Finite Group Databasebeta

← #11895780

Subgroups — #11895780

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590769C212yesmaximal, complemented
8#10590768C212yesmaximal, complemented
9#10590765C212yesmaximal, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#81088—31nomaximal
13#79969—31nomaximal
14C2×#3799—21no—
15C2×#3745C2212yes—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63911C2212yes—
22#63910—22no—
23#63909—21no—
24#63900—21no—
25#63894C2212yes—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33C3×#821C2212yes—
34C3×#817C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63564C2212yes—
42#63563C2211yescharacteristic
43#5730—31no—
44#5579—31no—
45#5577—31no—
46#5553—31no—
47C3×#476—31no—
48C3×#446—31no—
49#5088—31no—
50C4×#213—31no—
51#4871—32no—
52#4869—32no—
53#4847—32no—
54#4843—31no—
55#4843—31no—
56#4843—32no—
57#4843—61no—
58#4842D311yescharacteristic, complemented
59#4831D311yescharacteristic, complemented
60#4786—32no—
61#4764—32no—
62#4713—32no—
63#4711—32no—
64#4694—31no—
65C4×D24—31no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78C2×#624—22no—
79#3799—44no—
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3745—24no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3722—22no—
98#3714—22no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105#946—61no—
106#946—62no—
107#940—32no—
108C2×#213—31no—
109#930—61no—
110C2×D24—31no—
111C2×D24—32no—
112C2×D24—32no—
113C2×D24—62no—
114#897—61no—
115#896—62no—
116#895—62no—
117#895—61no—
118#893—32no—
119#893—32no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—61no—
122#890—32no—
123#884—62no—
124#874—32no—
125#874—31no—
126#874—31no—
127#874—61no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—32no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12C2×D311yescharacteristic
134#870—32no—
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C2×D311yescharacteristic
142C3×#102—32no—
143C3×#97—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—32no—
148#821—32no—
149#821—31no—
150#821—32no—
151#821—32no—
152#821—62no—
153#821C2×D312yes—
154#818—31no—
155#817C2×D312yes—
156#815C2×D312yes—
157Dic3⋊C8C2×D312yes—
158#809—31no—
159#809—32no—
160#809—32no—
161#807—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3⋊D3—22no—
165C22×C3×D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—42no—
174C4⋊(C3⋊D3)—81no—
175C4⋊(C3⋊D3)#4112yescomplemented
176C4×C3⋊D3—42no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—81no—
186#626—44no—
187#626—82no—
188#624—44no—
189#624—82no—
190C32×C8—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—91no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—31no—
199#459—92no—
200#459—91no—
201#446—31no—
202#442—92no—
203C4×D8—91no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C2×#67—62no—
209C2×#67—62no—
210#239—124no—
211#235—124no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12C22×D311yescharacteristic
227C2×C4×D3—21no—
228C2×C4×D3—62no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—121no—
235C2×Dic6—21no—
236C2×Dic6D1211yescharacteristic
237C2×C3×C8—22no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C22×D312yes—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#213—62no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—121no—
261C4⋊Dic3—21no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3D1211yescharacteristic
267C4⋊Dic3C22×D311yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4D1212yes—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D311yescharacteristic
276D24—64no—
277D24—64no—
278D24—62no—
279D24—124no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—22no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—41no—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C2×#41—181no—
300C2×D8—91no—
301C2×D8—92no—
302C4⋊Q8—31no—
303#127—92no—
304#127—91no—
305#125—92no—
306C22⋊Q8—182no—
307C22⋊Q8—181no—
308#121—182no—
309#121—181no—
310C4×Q8—31no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4—92no—
314C4×D4—91no—
315C2×C4⋊C4—181no—
316#107—91no—
317#106—32no—
318C4⋊C8—32no—
319C4⋊C8D3211yescharacteristic
320#102—32no—
321#102—91no—
322#102—92no—
323#102—92no—
324#102—91no—
325#102—92no—
326#97—32no—
327C4×C8—31no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—121no—
335C22×D3—122no—
336C3×Q8—62no—
337C3×Q8—241no—
338C3×D4—61no—
339C3×D4—61no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—122no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354#67—124no—
355#67—242no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—121no—
361C2×Dic3C2×D1212yes—
362C2×Dic3C2×D1212yes—
363D12—21no—
364D12—21no—
365D12—32no—
366D12—32no—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—62no—
371D12—62no—
372D12—62no—
373D12—62no—
374D12—121no—
375D12—122no—
376D12—122no—
377D12—124no—
378D12—122no—
379D12—122no—
380D12—242no—
381D12—241no—
382D12—241no—
383D12—242no—
384D12—242no—
385C4×D3—42no—
386C4×D3—124no—
387C4×D3—124no—
388C4×D3—122no—
389C4×D3—122no—
390C4×D3—242no—
391C4×D3—242no—
392C4×D3—242no—
393Dic6—22no—
394Dic6—81no—
395C3×C8—22no—
396C3×C8—22no—
397C3×C8—42no—
398C3×C8—61no—
399C3×C8—61no—
400C3⋊C8—21no—
401C3⋊C8—21no—
402C2×C32#54811yescharacteristic
403C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
404C2×C32#57611yescharacteristic
405C3⋊D3—42no—
406C3⋊D3—82no—
407C3×D3—81no—
408#41—364no—
409C2×Q8—31no—
410C2×Q8—61no—
411C2×D4—31no—
412C2×D4—91no—
413C2×D4—92no—
414C2×D4—182no—
415C2×D4—182no—
416C2×D4—181no—
417C2×D4—181no—
418C22×C4—61no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4—181no—
422D8—184no—
423D8—182no—
424C2×C8—31no—
425C2×C8—31no—
426C2×C8C2×D3212yes—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—32no—
430C4⋊C4—31no—
431C4⋊C4—61no—
432C4⋊C4—91no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C22⋊C4—61no—
436C22⋊C4—182no—
437C22⋊C4—182no—
438C22⋊C4—181no—
439C42—32no—
440C42C2×D3211yescharacteristic
441C22×C3—21no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C22×D1211yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—241no—
464C2×D3—241no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—22no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—41no—
474C3×C4—62no—
475C3×C4—62no—
476C3×C4—121no—
477C3×C4—122no—
478C3×C4#90812yes—
479C3×C4#91412yes—
480C3×C4#100711yescharacteristic
481C3×C4#100711yescharacteristic
482C3×C4D3×#4111yescharacteristic
483C3×C4D3×#4111yescharacteristic
484Dic3—22no—
485Dic3—22no—
486Dic3—41no—
487Dic3—42no—
488Dic3—121no—
489Dic3—121no—
490Dic3—241no—
491C32#336611yescharacteristic, complemented, Sylow
492C23—61no—
493C23—181no—
494C23—182no—
495Q8—62no—
496Q8—241no—
497D4—61no—
498D4—61no—
499D4—92no—
500D4—182no—
501D4—181no—
502D4—182no—
503D4—364no—
504D4—362no—
505D4—721no—
506D4—722no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—122no—
512C2×C4—181no—
513C2×C4—364no—
514C2×C4—362no—
515C2×C4—722no—
516C2×C4D3×D1211yescharacteristic
517C2×C4D3×D1211yescharacteristic
518C2×C4C22×D3211yescharacteristic
519C8—22no—
520C8—61no—
521C8—61no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—241no—
526C2×C3#557611yescharacteristic
527C2×C3#563311yescharacteristic
528C2×C3C2×#90811yescharacteristic
529C2×C3#575211yescharacteristic
530C2×C3C2×#91411yescharacteristic
531C2×C3#577411yescharacteristic
532D3—81no—
533D3—122no—
534D3—122no—
535D3—242no—
536D3—242no—
537D3—242no—
538D3—482no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—182no—
543C22—361no—
544C22—361no—
545C22—362no—
546C22—362no—
547C22—362no—
548C22C2×D3×D1211yescharacteristic
549C4—21no—
550C4—62no—
551C4—62no—
552C4—121no—
553C4—122no—
554C4—361no—
555C4#6379412yes—
556C4#6431211yescharacteristic
557C4#6431611yescharacteristic
558C3—21no—
559C3#7996911yescharacteristic, complemented
560C3#8108811yescharacteristic, complemented
561C2—241no—
562C2—362no—
563C2—722no—
564C2#1059432911yescharacteristic
565C2C2×#6379411yescharacteristic
566C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3366
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. #10593958C2semidirect
2. #10593902C2semidirect
3. #10592542C2semidirect
4. C3×#4842C2semidirect
5. C3×#4831C2semidirect
6. #10590882C2semidirect
7. #10590769C2semidirect
8. #10590768C2semidirect
9. #10590765C2semidirect
10. C4×#3714C2semidirect
11. #10590281C2semidirect
58. #4842D3semidirect
59. #4831D3semidirect
175. C4⋊(C3⋊D3)#41semidirect
491. C32#3366semidirect
559. C3#79969semidirect
560. C3#81088semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105939022
#105925422
C3×#48422
C3×#48312
#105908822
#105907692
#105907682
#105907652
C4×#37142
#105902812
#810883
#799693