Finite Group Databasebeta

← #11824457

Subgroups — #11824457

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×#874C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic, complemented
4C2×Dic3×D12C211yesmaximal, characteristic, complemented
5C2×#63886C214yesmaximal, complemented
6#10592638C211yesmaximal, characteristic, complemented
7C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8#10591391C214yesmaximal, complemented
9#10591318C211yesmaximal, characteristic, complemented
10#83177—31nomaximal
11#73799—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×#626C2212yes—
17C22×#626C2214yes—
18C22×#626C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2214yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#874—24no—
27C2×(C2×D3)⋊Dic3C2214yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29#63911—24no—
30#63911—24no—
31Dic3×D12—24no—
32#63886—216no—
33C3×C3⋊#95C2212yes—
34C2×C3×#127—31no—
35C2×#940—31no—
36C2×#940—31no—
37C2×#939—34no—
38C2×D4×Dic3—31no—
39C2×#895—34no—
40C2×#874—31no—
41C2×#874—31no—
42C2×#874D311yescharacteristic, complemented
43C2×C4×D12—31no—
44C3×C4×C4⋊C4—31no—
45#5223—34no—
46#5221—31no—
47#4939—31no—
48#4939—31no—
49#4939—31no—
50#4939—61no—
51C4×Dic3⋊C4D311yescharacteristic, complemented
52#4671—34no—
53C23×C3⋊D3C2312yes—
54C23×C3×D3C2312yes—
55C23×C3×D3C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2311yescharacteristic
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—28no—
68C2×C3×D12—28no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—22no—
72C2×C3×D12—44no—
73C2×C3×D12D414yescomplemented
74C2×#626—28no—
75C2×#626—28no—
76C2×#626—28no—
77C2×#626—24no—
78C2×#626—24no—
79C2×#626—44no—
80C2×#626—44no—
81C2×D3×Dic3—28no—
82C2×D3×Dic3—24no—
83C32×C42—22no—
84#3752—28no—
85C4⋊(C3⋊Dic3)—22no—
86C3×Dic3⋊C4D418yescomplemented
87C3×C4×Dic3—22no—
88C3×C4×Dic3D414yescomplemented
89(C2×D3)⋊Dic3—28no—
90(C2×D3)⋊Dic3—24no—
91#2541—91noSylow
92C22×C3×D4—31no—
93C22×C3×D4—31no—
94C22×C3×D4—34no—
95C22×#67—32no—
96C22×#67—34no—
97C22×#67—32no—
98C23×Dic3—32no—
99C22×D12—32no—
100C22×D12—31no—
101C22×D12—31no—
102C22×D12—34no—
103C22×D12—32no—
104C22×D12—61no—
105C22×D12C2×D311yescharacteristic
106C22×D12C2×D314yes—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—32no—
109C3×#127—64no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C42—21no—
112C2×C3×C42—31no—
113C2×C3×C42—31no—
114C2×C3×C42C2×D311yescharacteristic
115C2×C3×C42C2×D311yescharacteristic
116C2×#217—34no—
117C2×#217—32no—
118#940—64no—
119#940—64no—
120#939—616no—
121D4×Dic3—64no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—64no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×C4×Dic3C2×D311yescharacteristic
133#895—616no—
134#874—24no—
135#874—64no—
136#874—64no—
137C4×D12—64no—
138C3×#95—32no—
139C3⋊#95C2×D312yes—
140C23×C32C2411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—24no—
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—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D414yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4#4112yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—24no—
164C4⋊(C3⋊D3)—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D414yes—
170C2×C3×Dic3C2×D412yes—
171C2×C3×Dic3C2×D414yes—
172C3×D12—28no—
173C3×D12—416no—
174C3×D12—44no—
175#626—416no—
176#626—48no—
177#626—48no—
178D3×Dic3—48no—
179C2×#127—31no—
180C2×#127—91no—
181C2×#127—91no—
182C2×#121—94no—
183C2×C4×D4—91no—
184#392—94no—
185#390—91no—
186#390—91no—
187C4×C4⋊C4—31no—
188C24×C3—32no—
189C24×C3—32no—
190C23×D3—32no—
191C23×D3—32no—
192C23×D3—62no—
193C23×D3C22×D312yes—
194C23×D3C22×D312yes—
195C2×C3×D4—34no—
196C2×C3×D4—68no—
197C2×C3×D4—62no—
198C2×C3×D4—68no—
199C2×C3×D4—62no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—124no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—68no—
214C2×#67—68no—
215C2×#67—68no—
216C2×#67—64no—
217C2×#67—64no—
218C2×#67—124no—
219C2×#67—124no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—62no—
223C22×Dic3—64no—
224C22×Dic3—68no—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—28no—
231C2×D12—22no—
232C2×D12—28no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—44no—
236C2×D12—64no—
237C2×D12—64no—
238C2×D12—64no—
239C2×D12—68no—
240C2×D12—68no—
241C2×D12—68no—
242C2×D12—62no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—122no—
249C2×D12—122no—
250C2×D12—124no—
251C2×D12—124no—
252C2×D12#6714yescomplemented
253C2×C4×D3—64no—
254C2×C4×D3—68no—
255C3×C4⋊C4—38no—
256C3×C42—22no—
257C3×C42—22no—
258C3×C42—34no—
259C3×C42—42no—
260C3×C42—62no—
261#217—64no—
262#217—68no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—68no—
265(C2×D3)⋊C4—68no—
266(C2×D3)⋊C4—68no—
267(C2×D3)⋊C4—128no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—122no—
271Dic3⋊C4D1218yescomplemented
272C4×Dic3—22no—
273C4×Dic3D1214yescomplemented
274C22×C32C22×D411yescharacteristic
275C22×C32C22×D412yes—
276C22×C32C22×D411yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32H(5,𝔽2)12yes—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—44no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—44no—
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—24no—
295C32×C4#12114yescomplemented
296C3⋊Dic3—42no—
297C3×Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3#12714yescomplemented
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—34no—
303C22×D4—92no—
304C22×D4—94no—
305C22×D4—92no—
306C22×D4—91no—
307C23×C4—92no—
308#127—64no—
309#127—184no—
310#127—184no—
311#121—1816no—
312C4×D4—184no—
313C2×C4⋊C4—32no—
314C2×C4⋊C4—91no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—94no—
317C2×C22⋊C4—94no—
318C2×C42—31no—
319C2×C42—31no—
320C2×C42D3211yescharacteristic
321#95—32no—
322C23×C3—21no—
323C23×C3—34no—
324C23×C3—62no—
325C23×C3—64no—
326C23×C3—62no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—64no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—24no—
343C22×D3—22no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—62no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—64no—
352C22×D3—62no—
353C22×D3—64no—
354C22×D3—62no—
355C22×D3—124no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—124no—
359C22×D3C2×#6714yes—
360C3×D4—68no—
361C3×D4—1216no—
362C3×D4—124no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—32no—
372C2×C3×C4—34no—
373C2×C3×C4—32no—
374C2×C3×C4—34no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4C2×D1214yes—
381C2×C3×C4C2×D1212yes—
382C2×C3×C4D3×D414yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4#23712yes—
386C2×C3×C4#23912yes—
387C2×C3×C4C2×#6712yes—
388#67—1216no—
389#67—128no—
390#67—128no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—62no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—64no—
398C2×Dic3—122no—
399C2×Dic3—124no—
400C2×Dic3—128no—
401C2×Dic3C2×D1212yes—
402C2×Dic3C2×D1214yes—
403C2×Dic3C2×D1212yes—
404C2×Dic3C2×D1214yes—
405D12—28no—
406D12—416no—
407D12—44no—
408D12—128no—
409D12—128no—
410D12—1216no—
411D12—128no—
412D12—124no—
413D12—124no—
414C4×D3—128no—
415C2×C32C2×#12111yescharacteristic
416C2×C32C2×#12711yescharacteristic
417C2×C32#53511yescharacteristic
418C2×C32D4212yes—
419C2×C32#55012yes—
420C3⋊D3—82no—
421C3×D3—44no—
422C3×D3—82no—
423C24—32no—
424C24—32no—
425C24—92no—
426C2×D4—34no—
427C2×D4—68no—
428C2×D4—62no—
429C2×D4—62no—
430C2×D4—62no—
431C2×D4—68no—
432C2×D4—62no—
433C2×D4—62no—
434C2×D4—124no—
435C2×D4—188no—
436C2×D4—188no—
437C2×D4—184no—
438C2×D4—184no—
439C2×D4—188no—
440C2×D4—182no—
441C2×D4—182no—
442C2×D4—182no—
443C2×D4—364no—
444C2×D4—364no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—92no—
449C22×C4—184no—
450C22×C4—188no—
451C22×C4C2×D3212yes—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—38no—
454C4⋊C4—182no—
455C22⋊C4—184no—
456C22⋊C4—188no—
457C22⋊C4—188no—
458C42—22no—
459C42—34no—
460C42—62no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—64no—
467C22×C3—68no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—124no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—124no—
475C22×C3—124no—
476C22×C3C22×D1211yescharacteristic
477C22×C3C22×D1212yes—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C2×D3×D412yes—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×#23711yescharacteristic
482C22×C3#100412yes—
483C22×C3C2×#23911yescharacteristic
484C22×C3#100912yes—
485C22×C3C22×#6711yescharacteristic
486C2×D3—28no—
487C2×D3—24no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—44no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—44no—
494C2×D3—44no—
495C2×D3—42no—
496C2×D3—124no—
497C2×D3—128no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—124no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—124no—
505C2×D3—122no—
506C2×D3—124no—
507C2×D3—124no—
508C2×D3—242no—
509C2×D3—242no—
510C2×D3—244no—
511C3×C4—24no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—34no—
515C3×C4—44no—
516C3×C4—62no—
517C3×C4—64no—
518C3×C4#89514yescomplemented
519C3×C4#93914yescomplemented
520Dic3—22no—
521Dic3—24no—
522Dic3—122no—
523Dic3—122no—
524Dic3—242no—
525Dic3#87414yescomplemented
526C32#254111yescharacteristic, complemented, Sylow
527C23—34no—
528C23—62no—
529C23—62no—
530C23—64no—
531C23—64no—
532C23—62no—
533C23—64no—
534C23—62no—
535C23—64no—
536C23—62no—
537C23—182no—
538C23—184no—
539C23—182no—
540C23—184no—
541C23—182no—
542C23C22×D3211yescharacteristic
543D4—68no—
544D4—1216no—
545D4—124no—
546D4—368no—
547D4—3616no—
548D4—368no—
549D4—364no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—32no—
553C2×C4—34no—
554C2×C4—32no—
555C2×C4—34no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—184no—
560C2×C4—182no—
561C2×C4—368no—
562C2×C4#379612yes—
563C2×C4D3×D1214yes—
564C2×C4D3×D1212yes—
565C2×C4D3×#6712yes—
566C2×C3—21no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—124no—
572C2×C3—242no—
573C2×C3C2×#87411yescharacteristic
574C2×C3C2×#89511yescharacteristic
575C2×C3#552511yescharacteristic
576C2×C3D4×D1212yes—
577C2×C3#557712yes—
578C2×C3D3×#12711yescharacteristic
579C2×C3#571511yescharacteristic
580C2×C3#571812yes—
581C2×C3D4×#6712yes—
582C2×C3C2×#93911yescharacteristic
583D3—44no—
584D3—82no—
585D3—244no—
586D3—242no—
587D3—242no—
588C22—64no—
589C22—68no—
590C22—124no—
591C22—122no—
592C22—122no—
593C22—122no—
594C22—124no—
595C22—122no—
596C22—122no—
597C22—124no—
598C22—362no—
599C22—364no—
600C22—362no—
601C22—362no—
602C22—364no—
603C22C2×#379611yescharacteristic
604C22C2×D3×D1211yescharacteristic
605C22C2×D3×D1212yes—
606C22#6430712yes—
607C22C2×D3×#6711yescharacteristic
608C4—24no—
609C4—34no—
610C4—62no—
611C4—64no—
612C4—362no—
613C4#6388614yescomplemented
614C3—21no—
615C3#7379911yescharacteristic, complemented
616C3#8317711yescharacteristic, complemented
617C2—124no—
618C2—242no—
619C2—722no—
620C2#1059390012yes—
621C2D3×#87411yescharacteristic
622C2#1059400011yescharacteristic
623C2C2×#6388611yescharacteristic
624C2D12×#6712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#874C2semidirect
2. C2×#63911C2semidirect
3. C2×#63911C2semidirect
4. C2×Dic3×D12C2semidirect
5. C2×#63886C2semidirect
6. #10592638C2semidirect
7. C3×C4×Dic3⋊C4C2semidirect
8. #10591391C2semidirect
9. #10591318C2semidirect
42. C2×#874D3semidirect
51. C4×Dic3⋊C4D3semidirect
73. C2×C3×D12D4semidirect
86. C3×Dic3⋊C4D4semidirect
88. C3×C4×Dic3D4semidirect
252. C2×D12#67semidirect
271. Dic3⋊C4D12semidirect
273. C4×Dic3D12semidirect
295. C32×C4#121semidirect
299. C3×Dic3#127semidirect
518. C3×C4#895semidirect
519. C3×C4#939semidirect
525. Dic3#874semidirect
526. C32#2541semidirect
613. C4#63886semidirect
615. C3#73799semidirect
616. C3#83177semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8742
C2×#639112
C2×Dic3×D122
C2×#638862
#105926382
C3×C4×Dic3⋊C42
#105913912
#105913182
#831773
#737993