Finite Group Databasebeta

← #11886542

Subgroups — #11886542

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2#10595158C212yesmaximal, complemented
3C2×#63810C211yesmaximal, characteristic, complemented
4#10592856C211yesmaximal, characteristic, complemented
5C3×#5151C211yesmaximal, characteristic, complemented
6#10591520C212yesmaximal, complemented
7#10591450C212yesmaximal, complemented
8#10591438C212yesmaximal, complemented
9#10590831C211yesmaximal, characteristic, complemented
10Dic3×Dic12C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic, complemented
12#83924—31nomaximal
13#81790—31nomaximal
14C2×C3×#237C2212yes—
15C2×#3796C2212yes—
16C2×C32×D8C2211yescharacteristic
17#64147C2212yes—
18C2×C8×C3⋊D3C2211yescharacteristic
19C3×#940C2212yes—
20C2×C3×#214C2212yes—
21C2×C3×#213C2212yes—
22C3×#912—24no—
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#63979—22no—
27#63978—22no—
28Dic3×#67—22no—
29#63970—22no—
30#63908C2212yes—
31C4×#626C2211yescharacteristic
32Dic3×Dic6C2212yes—
33C2×#3715C2212yes—
34#63810—24no—
35#63659C2212yes—
36#63645C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63566C2212yes—
40#63563C2212yes—
41#63557C2211yescharacteristic
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
43C2×C3×#135—31no—
44#5834—32no—
45C2×#919—31no—
46C2×#912—31no—
47C2×#912D311yescharacteristic, complemented
48#5718—32no—
49C3×#493—31no—
50#5238—32no—
51Dic3×Q16—31no—
52#5172—32no—
53#5163—32no—
54#5158—32no—
55#5158—32no—
56#5157—31no—
57#5157—31no—
58#5157—31no—
59#5157—61no—
60#5151D311yescharacteristic, complemented
61#5115—31no—
62C8×#67—31no—
63#5075—32no—
64C4×Dic12—31no—
65C8×D12—31no—
66C2×C32×D4C2312yes—
67C2×#638—22no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—24no—
74C3×#237—42no—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×#626—22no—
79C2×#626D411yescharacteristic
80C2×#625—22no—
81C2×D3×Dic3—22no—
82#3796—24no—
83#3796—42no—
84C32×D8—22no—
85C2×C32×C8C2311yescharacteristic
86#3757—22no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C8×C3⋊D3—22no—
90C3×#214—24no—
91C3×#213—42no—
92C3×C4×Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12D414yescomplemented
96C3×D24—22no—
97C3×D3×C8—22no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3D411yescharacteristic
100#3722D411yescharacteristic
101(C2×D3)⋊Dic3—22no—
102(C2×D3)⋊Dic3D411yescharacteristic
103Dic32—22no—
104#3715—24no—
105#3287—91noSylow
106C2×C3×#41—32no—
107C2×#239—32no—
108C2×#237—32no—
109C2×#237C2×D312yes—
110C3×#135—64no—
111C2×C3×Q16—31no—
112C2×C3×SD16—32no—
113C2×C3×D8—21no—
114C2×C3×D8—32no—
115C2×C3×D8—31no—
116C2×C3×D8C2×D311yescharacteristic
117C2×C3×D8C2×D311yescharacteristic
118C22×C3×C8—31no—
119C3×#127—32no—
120Q8×Dic3—32no—
121C2×#215—32no—
122#940—62no—
123#940—62no—
124#940C2×D312yes—
125#939—62no—
126#939—62no—
127#938—32no—
128#938—32no—
129#938—32no—
130#938—62no—
131#938—62no—
132D4×Dic3—62no—
133C2×#214—32no—
134C2×#214C2×D312yes—
135C2×#213C2×D312yes—
136#930—32no—
137#930—62no—
138C4×#67—31no—
139C4×#67—62no—
140#919—64no—
141#912—24no—
142#912—64no—
143C2×Dic12C2×D311yescharacteristic
144C2×D24C2×D311yescharacteristic
145C2×D3×C8—31no—
146C2×D3×C8—31no—
147C2×D3×C8—61no—
148C2×D3×C8C2×D311yescharacteristic
149C4×D12—31no—
150C4×Dic6—32no—
151C3×C4×C8—31no—
152#835—32no—
153#832—32no—
154#832—32no—
155#832—32no—
156#832—62no—
157#830—31no—
158#821—32no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161(C2×D3)⋊C8—31no—
162#818—31no—
163#818—31no—
164#818—61no—
165#816—32no—
166Dic3⋊C8—31no—
167C8×Dic3C2×D311yescharacteristic
168C4⋊(C3⋊C8)—31no—
169C23×C32—22no—
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3C2×D411yescharacteristic
173C32×D4—22no—
174C32×D4—22no—
175C2×C32×C4C2411yescharacteristic
176#638—82no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C2×D411yescharacteristic
179C4×C3⋊D3—21no—
180C4×C3⋊D3—21no—
181C3×#67—44no—
182C3×#67—44no—
183C3×#67—82no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—44no—
186C2×C3×Dic3C2×D411yescharacteristic
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×D12—22no—
190C3×D12—22no—
191C3×C4×D3—21no—
192C3×C4×D3—21no—
193C3×Dic6—22no—
194C3×Dic6C2×D414yes—
195#626—22no—
196#626—44no—
197#625—82no—
198D3×Dic3—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—31no—
207#466—91no—
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—32no—
219C2×C3×D4—62no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C2×C3×D4C22×D312yes—
223C2×C3×D4C22×D312yes—
224C22×C3×C4—31no—
225C22×C3×C4—62no—
226C2×#67—22no—
227C2×#67—22no—
228C2×#67—22no—
229C2×#67—31no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—122no—
236C22×Dic3—22no—
237C22×Dic3—62no—
238#239—64no—
239#239—122no—
240#237—24no—
241#237—42no—
242#237—64no—
243#237—122no—
244C2×D12—31no—
245C2×D12—62no—
246C2×D12C22×D312yes—
247C2×C4×D3—31no—
248C2×C4×D3—31no—
249C2×C4×D3—61no—
250C2×C4×D3—62no—
251C2×C4×D3C22×D311yescharacteristic
252C2×Dic6C22×D312yes—
253C3×Q16—34no—
254C3×SD16—64no—
255C3×D8—22no—
256C3×D8—22no—
257C3×D8—42no—
258C3×D8—62no—
259C3×D8—122no—
260C2×C3×C8—21no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—62no—
264C2×C3×C8C22×D311yescharacteristic
265C2×C3×C8C22×D311yescharacteristic
266C3×C42—31no—
267#217—31no—
268#217—62no—
269#217—62no—
270#217—62no—
271#217—122no—
272#215—64no—
273#214—24no—
274#214—64no—
275#213—42no—
276(C2×D3)⋊C4—31no—
277(C2×D3)⋊C4—31no—
278(C2×D3)⋊C4—31no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—31no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285Dic3⋊C4—31no—
286Dic3⋊C4—62no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3C22×D311yescharacteristic
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295Dic12#6714yescomplemented
296D24—22no—
297D3×C8—22no—
298D3×C8—62no—
299D3×C8—62no—
300D3×C8—122no—
301C22×C32—42no—
302C22×C32—42no—
303C22×C32—42no—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—21no—
306C2×C3⋊D3—21no—
307C2×C3⋊D3—21no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C32×C4C22×D411yescharacteristic
315C32×C4H(5,𝔽2)11yescharacteristic
316C3⋊Dic3—21no—
317C3⋊Dic3—42no—
318C3×Dic3—24no—
319C3×Dic3—21no—
320C3×Dic3—21no—
321C3×Dic3#13512yescomplemented
322C2×#41—32no—
323C2×#41—92no—
324#135—64no—
325#135—184no—
326C2×Q16—31no—
327C2×SD16—32no—
328C2×SD16—92no—
329C2×D8—32no—
330C2×D8—31no—
331C2×D8D3211yescharacteristic
332C22×C8—31no—
333C22×C8—91no—
334#127—32no—
335#127—182no—
336#121—92no—
337#121—92no—
338#121—182no—
339#121—182no—
340C4×Q8—92no—
341C4×D4—91no—
342C4×D4—182no—
343#107—91no—
344C4⋊C8—91no—
345#103—92no—
346#102—92no—
347#102—92no—
348C22⋊C8—91no—
349C22⋊C8—91no—
350C4×C8—31no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—31no—
354C23×C3—42no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3—31no—
358C22×D3—31no—
359C22×D3—61no—
360C22×D3D3×D411yescharacteristic
361C3×Q8—34no—
362C3×Q8—62no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—22no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—62no—
370C3×D4—62no—
371C3×D4—124no—
372C3×D4—124no—
373C3×D4—242no—
374C2×C3×C4—21no—
375C2×C3×C4—31no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—124no—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—44no—
385#67—44no—
386#67—62no—
387#67—82no—
388#67—124no—
389#67—242no—
390#67—242no—
391#67—242no—
392#67—242no—
393#67—244no—
394C2×Dic3—22no—
395C2×Dic3—31no—
396C2×Dic3—31no—
397C2×Dic3—44no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3D3×D411yescharacteristic
404C2×Dic3D3×D411yescharacteristic
405C2×Dic3D3×D411yescharacteristic
406D12—22no—
407D12—22no—
408D12—62no—
409D12—124no—
410C4×D3—21no—
411C4×D3—21no—
412C4×D3—61no—
413C4×D3—61no—
414C4×D3—61no—
415C4×D3—61no—
416C4×D3—121no—
417C4×D3—121no—
418C4×D3—124no—
419Dic6—22no—
420Dic6C2×#6714yes—
421C3×C8—22no—
422C3×C8—61no—
423C3×C8—61no—
424C3×C8D3×D412yes—
425C3×C8C2×#6712yes—
426C3⋊C8—21no—
427C3⋊C8—21no—
428C3⋊C8—61no—
429C3⋊C8—61no—
430C3⋊C8—121no—
431C2×C32—82no—
432C2×C32D4211yescharacteristic
433C2×C32C2×#13511yescharacteristic
434C2×C32#57611yescharacteristic
435C3⋊D3—41no—
436C3×D3—41no—
437C3×D3—82no—
438#41—64no—
439#41—122no—
440#41—184no—
441#41—362no—
442C2×Q8—32no—
443C2×D4—32no—
444C2×D4—62no—
445C2×D4—62no—
446C2×D4—62no—
447C2×D4—91no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4C2×D3212yes—
452C22×C4—31no—
453C22×C4—62no—
454C22×C4—91no—
455C22×C4—182no—
456Q16—34no—
457SD16—64no—
458SD16—184no—
459D8—22no—
460D8—62no—
461D8—122no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—62no—
465C2×C8—91no—
466C2×C8—182no—
467C2×C8C2×D3211yescharacteristic
468C4⋊C4—91no—
469C4⋊C4—92no—
470C4⋊C4—182no—
471C22⋊C4—91no—
472C22⋊C4—91no—
473C22⋊C4—182no—
474C22⋊C4—182no—
475C42—31no—
476C42—182no—
477C22×C3—21no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—61no—
487C22×C3—82no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C2×D3—21no—
496C2×D3—21no—
497C2×D3—21no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—62no—
502C2×D3—61no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—61no—
506C2×D3—61no—
507C2×D3—61no—
508C2×D3—121no—
509C2×D3—121no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—32no—
513C3×C4—64no—
514C3×C4—61no—
515C3×C4—61no—
516C3×C4C2×D3×D411yescharacteristic
517C3×C4#100411yescharacteristic
518C3×C4#100411yescharacteristic
519C3×C4C22×#6711yescharacteristic
520Dic3—21no—
521Dic3—24no—
522Dic3—21no—
523Dic3—61no—
524Dic3—61no—
525Dic3—121no—
526Dic3—122no—
527Dic3—122no—
528Dic3—242no—
529Dic3#91212yescomplemented
530C32#328711yescharacteristic, complemented, Sylow
531C23—22no—
532C23—31no—
533C23—62no—
534C23—91no—
535Q8—34no—
536Q8—62no—
537D4—22no—
538D4—22no—
539D4—62no—
540D4—62no—
541D4—124no—
542D4—124no—
543D4—182no—
544D4—242no—
545D4—364no—
546D4—722no—
547D4—722no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—91no—
555C2×C4—124no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—182no—
559C2×C4—364no—
560C2×C4C22×D3211yescharacteristic
561C8—61no—
562C8—61no—
563C8—181no—
564C8D3×#6712yes—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—82no—
569C2×C3—82no—
570C2×C3—121no—
571C2×C3—162no—
572C2×C3—242no—
573C2×C3#571711yescharacteristic
574C2×C3C2×#91211yescharacteristic
575C2×C3#575711yescharacteristic
576C2×C3D3×#13511yescharacteristic
577C2×C3#576911yescharacteristic
578C2×C3D4×#6711yescharacteristic
579D3—41no—
580D3—82no—
581D3—122no—
582D3—121no—
583D3—121no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—61no—
588C22—61no—
589C22—61no—
590C22—122no—
591C22—122no—
592C22—122no—
593C22—181no—
594C22—181no—
595C22—181no—
596C22D32×D411yescharacteristic
597C4—32no—
598C4—61no—
599C4—61no—
600C4—64no—
601C4—181no—
602C4—362no—
603C4#6431311yescharacteristic
604C4C2×D3×#6711yescharacteristic
605C3—21no—
606C3#8179011yescharacteristic, complemented
607C3#8392411yescharacteristic, complemented
608C2—82no—
609C2—121no—
610C2—242no—
611C2—361no—
612C2D3×#91211yescharacteristic
613C2#1059473411yescharacteristic
614C2#1059529311yescharacteristic
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. #10595158C2semidirect
3. C2×#63810C2semidirect
4. #10592856C2semidirect
5. C3×#5151C2semidirect
6. #10591520C2semidirect
7. #10591450C2semidirect
8. #10591438C2semidirect
9. #10590831C2semidirect
10. Dic3×Dic12C2semidirect
11. C8×#626C2semidirect
47. C2×#912D3semidirect
60. #5151D3semidirect
95. C3×Dic12D4semidirect
295. Dic12#67semidirect
321. C3×Dic3#135semidirect
529. Dic3#912semidirect
530. C32#3287semidirect
606. C3#81790semidirect
607. 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
#105951582
C2×#638102
#105928562
C3×#51512
#105915202
#105914502
#105914382
#105908312
Dic3×Dic122
C8×#6262
#839243
#817903