Finite Group Databasebeta

← #11895766

Subgroups — #11895766

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590347C212yesmaximal, complemented
5#10590347C211yesmaximal, characteristic, complemented
6#10590344C212yesmaximal, complemented
7C4×#3713C211yesmaximal, characteristic, complemented
8#10590279C212yesmaximal, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#10590270C212yesmaximal, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83638—31nomaximal
13#83581—31nomaximal
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#946—21no—
17C3×#896—22no—
18C3×#895—21no—
19C3×#895—22no—
20C3×D3×C4⋊C4—21no—
21C3×#874C2211yescharacteristic
22C3×#874C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×#870C2212yes—
28C3×#869C2211yescharacteristic
29C2×#3713C2211yescharacteristic
30C2×#3713C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊C8))C2212yes—
33#63630C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63576C2211yescharacteristic
36#63574C2212yes—
37#63562C2212yes—
38#63562C2212yes—
39#63562C2212yes—
40#63562C2212yes—
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43C3×#554—31no—
44C3×#550—31no—
45#5579D311yescharacteristic, complemented
46#5577D311yescharacteristic, complemented
47#5088—31no—
48#5084—31no—
49#5072—31no—
50#5072—32no—
51#5071—32no—
52#5070—31no—
53#5067—32no—
54#5066—32no—
55#5024—31no—
56#5024—31no—
57#5024—61no—
58#5015—32no—
59#5015—31no—
60#5014—32no—
61#5014—32no—
62C4×#213—31no—
63C4×#213—31no—
64#5009—32no—
65#5008—31no—
66C2×C32×Q8D411yescharacteristic
67C3×#239—44no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4D412yes—
82C32×C42C2311yescharacteristic
83C32×C42C2312yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97#3713—22no—
98#3713—24no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×#127—32no—
105C3×#125—32no—
106C3×C22⋊Q8—61no—
107C3×C22⋊Q8—62no—
108C3×#121—61no—
109C3×#121—62no—
110C3×C4×Q8—21no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114C3×C4×D4—32no—
115C3×C4×D4—31no—
116C3×C4×D4—32no—
117C2×C3×C4⋊C4—61no—
118#946—21no—
119C2×#213—31no—
120C2×#213—31no—
121C2×#213—32no—
122C2×#213—32no—
123#896—22no—
124#895—21no—
125#895—22no—
126D3×C4⋊C4—21no—
127#874C2×D312yes—
128#874C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D311yescharacteristic
131C4×D12C2×D312yes—
132C4×D12C2×D312yes—
133#870C2×D312yes—
134#869C2×D311yescharacteristic
135#832—32no—
136#832—32no—
137#832—32no—
138#832—31no—
139#832—31no—
140#832—32no—
141#809—31no—
142#809—31no—
143#809—32no—
144#809—32no—
145#809—32no—
146#809—32no—
147#808—32no—
148#808—32no—
149#807—31no—
150#807—31no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)—31no—
155C4⋊(C3⋊C8)—61no—
156C4⋊(C3⋊C8)—62no—
157#803—32no—
158#803—32no—
159#803—62no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C32×Q8—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—44no—
181C3×D12—42no—
182C3×D12—81no—
183C3×D12—82no—
184C3×D12#4112yescomplemented
185C3×C4×D3—44no—
186C3×C4×D3—42no—
187C3×C4×D3—42no—
188C3×C4×D3—82no—
189C3×Dic6—81no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—22no—
192C3⋊(C3⋊C8)—21no—
193#554—31no—
194#550—31no—
195#490—92no—
196#486—91no—
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—21no—
206C2×C3×Q8—61no—
207C2×C3×Q8#6711yescharacteristic
208C2×C3×Q8#6711yescharacteristic
209C2×C3×D4—31no—
210C2×C3×D4—31no—
211C2×C3×D4—32no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C2×C3×D4—62no—
215C2×C3×D4—61no—
216C22×C3×C4—61no—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219C22×C3×C4—62no—
220#239—44no—
221C2×D12—22no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—22no—
225C2×D12C22×D311yescharacteristic
226C2×D12C22×D312yes—
227C2×D12C22×D311yescharacteristic
228C2×C4×D3—21no—
229C2×C4×D3—22no—
230C2×C4×D3—21no—
231C2×C4×D3—22no—
232C2×Dic6—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4#6711yescharacteristic
242C3×C4⋊C4#6711yescharacteristic
243C3×C4⋊C4#6712yes—
244C3×C4⋊C4#6712yes—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C22⋊C4—62no—
249C3×C42—21no—
250C3×C42—22no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D312yes—
254C3×C42C22×D312yes—
255#213—62no—
256#213—64no—
257#213—62no—
258#213—64no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—22no—
263C4⋊Dic3—21no—
264C4⋊Dic3C22×D311yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D312yes—
267Dic3⋊C4—22no—
268Dic3⋊C4—22no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—62no—
278C22×C32C22×D411yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—42no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4—21no—
290C32×C4—22no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—42no—
297C2×#41—61no—
298C2×D8—91no—
299C2×D8—92no—
300C4⋊Q8—31no—
301#127—31no—
302#127—32no—
303#125—32no—
304C22⋊Q8—61no—
305C22⋊Q8—62no—
306#121—61no—
307#121—62no—
308C4×Q8D3211yescharacteristic
309C4×D4—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—32no—
313C2×C4⋊C4—61no—
314#107—91no—
315#106—92no—
316C4⋊C8—91no—
317C4⋊C8—92no—
318#102—91no—
319#102—91no—
320#102—92no—
321#102—92no—
322#102—92no—
323#102—92no—
324#97—92no—
325C4×C8—91no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—22no—
331C22×D3—21no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×Q8—241no—
336C3×D4—32no—
337C3×D4—61no—
338C3×D4—62no—
339C3×D4—61no—
340C3×D4—62no—
341C3×D4—61no—
342C3×D4—124no—
343C3×D4—122no—
344C3×D4—241no—
345C3×D4—242no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—124no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4—242no—
358C2×C3×C4C2×#6712yes—
359C2×C3×C4C2×#6712yes—
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371D12—21no—
372D12—21no—
373D12—22no—
374D12—21no—
375D12—22no—
376D12—44no—
377D12—42no—
378D12—82no—
379D12—81no—
380D12#23912yescomplemented
381C4×D3—44no—
382C4×D3—42no—
383C4×D3—42no—
384C4×D3—82no—
385Dic6—81no—
386C3⋊C8—62no—
387C3⋊C8—61no—
388C3⋊C8—62no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—62no—
392C3⋊C8—61no—
393C3⋊C8—121no—
394C3⋊C8—122no—
395C2×C32#54811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32#57611yescharacteristic
398C3×D3—42no—
399C3×D3—82no—
400C3×D3—81no—
401#41—124no—
402C2×Q8—61no—
403C2×Q8#62511yescharacteristic
404C2×D4—31no—
405C2×D4—31no—
406C2×D4—32no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—62no—
411C22×C4—61no—
412C22×C4—62no—
413C22×C4—61no—
414C22×C4—62no—
415D8—182no—
416D8—184no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8—92no—
420C4⋊C4—32no—
421C4⋊C4—31no—
422C4⋊C4—31no—
423C4⋊C4—62no—
424C4⋊C4—61no—
425C4⋊C4—62no—
426C4⋊C4#62511yescharacteristic
427C4⋊C4#62512yes—
428C22⋊C4—61no—
429C22⋊C4—62no—
430C22⋊C4—61no—
431C22⋊C4—62no—
432C42C2×D3211yescharacteristic
433C42C2×D3212yes—
434C22×C3—21no—
435C22×C3—62no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—122no—
439C22×C3—121no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3C22×#6711yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4—122no—
470C3×C4#93212yes—
471C3×C4#94912yes—
472C3×C4C2×#23911yescharacteristic
473C3×C4#100711yescharacteristic
474C3×C4D3×#4111yescharacteristic
475C3×C4#101011yescharacteristic
476Dic3—41no—
477Dic3—41no—
478Dic3—42no—
479C32#336611yescharacteristic, complemented, Sylow
480C23—61no—
481C23—62no—
482C23—61no—
483Q8—22no—
484Q8—241no—
485D4—32no—
486D4—61no—
487D4—61no—
488D4—62no—
489D4—61no—
490D4—62no—
491D4—124no—
492D4—122no—
493D4—242no—
494D4—241no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—124no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—242no—
502C2×C4C2×#62511yescharacteristic
503C2×C4C2×#62512yes—
504C2×C4C2×#62512yes—
505C2×C4C2×#62511yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—181no—
508C8—181no—
509C8—182no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—122no—
514C2×C3—242no—
515C2×C3—241no—
516C2×C3C2×#93211yescharacteristic
517C2×C3#581711yescharacteristic
518C2×C3C2×#94911yescharacteristic
519C2×C3#583111yescharacteristic
520C2×C3#583511yescharacteristic
521C2×C3#583511yescharacteristic
522D3—42no—
523D3—82no—
524D3—81no—
525C22—62no—
526C22—121no—
527C22—121no—
528C22—122no—
529C22—121no—
530C22—121no—
531C22—122no—
532C22—122no—
533C22—121no—
534C22C22×#62511yescharacteristic
535C4—22no—
536C4—21no—
537C4—22no—
538C4—122no—
539C4—121no—
540C4—121no—
541C4#6382312yes—
542C4#6431511yescharacteristic
543C4D3×#23911yescharacteristic
544C3—21no—
545C3#8358111yescharacteristic, complemented
546C3#8363811yescharacteristic, complemented
547C2—122no—
548C2—242no—
549C2—241no—
550C2C2×#6382311yescharacteristic
551C2#1059540911yescharacteristic
552C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
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 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
2. C3×#5577C2semidirect
3. #10592723C2semidirect
4. #10590347C2semidirect
5. #10590347C2semidirect
6. #10590344C2semidirect
7. C4×#3713C2semidirect
8. #10590279C2semidirect
9. #10590277C2semidirect
10. #10590270C2semidirect
11. #10590266C2semidirect
45. #5579D3semidirect
46. #5577D3semidirect
184. C3×D12#41semidirect
380. D12#239semidirect
479. C32#3366semidirect
545. C3#83581semidirect
546. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#55772
#105927232
#105903472
#105903442
C4×#37132
#105902792
#105902772
#105902702
#105902662
#836383
#835813