Finite Group Databasebeta

← #11895973

Subgroups — #11895973

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10591409C212yesmaximal, complemented
8#10591405C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83587—31nomaximal
13#81590—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3754C2212yes—
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63873—21no—
26#63869C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3716C2211yescharacteristic
31#63659C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63576C2212yes—
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5721—31no—
45#5718D311yescharacteristic
46#5567—31no—
47C3×#486—31no—
48#5087—31no—
49#5075—31no—
50#5075—31no—
51#5075—32no—
52#5075—61no—
53#5071—32no—
54#5070D311yescharacteristic, complemented
55#5024—31no—
56#5018—32no—
57C4×#214—31no—
58#5009—32no—
59#5007—31no—
60#4764—32no—
61#4763—32no—
62#4762—32no—
63#4757—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C32×C42C2311yescharacteristic
79#3754—24no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3716—22no—
99#3368—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—
112Q8×Dic3—61no—
113#944—61no—
114#944—61no—
115#940C2×D312yes—
116#939—22no—
117#938—21no—
118D4×Dic3C2×D312yes—
119C2×#214—32no—
120C2×#214—32no—
121C2×#214—31no—
122C2×#214—62no—
123C2×#204—31no—
124#890—32no—
125#889—62no—
126#889—62no—
127#887—32no—
128#887—61no—
129C4×D12C2×D311yescharacteristic
130#870—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
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#817—31no—
149#816—31no—
150#815—32no—
151Dic3⋊C8—32no—
152#810—31no—
153#809—32no—
154#808—31no—
155#807—32no—
156#807—32no—
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—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174#634—21no—
175#634#4112yescomplemented
176C3×#67—44no—
177C3×#67—82no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3×Dic6—42no—
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192#550—31no—
193#490—92no—
194#486—31no—
195#478—92no—
196#474—91no—
197#460—92no—
198#460—91no—
199#446—91no—
200#440—92no—
201C4×SD16—91no—
202C3×#41—124no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—31no—
211C2×C3×D4—41no—
212C2×C3×D4—41no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C22×D312yes—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219C2×#67—22no—
220C2×#67—22no—
221C22×Dic3—22no—
222#237—44no—
223C2×D12C22×D311yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6#6711yescharacteristic
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—22no—
244#214—62no—
245#214—64no—
246#214—64no—
247#214—124no—
248(C2×D3)⋊C4—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3#6711yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—121no—
265Dic3⋊C4#6712yes—
266C4×Dic3—62no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—62no—
270C4×Dic3—121no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277#204—62no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—41no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×#41—61no—
296C2×SD16—91no—
297C2×SD16—92no—
298C4⋊Q8—31no—
299C4⋊Q8—181no—
300#127—32no—
301#127D3211yescharacteristic
302#125—92no—
303#125—182no—
304#121—61no—
305#121—62no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—91no—
309C4×Q8—181no—
310C4×D4—32no—
311C4×D4—31no—
312#107—92no—
313#106—91no—
314C4⋊C8—92no—
315C4⋊C8—91no—
316#103—91no—
317#102—32no—
318#102—32no—
319#102—92no—
320#102—91no—
321#102—92no—
322#97—92no—
323C4×C8—31no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—42no—
327C23×C3—61no—
328C22×D3—21no—
329C3×Q8—62no—
330C3×Q8—122no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—42no—
339C3×D4—61no—
340C3×D4—61no—
341C3×D4—82no—
342C3×D4—81no—
343C3×D4—81no—
344C3×D4—82no—
345C3×D4—124no—
346C3×D4—242no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—124no—
355C2×C3×C4—122no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362#67—44no—
363#67—82no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—44no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3C2×#6712yes—
374C2×Dic3C2×#6712yes—
375D12—21no—
376D12—21no—
377C4×D3—42no—
378Dic6—22no—
379Dic6—32no—
380Dic6—32no—
381Dic6—42no—
382Dic6—62no—
383Dic6—61no—
384Dic6—61no—
385Dic6—121no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C2×C32—82no—
394C2×C32#54811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32#57711yescharacteristic
397C3×D3—81no—
398#41—124no—
399C2×Q8—31no—
400C2×Q8—61no—
401C2×Q8—91no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—31no—
405C2×D4—62no—
406C2×D4—62no—
407C2×D4C2×D3212yes—
408C22×C4—62no—
409C22×C4—61no—
410SD16—182no—
411SD16—184no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—92no—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C22⋊C4—62no—
426C22⋊C4—61no—
427C42—32no—
428C42—182no—
429C42—181no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—82no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—41no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—121no—
458C3×C4—122no—
459C3×C4#91112yes—
460C3×C4#93212yes—
461C3×C4D3×#4111yescharacteristic
462C3×C4D3×#4111yescharacteristic
463C3×C4#101011yescharacteristic
464C3×C4#101011yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—42no—
468Dic3—41no—
469Dic3—62no—
470Dic3—62no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474Dic3—241no—
475C32#336811yescharacteristic, complemented, Sylow
476C23—22no—
477C23—61no—
478Q8—62no—
479Q8—92no—
480Q8—122no—
481Q8—181no—
482D4—22no—
483D4—22no—
484D4—42no—
485D4—61no—
486D4—61no—
487D4—81no—
488D4—124no—
489D4—242no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—124no—
495C2×C4—122no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4D3×#6711yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—61no—
502C8—61no—
503C8—182no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—82no—
508C2×C3—82no—
509C2×C3—162no—
510C2×C3—241no—
511C2×C3#567711yescharacteristic
512C2×C3C2×#91111yescharacteristic
513C2×C3#576211yescharacteristic
514C2×C3C2×#93211yescharacteristic
515C2×C3#583111yescharacteristic
516C2×C3#583611yescharacteristic
517D3—81no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22C2×D3×#6711yescharacteristic
525C4—21no—
526C4—62no—
527C4—62no—
528C4—121no—
529C4—122no—
530C4—182no—
531C4—361no—
532C4#6393212yes—
533C4#6430911yescharacteristic
534C4#6431211yescharacteristic
535C3—21no—
536C3#8159011yescharacteristic, complemented
537C3#8358711yescharacteristic, complemented
538C2—82no—
539C2—241no—
540C2#1059510511yescharacteristic
541C2C2×#6393211yescharacteristic
542C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3368
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
2. #10593864C2semidirect
3. #10592774C2semidirect
4. C3×#5070C2semidirect
5. #10591477C2semidirect
6. #10591439C2semidirect
7. #10591409C2semidirect
8. #10591405C2semidirect
9. C4×#3716C2semidirect
10. #10590269C2semidirect
11. #10590258C2semidirect
54. #5070D3semidirect
175. #634#41semidirect
475. C32#3368semidirect
536. C3#81590semidirect
537. C3#83587semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105938642
#105927742
C3×#50702
#105914772
#105914392
#105914092
#105914052
C4×#37162
#105902692
#105902582
#835873
#815903