Finite Group Databasebeta

← #11895778

Subgroups — #11895778

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590589C212yesmaximal, complemented
6#10590550C212yesmaximal, complemented
7#10590547C212yesmaximal, complemented
8#10590470C212yesmaximal, complemented
9#10590349C211yesmaximal, characteristic, complemented
10C4×#3713C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83638—31nomaximal
13#81088—31nomaximal
14C2×#3799—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64083C2211yescharacteristic
17C3×#946—22no—
18C3×#897—21no—
19C3×#893C2212yes—
20C3×D3×C4⋊C4—21no—
21C3×#890C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63911C2212yes—
26#63910—22no—
27#63909—21no—
28#63894C2212yes—
29C2×#3714C2212yes—
30C2×#3713C2211yescharacteristic
31#63636C2212yes—
32#63636C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#809C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic, complemented
45#5577—31no—
46#5553—31no—
47C3×#476—31no—
48#5088—31no—
49#5088—31no—
50#5088—61no—
51#5084D311yescharacteristic, complemented
52#5067—32no—
53#5066—32no—
54#5024—31no—
55#5015—32no—
56#5015—31no—
57#5014—32no—
58C4×#213—31no—
59C4×#213—31no—
60#4871—32no—
61#4869—32no—
62#4843—31no—
63#4831—31no—
64#4786—32no—
65#4764—32no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6D411yescharacteristic
76C2×#626—22no—
77C2×#626—22no—
78C2×#624—22no—
79#3799—44no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96#3722—22no—
97#3714—24no—
98#3713—22no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×#125—32no—
106C3×C22⋊Q8—61no—
107C3×C22⋊Q8—62no—
108C3×C4×Q8—31no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4—31no—
112C2×C3×C4⋊C4—61no—
113#946—22no—
114#940—32no—
115C2×#213—31no—
116C2×#213—31no—
117C2×#213—32no—
118#930—61no—
119C2×D24—32no—
120#897—21no—
121#895—62no—
122#895—61no—
123#893—32no—
124#893C2×D312yes—
125D3×C4⋊C4—21no—
126#890C2×D312yes—
127#884—62no—
128#874—32no—
129#874—31no—
130#874—31no—
131#874—61no—
132C4×D12—32no—
133C4×D12C2×D311yescharacteristic
134C4×D12C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#832—31no—
140#832—31no—
141#821—32no—
142#815—32no—
143Dic3⋊C8—32no—
144#809—31no—
145#809—31no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809—62no—
153#809C2×D312yes—
154#808C2×D312yes—
155#807—31no—
156#807—31no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C32×Q8—81no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—42no—
174C4⋊(C3⋊D3)—81no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12#4112yescomplemented
183C3×C4×D3—42no—
184C3×C4×D3—42no—
185C3×C4×D3—82no—
186C3×Dic6—22no—
187#626—44no—
188#626—82no—
189#624—44no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—21no—
192C3×C3⋊C8—22no—
193#554—31no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—31no—
199#459—92no—
200#459—91no—
201#446—91no—
202#442—92no—
203C4×D8—91no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×D4—31no—
209C2×C3×D4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215#239—124no—
216#235—124no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—121no—
227C2×D12—121no—
228C2×D12C22×D311yescharacteristic
229C2×D12C22×D311yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—22no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×Dic6#6711yescharacteristic
236C2×C3×C8—32no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C22×D312yes—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4—61no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#213—64no—
257#213—62no—
258#213—62no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—21no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3—22no—
265C4⋊Dic3#6711yescharacteristic
266C4⋊Dic3C22×D311yescharacteristic
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—22no—
269Dic3⋊C4#6712yes—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8C22×D312yes—
278D24—64no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C2×#41—181no—
299C2×D8—92no—
300C2×D8—91no—
301C4⋊Q8D3211yescharacteristic
302#127—92no—
303#127—91no—
304#125—32no—
305C22⋊Q8—61no—
306C22⋊Q8—62no—
307#121—182no—
308#121—181no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—31no—
313C4×D4—92no—
314C2×C4⋊C4—61no—
315#107—91no—
316#106—32no—
317C4⋊C8—31no—
318C4⋊C8—92no—
319#102—32no—
320#102—92no—
321#102—91no—
322#102—91no—
323#102—92no—
324#102—92no—
325#97—92no—
326C4×C8—91no—
327C23×C3—61no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—21no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—122no—
334C3×Q8—62no—
335C3×Q8—81no—
336C3×Q8—81no—
337C3×Q8—82no—
338C3×D4—32no—
339C3×D4—61no—
340C3×D4—61no—
341C3×D4—61no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—42no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—122no—
353C2×C3×C4—122no—
354C2×C3×C4—242no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—124no—
362#67—242no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—21no—
368D12—21no—
369D12—21no—
370D12—62no—
371D12—62no—
372D12—62no—
373D12—62no—
374D12—122no—
375D12—122no—
376D12—124no—
377D12—122no—
378D12—122no—
379D12—242no—
380D12—241no—
381D12—241no—
382D12—242no—
383D12—242no—
384D12#23912yescomplemented
385C4×D3—42no—
386C4×D3—42no—
387C4×D3—82no—
388C4×D3—124no—
389C4×D3—124no—
390Dic6—22no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—121no—
398C3⋊C8—121no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—82no—
403C3×D3—42no—
404C3×D3—81no—
405#41—364no—
406C2×Q8—21no—
407C2×Q8—31no—
408C2×D4—31no—
409C2×D4—31no—
410C2×D4—92no—
411C2×D4—182no—
412C2×D4—182no—
413C2×D4—181no—
414C2×D4—181no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—182no—
419D8—184no—
420D8—182no—
421C2×C8—32no—
422C2×C8—91no—
423C2×C8—91no—
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—32no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—62no—
430C4⋊C4—62no—
431C4⋊C4C2×D3212yes—
432C22⋊C4—62no—
433C22⋊C4—61no—
434C22⋊C4—61no—
435C22⋊C4—182no—
436C42—32no—
437C42C2×D3211yescharacteristic
438C22×C3—21no—
439C22×C3—62no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C22×#6711yescharacteristic
447C2×D3—22no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—242no—
460C2×D3—242no—
461C2×D3—242no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—62no—
471C3×C4—62no—
472C3×C4—82no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4#91412yes—
476C3×C4#94912yes—
477C3×C4C2×#23911yescharacteristic
478C3×C4#100711yescharacteristic
479C3×C4#100711yescharacteristic
480C3×C4D3×#4111yescharacteristic
481Dic3—22no—
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—61no—
487C23—61no—
488C23—182no—
489Q8—62no—
490Q8—81no—
491D4—32no—
492D4—61no—
493D4—61no—
494D4—61no—
495D4—182no—
496D4—182no—
497D4—364no—
498D4—362no—
499D4—721no—
500D4—722no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—242no—
509C2×C4—364no—
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—62no—
514C8—181no—
515C8—181no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—122no—
520C2×C3—241no—
521C2×C3#563311yescharacteristic
522C2×C3C2×#91411yescharacteristic
523C2×C3#577411yescharacteristic
524C2×C3#581711yescharacteristic
525C2×C3C2×#94911yescharacteristic
526C2×C3#583511yescharacteristic
527D3—42no—
528D3—81no—
529D3—242no—
530D3—242no—
531D3—482no—
532C22—62no—
533C22—121no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22—362no—
539C22—362no—
540C22—362no—
541C22C2×D3×#6711yescharacteristic
542C4—21no—
543C4—42no—
544C4—62no—
545C4—62no—
546C4—121no—
547C4—121no—
548C4#6393912yes—
549C4#6431611yescharacteristic
550C4D3×#23911yescharacteristic
551C3—21no—
552C3#8108811yescharacteristic, complemented
553C3#8363811yescharacteristic, complemented
554C2—122no—
555C2—241no—
556C2—722no—
557C2#1059509711yescharacteristic
558C2C2×#6393911yescharacteristic
559C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3366
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×#5730C2semidirect
2. #10593902C2semidirect
3. #10592787C2semidirect
4. C3×#5084C2semidirect
5. #10590589C2semidirect
6. #10590550C2semidirect
7. #10590547C2semidirect
8. #10590470C2semidirect
9. #10590349C2semidirect
10. C4×#3713C2semidirect
11. #10590259C2semidirect
44. #5730D3semidirect
51. #5084D3semidirect
182. C3×D12#41semidirect
384. D12#239semidirect
485. C32#3366semidirect
552. C3#81088semidirect
553. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105939022
#105927872
C3×#50842
#105905892
#105905502
#105905472
#105904702
#105903492
C4×#37132
#105902592
#836383
#810883