Finite Group Databasebeta

← #11824460

Subgroups — #11824460

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×#63970C214yesmaximal, complemented
4C2×#63914C211yesmaximal, characteristic, complemented
5C2×Dic3×D12C211yesmaximal, characteristic, complemented
6#10592920C211yesmaximal, characteristic, complemented
7#10591723C214yesmaximal, complemented
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591318C211yesmaximal, characteristic, complemented
10#83188—31nomaximal
11#83177—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67C2212yes—
14C22×C3×#67C2214yes—
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×#625C2214yes—
19C22×D3×Dic3C2212yes—
20C2×#3757C2214yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C3×#940—24no—
24C3×#940—24no—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27#63970—216no—
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31#63914—24no—
32Dic3×D12—24no—
33#63579C2212yes—
34C2×C3×#127—31no—
35C2×C3×#127—31no—
36C2×#940—31no—
37C2×#940—31no—
38C2×#940D311yescharacteristic, complemented
39C2×#940D311yescharacteristic, complemented
40C2×#939—34no—
41C2×#938—34no—
42C2×D4×Dic3—31no—
43C2×C4×D12—31no—
44#5223—34no—
45#5223—34no—
46#5221—31no—
47#5221—31no—
48#5221—31no—
49#5221—61no—
50#4939—31no—
51C4×C4⋊Dic3—31no—
52C4×Dic3⋊C4—31no—
53C24×C32C2312yes—
54C23×C3×D3C2312yes—
55C23×C3×D3C2312yes—
56C2×C32×D4—22no—
57C2×C32×D4—22no—
58C2×C32×D4—22no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2312yes—
62C2×C3×#67—28no—
63C2×C3×#67—24no—
64C2×C3×#67—24no—
65C2×C3×#67—28no—
66C2×C3×#67—28no—
67C2×C3×#67—44no—
68C2×C3×#67—44no—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12D414yescomplemented
78C2×#625—28no—
79C2×#625—28no—
80C2×#625—44no—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—28no—
83#3757—28no—
84C4⋊(C3⋊Dic3)—22no—
85C4×C3⋊Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3D414yescomplemented
88Dic3⋊Dic3D418yescomplemented
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—28no—
91#2541—91noSylow
92C22×C3×D4—21no—
93C22×C3×D4—32no—
94C22×C3×D4—34no—
95C22×C3×D4—32no—
96C22×C3×D4—31no—
97C22×C3×D4—31no—
98C22×C3×D4C2×D311yescharacteristic
99C22×C3×D4C2×D311yescharacteristic
100C22×#67—34no—
101C22×#67—34no—
102C22×#67C2×D312yes—
103C22×#67C2×D314yes—
104C22×#67C2×D312yes—
105C23×Dic3—32no—
106C22×D12C2×D311yescharacteristic
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—32no—
109C3×#127—64no—
110C3×#127—64no—
111C2×C3×C42—31no—
112C2×C3×C42—31no—
113C2×#217—34no—
114C2×#217—34no—
115C2×#217—34no—
116C2×#217—32no—
117C2×#217—64no—
118#940—24no—
119#940—24no—
120#940—64no—
121#940—64no—
122#939—616no—
123#938—616no—
124D4×Dic3—64no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—32no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—61no—
131C2×Dic3⋊C4—32no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136C2×C4×Dic3C2×D311yescharacteristic
137C4×D12—64no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C23×C32—22no—
141C23×C32—24no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32—24no—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—24no—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—24no—
155C22×C3×D3C2×D414yes—
156C32×D4—44no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4#4112yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—24no—
164C2×C3⋊Dic3C2×D414yes—
165C3×#67—416no—
166C3×#67—48no—
167C3×#67—48no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D414yes—
172C2×C3×Dic3C2×D414yes—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—28no—
176C3×D12—44no—
177#625—416no—
178D3×Dic3—48no—
179C2×#127—31no—
180C2×#127—31no—
181C2×#127—91no—
182C2×#121—94no—
183C2×C4×D4—91no—
184#392—94no—
185#390—91no—
186#390—91no—
187C4×C4⋊C4—91no—
188C24×C3—22no—
189C24×C3—32no—
190C24×C3—32no—
191C24×C3C22×D312yes—
192C24×C3C22×D312yes—
193C23×D3C22×D312yes—
194C23×D3C22×D312yes—
195C2×C3×D4—24no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—34no—
203C2×C3×D4—42no—
204C2×C3×D4—42no—
205C2×C3×D4—68no—
206C2×C3×D4—68no—
207C2×C3×D4—64no—
208C2×C3×D4—64no—
209C2×C3×D4—68no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C2×C3×D4—124no—
216C2×C3×D4—124no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—28no—
224C2×#67—28no—
225C2×#67—28no—
226C2×#67—24no—
227C2×#67—24no—
228C2×#67—44no—
229C2×#67—44no—
230C2×#67—68no—
231C2×#67—68no—
232C2×#67—68no—
233C2×#67—68no—
234C2×#67—124no—
235C2×#67—124no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—68no—
243C22×Dic3—64no—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D311yescharacteristic
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—22no—
251C2×D12—22no—
252C2×D12#6714yescomplemented
253C2×C4×D3—64no—
254C2×C4×D3—68no—
255C3×C42—34no—
256C3×C42—62no—
257#217—68no—
258#217—68no—
259#217—68no—
260#217—64no—
261#217—128no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—68no—
264C4⋊Dic3—38no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—122no—
268Dic3⋊C4—38no—
269C4×Dic3—22no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—122no—
273C4×Dic3#6714yescomplemented
274C22×C32—42no—
275C22×C32—44no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32—44no—
279C22×C32C22×D412yes—
280C22×C32C22×D411yescharacteristic
281C22×C32C22×D411yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32H(5,𝔽2)12yes—
284C2×C3×D3—24no—
285C2×C3×D3—28no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—44no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—44no—
293C2×C3×D3—44no—
294C32×C4#12114yescomplemented
295C3⋊Dic3—24no—
296C3⋊Dic3—42no—
297C3×Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3#12714yescomplemented
300C22×D4—32no—
301C22×D4—34no—
302C22×D4—32no—
303C22×D4—31no—
304C22×D4—31no—
305C22×D4—94no—
306C22×D4D3211yescharacteristic
307C23×C4—92no—
308#127—64no—
309#127—64no—
310#127—184no—
311#121—1816no—
312C4×D4—184no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—91no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—94no—
317C2×C22⋊C4—94no—
318C2×C42—31no—
319C2×C42—31no—
320C2×C42—91no—
321#95—92no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—34no—
335C23×C3—44no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—44no—
339C23×C3—64no—
340C23×C3—62no—
341C23×C3—64no—
342C23×C3—62no—
343C23×C3—64no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—64no—
347C23×C3—62no—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—22no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—24no—
358C22×D3—22no—
359C22×D3C2×#6714yes—
360C3×D4—48no—
361C3×D4—44no—
362C3×D4—44no—
363C3×D4—68no—
364C3×D4—128no—
365C3×D4—1216no—
366C3×D4—128no—
367C3×D4—124no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—34no—
374C2×C3×C4—32no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4D3×D412yes—
379C2×C3×C4D3×D412yes—
380C2×C3×C4#23712yes—
381C2×C3×C4#23712yes—
382C2×C3×C4C2×#6712yes—
383C2×C3×C4C2×#6712yes—
384#67—416no—
385#67—48no—
386#67—48no—
387#67—1216no—
388#67—1216no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—64no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—124no—
407C2×Dic3—128no—
408C2×Dic3D3×D414yes—
409C2×Dic3D3×D414yes—
410C2×Dic3C2×#6712yes—
411C2×Dic3C2×#6712yes—
412D12—28no—
413D12—44no—
414C4×D3—128no—
415C2×C32—82no—
416C2×C32C2×#12111yescharacteristic
417C2×C32C2×#12711yescharacteristic
418C2×C32#53511yescharacteristic
419C2×C32D4212yes—
420C2×C32#55012yes—
421C3×D3—44no—
422C3×D3—82no—
423C24—32no—
424C24—32no—
425C24C2×D3212yes—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—34no—
430C2×D4—68no—
431C2×D4—68no—
432C2×D4—64no—
433C2×D4—64no—
434C2×D4—68no—
435C2×D4—62no—
436C2×D4—62no—
437C2×D4—62no—
438C2×D4—62no—
439C2×D4—62no—
440C2×D4—124no—
441C2×D4—124no—
442C2×D4—188no—
443C2×D4—188no—
444C2×D4—364no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—92no—
449C22×C4—92no—
450C22×C4—184no—
451C22×C4—188no—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—98no—
454C4⋊C4—182no—
455C22⋊C4—184no—
456C22⋊C4—188no—
457C22⋊C4—188no—
458C42—34no—
459C42—62no—
460C42—182no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—44no—
467C22×C3—48no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3—44no—
473C22×C3—42no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—68no—
479C22×C3—64no—
480C22×C3—82no—
481C22×C3—82no—
482C22×C3—84no—
483C22×C3—124no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—124no—
489C22×C3—124no—
490C22×C3—122no—
491C22×C3C2×D3×D412yes—
492C22×C3C2×D3×D412yes—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×#23711yescharacteristic
496C22×C3C2×#23711yescharacteristic
497C22×C3#100412yes—
498C22×C3#100412yes—
499C22×C3C22×#6711yescharacteristic
500C22×C3C22×#6711yescharacteristic
501C2×D3—28no—
502C2×D3—24no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—44no—
506C2×D3—44no—
507C2×D3—44no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C3×C4—24no—
512C3×C4—34no—
513C3×C4—62no—
514C3×C4—64no—
515C3×C4#93814yescomplemented
516C3×C4#93914yescomplemented
517Dic3—24no—
518Dic3—22no—
519Dic3—64no—
520Dic3—64no—
521Dic3—124no—
522Dic3—122no—
523Dic3—122no—
524Dic3—242no—
525Dic3#94014yescomplemented
526C32#254111yescharacteristic, complemented, Sylow
527C23—24no—
528C23—24no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—34no—
533C23—64no—
534C23—64no—
535C23—62no—
536C23—62no—
537C23—64no—
538C23—64no—
539C23—62no—
540C23—62no—
541C23—62no—
542C23C22×D3211yescharacteristic
543D4—44no—
544D4—68no—
545D4—128no—
546D4—1216no—
547D4—128no—
548D4—124no—
549D4—3616no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—32no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—94no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4—184no—
561C2×C4—182no—
562C2×C4—368no—
563C2×C4#380512yes—
564C2×C4D3×#6712yes—
565C2×C4D3×#6712yes—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—84no—
572C2×C3—82no—
573C2×C3—82no—
574C2×C3—124no—
575C2×C3—242no—
576C2×C3D3×#12711yescharacteristic
577C2×C3#571511yescharacteristic
578C2×C3#571712yes—
579C2×C3#571812yes—
580C2×C3#571812yes—
581C2×C3C2×#93811yescharacteristic
582C2×C3D4×#6712yes—
583C2×C3C2×#93911yescharacteristic
584C2×C3C2×#94011yescharacteristic
585C2×C3#580511yescharacteristic
586D3—44no—
587D3—82no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—44no—
593C22—64no—
594C22—68no—
595C22—124no—
596C22—122no—
597C22—122no—
598C22—124no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—124no—
603C22D32×D412yes—
604C22#6431312yes—
605C22C2×#380511yescharacteristic
606C22C2×D3×#6711yescharacteristic
607C22C2×D3×#6711yescharacteristic
608C4—34no—
609C4—62no—
610C4—64no—
611C4—184no—
612C4—362no—
613C4#6397014yescomplemented
614C3—21no—
615C3#8317711yescharacteristic, complemented
616C3#8318811yescharacteristic, complemented
617C2—82no—
618C2—124no—
619C2—242no—
620C2#1059514412yes—
621C2#1059523311yescharacteristic
622C2D3×#94011yescharacteristic
623C2#1059529312yes—
624C2C2×#6397011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. C2×C3×#940C2semidirect
3. C2×#63970C2semidirect
4. C2×#63914C2semidirect
5. C2×Dic3×D12C2semidirect
6. #10592920C2semidirect
7. #10591723C2semidirect
8. C4×Dic3⋊Dic3C2semidirect
9. #10591318C2semidirect
38. C2×#940D3semidirect
39. C2×#940D3semidirect
77. C2×C3×D12D4semidirect
87. C3×C4×Dic3D4semidirect
88. Dic3⋊Dic3D4semidirect
252. C2×D12#67semidirect
273. C4×Dic3#67semidirect
294. C32×C4#121semidirect
299. C3×Dic3#127semidirect
515. C3×C4#938semidirect
516. C3×C4#939semidirect
525. Dic3#940semidirect
526. C32#2541semidirect
613. C4#63970semidirect
615. C3#83177semidirect
616. C3#83188semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#639702
C2×#639142
C2×Dic3×D122
#105929202
#105917232
C4×Dic3⋊Dic32
#105913182
#831883
#831773