×Dic3—82no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#559—91no—
190#554—91no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—31no—
198C4×SD16—31no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C22×Dic3—62no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—121no—
213C2×D12—121no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6D1211yescharacteristic
223C2×Dic6C22×D311yescharacteristic
224C3×SD16—62no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—61no—
238C3×C42—21no—
239C3×C42—32no—
240C3×C42—61no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#213—64no—
245(C2×D3)⋊C4—21no—
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—62no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3D1211yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4D1212yes—
268C4×Dic3—21no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271D24—64no—
272#204—22no—
273C22×C32C22×D411yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3×D3—22no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C32×C4—21no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C2×SD16—31no—
291C2×D8—92no—
292C4⋊Q8—91no—
293#127—91no—
294#125—92no—
295#124—92no—
296#124—181no—
297#123—182no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—31no—
302C4×D4—31no—
303C4×D4—92no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C4⋊C4—181no—
307#107—92no—
308#106—31no—
309C4⋊C8—32no—
310C4⋊C8—31no—
311#103—31no—
312#103—92no—
313#102—31no—
314#102—92no—
315#102—92no—
316#102—92no—
317C4×C8—32no—
318C4×C8D3211yescharacteristic
319C23×C3—61no—
320C22×D3—21no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—122no—
324C3×Q8—62no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—32no—
328C3×D4—61no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—242no—
351C2×Dic3C2×D1212yes—
352C2×Dic3C2×D1212yes—
353D12—21no—
354D12—62no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—122no—
359D12—122no—
360D12—122no—
361D12—122no—
362D12—242no—
363D12—241no—
364D12—241no—
365D12—242no—
366D12#23512yes—
367C4×D3—42no—
368C4×D3—242no—
369C4×D3—242no—
370C4×D3—242no—
371Dic6—22no—
372Dic6—21no—
373Dic6—21no—
374Dic6—241no—
375Dic6—241no—
376Dic6—242no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C3×C8—21no—
381C3×C8—41no—
382C3×C8—41no—
383C3×C8—62no—
384C3⋊C8—22no—
385C2×C32#54811yescharacteristic
386C2×C32C2×#13511yescharacteristic
387C2×C32#57611yescharacteristic
388C3⋊D3—82no—
389C3×D3—42no—
390C2×Q8—31no—
391C2×Q8—31no—
392C2×Q8—181no—
393C2×D4—31no—
394C2×D4—92no—
395C2×D4—181no—
396C2×D4—181no—
397C22×C4—61no—
398C22×C4—182no—
399C22×C4—182no—
400SD16—62no—
401D8—184no—
402C2×C8—32no—
403C2×C8C2×D3211yescharacteristic
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—31no—
409C4⋊C4—61no—
410C4⋊C4—92no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—181no—
414C22⋊C4—61no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C42—32no—
420C42—61no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—62no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C22×D1211yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—242no—
438C2×D3—242no—
439C2×D3—242no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—121no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4#90412yes—
452C3×C4#91612yes—
453C3×C4C2×#23511yescharacteristic
454C3×C4#100711yescharacteristic
455C3×C4D3×#4111yescharacteristic
456C3×C4#101011yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—41no—
460Dic3—41no—
461Dic3—41no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32#336111yescharacteristic, complemented, Sylow
466C23—61no—
467C23—182no—
468Q8—62no—
469Q8—61no—
470Q8—61no—
471Q8—721no—
472D4—32no—
473D4—61no—
474D4—182no—
475D4—182no—
476D4—362no—
477D4—721no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—122no—
484C2×C4—182no—
485C2×C4—722no—
486C2×C4—722no—
487C2×C4D3×D1211yescharacteristic
488C2×C4D3×D1211yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—21no—
491C8—21no—
492C8—62no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—122no—
497C2×C3#555211yescharacteristic
498C2×C3#557611yescharacteristic
499C2×C3C2×#90411yescharacteristic
500C2×C3#575211yescharacteristic
501C2×C3C2×#91611yescharacteristic
502C2×C3#576911yescharacteristic
503D3—42no—
504D3—242no—
505D3—242no—
506D3—482no—
507C22—62no—
508C22—121no—
509C22—121no—
510C22—362no—
511C22—362no—
512C22—362no—
513C22C2×D3×D1211yescharacteristic
514C4—21no—
515C4—62no—
516C4—62no—
517C4—121no—
518C4—121no—
519C4—121no—
520C4—362no—
521C4#6380612yes—
522C4#6429711yescharacteristic
523C4D3×#23511yescharacteristic
524C3—21no—
525C3#7962111yescharacteristic, complemented
526C3#7992711yescharacteristic, complemented
527C2—122no—
528C2—722no—
529C2#1059389911yescharacteristic
530C2#1059468011yescharacteristic
531C2C2×#6380611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590349C2
hypercenterC4×C8D32
hypocenterC32#3361
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
1. #10593963C2semidirect
2. #10593960C2semidirect
3. #10592393C2semidirect
4. C3×C4×#204C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590872C2semidirect
7. #10590769C2semidirect
8. #10590754C2semidirect
9. #10590745C2semidirect
11. #10590283C2semidirect
64. C4×#204D3semidirect
65. C8×Dic6D3semidirect
465. C32#3361semidirect
525. C3#79621semidirect
526. C3#79927semidirect

Maximal subgroups

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

subgroupindex
#105939632
#105939602
#105923932
C3×C4×#2042
C3×C8×Dic62
#105908722
#105907692
#105907542
#105907452
#105903492
#105902832
#799273
#796213