Finite Group Databasebeta

← #11864667

Subgroups — #11864667

Order 1152.

2136 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×2−1+4C211yesmaximal, characteristic, complemented
2#10596304C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×#64151C211yesmaximal, characteristic, complemented
5#10592938C212yesmaximal, complemented
6#10592937C212yesmaximal, complemented
7#10592933C211yesmaximal, characteristic, complemented
8#10592931C211yesmaximal, characteristic, complemented
9#10592927C212yesmaximal, complemented
10#10592926C212yesmaximal, complemented
11C2×#63662C211yesmaximal, characteristic, complemented
12#84114—34nomaximal
13C32×2−1+4—24no—
14C32×2−1+4—24no—
15C2×C32×#41—21no—
16C2×C32×#41—22no—
17C2×C32×#41C2212yes—
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C22×C32×Q8—21no—
21C22×C32×Q8C2212yes—
22C22×C32×Q8C2211yescharacteristic
23C2×#3828C2211yescharacteristic
24#64159—24no—
25#64155—21no—
26C2×#3756C2211yescharacteristic
27C2×#3756C2212yes—
28#64151—24no—
29C2×#3755C2211yescharacteristic
30C2×#3755C2212yes—
31#64148—22no—
32#64147—21no—
33C2×#3754C2211yescharacteristic
34C2×#3753C2211yescharacteristic
35#64139C2212yes—
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
37#64133C2212yes—
38C2×#3748C2211yescharacteristic
39C22×C3⋊(C3⋊C8)C2211yescharacteristic
40#63662C2212yes—
41#63662C2212yes—
42#63662C2212yes—
43#63659C2212yes—
44#63657C2212yes—
45#63657C2212yes—
46C2×C3×2−1+4D314yescomplemented
47#5833—34no—
48C2×#950—34no—
49C2×#942—34no—
50#5239—38no—
51#5238—38no—
52#5234—34no—
53#5232—34no—
54#5228—38no—
55#5227—38no—
56C2×#835—34no—
57C32×#41—216no—
58C32×#41—28no—
59C32×#41—24no—
60C32×#41—24no—
61C32×#41—22no—
62C32×#41—22no—
63C32×#41—22no—
64C32×#41D414yescomplemented
65C2×C32×Q8—28no—
66C2×C32×Q8—24no—
67C2×C32×Q8—24no—
68C2×C32×Q8—22no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8D411yescharacteristic
72C2×C32×Q8D414yescomplemented
73C2×C32×Q8C2311yescharacteristic
74C2×C32×Q8C2312yes—
75C2×C32×D4—22no—
76C2×C32×D4—21no—
77C2×C32×D4D411yescharacteristic
78C2×C32×D4D412yes—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—22no—
81C22×C32×C4—21no—
82C22×C32×C4—22no—
83C22×C32×C4—21no—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C2×#638—21no—
87C2×#638—22no—
88C22×C3⋊Dic3—21no—
89#3828—22no—
90#3828—22no—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4×C3⋊D3—21no—
93C2×#634C2311yescharacteristic
94#3757—22no—
95#3756—24no—
96#3756—22no—
97#3755—24no—
98#3755—22no—
99#3754—22no—
100#3753—22no—
101#3752—22no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)C2312yes—
104#3750—22no—
105#3748—22no—
106C2×C3⋊(C3⋊C8)—22no—
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2312yes—
110#3013—91noSylow
111C3×2−1+4—216no—
112C3×2−1+4—216no—
113C2×C3×#41—24no—
114C2×C3×#41—28no—
115C2×C3×#41C2×D318yes—
116C2×C3×#41C2×D314yes—
117C2×C3×#41C2×D314yes—
118C22×C3×Q8—24no—
119C22×C3×Q8C2×D318yes—
120C22×C3×Q8C2×D314yes—
121C2×#235—34no—
122#950—616no—
123#946—64no—
124C2×#216—34no—
125C2×#216—38no—
126#942—616no—
127C2×#215—34no—
128C2×#215—38no—
129#939—68no—
130#938—64no—
131C2×#214—34no—
132C2×#213—34no—
133#930—38no—
134C2×C4⋊Dic3—34no—
135#924—38no—
136C2×#208—34no—
137C22×C3⋊C8—34no—
138#835—38no—
139#835—38no—
140#835—38no—
141#832—38no—
142#830—38no—
143#830—38no—
144C23×C32—21no—
145C23×C32C2×D412yes—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—21no—
148C32×Q8—28no—
149C32×Q8—22no—
150C32×Q8—24no—
151C32×Q8—21no—
152C32×Q8—22no—
153C32×Q8C2×D412yes—
154C32×Q8C2×D414yes—
155C32×D4—28no—
156C32×D4—24no—
157C32×D4—24no—
158C32×D4—22no—
159C32×D4—21no—
160C32×D4C2×D412yes—
161C2×C32×C4—28no—
162C2×C32×C4—28no—
163C2×C32×C4—24no—
164C2×C32×C4—22no—
165C2×C32×C4—21no—
166C2×C32×C4—24no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2411yescharacteristic
174#638—42no—
175#638—82no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—81no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—21no—
181C4×C3⋊D3—42no—
182#634—21no—
183#634—21no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—22no—
187C2×2−1+4C3⋊D311yescharacteristic, complemented
188C2×#137—91no—
189C2×#135—91no—
190#537—91no—
191#452—92no—
192#451—92no—
193#449—92no—
194#448—92no—
195#417—91no—
196C2×#103—91no—
197#408—91no—
198C3×#41—264no—
199C3×#41—232no—
200C3×#41—216no—
201C3×#41—216no—
202C3×#41—28no—
203C3×#41—28no—
204C3×#41—28no—
205C3×#41#67116yescomplemented
206C2×C3×Q8—232no—
207C2×C3×Q8—216no—
208C2×C3×Q8—216no—
209C2×C3×Q8—28no—
210C2×C3×Q8—24no—
211C2×C3×Q8—28no—
212C2×C3×Q8#6714yes—
213C2×C3×Q8#67116yescomplemented
214C2×C3×Q8C22×D314yes—
215C2×C3×Q8C22×D318yes—
216C2×C3×D4—28no—
217C2×C3×D4—24no—
218C2×C3×D4#6714yes—
219C2×C3×D4#6718yes—
220C2×C3×D4C22×D314yes—
221C22×C3×C4—28no—
222C22×C3×C4—24no—
223C22×C3×C4—28no—
224C22×C3×C4—24no—
225C22×C3×C4C22×D318yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228C2×#67—68no—
229C22×Dic3—64no—
230#235—68no—
231#235—68no—
232C2×D12—34no—
233C2×C4×D3—64no—
234C2×Dic6—34no—
235#217—68no—
236#216—616no—
237#216—68no—
238#215—616no—
239#215—68no—
240#214—68no—
241#213—68no—
242(C2×D3)⋊C4—68no—
243C4⋊Dic3—38no—
244C4⋊Dic3—64no—
245Dic3⋊C4—68no—
246#208—68no—
247C2×C3⋊C8—38no—
248C2×C3⋊C8—34no—
249C2×C3⋊C8—34no—
250C2×C3⋊C8—68no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32—22no—
256C22×C32—22no—
257C22×C32—41no—
258C22×C32—41no—
259C22×C32#12012yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C32×C4—24no—
265C32×C4—22no—
266C32×C4—22no—
267C32×C4#12012yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C22×D411yescharacteristic
270C3⋊Dic3—41no—
271C3⋊Dic3—42no—
2722−1+4—24no—
2732−1+4—24no—
274C2×#41—21no—
275C2×#41—22no—
276C2×#41—91no—
277C2×#41C2×C3⋊D312yes—
278C2×#41C2×C3⋊D311yescharacteristic
279C2×#41C2×C3⋊D311yescharacteristic
280C22×Q8—21no—
281C22×Q8C2×C3⋊D312yes—
282C22×Q8C2×C3⋊D311yescharacteristic
283#137—184no—
284#135—184no—
285C2×Q16—91no—
286C2×Q16—92no—
287C2×SD16—91no—
288C2×SD16—92no—
289C2×SD16—91no—
290C2×D8—91no—
291C2×M16—91no—
292C22×C8—91no—
293C22⋊Q8—92no—
294C22⋊Q8—181no—
295#121—92no—
296#121—181no—
297#121—182no—
298C2×C4⋊C4—91no—
299#103—92no—
300#103—92no—
301#103—92no—
302#102—92no—
303C22⋊C8—92no—
304C22⋊C8—92no—
305C23×C3—24no—
306C23×C3C2×#6718yes—
307C23×C3C2×#6714yes—
308C22×D3—64no—
309C3×Q8—232no—
310C3×Q8—28no—
311C3×Q8—216no—
312C3×Q8—24no—
313C3×Q8—28no—
314C3×Q8C2×#6718yes—
315C3×Q8C2×#67116yes—
316C3×D4—232no—
317C3×D4—216no—
318C3×D4—216no—
319C3×D4—28no—
320C3×D4—24no—
321C3×D4C2×#6718yes—
322C2×C3×C4—232no—
323C2×C3×C4—232no—
324C2×C3×C4—216no—
325C2×C3×C4—28no—
326C2×C3×C4—24no—
327C2×C3×C4—216no—
328C2×C3×C4—28no—
329C2×C3×C4—28no—
330C2×C3×C4C2×#6718yes—
331C2×C3×C4C2×#6714yes—
332C2×C3×C4C2×#6718yes—
333C2×C3×C4C2×#6718yes—
334C2×C3×C4C23×D314yes—
335#67—128no—
336#67—248no—
337C2×Dic3—64no—
338C2×Dic3—68no—
339C2×Dic3—244no—
340D12—64no—
341D12—64no—
342C4×D3—128no—
343Dic6—64no—
344Dic6—64no—
345C3⋊C8—64no—
346C3⋊C8—64no—
347C3⋊C8—68no—
348C2×C32—22no—
349C2×C32—42no—
350C2×C32—42no—
351C2×C32C2×#12011yescharacteristic
352C2×C32#57711yescharacteristic
353C2×C32#57811yescharacteristic
354C3⋊D3—81no—
355#41—216no—
356#41—28no—
357#41—24no—
358#41—24no—
359#41—22no—
360#41—22no—
361#41—22no—
362#41—182no—
363#41—182no—
364#41#63814yescomplemented
365C2×Q8—28no—
366C2×Q8—24no—
367C2×Q8—24no—
368C2×Q8—22no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—91no—
372C2×Q8#63811yescharacteristic
373C2×Q8#63814yescomplemented
374C2×Q8C22×C3⋊D311yescharacteristic
375C2×Q8C22×C3⋊D312yes—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—91no—
379C2×D4—181no—
380C2×D4—182no—
381C2×D4#63812yes—
382C2×D4#63811yescharacteristic
383C2×D4C22×C3⋊D311yescharacteristic
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4C22×C3⋊D312yes—
391C22×C4C22×C3⋊D311yescharacteristic
392Q16—182no—
393Q16—184no—
394SD16—182no—
395SD16—184no—
396SD16—182no—
397D8—182no—
398M16—182no—
399C2×C8—92no—
400C2×C8—91no—
401C2×C8—91no—
402C2×C8—182no—
403C4⋊C4—92no—
404C4⋊C4—181no—
405C4⋊C4—182no—
406C22⋊C4—182no—
407C22⋊C4—182no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—28no—
411C22×C3—28no—
412C22×C3—28no—
413C22×C3—28no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3#95318yes—
417C22×C3C22×#6714yes—
418C2×D3—124no—
419C2×D3—124no—
420C2×D3—124no—
421C3×C4—216no—
422C3×C4—28no—
423C3×C4—28no—
424C3×C4#95318yes—
425C3×C4C22×#6714yes—
426C3×C4C22×#6714yes—
427Dic3—128no—
428Dic3—124no—
429C32#301311yescharacteristic, complemented, Sylow
430C23—21no—
431C23—181no—
432C23C2×#63812yes—
433C23C2×#63811yescharacteristic
434Q8—28no—
435Q8—21no—
436Q8—22no—
437Q8—22no—
438Q8—24no—
439Q8—181no—
440Q8—181no—
441Q8C2×#63812yes—
442Q8C2×#63814yes—
443D4—28no—
444D4—24no—
445D4—24no—
446D4—21no—
447D4—22no—
448D4—181no—
449D4—181no—
450D4—362no—
451D4—722no—
452D4C2×#63812yes—
453C2×C4—28no—
454C2×C4—28no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—182no—
462C2×C4—181no—
463C2×C4—362no—
464C2×C4—721no—
465C2×C4C2×#63812yes—
466C2×C4C2×#63812yes—
467C2×C4C2×#63812yes—
468C2×C4C2×#63811yescharacteristic
469C2×C4C23×C3⋊D311yescharacteristic
470C8—181no—
471C8—181no—
472C8—182no—
473C2×C3—28no—
474C2×C3—48no—
475C2×C3—48no—
476C2×C3#583714yes—
477C2×C3#583814yes—
478C2×C3C2×#95314yes—
479D3—244no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—41no—
487C22—41no—
488C22—361no—
489C22—361no—
490C22—361no—
491C22#6416212yes—
492C22C22×#63811yescharacteristic
493C4—24no—
494C4—22no—
495C4—22no—
496C4—362no—
497C4—361no—
498C4#6416212yes—
499C4C22×#63811yescharacteristic
500C4C22×#63811yescharacteristic
501C3#8411414yescomplemented
502C2—22no—
503C2—42no—
504C2—42no—
505C2—721no—
506C2#1059630811yescharacteristic
507C2#1059630911yescharacteristic
508C2C2×#6416211yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×2−1+4C2
socleC22×C32C22×D4
hypercenterC2×2−1+4C3⋊D3
hypocenterC32#3013
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C32×2−1+4C2semidirect
2. #10596304C2semidirect
3. C2×#64159C2semidirect
4. C2×#64151C2semidirect
5. #10592938C2semidirect
6. #10592937C2semidirect
7. #10592933C2semidirect
8. #10592931C2semidirect
9. #10592927C2semidirect
10. #10592926C2semidirect
11. C2×#63662C2semidirect
46. C2×C3×2−1+4D3semidirect
64. C32×#41D4semidirect
72. C2×C32×Q8D4semidirect
187. C2×2−1+4C3⋊D3semidirect
205. C3×#41#67semidirect
213. C2×C3×Q8#67semidirect
364. #41#638semidirect
373. C2×Q8#638semidirect
429. C32#3013semidirect
501. C3#84114semidirect

Maximal subgroups

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

subgroupindex
C2×C32×2−1+42
#105963042
C2×#641592
C2×#641512
#105929382
#105929372
#105929332
#105929312
#105929272
#105929262
C2×#636622
#841143