Finite Group Databasebeta

← #11895774

Subgroups — #11895774

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590767C212yesmaximal, complemented
8#10590765C212yesmaximal, complemented
9#10590746C212yesmaximal, complemented
10#10590355C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81586—31nomaximal
13#79969—31nomaximal
14C2×#3796—21no—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#874C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63916—21no—
22#63911C2212yes—
23#63900—21no—
24#63894C2212yes—
25Dic3×D12C2212yes—
26#63888—22no—
27#63886—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63648C2211yescharacteristic
34#63645C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63564C2212yes—
42#63563C2212yes—
43#5730—31no—
44#5718—31no—
45#5579—31no—
46#5577—31no—
47C3×#486—31no—
48C3×#446—31no—
49#5084—31no—
50#5072—31no—
51#4847—32no—
52#4843—31no—
53#4843—32no—
54#4842—31no—
55#4786—32no—
56#4785—32no—
57#4766—32no—
58#4764—32no—
59#4713—32no—
60#4711—32no—
61#4694D311yescharacteristic, complemented
62C4×D24—31no—
63C4×D24—31no—
64C4×D24—61no—
65#4679D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78C2×D3×Dic3—22no—
79#3796—44no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3745—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97(C2×D3)⋊Dic3—22no—
98#3714—24no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×C4×Q8—31no—
105#946—61no—
106#946—62no—
107#940—32no—
108#939—62no—
109#938—61no—
110D4×Dic3—32no—
111C2×#213—32no—
112C2×D24—32no—
113C2×D24—31no—
114C2×D24—31no—
115C2×D24—61no—
116#897—61no—
117#896—62no—
118#895—62no—
119#895—61no—
120#893—32no—
121D3×C4⋊C4—61no—
122D3×C4⋊C4—61no—
123#890—32no—
124#874—32no—
125#874C2×D311yescharacteristic
126C4×D12—32no—
127C4×D12—31no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12—61no—
134#870—32no—
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140C3×#102—32no—
141C3×#97—32no—
142C3×C4×C8—21no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#832—32no—
146#821—32no—
147#821—31no—
148#821—31no—
149#821—31no—
150#821—31no—
151#821—32no—
152#821—61no—
153#821—61no—
154#821C2×D312yes—
155#821C2×D312yes—
156#818—31no—
157#818—31no—
158#818—61no—
159#817—32no—
160#815C2×D312yes—
161Dic3⋊C8C2×D312yes—
162#809—32no—
163#808—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yescomplemented
177C4×C3⋊D3—42no—
178C4×C3⋊D3—42no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×Dic6—22no—
187C3×Dic6—81no—
188#626—44no—
189#626—82no—
190#624—82no—
191D3×Dic3—44no—
192C32×C8—21no—
193C32×C8—21no—
194C3×C3⋊C8—22no—
195#554—91no—
196#550—91no—
197#490—92no—
198#486—31no—
199#478—92no—
200#476—91no—
201#459—92no—
202#459—91no—
203#446—31no—
204#442—92no—
205C4×D8—91no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×#67—62no—
212C2×#67—62no—
213C22×Dic3—62no—
214#239—124no—
215#237—124no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—31no—
219C2×D12—31no—
220C2×D12—31no—
221C2×D12—31no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12C22×D312yes—
227C2×C4×D3—62no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—121no—
235C2×C4×D3—121no—
236C2×Dic6—21no—
237C2×Dic6D1211yescharacteristic
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C3×C4⋊C4—31no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—61no—
249C3×C42—21no—
250C3×C42—32no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—62no—
254#213—64no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—121no—
263(C2×D3)⋊C4—121no—
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3D1211yescharacteristic
273C4⋊Dic3C22×D312yes—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4D1212yes—
278C4×Dic3C22×D312yes—
279C2×C3⋊C8C22×D312yes—
280D24—62no—
281D24—62no—
282D24—64no—
283D24—64no—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—22no—
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C32×C4—21no—
295C32×C4AGL(1,ℤ/8)12yes—
296C32×C4C2×#4111yescharacteristic
297C32×C42−1+411yescharacteristic
298C3⋊Dic3—41no—
299C3⋊Dic3—41no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C2×#41—181no—
304C2×D8—92no—
305C2×D8—91no—
306C4⋊Q8—31no—
307#127—31no—
308#127—92no—
309#125—92no—
310C22⋊Q8—182no—
311C22⋊Q8—181no—
312#121—181no—
313#121—182no—
314C4×Q8—31no—
315C4×D4—92no—
316C4×D4—92no—
317C4×D4—91no—
318C4×D4—91no—
319C2×C4⋊C4—181no—
320#107—91no—
321#106—92no—
322C4⋊C8—32no—
323C4⋊C8—31no—
324#102—32no—
325#102—32no—
326#102—92no—
327#102—92no—
328#102—91no—
329#102—91no—
330#97—32no—
331C4×C8D3211yescharacteristic
332C23×C3—62no—
333C22×D3—22no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—121no—
339C22×D3—121no—
340C3×Q8—62no—
341C3×Q8—241no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—122no—
345C3×D4—241no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—62no—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—124no—
359#67—242no—
360C2×Dic3—22no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—124no—
368C2×Dic3C2×D1212yes—
369C2×Dic3C2×D1212yes—
370D12—22no—
371D12—22no—
372D12—32no—
373D12—32no—
374D12—42no—
375D12—62no—
376D12—62no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—61no—
381D12—61no—
382D12—61no—
383D12—81no—
384D12—121no—
385D12—121no—
386D12—124no—
387D12—242no—
388C4×D3—124no—
389C4×D3—122no—
390C4×D3—122no—
391C4×D3—122no—
392C4×D3—122no—
393C4×D3—242no—
394C4×D3—242no—
395C4×D3—242no—
396C4×D3—242no—
397Dic6—22no—
398Dic6—81no—
399C3×C8—22no—
400C3×C8—21no—
401C3×C8—21no—
402C3×C8—21no—
403C3×C8—21no—
404C3×C8—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C2×C32#54811yescharacteristic
408C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
409C2×C32#57611yescharacteristic
410C3⋊D3—42no—
411C3⋊D3—81no—
412C3×D3—82no—
413#41—364no—
414C2×Q8—31no—
415C2×Q8—61no—
416C2×D4—32no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—91no—
420C2×D4—91no—
421C2×D4—182no—
422C2×D4—182no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—181no—
426C22×C4—181no—
427D8—182no—
428D8—184no—
429C2×C8—32no—
430C2×C8C2×D3211yescharacteristic
431C2×C8C2×D3211yescharacteristic
432C4⋊C4—31no—
433C4⋊C4—32no—
434C4⋊C4—32no—
435C4⋊C4—61no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—182no—
439C4⋊C4—182no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C42—32no—
445C42C2×D3211yescharacteristic
446C22×C3—21no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3C22×D1211yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—122no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—241no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—241no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—21no—
478C3×C4—41no—
479C3×C4—62no—
480C3×C4—62no—
481C3×C4—122no—
482C3×C4#90812yes—
483C3×C4#91412yes—
484C3×C4#100711yescharacteristic
485C3×C4D3×#4111yescharacteristic
486C3×C4D3×#4111yescharacteristic
487C3×C4#101011yescharacteristic
488Dic3—22no—
489Dic3—22no—
490Dic3—42no—
491Dic3—121no—
492Dic3—121no—
493Dic3—121no—
494Dic3—121no—
495Dic3—241no—
496Dic3—241no—
497C32#336611yescharacteristic, complemented, Sylow
498C23—62no—
499C23—181no—
500C23—181no—
501Q8—62no—
502Q8—241no—
503D4—62no—
504D4—62no—
505D4—92no—
506D4—122no—
507D4—181no—
508D4—181no—
509D4—181no—
510D4—241no—
511D4—364no—
512D4—722no—
513C2×C4—32no—
514C2×C4—32no—
515C2×C4—62no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—364no—
519C2×C4—362no—
520C2×C4—362no—
521C2×C4—722no—
522C2×C4D3×D1211yescharacteristic
523C2×C4D3×D1211yescharacteristic
524C2×C4C22×D3211yescharacteristic
525C8—21no—
526C8—21no—
527C8—62no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—242no—
532C2×C3#557611yescharacteristic
533C2×C3#567711yescharacteristic
534C2×C3C2×#90811yescharacteristic
535C2×C3#575211yescharacteristic
536C2×C3#575711yescharacteristic
537C2×C3C2×#91411yescharacteristic
538D3—82no—
539D3—122no—
540D3—122no—
541D3—242no—
542D3—242no—
543D3—241no—
544D3—241no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—182no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—361no—
554C22C2×D3×D1211yescharacteristic
555C4—21no—
556C4—62no—
557C4—62no—
558C4—122no—
559C4—361no—
560C4—361no—
561C4#6379412yes—
562C4#6429711yescharacteristic
563C4#6430611yescharacteristic
564C3—21no—
565C3#7996911yescharacteristic, complemented
566C3#8158611yescharacteristic, complemented
567C2—242no—
568C2—362no—
569C2—721no—
570C2#1059390111yescharacteristic
571C2C2×#6379411yescharacteristic
572C2#1059467811yescharacteristic
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. #10593900C2semidirect
3. C4×#3745C2semidirect
4. C3×#4694C2semidirect
5. C3×#4679C2semidirect
6. #10590882C2semidirect
7. #10590767C2semidirect
8. #10590765C2semidirect
9. #10590746C2semidirect
10. #10590355C2semidirect
11. #10590300C2semidirect
61. #4694D3semidirect
65. #4679D3semidirect
176. C4⋊(C3⋊D3)#41semidirect
497. C32#3366semidirect
565. C3#79969semidirect
566. C3#81586semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105939002
C4×#37452
C3×#46942
C3×#46792
#105908822
#105907672
#105907652
#105907462
#105903552
#105903002
#815863
#799693