Finite Group Databasebeta

← #11898305

Subgroups — #11898305

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591618C212yesmaximal, complemented
6#10591564C212yesmaximal, complemented
7#10590549C212yesmaximal, complemented
8#10590453C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590375C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83685—31nomaximal
13#80378—31nomaximal
14C2×#3796—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#944C2212yes—
19C2×C3×#215C2212yes—
20C3×#889—22no—
21C3×#887C2212yes—
22C3×#874C2211yescharacteristic
23C3×#870—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63916—21no—
28#63911C2212yes—
29Dic3×D12C2212yes—
30#63886—22no—
31C2×#3717C2212yes—
32C2×#3715C2212yes—
33C2×#3715C2212yes—
34#63662C2211yescharacteristic
35#63636C2211yescharacteristic
36#63635C2211yescharacteristic
37C4×C3⋊(C3⋊C8)C2211yescharacteristic
38C3×#809C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63566C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5718—31no—
45#5577—31no—
46#5567D311yescharacteristic, complemented
47C3×#460—31no—
48#5175—32no—
49#5162—32no—
50#5085—32no—
51#5085—31no—
52#5083—32no—
53#5083—31no—
54#5076—31no—
55#5027—32no—
56#5027D311yescharacteristic, complemented
57C4×#215—31no—
58C4×#215—31no—
59C4×#215—32no—
60C4×#215—61no—
61Q8×C3⋊C8—31no—
62#4841—31no—
63#4830—31no—
64#4762—32no—
65#4758—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82#3755—22no—
83#3752—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#215—42no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98(C2×D3)⋊Dic3—22no—
99#3717—42no—
100#3715—24no—
101#3715—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#237—61no—
105C2×C3×SD16—32no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—31no—
108C3×#127—31no—
109C3×#125—61no—
110C3×#125—62no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—61no—
115C3×C4×Q8C2×D311yescharacteristic
116C3×C4×Q8C2×D311yescharacteristic
117#944C2×D312yes—
118C2×#215—31no—
119C2×#215—31no—
120C2×#215—32no—
121C2×#215—32no—
122C2×#215—32no—
123C2×#215—61no—
124C2×#215C2×D312yes—
125#940—32no—
126#939—62no—
127#938—61no—
128D4×Dic3—32no—
129C2×#214—32no—
130C2×#214—32no—
131C2×#204—32no—
132#895—62no—
133#895—61no—
134#889—22no—
135#887C2×D312yes—
136#874—32no—
137#874C2×D311yescharacteristic
138C4×D12—32no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142#870—21no—
143#869C2×D311yescharacteristic
144C4×Dic6—21no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—31no—
147C3×#102—32no—
148#835—31no—
149#835—31no—
150#835—32no—
151#835—61no—
152#816—32no—
153Dic3⋊C8—32no—
154C8×Dic3—32no—
155#809—31no—
156#809—31no—
157#809—61no—
158#809C2×D312yes—
159#808—31no—
160#808—31no—
161#808—61no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8—31no—
165C4×C3⋊C8—31no—
166C4×C3⋊C8—32no—
167C4×C3⋊C8—61no—
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
170C32×Q8—21no—
171C32×Q8—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—21no—
180C4×C3⋊D3—42no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×D12—22no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6SD1614yescomplemented
191#626—44no—
192#626—82no—
193D3×Dic3—44no—
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)#4112yescomplemented
196C3×C3⋊C8—22no—
197#557—31no—
198#550—91no—
199#492—91no—
200#492—92no—
201#461—91no—
202#461—92no—
203#460—31no—
204#460—92no—
205C8×Q8—91no—
206C4×SD16—92no—
207C4×SD16—91no—
208C2×C3×Q8—21no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×Q8C22×D311yescharacteristic
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×D4—32no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×#67—62no—
217C2×#67—62no—
218C22×Dic3—62no—
219#239—124no—
220#237—124no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—31no—
224C2×D12—31no—
225C2×D12—61no—
226C2×D12—62no—
227C2×D12—62no—
228C2×D12C22×D312yes—
229C2×C4×D3—62no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—121no—
233C2×Dic6#6711yescharacteristic
234C2×Dic6C22×D312yes—
235C3×SD16—122no—
236C2×C3×C8—32no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—41no—
255C3×C42—62no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—62no—
259#215—42no—
260#215—64no—
261#215—62no—
262#215—62no—
263#215—64no—
264#215—122no—
265#215—122no—
266#214—64no—
267#214—122no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—121no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277C4⋊Dic3#6711yescharacteristic
278Dic3⋊C4—22no—
279Dic3⋊C4—22no—
280Dic3⋊C4—22no—
281Dic3⋊C4#6712yes—
282C4×Dic3—22no—
283C4×Dic3C22×D312yes—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8C22×D312yes—
291#204—122no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4—41no—
302C32×C4C2×SD1612yes—
303C32×C4C2×#4111yescharacteristic
304C32×C4H(5,𝔽2)11yescharacteristic
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3C2×SD1614yes—
309C2×#41—181no—
310C2×SD16—32no—
311C2×SD16—92no—
312C2×SD16—92no—
313C2×SD16—91no—
314C2×SD16—92no—
315C4⋊Q8—32no—
316C4⋊Q8—31no—
317#127—31no—
318#127—92no—
319#125—61no—
320#125—62no—
321#121—181no—
322#121—182no—
323C4×Q8—31no—
324C4×Q8—32no—
325C4×Q8—61no—
326C4×Q8D3211yescharacteristic
327C4×D4—92no—
328C4×D4—91no—
329#106—91no—
330C4⋊C8—31no—
331C4⋊C8—92no—
332#103—92no—
333#103—91no—
334#102—32no—
335#102—91no—
336C4×C8—92no—
337C4×C8—91no—
338C23×C3—62no—
339C22×D3—22no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—121no—
343C3×Q8—22no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—21no—
348C3×Q8—34no—
349C3×Q8—41no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×D4—62no—
353C3×D4—62no—
354C3×D4—122no—
355C3×D4—241no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—62no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—124no—
375#67—242no—
376C2×Dic3—22no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—121no—
380C2×Dic3—124no—
381C2×Dic3C2×#6712yes—
382C2×Dic3C2×#6712yes—
383D12—22no—
384D12—22no—
385D12—42no—
386D12—62no—
387D12—61no—
388D12—61no—
389D12—61no—
390D12—61no—
391D12—81no—
392D12—121no—
393D12—124no—
394D12—242no—
395C4×D3—124no—
396C4×D3—122no—
397C4×D3—122no—
398C4×D3—242no—
399Dic6—22no—
400Dic6—22no—
401Dic6#21514yescomplemented
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—32no—
405C3⋊C8—32no—
406C3⋊C8—62no—
407C3⋊C8—61no—
408C3⋊C8—61no—
409C3⋊C8—121no—
410C2×C32#55011yescharacteristic
411C2×C32C22×SD1611yescharacteristic
412C2×C32#57711yescharacteristic
413C3⋊D3—81no—
414C3×D3—82no—
415#41—364no—
416C2×Q8—31no—
417C2×Q8—32no—
418C2×Q8C2×D3211yescharacteristic
419C2×D4—32no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—91no—
423C2×D4—182no—
424C2×D4—182no—
425C22×C4—182no—
426C22×C4—181no—
427SD16—122no—
428SD16—184no—
429SD16—182no—
430SD16—362no—
431SD16—362no—
432C2×C8—32no—
433C2×C8—91no—
434C2×C8—91no—
435C4⋊C4—21no—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—91no—
444C4⋊C4C2×D3211yescharacteristic
445C22⋊C4—182no—
446C22⋊C4—181no—
447C42—21no—
448C42—32no—
449C42—62no—
450C42C2×D3211yescharacteristic
451C22×C3—21no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3C2×D3×D411yescharacteristic
456C22×C3C22×#6711yescharacteristic
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—122no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—241no—
468C2×D3—241no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—22no—
474C3×C4—34no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—62no—
482C3×C4—81no—
483C3×C4—122no—
484C3×C4D3×SD1612yes—
485C3×C4C2×#21512yes—
486C3×C4#100411yescharacteristic
487C3×C4D3×#4111yescharacteristic
488C3×C4D3×#4111yescharacteristic
489C3×C4#100911yescharacteristic
490Dic3—22no—
491Dic3—42no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3C2×#21514yes—
496C32#339211yescharacteristic, complemented, Sylow
497C23—62no—
498C23—181no—
499Q8—21no—
500Q8—21no—
501Q8—34no—
502Q8—62no—
503Q8—62no—
504D4—62no—
505D4—62no—
506D4—122no—
507D4—181no—
508D4—181no—
509D4—241no—
510D4—364no—
511D4—722no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—62no—
517C2×C4—181no—
518C2×C4—364no—
519C2×C4—362no—
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—62no—
524C8—92no—
525C8—181no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—242no—
530C2×C3#559911yescharacteristic
531C2×C3C2×D3×SD1611yescharacteristic
532C2×C3#577511yescharacteristic
533C2×C3C22×#21511yescharacteristic
534C2×C3#583411yescharacteristic
535C2×C3#583711yescharacteristic
536D3—82no—
537D3—242no—
538D3—241no—
539D3—241no—
540C22—122no—
541C22—122no—
542C22—122no—
543C22—361no—
544C22—361no—
545C22—361no—
546C22C2×D3×#6711yescharacteristic
547C4—21no—
548C4—34no—
549C4—41no—
550C4—41no—
551C4—62no—
552C4—122no—
553C4—361no—
554C4D3×#21512yes—
555C4#6430611yescharacteristic
556C4#6430711yescharacteristic
557C3—21no—
558C3#8037811yescharacteristic, complemented
559C3#8368511yescharacteristic, complemented
560C2—242no—
561C2—721no—
562C2#1059500611yescharacteristic
563C2C2×D3×#21511yescharacteristic
564C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4×Q8D32
hypocenterC32#3392
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
1. C3×#5567C2semidirect
3. C4×#3755C2semidirect
4. C3×#5027C2semidirect
5. #10591618C2semidirect
6. #10591564C2semidirect
7. #10590549C2semidirect
8. #10590453C2semidirect
9. #10590379C2semidirect
10. #10590375C2semidirect
11. #10590250C2semidirect
46. #5567D3semidirect
56. #5027D3semidirect
190. C3×Dic6SD16semidirect
195. C3⋊(C3⋊C8)#41semidirect
401. Dic6#215semidirect
496. C32#3392semidirect
558. C3#80378semidirect
559. C3#83685semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
#105939002
C4×#37552
C3×#50272
#105916182
#105915642
#105905492
#105904532
#105903792
#105903752
#105902502
#836853
#803783