Finite Group Databasebeta

← #11906043

Subgroups — #11906043

Order 1152.

3097 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C212yesmaximal, complemented
2C2×#64078C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C3×C4×#235C211yesmaximal, characteristic, complemented
5#10594907C218yesmaximal, complemented
6#10594856C212yesmaximal, complemented
7Dic6×D12C214yesmaximal, complemented
8#10593897C212yesmaximal, complemented
9#10593895C214yesmaximal, complemented
10#10593894C214yesmaximal, complemented
11D3×#869C212yesmaximal, complemented
12#86243—31nomaximal
13#85827—31nomaximal
14C22×#634C2212yes—
15C2×C3×#235C2212yes—
16C2×C3×#235C2211yescharacteristic
17C2×#3805C2218yes—
18#64298—216no—
19C2×#3795C2214yes—
20C2×#3795C2214yes—
21C2×D3×Dic6C2214yes—
22C2×D3×Dic6C2214yes—
23C2×C32×C42C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2214yes—
25#64078C2212yes—
26#64078C2212yes—
27#64078C2214yes—
28C3×#930C2214yes—
29C3×C4×#67C2214yes—
30C3×#926C2211yescharacteristic
31C3×#875C2212yes—
32C3×#874C2211yescharacteristic
33C3×C4×D12C2212yes—
34C3×C4×D12C2214yes—
35C3×#872C2212yes—
36C3×C42×D3C2212yes—
37C3×#869C2211yescharacteristic
38C3×C4×Dic6C2212yes—
39#63962C2218yes—
40#63918C2218yes—
41#63908C2218yes—
42#63893C22116yes—
43Dic3×D12C2218yes—
44#63891C22116yes—
45D3×C4⋊Dic3C2218yes—
46#63866C2214yes—
47#63860C2214yes—
48#63857C2218yes—
49C2×#1010—32no—
50C2×#1010—32no—
51C3×#532—31no—
52C3×C4×#41—31no—
53#5825—32no—
54D3×C4⋊Q8—32no—
55#5716—32no—
56#5675—34no—
57#5611—38no—
58Q8×D12—34no—
59#5555—38no—
60#5555—34no—
61#5551—34no—
62D4×Dic6—34no—
63#5526—32no—
64#5526—34no—
65#5477—32no—
66#5477D311yescharacteristic, complemented
67C4×#235D311yescharacteristic, complemented
68C2×#869—31no—
69C2×#869—31no—
70C2×#869—32no—
71C2×#869—61no—
72C22×C32×C4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3C2314yes—
75C2×#634—28no—
76C2×#634C2314yes—
77C2×#634C2314yes—
78C2×C3×#67C2314yes—
79C2×C3×#67C2312yes—
80C3×#235—28no—
81C3×#235D418yescomplemented
82C2×C3×D12C2312yes—
83C2×C3×D12C2314yes—
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3C2314yes—
86C2×C3×C4×D3C2314yes—
87C2×C3×C4×D3C2312yes—
88C2×C3×Dic6C2312yes—
89C2×C3×Dic6C2311yescharacteristic
90C2×#627C2318yes—
91C2×#625C2318yes—
92#3805—232no—
93C2×D3×Dic3C2318yes—
94C2×D3×Dic3C2318yes—
95#3795—216no—
96#3795—216no—
97D3×Dic6—216no—
98D3×Dic6—216no—
99C32×C42C2312yes—
100C32×C42C2311yescharacteristic
101C32×C42C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2318yes—
103C4⋊(C3⋊Dic3)C2318yes—
104C3×#217C2312yes—
105C3×(C2×D3)⋊C4C2314yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×C4⋊Dic3C2312yes—
108C3×C4⋊Dic3C2314yes—
109C3×Dic3⋊C4C2314yes—
110C3×C4×Dic3C2312yes—
111C3×C4×Dic3C2314yes—
112Dic3⋊Dic3C23116yes—
113(C2×D3)⋊Dic3C23116yes—
114#3499—91noSylow
115C2×C3×#41—31no—
116C2×C3×#41—32no—
117#1010—616no—
118#1010—616no—
119C2×D3×Q8—34no—
120C2×D3×Q8—34no—
121C2×#237—38no—
122C2×#237—38no—
123C2×#237—34no—
124C2×#237—34no—
125C2×#235—34no—
126C2×#235—34no—
127C2×#235C2×D312yes—
128C2×#235C2×D311yescharacteristic
129C22×Dic6—32no—
130C22×Dic6—32no—
131C22×Dic6—34no—
132C22×Dic6—34no—
133C22×Dic6—62no—
134C3×C4⋊Q8—31no—
135C3×#127—31no—
136C3×#124—32no—
137C3×#121—34no—
138C3×C4×Q8—32no—
139C3×C4×D4—34no—
140C3×C4×D4—34no—
141C3×C4×D4—32no—
142C3×#117—31no—
143C3×#117—32no—
144C2×C3×C42—21no—
145C2×C3×C42—32no—
146C2×C3×C42C2×D311yescharacteristic
147C2×C3×C42C2×D311yescharacteristic
148#944—34no—
149#938—38no—
150#936—34no—
151#935—38no—
152D4×Dic3—38no—
153#930—38no—
154#930C2×D314yes—
155C4×#67C2×D314yes—
156#926C2×D311yescharacteristic
157C2×C4⋊Dic3—34no—
158C2×C4⋊Dic3—34no—
159C2×C4⋊Dic3—38no—
160C2×C4⋊Dic3—64no—
161#924—38no—
162#897—38no—
163#897—316no—
164D3×C4⋊C4—38no—
165#888—38no—
166#886—38no—
167#886—316no—
168#883—316no—
169#878—316no—
170#875—34no—
171#875C2×D312yes—
172#874C2×D311yescharacteristic
173C4×D12—38no—
174C4×D12C2×D312yes—
175C4×D12C2×D314yes—
176#872C2×D312yes—
177C42×D3C2×D312yes—
178#869—34no—
179#869—32no—
180#869—32no—
181#869—32no—
182#869—32no—
183#869—34no—
184#869—34no—
185#869—38no—
186#869—62no—
187#869—62no—
188#869—64no—
189#869C2×D311yescharacteristic
190C4×Dic6C2×D312yes—
191C23×C32C2411yescharacteristic
192C22×C3×D3C2414yes—
193C22×C3×D3C2412yes—
194C2×C32×C4—24no—
195C2×C32×C4C2×D414yes—
196C2×C32×C4C2412yes—
197C2×C32×C4C2411yescharacteristic
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2412yes—
200C2×C3⋊Dic3—28no—
201C2×C3⋊Dic3C2418yes—
202#634—28no—
203#634—28no—
204C3×#67—28no—
205C3×#67C2×D418yes—
206C2×C3×Dic3C2414yes—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2412yes—
209C3×D12—24no—
210C3×D12—28no—
211C3×D12C2×D414yes—
212C3×C4×D3—28no—
213C3×C4×D3—28no—
214C3×C4×D3C2×D418yes—
215C3×Dic6—24no—
216C3×Dic6C2×D414yes—
217#627—216no—
218#625—216no—
219D3×Dic3—216no—
220D3×Dic3—216no—
221C2×2−1+4—92no—
222D4×Q8—94no—
223#547—94no—
224#547—98no—
225#536—94no—
226#536—92no—
227#532—31no—
228#532—92no—
229C2×C4⋊Q8—92no—
230C2×C4⋊Q8—91no—
231C4×#41—31no—
232C3×#41—38no—
233C3×#41—68no—
234C2×C3×Q8—31no—
235C2×C3×Q8—32no—
236C2×C3×D4—32no—
237C2×C3×D4—34no—
238C2×C3×D4—31no—
239C2×C3×D4—34no—
240C2×C3×D4—32no—
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—32no—
244C22×C3×C4—34no—
245C22×C3×C4—34no—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—38no—
251C2×#67—38no—
252C2×#67C22×D314yes—
253C2×#67C22×D312yes—
254C22×Dic3—34no—
255C22×Dic3—34no—
256C22×Dic3—38no—
257C22×Dic3—38no—
258C22×Dic3—64no—
259D3×Q8—616no—
260D3×Q8—616no—
261#237—616no—
262#237—632no—
263#237—632no—
264#237—616no—
265#235—28no—
266#235—616no—
267#235—616no—
268#235D1218yescomplemented
269C2×D12C22×D314yes—
270C2×D12C22×D312yes—
271C2×D12C22×D311yescharacteristic
272C2×C4×D3—38no—
273C2×C4×D3—38no—
274C2×C4×D3C22×D314yes—
275C2×C4×D3C22×D314yes—
276C2×C4×D3C22×D312yes—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—34no—
280C2×Dic6—34no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—64no—
284C2×Dic6—64no—
285C2×Dic6—616no—
286C2×Dic6—68no—
287C2×Dic6—68no—
288C2×Dic6—616no—
289C2×Dic6—128no—
290C2×Dic6C22×D312yes—
291C2×Dic6C22×D311yescharacteristic
292C3×C4⋊C4—34no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4—32no—
295C3×C22⋊C4—32no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—34no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—22no—
301C3×C42—34no—
302C3×C42—32no—
303C3×C42C22×D312yes—
304C3×C42C22×D311yescharacteristic
305C3×C42C22×D311yescharacteristic
306C3×C42C22×D311yescharacteristic
307C3×C42C22×D312yes—
308C3×C42C22×D311yescharacteristic
309#217—316no—
310#217C22×D312yes—
311(C2×D3)⋊C4—316no—
312(C2×D3)⋊C4C22×D314yes—
313(C2×D3)⋊C4C22×D318yes—
314C4⋊Dic3—38no—
315C4⋊Dic3—38no—
316C4⋊Dic3—38no—
317C4⋊Dic3—38no—
318C4⋊Dic3—316no—
319C4⋊Dic3—68no—
320C4⋊Dic3—68no—
321C4⋊Dic3C22×D312yes—
322C4⋊Dic3C22×D314yes—
323Dic3⋊C4—316no—
324Dic3⋊C4C22×D314yes—
325C4×Dic3C22×D314yes—
326C4×Dic3C22×D312yes—
327C22×C32—22no—
328C22×C32C22×D412yes—
329C22×C32C2511yescharacteristic
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—28no—
333C2×C3×D3C22×D414yes—
334C32×C4—22no—
335C32×C4C22×D412yes—
336C32×C4C22×D412yes—
337C32×C42−1+414yescomplemented
338C3⋊Dic3—28no—
339C3×Dic3—24no—
340C3×Dic3—24no—
341C3×Dic3C22×D414yes—
3422−1+4—1816no—
343C2×#41—31no—
344C2×#41—32no—
345C2×#41—94no—
346C2×#41—94no—
347C2×#41—98no—
348C22×Q8—94no—
349C22×Q8—94no—
350C22×Q8—92no—
351C4⋊Q8—31no—
352C4⋊Q8—98no—
353C4⋊Q8—94no—
354C4⋊Q8—92no—
355C4⋊Q8—92no—
356C4⋊Q8—94no—
357#127—31no—
358#124—32no—
359#124—94no—
360#123—916no—
361#123—98no—
362C22⋊Q8—916no—
363C22⋊Q8—98no—
364#121—34no—
365#121—98no—
366C4×Q8—32no—
367C4×D4—34no—
368C4×D4—32no—
369C4×D4—34no—
370C4×D4—98no—
371#117—31no—
372#117—32no—
373C2×C4⋊C4—98no—
374C2×C4⋊C4—94no—
375C2×C42—32no—
376C2×C42D3211yescharacteristic
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—34no—
380C23×C3C23×D311yescharacteristic
381C23×C3C23×D311yescharacteristic
382C22×D3C23×D314yes—
383C22×D3C23×D312yes—
384C3×Q8—34no—
385C3×Q8—64no—
386C3×D4—38no—
387C3×D4—34no—
388C3×D4—68no—
389C3×D4—64no—
390C3×D4—68no—
391C2×C3×C4—28no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—24no—
399C2×C3×C4—32no—
400C2×C3×C4—38no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—68no—
404C2×C3×C4—68no—
405C2×C3×C4C2×D1214yes—
406C2×C3×C4D3×D414yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415#67—28no—
416#67—616no—
417#67—616no—
418#67C2×D1218yes—
419C2×Dic3—38no—
420C2×Dic3—38no—
421C2×Dic3—68no—
422C2×Dic3—616no—
423C2×Dic3—68no—
424C2×Dic3—68no—
425C2×Dic3—616no—
426C2×Dic3—128no—
427C2×Dic3C23×D314yes—
428C2×Dic3C23×D314yes—
429C2×Dic3C23×D312yes—
430D12—24no—
431D12—28no—
432D12C2×D1214yes—
433C4×D3—28no—
434C4×D3—28no—
435C4×D3—616no—
436C4×D3—616no—
437C4×D3C2×D1218yes—
438Dic6—24no—
439Dic6—616no—
440Dic6—68no—
441Dic6—68no—
442Dic6—68no—
443Dic6—68no—
444Dic6—616no—
445Dic6—128no—
446Dic6—128no—
447Dic6C2×D1214yes—
448C2×C32—22no—
449C2×C32C23×D411yescharacteristic
450C2×C32C2×2−1+412yes—
451C3×D3—24no—
452C3×D3—44no—
453#41—38no—
454#41—68no—
455#41—1816no—
456#41—1816no—
457#41—1832no—
458C2×Q8—31no—
459C2×Q8—32no—
460C2×Q8—98no—
461C2×Q8—94no—
462C2×Q8—94no—
463C2×Q8—1816no—
464C2×Q8—1816no—
465C2×Q8—188no—
466C2×D4—32no—
467C2×D4—34no—
468C2×D4—31no—
469C2×D4—34no—
470C2×D4—32no—
471C2×D4—98no—
472C22×C4—32no—
473C22×C4—34no—
474C22×C4—34no—
475C22×C4—98no—
476C22×C4—98no—
477C22×C4—94no—
478C22×C4C2×D3212yes—
479C22×C4C2×D3211yescharacteristic
480C4⋊C4—34no—
481C4⋊C4—34no—
482C4⋊C4—32no—
483C4⋊C4—916no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C22⋊C4—32no—
487C22⋊C4—34no—
488C22⋊C4—38no—
489C22⋊C4—916no—
490C42—32no—
491C42—34no—
492C42C2×D3211yescharacteristic
493C42C2×D3211yescharacteristic
494C42C2×D3212yes—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—21no—
500C22×C3—34no—
501C22×C3—64no—
502C22×C3—64no—
503C22×C3—68no—
504C22×C3C22×D1212yes—
505C22×C3C2×D3×D412yes—
506C22×C3C24×D311yescharacteristic
507C22×C3C24×D311yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—28no—
511C2×D3C22×D1214yes—
512C3×C4—24no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—24no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—34no—
519C3×C4—64no—
520C3×C4—64no—
521C3×C4C22×D1212yes—
522C3×C4C22×D1212yes—
523C3×C4C2×D3×D412yes—
524C3×C4C2×D3×D412yes—
525C3×C4#101014yescomplemented
526C3×C4#101014yescomplemented
527Dic3—24no—
528Dic3—24no—
529Dic3—68no—
530Dic3—68no—
531Dic3—128no—
532Dic3C22×D1214yes—
533C32#349911yescharacteristic, complemented, Sylow
534C23—32no—
535C23—34no—
536C23C22×D3211yescharacteristic
537Q8—34no—
538Q8—64no—
539Q8—1816no—
540Q8—188no—
541Q8—188no—
542D4—38no—
543D4—34no—
544D4—68no—
545D4—68no—
546D4—64no—
547D4—1816no—
548C2×C4—24no—
549C2×C4—32no—
550C2×C4—38no—
551C2×C4—34no—
552C2×C4—34no—
553C2×C4—68no—
554C2×C4—68no—
555C2×C4—98no—
556C2×C4—1816no—
557C2×C4—1816no—
558C2×C4—188no—
559C2×C4D3×D1214yes—
560C2×C4C22×D3212yes—
561C2×C4C22×D3212yes—
562C2×C4C22×D3211yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C2×C3—24no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—64no—
570C2×C3—124no—
571C2×C3C23×D1211yescharacteristic
572C2×C3C22×D3×D411yescharacteristic
573C2×C3C2×#101012yes—
574C2×C3C2×#101012yes—
575D3—24no—
576D3—44no—
577C22—22no—
578C22—34no—
579C22—64no—
580C22—68no—
581C22—64no—
582C22C2×D3×D1212yes—
583C22C23×D3211yescharacteristic
584C4—22no—
585C4—34no—
586C4—64no—
587C4—64no—
588C4—188no—
589C4#6429814yescomplemented
590C4C2×D3×D1212yes—
591C4C2×D3×D1212yes—
592C3—21no—
593C3#8582711yescharacteristic, complemented
594C3#8624311yescharacteristic, complemented
595C2—22no—
596C2—64no—
597C2—124no—
598C2C2×#6429812yes—
599C2C22×D3×D1211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. C2×#64078C2semidirect
3. C3×#5477C2semidirect
4. C3×C4×#235C2semidirect
5. #10594907C2semidirect
6. #10594856C2semidirect
7. Dic6×D12C2semidirect
8. #10593897C2semidirect
9. #10593895C2semidirect
10. #10593894C2semidirect
11. D3×#869C2semidirect
66. #5477D3semidirect
67. C4×#235D3semidirect
81. C3×#235D4semidirect
268. #235D12semidirect
337. C32×C42−1+4semidirect
525. C3×C4#1010semidirect
526. C3×C4#1010semidirect
533. C32#3499semidirect
589. C4#64298semidirect
593. C3#85827semidirect
594. C3#86243semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C2×#640782
C3×#54772
C3×C4×#2352
#105949072
#105948562
Dic6×D122
#105938972
#105938952
#105938942
D3×#8692
#862433
#858273