Finite Group Databasebeta

← #11895771

Subgroups — #11895771

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
1C3×#5718C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591429C212yesmaximal, complemented
7#10591411C212yesmaximal, complemented
8#10591404C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83581—31nomaximal
13#81586—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3753C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2211yescharacteristic
31#63659C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5730—31no—
45#5718D311yescharacteristic, complemented
46#5579—31no—
47C3×#486—31no—
48#5084—31no—
49#5072—31no—
50#5072—31no—
51#5072—32no—
52#5072—61no—
53#5071—32no—
54#5070D311yescharacteristic, complemented
55#5024—31no—
56#5014—32no—
57C4×#213—31no—
58#5009—32no—
59#5008—31no—
60#4786—32no—
61#4785—32no—
62#4766—32no—
63#4764—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C3×#237—44no—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6D411yescharacteristic
79C2×#624—22no—
80C32×C42C2311yescharacteristic
81#3753—24no—
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3714—22no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C3×C4⋊Q8—31no—
103C3×#127—21no—
104C3×#127—32no—
105C3×#127C2×D311yescharacteristic
106C3×#127C2×D311yescharacteristic
107C3×#121—61no—
108C3×#121—62no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112#946—61no—
113#946—62no—
114#940C2×D312yes—
115#939—22no—
116#938—21no—
117D4×Dic3C2×D312yes—
118C2×#213—32no—
119C2×#213—32no—
120C2×#213—31no—
121C2×#213—62no—
122C2×D24—31no—
123#897—61no—
124#896—62no—
125#893—32no—
126D3×C4⋊C4—61no—
127D3×C4⋊C4—61no—
128#890—32no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12C2×D311yescharacteristic
134#870—32no—
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#102—32no—
138C3×#102—32no—
139C3×C4×C8—31no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—31no—
144#832—62no—
145#832C2×D312yes—
146#832C2×D312yes—
147#821—31no—
148#821—31no—
149#818—31no—
150#815—32no—
151Dic3⋊C8—32no—
152#809—32no—
153#809—31no—
154#808—32no—
155#808—32no—
156#807—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—22no—
164C22×C3⋊D3—21no—
165C22×C3×D3—21no—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—42no—
169C32×D4—81no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)#4112yescomplemented
176C4×C3⋊D3—42no—
177C3×#67—44no—
178C3×#67—82no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—44no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—42no—
187C3×Dic6—22no—
188C3×Dic6—81no—
189#624—82no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—91no—
194#550—31no—
195#490—92no—
196#486—31no—
197#478—92no—
198#476—91no—
199#459—92no—
200#459—91no—
201#446—91no—
202#442—92no—
203C4×D8—91no—
204C3×#41—124no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—22no—
212C2×C3×D4—31no—
213C2×C3×D4—41no—
214C2×C3×D4—41no—
215C2×C3×D4—62no—
216C2×C3×D4—62no—
217C2×C3×D4C22×D312yes—
218C2×C3×D4C22×D312yes—
219C22×C3×C4—62no—
220C22×C3×C4—61no—
221C2×#67—22no—
222C2×#67—22no—
223C22×Dic3—22no—
224#237—44no—
225C2×D12—31no—
226C2×D12—31no—
227C2×D12—61no—
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—121no—
235C2×Dic6—21no—
236C2×Dic6#6711yescharacteristic
237C2×C3×C8—31no—
238C2×C3×C8—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—61no—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#217—22no—
251#213—62no—
252#213—64no—
253#213—64no—
254#213—124no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
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⋊Dic3#6711yescharacteristic
267C4⋊Dic3C22×D311yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4#6712yes—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279D24—62no—
280C22×C32—42no—
281C22×C32—42no—
282C22×C32—42no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
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—61no—
300C2×D8—91no—
301C2×D8—92no—
302C4⋊Q8—31no—
303#127—32no—
304#127D3211yescharacteristic
305#125—92no—
306C22⋊Q8—182no—
307C22⋊Q8—181no—
308#121—61no—
309#121—62no—
310C4×Q8—31no—
311C4×D4—32no—
312C4×D4—31no—
313C4×D4—92no—
314C4×D4—91no—
315C2×C4⋊C4—181no—
316#107—91no—
317#106—92no—
318C4⋊C8—92no—
319C4⋊C8—91no—
320#102—32no—
321#102—32no—
322#102—91no—
323#102—92no—
324#102—91no—
325#102—92no—
326#97—92no—
327C4×C8—31no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—42no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—121no—
336C3×Q8—62no—
337C3×Q8—241no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—61no—
347C3×D4—61no—
348C3×D4—82no—
349C3×D4—81no—
350C3×D4—81no—
351C3×D4—82no—
352C3×D4—124no—
353C3×D4—242no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—124no—
362C2×C3×C4—122no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—44no—
370#67—82no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373C2×Dic3—44no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—121no—
377C2×Dic3C2×#6712yes—
378C2×Dic3C2×#6712yes—
379D12—21no—
380D12—21no—
381D12—32no—
382D12—32no—
383D12—62no—
384D12—61no—
385D12—61no—
386D12—121no—
387C4×D3—42no—
388C4×D3—122no—
389C4×D3—122no—
390C4×D3—242no—
391C4×D3—242no—
392C4×D3—242no—
393Dic6—22no—
394Dic6—81no—
395C3×C8—61no—
396C3×C8—61no—
397C3⋊C8—21no—
398C3⋊C8—21no—
399C3⋊C8—62no—
400C3⋊C8—62no—
401C3⋊C8—122no—
402C2×C32—82no—
403C2×C32#54811yescharacteristic
404C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C32#57611yescharacteristic
406C3⋊D3—42no—
407C3×D3—81no—
408#41—124no—
409C2×Q8—31no—
410C2×Q8—61no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—31no—
414C2×D4—62no—
415C2×D4—62no—
416C2×D4—91no—
417C2×D4C2×D3212yes—
418C22×C4—62no—
419C22×C4—61no—
420C22×C4—182no—
421C22×C4—181no—
422D8—182no—
423D8—184no—
424C2×C8—31no—
425C2×C8—31no—
426C2×C8—92no—
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—62no—
436C22⋊C4—61no—
437C22⋊C4—182no—
438C22⋊C4—181no—
439C42—32no—
440C42C2×D3211yescharacteristic
441C22×C3—21no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—82no—
449C22×C3—82no—
450C22×C3—82no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×#6711yescharacteristic
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—122no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—241no—
467C2×D3—241no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—41no—
474C3×C4—62no—
475C3×C4—62no—
476C3×C4—121no—
477C3×C4—122no—
478C3×C4#91412yes—
479C3×C4#93212yes—
480C3×C4D3×#4111yescharacteristic
481C3×C4D3×#4111yescharacteristic
482C3×C4#101011yescharacteristic
483C3×C4#101011yescharacteristic
484Dic3—22no—
485Dic3—22no—
486Dic3—42no—
487Dic3—41no—
488Dic3—121no—
489Dic3—121no—
490Dic3—241no—
491C32#336611yescharacteristic, complemented, Sylow
492C23—22no—
493C23—61no—
494C23—181no—
495Q8—62no—
496Q8—241no—
497D4—22no—
498D4—22no—
499D4—42no—
500D4—61no—
501D4—61no—
502D4—81no—
503D4—92no—
504D4—124no—
505D4—181no—
506D4—242no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—124no—
512C2×C4—122no—
513C2×C4—181no—
514C2×C4—362no—
515C2×C4—722no—
516C2×C4D3×#6711yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4C22×D3211yescharacteristic
519C8—61no—
520C8—61no—
521C8—182no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—82no—
526C2×C3—82no—
527C2×C3—162no—
528C2×C3—241no—
529C2×C3#567711yescharacteristic
530C2×C3#575711yescharacteristic
531C2×C3C2×#91411yescharacteristic
532C2×C3C2×#93211yescharacteristic
533C2×C3#583111yescharacteristic
534C2×C3#583511yescharacteristic
535D3—81no—
536D3—122no—
537D3—122no—
538D3—242no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—182no—
546C22—361no—
547C22—361no—
548C22C2×D3×#6711yescharacteristic
549C4—21no—
550C4—62no—
551C4—62no—
552C4—122no—
553C4—121no—
554C4—361no—
555C4#6393412yes—
556C4#6430911yescharacteristic
557C4#6431211yescharacteristic
558C3—21no—
559C3#8158611yescharacteristic, complemented
560C3#8358111yescharacteristic, complemented
561C2—82no—
562C2—241no—
563C2—362no—
564C2#1059509611yescharacteristic
565C2C2×#6393411yescharacteristic
566C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5718C2semidirect
2. #10593958C2semidirect
3. #10592771C2semidirect
4. C3×#5070C2semidirect
5. #10591477C2semidirect
6. #10591429C2semidirect
7. #10591411C2semidirect
8. #10591404C2semidirect
9. C4×#3714C2semidirect
10. #10590266C2semidirect
11. #10590258C2semidirect
45. #5718D3semidirect
54. #5070D3semidirect
175. C4⋊(C3⋊D3)#41semidirect
491. C32#3366semidirect
559. C3#81586semidirect
560. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939582
#105927712
C3×#50702
#105914772
#105914292
#105914112
#105914042
C4×#37142
#105902662
#105902582
#835813
#815863