Finite Group Databasebeta

← #11788182

Subgroups — #11788182

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#71711—31nomaximal
9#68756—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C32×#117C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#897C412yescomplemented
19C3×#895C412yescomplemented
20C3×#886—21no—
21C3×#882—21no—
22C3×C4×D12—22no—
23C2×Dic32—21no—
24C4×D3×Dic3—22no—
25C4×D3×Dic3—22no—
26#63569—22no—
27#63568—22no—
28(C2×D3)⋊(C3⋊C8)—22no—
29C3×#525—31no—
30C22×C4×Dic3—31no—
31#5524D311yescharacteristic
32C2×C42×D3—31no—
33C2×#837—31no—
34C2×#837—31no—
35#5207—31no—
36C2×#825—31no—
37#5126—31no—
38C2×#805—31no—
39C3×#339—31no—
40#4532—31no—
41#4532—31no—
42#4532—61no—
43#4532D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C2×C3×D12—22no—
55C2×C3×D12C2×C411yescharacteristic, complemented
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3D412yes—
63C2×C3×Dic6C2×C411yescharacteristic, complemented
64C2×D3×Dic3—28no—
65C2×D3×Dic3—24no—
66C32×C4⋊C4C2×C412yescomplemented
67C32×C22⋊C4—21no—
68C32×C42—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3D412yescomplemented
71#3748—21no—
72#3748—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C3×(C2×D3)⋊C4—22no—
75C3×(C2×D3)⋊C4—22no—
76C3×C4⋊Dic3—22no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3D412yescomplemented
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82Dic32—24no—
83#1896—91noSylow
84C2×C3×#41—31no—
85C23×C3×C4—31no—
86C23×Dic3—61no—
87C2×#235C2×D311yescharacteristic
88C22×C4×D3—61no—
89C22×C4×D3C2×D311yescharacteristic
90C2×C3×M16—31no—
91C3×#123—61no—
92C3×C22⋊Q8—32no—
93C3×#121—32no—
94C3×#120—61no—
95C3×C4×D4—62no—
96C3×#117—21no—
97C3×#117C2×D311yescharacteristic
98C3×#117C2×D311yescharacteristic
99C2×C3×C42—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3—62no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—62no—
107C2×C4×Dic3C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#208C2×D311yescharacteristic
112#897Dic312yescomplemented
113#895Dic312yescomplemented
114#886—21no—
115#882—21no—
116C4×D12—22no—
117C42×D3—62no—
118C42×D3—62no—
119#837—62no—
120#837—62no—
121#830—62no—
122#825—62no—
123(C2×D3)⋊C8—62no—
124#805—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—24no—
129C22×C3×D3—21no—
130C22×C3×D3C22⋊C412yes—
131C2×C32×C4—22no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3—22no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3C22⋊C412yes—
148C3×D12—21no—
149C3×D12—21no—
150C3×D12—44no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—22no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×Dic6—21no—
158C3×Dic6—21no—
159D3×Dic3—216no—
160C3⋊(C3⋊C8)—41no—
161C3×C3⋊C8—41no—
162#525—31no—
163C22×C42—91no—
164C2×#104—91no—
165C2×#104—91no—
166#407—91no—
167#339—31no—
168#339—91no—
169C24×C3—31no—
170C23×D3#6711yescharacteristic
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×D4—31no—
177C2×C3×D4—62no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—31no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3—64no—
194C22×Dic3—68no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3#6711yescharacteristic
199#235—21no—
200#235—21no—
201#235—21no—
202#235—21no—
203C2×D12—22no—
204C2×D12C2×Dic311yescharacteristic, complemented
205C2×C4×D3—21no—
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×C4×D3—64no—
211C2×C4×D3—68no—
212C2×C4×D3C2×Dic312yes—
213C2×C4×D3#6712yes—
214C2×Dic6C2×Dic311yescharacteristic, complemented
215C3×M16—61no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4C4×D312yescomplemented
221C3×C4⋊C4C2×Dic312yescomplemented
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—41no—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—32no—
230C3×C42—41no—
231C3×C42—61no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—22no—
234C4⋊Dic3—22no—
235C4×Dic3—21no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—62no—
239C4×Dic3—64no—
240C4×Dic3—64no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—121no—
244C4×Dic3D1212yescomplemented
245#208—21no—
246#208—21no—
247#208—62no—
248#208—61no—
249#208—61no—
250#208—61no—
251#208—61no—
252#208—121no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—121no—
257C22×C32—22no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12311yescharacteristic
261C2×C3×D3—24no—
262C2×C3×D3—24no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—42no—
267C2×C3×D3#10414yescomplemented
268C32×C4—42no—
269C32×C4C4×D411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C3⋊Dic3—24no—
274C3×Dic3—24no—
275C3×Dic3—22no—
276C3×Dic3—41no—
277C2×#41—31no—
278C23×C4—31no—
279C23×C4—181no—
280C2×M16—31no—
281C2×M16—91no—
282#123—61no—
283C22⋊Q8—32no—
284#121—32no—
285#120—61no—
286C4×D4—62no—
287#117D3211yescharacteristic
288C2×C42—31no—
289C2×C42—91no—
290C2×C42—182no—
291C2×C42—182no—
292C2×C42—181no—
293#104—182no—
294#104—182no—
295C22⋊C8—182no—
296C23×C3—21no—
297C23×C3—32no—
298C23×C3—64no—
299C23×C3—61no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—24no—
307C22×D3—21no—
308C22×D3#21712yes—
309C3×Q8—61no—
310C3×Q8—61no—
311C3×D4—61no—
312C3×D4—61no—
313C3×D4—124no—
314C3×D4—121no—
315C3×D4—121no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—64no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23911yescharacteristic
347C2×C3×C4C22×Dic311yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349#67—41no—
350#67—41no—
351C2×Dic3—24no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—616no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—122no—
362C2×Dic3—124no—
363C2×Dic3#21712yes—
364D12—21no—
365D12—21no—
366D12—44no—
367C4×D3—22no—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—22no—
371C4×D3—41no—
372C4×D3—41no—
373C4×D3—616no—
374Dic6—21no—
375Dic6—21no—
376C3×C8—121no—
377C3⋊C8—41no—
378C3⋊C8—122no—
379C3⋊C8—121no—
380C3⋊C8—121no—
381C2×C32—21no—
382C2×C32—21no—
383C2×C32#38611yescharacteristic
384C2×C32C2×#10412yes—
385C3×D3—24no—
386C3×D3—81no—
387C24—31no—
388#41—61no—
389#41—61no—
390#41—61no—
391#41—61no—
392C2×Q8—31no—
393C2×D4—31no—
394C2×D4—62no—
395C2×D4—61no—
396C22×C4—31no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—184no—
406C22×C4—188no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409M16—61no—
410M16—61no—
411M16—181no—
412M16—181no—
413C2×C8—61no—
414C2×C8—181no—
415C4⋊C4—62no—
416C4⋊C4D3×Dic312yescomplemented
417C22⋊C4—21no—
418C22⋊C4—62no—
419C22⋊C4—62no—
420C42—21no—
421C42—32no—
422C42—61no—
423C42—92no—
424C42—184no—
425C42—181no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—34no—
432C22×C3—42no—
433C22×C3—64no—
434C22×C3—64no—
435C22×C3—62no—
436C22×C3—62no—
437C22×C3—121no—
438C22×C3—122no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3#88211yescharacteristic
441C22×C3#89411yescharacteristic
442C22×C3#93511yescharacteristic
443C22×C3#93711yescharacteristic
444C22×C3C2×#21711yescharacteristic
445C2×D3—24no—
446C2×D3—24no—
447C2×D3—22no—
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3#83714yescomplemented
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—64no—
459C3×C4—62no—
460C3×C4—82no—
461C3×C4—121no—
462C3×C4C4×D1211yescharacteristic
463C3×C4#88411yescharacteristic
464C3×C4#89311yescharacteristic
465C3×C4#89511yescharacteristic
466C3×C4D4×Dic311yescharacteristic
467C3×C4D4×Dic311yescharacteristic
468C3×C4#93911yescharacteristic
469C3×C4#93911yescharacteristic
470Dic3—24no—
471Dic3—22no—
472Dic3—41no—
473Dic3—64no—
474Dic3—64no—
475Dic3—124no—
476C32#189611yescharacteristic, complemented, Sylow
477C23—32no—
478C23—64no—
479C23—61no—
480C23—61no—
481C23—61no—
482C23D3×#6711yescharacteristic
483Q8—61no—
484Q8—61no—
485D4—61no—
486D4—61no—
487D4—124no—
488D4—121no—
489D4—121no—
490C2×C4—22no—
491C2×C4—32no—
492C2×C4—64no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—1816no—
504C2×C4—184no—
505C2×C4—182no—
506C2×C4#379511yescharacteristic
507C2×C4#379611yescharacteristic
508C2×C4D3×D1211yescharacteristic
509C2×C4#380211yescharacteristic
510C2×C4C2×D3×Dic311yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C8—121no—
513C8—361no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—64no—
523C2×C3—241no—
524C2×C3#466511yescharacteristic
525C2×C3D3×#10412yes—
526C2×C3#522011yescharacteristic
527C2×C3C2×#83712yes—
528D3—24no—
529D3—81no—
530C22—22no—
531C22—34no—
532C22—64no—
533C22—64no—
534C22—62no—
535C22—62no—
536C22—121no—
537C22—122no—
538C22#6388411yescharacteristic
539C22#6392211yescharacteristic
540C22D3×#21711yescharacteristic
541C4—42no—
542C4—64no—
543C4—62no—
544C4—121no—
545C4—184no—
546C4#6388511yescharacteristic
547C4#6388611yescharacteristic
548C4Dic3×D1211yescharacteristic
549C4#6389811yescharacteristic
550C3—21no—
551C3#6875611yescharacteristic, complemented
552C3#7171111yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—64no—
556C2—241no—
557C2#1059137611yescharacteristic
558C2D3×#83712yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5524C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Dic3C2semidirect
3. C2×#63569C2semidirect
4. C2×#63568C2semidirect
5. #10591069C2semidirect
6. #10589398C2semidirect
7. C3×#4532C2semidirect
18. C3×#897C4semidirect
19. C3×#895C4semidirect
43. #4532D3semidirect
55. C2×C3×D12C2×C4semidirect
63. C2×C3×Dic6C2×C4semidirect
66. C32×C4⋊C4C2×C4semidirect
70. C4×C3⋊Dic3D4semidirect
78. C3×C4×Dic3D4semidirect
112. #897Dic3semidirect
113. #895Dic3semidirect
204. C2×D12C2×Dic3semidirect
214. C2×Dic6C2×Dic3semidirect
220. C3×C4⋊C4C4×D3semidirect
221. C3×C4⋊C4C2×Dic3semidirect
244. C4×Dic3D12semidirect
267. C2×C3×D3#104semidirect
416. C4⋊C4D3×Dic3semidirect
451. C2×D3#837semidirect
476. C32#1896semidirect
551. C3#68756semidirect
552. C3#71711semidirect

Maximal subgroups

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

subgroupindex
C3×#55242
C2×C4×D3×Dic32
C2×#635692
C2×#635682
#105910692
#105893982
C3×#45322
#717113
#687563