Finite Group Databasebeta

← #11886544

Subgroups — #11886544

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2#10595236C212yesmaximal, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4#10592850C211yesmaximal, characteristic, complemented
5C3×#5157C211yesmaximal, characteristic, complemented
6#10591521C212yesmaximal, complemented
7#10591452C212yesmaximal, complemented
8#10591444C212yesmaximal, complemented
9#10590832C211yesmaximal, characteristic, complemented
10#10590818C211yesmaximal, characteristic, complemented
11C8×#625C211yesmaximal, characteristic, complemented
12#83924—31nomaximal
13#80735—31nomaximal
14C2×C3×#237C2212yes—
15C2×#3799C2212yes—
16C2×C32×D8C2211yescharacteristic
17#64149C2212yes—
18C2×#3753C2212yes—
19C2×#3745C2211yescharacteristic
20C3×#938C2212yes—
21C2×C3×#214C2212yes—
22C3×#912—24no—
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#63979—22no—
27#63978—22no—
28#63958—22no—
29#63952—22no—
30#63909C2212yes—
31C4×#625C2211yescharacteristic
32#63843C2212yes—
33C2×#3717C2212yes—
34#63808—24no—
35C8×C3⋊Dic3C2211yescharacteristic
36C3×#832C2212yes—
37C3×#818C2211yescharacteristic
38#63572C2211yescharacteristic
39#63565C2212yes—
40#63564C2212yes—
41(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
43C2×C3×#135—31no—
44#5834—32no—
45C2×#919—31no—
46C2×#912D311yescharacteristic, complemented
47C2×#904—31no—
48#5599—32no—
49C3×#466—31no—
50#5238—32no—
51Dic3×Q16—31no—
52#5172—32no—
53#5163—32no—
54#5157D311yescharacteristic, complemented
55#5151—31no—
56#5151—31no—
57#5151—61no—
58#5115—31no—
59C8×#67—31no—
60C8×#67—31no—
61#5037—32no—
62#4883—31no—
63#4873—31no—
64#4781—32no—
65#4762—32no—
66C2×C32×D4C2312yes—
67C2×#638—22no—
68C2×#638—22no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—24no—
74C3×#237—42no—
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×#626—22no—
79C2×#626—22no—
80C2×#625D411yescharacteristic
81C2×#624—22no—
82#3799—24no—
83#3799—42no—
84C32×D8—22no—
85C2×C32×C8C2311yescharacteristic
86#3753—42no—
87C4×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89#3745—22no—
90C3×#217—22no—
91C3×#214—24no—
92C3×C4⋊Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12D414yescomplemented
96C3×D3×C8—22no—
97C3×D3×C8—22no—
98#3724D411yescharacteristic
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3D411yescharacteristic
102(C2×D3)⋊Dic3D411yescharacteristic
103Dic32—22no—
104#3717—24no—
105#3287—91noSylow
106C2×C3×#41—32no—
107C2×#239—32no—
108C2×#237C2×D312yes—
109C2×#235—32no—
110C3×#135—64no—
111C2×C3×Q16—31no—
112C2×C3×SD16—32no—
113C2×C3×D8—21no—
114C2×C3×D8C2×D311yescharacteristic
115C2×C3×D8C2×D311yescharacteristic
116C22×C3×C8—31no—
117C22×C3×C8—31no—
118C3×#121—32no—
119Q8×Dic3—32no—
120C2×#215—32no—
121#940—32no—
122#940—32no—
123#940—62no—
124#940—62no—
125#940—62no—
126#939—62no—
127#938—62no—
128#938C2×D312yes—
129C2×#214C2×D312yes—
130C2×#213—32no—
131C2×#213—32no—
132C2×#213—62no—
133#930—32no—
134#930—62no—
135C4×#67—31no—
136C4×#67—31no—
137C4×#67—62no—
138#919—64no—
139#912—24no—
140C2×Dic12C2×D311yescharacteristic
141#904—64no—
142C2×D24—31no—
143C2×D24—31no—
144C2×D24—61no—
145C2×#204—32no—
146C2×D3×C8C2×D311yescharacteristic
147C2×D3×C8C2×D311yescharacteristic
148#895—32no—
149#887—32no—
150#884—62no—
151#67⋊C4—62no—
152C3×#107—31no—
153C3×#102—32no—
154#835—32no—
155#832C2×D312yes—
156#830—31no—
157#830—31no—
158#821—32no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161#818C2×D311yescharacteristic
162Dic3⋊C8—31no—
163Dic3⋊C8—31no—
164C8×Dic3—31no—
165C8×Dic3—31no—
166C8×Dic3—61no—
167#810—32no—
168#809—32no—
169C23×C32—22no—
170C22×C3⋊D3—22no—
171C22×C3×D3C2×D411yescharacteristic
172C22×C3×D3C2×D411yescharacteristic
173C32×D4—22no—
174C32×D4—22no—
175C2×C32×C4C2411yescharacteristic
176#638—44no—
177#638—82no—
178C2×C3⋊Dic3C2×D411yescharacteristic
179C2×C3⋊Dic3C2×D411yescharacteristic
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—22no—
182C3×#67—44no—
183C3×#67—82no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—44no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×C4×D3—21no—
190C3×C4×D3—21no—
191C3×C4×D3—21no—
192C3×C4×D3—21no—
193C3×Dic6—22no—
194C3×Dic6C2×D414yes—
195#626—44no—
196#626—82no—
197#625—22no—
198#624—44no—
199C32×C8C2×D412yes—
200C3⋊(C3⋊C8)—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C2×#135—31no—
204C2×#135—91no—
205#550—92no—
206#493—91no—
207#466—31no—
208#466—91no—
209#460—92no—
210#449—92no—
211#449—92no—
212C4×Q16—91no—
213C8×D4—91no—
214C3×#41—64no—
215C3×#41—122no—
216C2×C3×Q8—32no—
217C2×C3×D4—22no—
218C2×C3×D4—62no—
219C2×C3×D4—62no—
220C2×C3×D4C22×D312yes—
221C2×C3×D4C22×D312yes—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—62no—
225C2×#67—22no—
226C2×#67—22no—
227C2×#67—31no—
228C2×#67—31no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—122no—
236C2×#67—122no—
237C22×Dic3—22no—
238#239—64no—
239#239—122no—
240#237—24no—
241#237—42no—
242#235—64no—
243#235—122no—
244C2×D12—32no—
245C2×D12—32no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3C22×D311yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×Dic6C22×D312yes—
254C3×Q16—34no—
255C3×SD16—64no—
256C3×D8—22no—
257C3×D8—22no—
258C3×D8—42no—
259C2×C3×C8—21no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—62no—
263C2×C3×C8—62no—
264C2×C3×C8C22×D311yescharacteristic
265C2×C3×C8C22×D311yescharacteristic
266C3×C4⋊C4—32no—
267C3×C22⋊C4—62no—
268#217—22no—
269#217—31no—
270#217—31no—
271#215—64no—
272#214—24no—
273#213—122no—
274#213—122no—
275#213—124no—
276(C2×D3)⋊C4—31no—
277(C2×D3)⋊C4—31no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3C22×D312yes—
282Dic3⋊C4—31no—
283Dic3⋊C4—31no—
284Dic3⋊C4—62no—
285C4×Dic3—31no—
286C4×Dic3—31no—
287C4×Dic3—61no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295Dic12#6714yescomplemented
296D24—62no—
297D24—62no—
298D24—122no—
299#204—64no—
300D3×C8—22no—
301D3×C8—22no—
302C22×C32—42no—
303C22×C32—42no—
304C22×C32—42no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—21no—
314C2×C3×D3—21no—
315C32×C4C22×D411yescharacteristic
316C32×C4H(5,𝔽2)11yescharacteristic
317C3⋊Dic3—21no—
318C3⋊Dic3#13512yescomplemented
319C3×Dic3—21no—
320C3×Dic3—24no—
321C3×Dic3—21no—
322C3×Dic3—42no—
323C2×#41—32no—
324C2×#41—92no—
325#135—64no—
326#135—184no—
327C2×Q16—31no—
328C2×SD16—32no—
329C2×SD16—92no—
330C2×D8—92no—
331C2×D8—91no—
332C2×D8D3211yescharacteristic
333C22×C8—31no—
334C22×C8—31no—
335#127—92no—
336#127—182no—
337#121—32no—
338#121—92no—
339#121—182no—
340#121—182no—
341C4×Q8—92no—
342C4×D4—91no—
343C4×D4—182no—
344#107—31no—
345C4⋊C8—91no—
346#103—92no—
347#102—32no—
348#102—92no—
349C22⋊C8—91no—
350C22⋊C8—91no—
351C4×C8—91no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—31no—
355C23×C3—31no—
356C23×C3—42no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—122no—
360C22×D3D3×D411yescharacteristic
361C22×D3D3×D411yescharacteristic
362C3×Q8—34no—
363C3×Q8—62no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—22no—
367C3×D4—22no—
368C3×D4—42no—
369C3×D4—42no—
370C3×D4—124no—
371C3×D4—242no—
372C2×C3×C4—21no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—124no—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—44no—
385#67—62no—
386#67—62no—
387#67—82no—
388#67—124no—
389#67—124no—
390#67—124no—
391#67—244no—
392#67—242no—
393#67—242no—
394#67—242no—
395#67—244no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—44no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3D3×D411yescharacteristic
406C2×Dic3D3×D411yescharacteristic
407D12—62no—
408D12—62no—
409D12—62no—
410D12—62no—
411D12—122no—
412D12—122no—
413D12—124no—
414D12—242no—
415C4×D3—21no—
416C4×D3—21no—
417C4×D3—21no—
418C4×D3—21no—
419C4×D3—124no—
420C4×D3—124no—
421Dic6—22no—
422Dic6C2×#6714yes—
423C3×C8—22no—
424C3×C8—61no—
425C3×C8—61no—
426C3×C8D3×D412yes—
427C3×C8C2×#6712yes—
428C3⋊C8—21no—
429C3⋊C8—21no—
430C3⋊C8—62no—
431C3⋊C8—61no—
432C3⋊C8—61no—
433C2×C32—82no—
434C2×C32D4211yescharacteristic
435C2×C32C2×#13511yescharacteristic
436C2×C32#57611yescharacteristic
437C3⋊D3—82no—
438C3×D3—41no—
439C3×D3—41no—
440#41—64no—
441#41—122no—
442#41—184no—
443#41—362no—
444C2×Q8—32no—
445C2×D4—62no—
446C2×D4—62no—
447C2×D4—91no—
448C2×D4—92no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—182no—
453C2×D4C2×D3212yes—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—62no—
457C22×C4—182no—
458Q16—34no—
459SD16—64no—
460SD16—184no—
461D8—22no—
462D8—182no—
463D8—362no—
464C2×C8—31no—
465C2×C8—31no—
466C2×C8—62no—
467C2×C8—62no—
468C2×C8—91no—
469C2×C8C2×D3211yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—91no—
472C4⋊C4—182no—
473C22⋊C4—62no—
474C22⋊C4—91no—
475C22⋊C4—91no—
476C22⋊C4—182no—
477C42—91no—
478C42—182no—
479C22×C3—21no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—61no—
487C22×C3—61no—
488C22×C3—61no—
489C22×C3—61no—
490C22×C3—61no—
491C22×C3—61no—
492C22×C3—82no—
493C22×C3—82no—
494C22×C3—82no—
495C22×C3C2×D3×D411yescharacteristic
496C22×C3C2×D3×D411yescharacteristic
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—21no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—242no—
510C2×D3—242no—
511C2×D3—242no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—61no—
515C3×C4—64no—
516C3×C4—61no—
517C3×C4—122no—
518C3×C4C2×D3×D411yescharacteristic
519C3×C4#100411yescharacteristic
520C3×C4#100911yescharacteristic
521C3×C4C22×#6711yescharacteristic
522Dic3—24no—
523Dic3—21no—
524Dic3—21no—
525Dic3—32no—
526Dic3—32no—
527Dic3—42no—
528Dic3—62no—
529Dic3—62no—
530Dic3—61no—
531Dic3—61no—
532C32#328711yescharacteristic, complemented, Sylow
533C23—22no—
534C23—31no—
535C23—31no—
536C23—182no—
537Q8—34no—
538Q8—62no—
539D4—22no—
540D4—22no—
541D4—124no—
542D4—182no—
543D4—182no—
544D4—182no—
545D4—242no—
546D4—364no—
547D4—364no—
548D4—722no—
549D4—722no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—91no—
559C2×C4—91no—
560C2×C4—124no—
561C2×C4—364no—
562C2×C4C22×D3211yescharacteristic
563C8—61no—
564C8—61no—
565C8—181no—
566C8D3×#6712yes—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—82no—
571C2×C3—82no—
572C2×C3—121no—
573C2×C3—121no—
574C2×C3—162no—
575C2×C3#560911yescharacteristic
576C2×C3#575711yescharacteristic
577C2×C3D3×#13511yescharacteristic
578C2×C3D3×#13511yescharacteristic
579C2×C3#576911yescharacteristic
580C2×C3D4×#6711yescharacteristic
581D3—41no—
582D3—41no—
583D3—242no—
584D3—242no—
585D3—482no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—61no—
590C22—61no—
591C22—61no—
592C22—61no—
593C22—61no—
594C22—61no—
595C22—362no—
596C22—362no—
597C22—362no—
598C22D32×D411yescharacteristic
599C4—61no—
600C4—61no—
601C4—64no—
602C4—92no—
603C4—122no—
604C4—181no—
605C4#6431411yescharacteristic
606C4C2×D3×#6711yescharacteristic
607C3—21no—
608C3#8073511yescharacteristic, complemented
609C3#8392411yescharacteristic, complemented
610C2—82no—
611C2—121no—
612C2—121no—
613C2—722no—
614C2#1059473011yescharacteristic
615C2#1059473411yescharacteristic
616C2#1059528811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3287
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. #10595236C2semidirect
3. C2×#63808C2semidirect
4. #10592850C2semidirect
5. C3×#5157C2semidirect
6. #10591521C2semidirect
7. #10591452C2semidirect
8. #10591444C2semidirect
9. #10590832C2semidirect
10. #10590818C2semidirect
11. C8×#625C2semidirect
46. C2×#912D3semidirect
54. #5157D3semidirect
95. C3×Dic12D4semidirect
295. Dic12#67semidirect
318. C3⋊Dic3#135semidirect
532. C32#3287semidirect
608. C3#80735semidirect
609. C3#83924semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
#105952362
C2×#638082
#105928502
C3×#51572
#105915212
#105914522
#105914442
#105908322
#105908182
C8×#6252
#839243
#807353