Finite Group Databasebeta

← #11824461

Subgroups — #11824461

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×#893C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C2×#63906C214yesmaximal, complemented
6#10592687C211yesmaximal, characteristic, complemented
7C3×#4988C211yesmaximal, characteristic, complemented
8#10591393C214yesmaximal, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#82378—31nomaximal
11#76348—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×#626C2212yes—
17C22×#626C2214yes—
18C22×#626C2212yes—
19C22×#625C2214yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2214yes—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#893—24no—
28C2×Dic3⋊Dic3C2212yes—
29#63914—24no—
30#63911—24no—
31#63911—24no—
32#63906—216no—
33#63579C2212yes—
34C2×C3×C4×D4—31no—
35C2×#940—31no—
36C2×#940—31no—
37C2×#940—31no—
38C2×#940—31no—
39C2×#930—34no—
40C2×#893D311yescharacteristic, complemented
41C2×#884—34no—
42C2×#874—31no—
43C2×#874—31no—
44C3×#390—31no—
45#4988—31no—
46#4988—31no—
47#4988—61no—
48#4988D311yescharacteristic, complemented
49#4960—34no—
50#4960—34no—
51C4×C4⋊Dic3—31no—
52C4×Dic3⋊C4—31no—
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×Dic3C2311yescharacteristic
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12D414yescomplemented
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—28no—
73C2×#626—28no—
74C2×#626—28no—
75C2×#626—28no—
76C2×#626—24no—
77C2×#626—24no—
78C2×#626—44no—
79C2×#626—44no—
80C2×#625—28no—
81C2×#625—28no—
82C2×#625—44no—
83C32×C4⋊C4—22no—
84#3752—28no—
85C4×C3⋊Dic3—22no—
86C3×(C2×D3)⋊C4—24no—
87C3×(C2×D3)⋊C4—28no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3D414yescomplemented
90Dic3⋊Dic3D418yescomplemented
91#2541—91noSylow
92C22×C3×D4—31no—
93C22×C3×D4—31no—
94C23×C3×C4—32no—
95C22×#67—34no—
96C22×#67—34no—
97C22×#67—32no—
98C22×#67—34no—
99C22×#67—32no—
100C22×D12—32no—
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—34no—
104C22×D12—32no—
105C22×D12—61no—
106C22×D12C2×D311yescharacteristic
107C22×D12C2×D311yescharacteristic
108C22×C4×D3C2×D312yes—
109C3×C4×D4—64no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—34no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117#940—64no—
118#940—64no—
119#940—64no—
120#940—64no—
121#930—616no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—64no—
125C2×(C2×D3)⋊C4C2×D312yes—
126C2×(C2×D3)⋊C4C2×D314yes—
127C2×C4⋊Dic3—32no—
128C2×Dic3⋊C4—32no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3C2×D311yescharacteristic
133C2×C4×Dic3C2×D311yescharacteristic
134#893—24no—
135#884—616no—
136#874—64no—
137#874—64no—
138C3⋊#95—32no—
139C3⋊#95—32no—
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—24no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4#4112yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D414yes—
164C4⋊(C3⋊D3)—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D414yes—
169C2×C3×Dic3C2×D414yes—
170C2×C3×Dic3C2×D412yes—
171C2×C3×Dic3C2×D412yes—
172C3×D12—28no—
173C3×D12—44no—
174C3×C4×D3—48no—
175#626—416no—
176#626—48no—
177#626—48no—
178#625—416no—
179C2×#127—91no—
180C2×#127—91no—
181C2×#127—91no—
182C2×#121—94no—
183C2×C4×D4—31no—
184#392—94no—
185#390—31no—
186#390—91no—
187C4×C4⋊C4—91no—
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—62no—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—62no—
200C2×C3×D4—62no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—68no—
207C22×C3×C4—64no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—68no—
213C2×#67—68no—
214C2×#67—68no—
215C2×#67—68no—
216C2×#67—68no—
217C2×#67—68no—
218C2×#67—68no—
219C2×#67—64no—
220C2×#67—64no—
221C2×#67—124no—
222C2×#67—124no—
223C2×#67—124no—
224C2×#67—124no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—62no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C2×D12—22no—
232C2×D12—22no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—22no—
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×D12D1214yescomplemented
253C2×C4×D3—28no—
254C2×C4×D3—24no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—42no—
258C3×C22⋊C4—68no—
259C3×C22⋊C4—64no—
260C3×C42—34no—
261C3×C42—62no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—68no—
265(C2×D3)⋊C4—68no—
266(C2×D3)⋊C4—128no—
267C4⋊Dic3—38no—
268Dic3⋊C4—38no—
269C4×Dic3—22no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—122no—
273C4×Dic3#6714yescomplemented
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—42no—
295C32×C4#12114yescomplemented
296C3⋊Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3#12714yescomplemented
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—92no—
303C22×D4—94no—
304C22×D4—92no—
305C22×D4—94no—
306C22×D4—91no—
307C23×C4—32no—
308#127—184no—
309#127—184no—
310#127—184no—
311#121—1816no—
312C4×D4—64no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4D3211yescharacteristic
315C2×C22⋊C4—32no—
316C2×C22⋊C4—34no—
317C2×C22⋊C4—94no—
318C2×C42—31no—
319C2×C42—31no—
320C2×C42—91no—
321#95—92no—
322C23×C3—21no—
323C23×C3—34no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—64no—
327C23×C3—64no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—64no—
331C23×C3—64no—
332C23×C3—62no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—24no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—64no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—62no—
355C22×D3—124no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—124no—
359C22×D3C2×D1214yes—
360C3×D4—68no—
361C3×D4—124no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—34no—
370C2×C3×C4—32no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—44no—
374C2×C3×C4—42no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—128no—
379C2×C3×C4C2×D1212yes—
380C2×C3×C4#23512yes—
381C2×C3×C4#23512yes—
382C2×C3×C4D3×D412yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4C2×#6712yes—
385#67—1216no—
386#67—128no—
387#67—1216no—
388#67—1216no—
389#67—128no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3D3×D414yes—
403C2×Dic3D3×D414yes—
404C2×Dic3C2×#6712yes—
405C2×Dic3C2×#6712yes—
406D12—28no—
407D12—44no—
408D12—128no—
409D12—128no—
410D12—1216no—
411D12—128no—
412D12—124no—
413D12—124no—
414C4×D3—48no—
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—62no—
428C2×D4—62no—
429C2×D4—62no—
430C2×D4—62no—
431C2×D4—62no—
432C2×D4—188no—
433C2×D4—188no—
434C2×D4—184no—
435C2×D4—184no—
436C2×D4—188no—
437C2×D4—188no—
438C2×D4—188no—
439C2×D4—182no—
440C2×D4—182no—
441C2×D4—182no—
442C2×D4—364no—
443C2×D4—364no—
444C2×D4—364no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—64no—
449C22×C4—68no—
450C22×C4—92no—
451C22×C4C2×D3212yes—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—22no—
454C4⋊C4—98no—
455C22⋊C4—64no—
456C22⋊C4—68no—
457C22⋊C4—188no—
458C42—34no—
459C42—62no—
460C42—182no—
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—124no—
474C22×C3—124no—
475C22×C3—122no—
476C22×C3C22×D1211yescharacteristic
477C22×C3C2×#23511yescharacteristic
478C22×C3C2×#23511yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C22×C3C2×D3×D412yes—
481C22×C3C2×D3×D412yes—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3#100912yes—
484C22×C3#100912yes—
485C22×C3C22×#6711yescharacteristic
486C2×D3—24no—
487C2×D3—28no—
488C2×D3—42no—
489C2×D3—44no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—44no—
495C2×D3—44no—
496C2×D3—124no—
497C2×D3—128no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—124no—
504C2×D3—124no—
505C2×D3—124no—
506C2×D3—122no—
507C2×D3—124no—
508C2×D3—244no—
509C2×D3—242no—
510C2×D3—242no—
511C3×C4—24no—
512C3×C4—34no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—62no—
516C3×C4—64no—
517C3×C4—82no—
518C3×C4#88414yescomplemented
519C3×C4#93014yescomplemented
520Dic3—22no—
521Dic3—24no—
522Dic3—64no—
523Dic3—64no—
524Dic3—124no—
525Dic3#94014yescomplemented
526C32#254111yescharacteristic, complemented, Sylow
527C23—34no—
528C23—62no—
529C23—64no—
530C23—64no—
531C23—62no—
532C23—62no—
533C23—62no—
534C23—64no—
535C23—64no—
536C23—62no—
537C23—182no—
538C23—182no—
539C23—184no—
540C23—184no—
541C23—182no—
542C23C22×D3211yescharacteristic
543D4—68no—
544D4—124no—
545D4—368no—
546D4—3616no—
547D4—368no—
548D4—3616no—
549D4—364no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—34no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—32no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—94no—
560C2×C4—128no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4#379812yes—
564C2×C4D3×D1212yes—
565C2×C4D3×#6712yes—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—124no—
572C2×C3—242no—
573C2×C3C2×#88411yescharacteristic
574C2×C3D4×D1212yes—
575C2×C3#555312yes—
576C2×C3#555312yes—
577C2×C3#560912yes—
578C2×C3#567411yescharacteristic
579C2×C3D3×#12711yescharacteristic
580C2×C3C2×#93011yescharacteristic
581C2×C3C2×#94011yescharacteristic
582C2×C3#583011yescharacteristic
583D3—44no—
584D3—82no—
585D3—244no—
586D3—242no—
587D3—242no—
588C22—68no—
589C22—64no—
590C22—122no—
591C22—122no—
592C22—124no—
593C22—124no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—124no—
598C22—364no—
599C22—362no—
600C22—362no—
601C22—362no—
602C22—364no—
603C22C2×#379811yescharacteristic
604C22C2×D3×D1211yescharacteristic
605C22D32×D412yes—
606C22#6432012yes—
607C22C2×D3×#6711yescharacteristic
608C4—34no—
609C4—42no—
610C4—64no—
611C4—62no—
612C4—184no—
613C4#6390614yescomplemented
614C3—21no—
615C3#7634811yescharacteristic, complemented
616C3#8237811yescharacteristic, complemented
617C2—124no—
618C2—242no—
619C2—722no—
620C2#1059452012yes—
621C2#1059462112yes—
622C2C2×#6390611yescharacteristic
623C2D3×#94011yescharacteristic
624C2#1059542611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. C2×#63914C2semidirect
3. C2×#63911C2semidirect
4. C2×#63911C2semidirect
5. C2×#63906C2semidirect
6. #10592687C2semidirect
7. C3×#4988C2semidirect
8. #10591393C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
40. C2×#893D3semidirect
48. #4988D3semidirect
70. C2×C3×D12D4semidirect
89. C3×C4×Dic3D4semidirect
90. Dic3⋊Dic3D4semidirect
252. C2×D12D12semidirect
273. C4×Dic3#67semidirect
295. C32×C4#121semidirect
299. C3×Dic3#127semidirect
518. C3×C4#884semidirect
519. C3×C4#930semidirect
525. Dic3#940semidirect
526. C32#2541semidirect
613. C4#63906semidirect
615. C3#76348semidirect
616. C3#82378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639142
C2×#639112
C2×#639062
#105926872
C3×#49882
#105913932
C4×Dic3⋊Dic32
#823783
#763483