Finite Group Databasebeta

← #11895762

Subgroups — #11895762

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
1C3×#5553C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591429C212yesmaximal, complemented
7#10590589C212yesmaximal, complemented
8#10590545C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83581—31nomaximal
13#81088—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3753C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#940C2212yes—
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2212yes—
31#63659C2211yescharacteristic
32#63636C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×#808C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5730—31no—
45#5579—31no—
46#5553D311yescharacteristic, complemented
47C3×#476—31no—
48#5088—31no—
49#5072—32no—
50#5072—31no—
51#5071—32no—
52#5070—31no—
53#5024—31no—
54#5014—32no—
55C4×#213—31no—
56C4×#213—31no—
57C4×#213—61no—
58#5009—32no—
59#5008D311yescharacteristic, complemented
60#4871—32no—
61#4869—32no—
62#4843—31no—
63#4831—31no—
64#4786—32no—
65#4764—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C3×#235—44no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6D411yescharacteristic
79C2×#624—22no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3753—22no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3714—24no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C3×C4⋊Q8—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112#946—61no—
113#946—62no—
114#940C2×D312yes—
115C2×#213—31no—
116C2×#213—31no—
117C2×#213—32no—
118C2×#213—61no—
119#930—21no—
120C2×D24—32no—
121#897—61no—
122#896—62no—
123#893—32no—
124#893C2×D312yes—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—61no—
127#890—32no—
128#884—22no—
129#874C2×D311yescharacteristic
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—32no—
133C4×D12—61no—
134#870—32no—
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140#832—31no—
141#832—31no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—61no—
146#832C2×D312yes—
147#821—32no—
148#815—32no—
149Dic3⋊C8—32no—
150#809—32no—
151#809—32no—
152#809—31no—
153#809—31no—
154#809—61no—
155#808C2×D312yes—
156#807—31no—
157#807—31no—
158#807—61no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161#803—32no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
165C23×C32—21no—
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C32×D4—21no—
169C32×D4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)#4112yescomplemented
178C4×C3⋊D3—42no—
179C3×#67—44no—
180C3×#67—82no—
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×C4×D3—44no—
189C3×Dic6—22no—
190C3×Dic6—81no—
191#624—82no—
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)—21no—
194C3×C3⋊C8—22no—
195#554—91no—
196#550—31no—
197#490—92no—
198#486—91no—
199#478—92no—
200#476—31no—
201#459—92no—
202#459—91no—
203#446—91no—
204#442—92no—
205C4×D8—91no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—61no—
209C2×C3×D4—21no—
210C2×C3×D4—32no—
211C2×C3×D4—62no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4C22×D311yescharacteristic
216C2×C3×D4C22×D311yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—41no—
220C22×C3×C4—62no—
221C2×#67—22no—
222C2×#67—22no—
223#235—44no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—31no—
227C2×D12—31no—
228C2×D12—61no—
229C2×D12C22×D312yes—
230C2×C4×D3—22no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—121no—
236C2×Dic6—21no—
237C2×Dic6#6711yescharacteristic
238C2×C3×C8—32no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—41no—
249C3×C22⋊C4—62no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#213—64no—
255#213—62no—
256#213—62no—
257#213—64no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—121no—
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3#6711yescharacteristic
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4#6712yes—
275C4×Dic3C22×D312yes—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—61no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8C22×D312yes—
283D24—64no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—22no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4AGL(1,ℤ/8)12yes—
297C32×C4C2×#4111yescharacteristic
298C32×C42−1+411yescharacteristic
299C3⋊Dic3—41no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C2×#41—61no—
304C2×D8—92no—
305C2×D8—91no—
306C4⋊Q8—31no—
307#127—32no—
308#127—31no—
309#125—92no—
310C22⋊Q8—182no—
311C22⋊Q8—181no—
312#121—62no—
313#121—61no—
314C4×Q8—31no—
315C4×D4—32no—
316C4×D4—92no—
317C4×D4—91no—
318C4×D4D3211yescharacteristic
319C2×C4⋊C4—181no—
320#107—91no—
321#106—32no—
322C4⋊C8—31no—
323C4⋊C8—92no—
324#102—32no—
325#102—92no—
326#102—92no—
327#102—92no—
328#102—91no—
329#102—91no—
330#97—92no—
331C4×C8—91no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—41no—
335C23×C3—62no—
336C22×D3—22no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—121no—
340C3×Q8—62no—
341C3×Q8—241no—
342C3×D4—22no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—41no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—124no—
351C3×D4—122no—
352C3×D4—241no—
353C3×D4—242no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—41no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—62no—
365C2×C3×C4—82no—
366C2×C3×C4—124no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—44no—
374#67—82no—
375C2×Dic3—22no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—121no—
379C2×Dic3C2×#6712yes—
380C2×Dic3C2×#6712yes—
381D12—22no—
382D12—22no—
383D12—32no—
384D12—32no—
385D12—42no—
386D12—62no—
387D12—61no—
388D12—61no—
389D12—81no—
390D12—121no—
391C4×D3—44no—
392C4×D3—122no—
393C4×D3—122no—
394C4×D3—242no—
395C4×D3—242no—
396C4×D3—242no—
397Dic6—22no—
398Dic6—81no—
399C3×C8—62no—
400C3⋊C8—22no—
401C3⋊C8—62no—
402C3⋊C8—61no—
403C3⋊C8—61no—
404C3⋊C8—61no—
405C3⋊C8—61no—
406C3⋊C8—121no—
407C2×C32—81no—
408C2×C32#54811yescharacteristic
409C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
410C2×C32#57611yescharacteristic
411C3⋊D3—42no—
412C3×D3—82no—
413#41—124no—
414C2×Q8—31no—
415C2×Q8—61no—
416C2×D4—32no—
417C2×D4—62no—
418C2×D4—62no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—91no—
422C2×D4C2×D3211yescharacteristic
423C22×C4—21no—
424C22×C4—62no—
425C22×C4—182no—
426C22×C4—181no—
427D8—184no—
428D8—182no—
429C2×C8—32no—
430C2×C8—91no—
431C2×C8—91no—
432C4⋊C4—31no—
433C4⋊C4—32no—
434C4⋊C4—32no—
435C4⋊C4—61no—
436C4⋊C4—91no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4C2×D3211yescharacteristic
440C22⋊C4—21no—
441C22⋊C4—62no—
442C22⋊C4—182no—
443C22⋊C4—181no—
444C42—32no—
445C42C2×D3211yescharacteristic
446C22×C3—21no—
447C22×C3—42no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—81no—
455C22×C3—81no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C22×#6711yescharacteristic
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—241no—
472C2×D3—241no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—22no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—62no—
482C3×C4—62no—
483C3×C4—81no—
484C3×C4—122no—
485C3×C4#91412yes—
486C3×C4#93212yes—
487C3×C4#100711yescharacteristic
488C3×C4D3×#4111yescharacteristic
489C3×C4D3×#4111yescharacteristic
490C3×C4#101011yescharacteristic
491Dic3—22no—
492Dic3—22no—
493Dic3—42no—
494Dic3—121no—
495Dic3—121no—
496Dic3—241no—
497C32#336611yescharacteristic, complemented, Sylow
498C23—21no—
499C23—62no—
500C23—181no—
501Q8—62no—
502Q8—241no—
503D4—21no—
504D4—21no—
505D4—62no—
506D4—62no—
507D4—92no—
508D4—124no—
509D4—122no—
510D4—181no—
511D4—241no—
512D4—242no—
513C2×C4—21no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—42no—
517C2×C4—62no—
518C2×C4—124no—
519C2×C4—181no—
520C2×C4—362no—
521C2×C4—722no—
522C2×C4D3×#6711yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C2×C4C22×D3211yescharacteristic
525C8—62no—
526C8—181no—
527C8—181no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—82no—
532C2×C3—81no—
533C2×C3—81no—
534C2×C3—242no—
535C2×C3#563311yescharacteristic
536C2×C3C2×#91411yescharacteristic
537C2×C3#577411yescharacteristic
538C2×C3C2×#93211yescharacteristic
539C2×C3#583111yescharacteristic
540C2×C3#583511yescharacteristic
541D3—82no—
542D3—122no—
543D3—122no—
544D3—242no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—182no—
552C22—361no—
553C22—361no—
554C22C2×D3×#6711yescharacteristic
555C4—21no—
556C4—41no—
557C4—62no—
558C4—62no—
559C4—122no—
560C4—361no—
561C4#6393412yes—
562C4#6429711yescharacteristic
563C4#6430611yescharacteristic
564C3—21no—
565C3#8108811yescharacteristic, complemented
566C3#8358111yescharacteristic, complemented
567C2—81no—
568C2—242no—
569C2—362no—
570C2#1059483011yescharacteristic
571C2C2×#6393411yescharacteristic
572C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5553C2semidirect
2. #10593958C2semidirect
3. C4×#3753C2semidirect
4. C3×#5008C2semidirect
5. #10591477C2semidirect
6. #10591429C2semidirect
7. #10590589C2semidirect
8. #10590545C2semidirect
9. #10590355C2semidirect
10. #10590277C2semidirect
11. #10590259C2semidirect
46. #5553D3semidirect
59. #5008D3semidirect
177. C4⋊(C3⋊D3)#41semidirect
497. C32#3366semidirect
565. C3#81088semidirect
566. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105939582
C4×#37532
C3×#50082
#105914772
#105914292
#105905892
#105905452
#105903552
#105902772
#105902592
#835813
#810883