Finite Group Databasebeta

← #11787696

Subgroups — #11787696

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2C2×#63827C211yesmaximal, characteristic
3C3×#4973C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591099C211yesmaximal, characteristic, complemented
6#10589396C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71666—31nomaximal
9#69693—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×C4×#67—22no—
16C3×#926C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C3×#893—21no—
19C3×#892—21no—
20C3×D3×C4⋊C4—21no—
21C3×#887—21no—
22C2×#3718—21no—
23#63827—22no—
24#63827C414yescomplemented
25C2×#3715—21no—
26C3×C3⋊#95—22no—
27#63569—22no—
28#63565—21no—
29#63565—21no—
30C3×#520—31no—
31C2×#951—31no—
32C2×#942—31no—
33#5504D311yescharacteristic
34C3×#391—31no—
35C2×#837—31no—
36#5225—31no—
37#5004—31no—
38#4973D311yescharacteristic, complemented
39C2×#805—31no—
40#4532—31no—
41#4530—31no—
42#4530—31no—
43#4530—61no—
44#4523—31no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235C2×C412yes—
53C3×#235D412yes—
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—22no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2×C412yescomplemented
63C2×C3×Dic6D411yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66#3748—21no—
67#3748—21no—
68#3748—21no—
69#3748C2×C412yescomplemented
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3D411yescharacteristic
75C3×C4⋊Dic3D411yescharacteristic
76C3×Dic3⋊C4—22no—
77C3×C4×Dic3—22no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81#3718—24no—
82#3715—24no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C22×C3×Q8—31no—
86C2×#235C2×D311yescharacteristic
87C22×Dic6C2×D311yescharacteristic
88C3×C4×Q8—61no—
89C3×C4×D4—61no—
90C3×C4×D4—62no—
91C3×#117—31no—
92C3×#117—61no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C42—31no—
98#951—34no—
99#951—62no—
100C2×#216—61no—
101C2×#216—61no—
102#942—34no—
103#942—62no—
104C2×#215—61no—
105C2×#214—61no—
106C4×#67—22no—
107#926C2×D311yescharacteristic
108C2×C4×Dic3C2×D311yescharacteristic
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114C2×#208—61no—
115#893—21no—
116#892—21no—
117D3×C4⋊C4—21no—
118#887—21no—
119C3×#95—62no—
120#837—62no—
121#835—61no—
122#835—61no—
123C3⋊#95—22no—
124#810—61no—
125#810—61no—
126#805—62no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4—22no—
130C2×C32×C4—42no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C3×#67—22no—
138C3×#67—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—21no—
149C3×D12C22⋊C412yes—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—82no—
153C3×Dic6—21no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158C3×Dic6C22⋊C412yes—
159C3⋊(C3⋊C8)—22no—
160C3⋊(C3⋊C8)—41no—
161C2×#137—91no—
162#520—31no—
163C2×#104—91no—
164#419—91no—
165#391—31no—
166#343—91no—
167#339—91no—
168C3×#41—32no—
169C3×#41—32no—
170C3×#41—61no—
171C3×#41—61no—
172C2×C3×Q8—32no—
173C2×C3×Q8—31no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—62no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4#6712yes—
188C22×C3×C4#6712yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194#235—21no—
195#235—21no—
196#235C4×D312yes—
197#235D1212yes—
198C2×D12#6711yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—22no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6C4×D312yescomplemented
207C2×Dic6#6711yescharacteristic
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—31no—
213C3×C4⋊C4—31no—
214C3×C4⋊C4—41no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C22⋊C4—61no—
219C3×C42—62no—
220C3×C42—61no—
221C3×C42—61no—
222C3×C42—61no—
223#217—21no—
224#216—64no—
225#216—64no—
226#215—64no—
227#214—64no—
228(C2×D3)⋊C4—22no—
229C4⋊Dic3#6711yescharacteristic
230C4⋊Dic3#6711yescharacteristic
231Dic3⋊C4—22no—
232C4×Dic3—22no—
233C4×Dic3—21no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236#208—32no—
237#208—32no—
238#208—62no—
239#208—61no—
240#208—61no—
241#208—62no—
242#208—61no—
243#208—61no—
244#208—61no—
245#208—61no—
246#208—121no—
247#208—121no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—121no—
253C2×C3⋊C8—121no—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32C4×D411yescharacteristic
257C22×C32#12011yescharacteristic
258C22×C32#12111yescharacteristic
259C2×C3×D3—22no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C32×C4—42no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12311yescharacteristic
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C3×Dic3—41no—
271C3×Dic3—41no—
272C2×#41—31no—
273C22×Q8—31no—
274#137—94no—
275#137—182no—
276C2×Q16—181no—
277C2×SD16—181no—
278C2×M16—91no—
279C2×M16—91no—
280C4×Q8—61no—
281C4×D4—61no—
282C4×D4—62no—
283#117—31no—
284#117—61no—
285C2×C4⋊C4—61no—
286C2×C4⋊C4D3211yescharacteristic
287C2×C42—31no—
288#104—182no—
289#103—181no—
290#103—181no—
291#95—62no—
292C23×C3—21no—
293C23×C3—61no—
294C23×C3C2×#6711yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—21no—
297C3×Q8—32no—
298C3×Q8—61no—
299C3×Q8—62no—
300C3×Q8—62no—
301C3×Q8—121no—
302C3×Q8—121no—
303C3×D4—32no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—61no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—61no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—82no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—242no—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4#23511yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343#67—22no—
344#67—22no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354D12—21no—
355D12(C2×D3)⋊C412yes—
356C4×D3—22no—
357C4×D3—22no—
358C4×D3—82no—
359Dic6—21no—
360Dic6—22no—
361Dic6—22no—
362Dic6—41no—
363Dic6—41no—
364Dic6(C2×D3)⋊C412yes—
365C3⋊C8—62no—
366C3⋊C8—62no—
367C3⋊C8—122no—
368C3⋊C8—122no—
369C3⋊C8—121no—
370C3⋊C8—121no—
371C2×C32—21no—
372C2×C32—21no—
373C2×C32#38611yescharacteristic
374C2×C32#45511yescharacteristic
375C2×C32#45611yescharacteristic
376C3×D3—42no—
377#41—32no—
378#41—32no—
379#41—61no—
380#41—61no—
381C2×Q8—32no—
382C2×Q8—31no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×D4—31no—
389C2×D4—61no—
390C22×C4—62no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4#62512yes—
395C22×C4C2×D3211yescharacteristic
396Q16—184no—
397SD16—184no—
398M16—92no—
399M16—181no—
400M16—181no—
401M16—181no—
402C2×C8—181no—
403C2×C8—181no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—31no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C42—62no—
412C42—61no—
413C42—61no—
414C42—61no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—62no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3C4×#6711yescharacteristic
428C22×C3C4×#6711yescharacteristic
429C22×C3#93011yescharacteristic
430C22×C3#93711yescharacteristic
431C22×C3#93811yescharacteristic
432C22×C3#95311yescharacteristic
433C2×D3—22no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—62no—
443C3×C4—82no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4—121no—
447C3×C4—121no—
448C3×C4D3×C22⋊C411yescharacteristic
449C3×C4#67⋊C411yescharacteristic
450C3×C4#88311yescharacteristic
451C3×C4#88411yescharacteristic
452C3×C4C2×(C2×D3)⋊C411yescharacteristic
453C3×C4C4×#6711yescharacteristic
454C3×C4#92911yescharacteristic
455C3×C4#93011yescharacteristic
456Dic3—22no—
457Dic3—42no—
458Dic3—42no—
459Dic3—41no—
460Dic3—41no—
461C32#188211yescharacteristic, complemented, Sylow
462C23—61no—
463C23C2×#62511yescharacteristic
464Q8—32no—
465Q8—61no—
466Q8—62no—
467Q8—62no—
468Q8—121no—
469Q8—121no—
470D4—32no—
471D4—62no—
472D4—62no—
473D4—61no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—242no—
488C2×C4#379511yescharacteristic
489C2×C4#379811yescharacteristic
490C2×C4C4×D3211yescharacteristic
491C2×C4D3×D1211yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—182no—
495C8—361no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—122no—
506C2×C3#495611yescharacteristic
507C2×C3#506111yescharacteristic
508C2×C3#509511yescharacteristic
509C2×C3#521311yescharacteristic
510C2×C3#524211yescharacteristic
511C2×C3#524611yescharacteristic
512D3—42no—
513C22—21no—
514C22—21no—
515C22—62no—
516C22—121no—
517C22—121no—
518C22C4×#62511yescharacteristic
519C22#6390811yescharacteristic
520C22#6397611yescharacteristic
521C4—42no—
522C4—62no—
523C4—122no—
524C4—121no—
525C4—122no—
526C4—121no—
527C4#6387911yescharacteristic
528C4#6390511yescharacteristic
529C4#6390611yescharacteristic
530C4D3×(C2×D3)⋊C411yescharacteristic
531C3—21no—
532C3#6969311yescharacteristic, complemented
533C3#7166611yescharacteristic, complemented
534C2—21no—
535C2—21no—
536C2—122no—
537C2#1059138111yescharacteristic
538C2#1059151211yescharacteristic
539C2#1059164811yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4973C2semidirect
5. #10591099C2semidirect
6. #10589396C2semidirect
7. #10589161C2semidirect
24. #63827C4semidirect
38. #4973D3semidirect
62. C2×C3×Dic6C2×C4semidirect
69. #3748C2×C4semidirect
206. C2×Dic6C4×D3semidirect
461. C32#1882semidirect
532. C3#69693semidirect
533. C3#71666semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C2×#638272
C3×#49732
C2×#635692
#105910992
#105893962
#105891612
#716663
#696933