Finite Group Databasebeta

← #11864365

Subgroups — #11864365

Order 1152.

1599 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10591461C214yesmaximal, complemented
7#10591458C214yesmaximal, complemented
8#10591084C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84105—31nomaximal
11#83859—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—22no—
14C3×#1004—24no—
15C3×#1004—24no—
16C2×C3×#237—21no—
17C2×C3×#237C2212yes—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2212yes—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23#64135C2211yescharacteristic, complemented
24C2×#3748C2211yescharacteristic, complemented
25C2×C3×#214—24no—
26C2×C3×#214C2214yescomplemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28#63961—22no—
29#63873—21no—
30#63863—21no—
31#63856C2214yescomplemented
32C2×#3718C2212yescomplemented
33#63827—24no—
34C2×#3715C2212yescomplemented
35#63659C2214yescomplemented
36#63566C2212yescomplemented
37#63563C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1004D311yescharacteristic
41C22×C3×SD16—31no—
42#5825—31no—
43C2×#951—31no—
44#5816—31no—
45C2×#942—31no—
46C22×#214D311yescharacteristic, complemented
47#5239—34no—
48#5234—31no—
49#5233—31no—
50#5218—34no—
51#5215—31no—
52#5215—31no—
53#5215—61no—
54#5173—34no—
55#5169—34no—
56#5113—31no—
57#5110—31no—
58C24×C32—21no—
59C23×C3×D3—22no—
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yes—
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—216no—
66C2×C3×#67—21no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67D412yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—21no—
72C3×#237—28no—
73C3×#237—24no—
74C3×#237—24no—
75C3×D3×D4—28no—
76C3×D3×D4—24no—
77C3×D3×D4—24no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yes—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—21no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6C2312yes—
91C2×C3×Dic6C2311yescharacteristic
92#3757—21no—
93C4⋊(C3⋊Dic3)C2312yes—
94C4×C3⋊Dic3—21no—
95#3748—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#214—28no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100#3724—24no—
101(C2×D3)⋊Dic3—24no—
102#3718—24no—
103#3715—24no—
104#3009—91noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—61no—
111C22×C3×Q8—31no—
112C22×C3×D4—21no—
113C22×C3×D4—32no—
114C22×C3×D4—61no—
115C22×C3×D4—62no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C2×D311yescharacteristic
118C22×#67—22no—
119#1004—24no—
120#1004—24no—
121C2×#237—21no—
122C2×#237C2×D312yes—
123C2×D3×D4—21no—
124C2×D3×D4C2×D312yes—
125C2×#235C2×D311yescharacteristic
126C2×#235C2×D311yescharacteristic
127C22×Dic6C2×D311yescharacteristic, complemented
128C2×C3×SD16—34no—
129C2×C3×SD16—64no—
130C22×C3×C8—31no—
131#951—64no—
132#947—61no—
133#946—34no—
134#944—61no—
135#944—61no—
136C2×#216—32no—
137C2×#216—32no—
138#942—64no—
139C2×#215—32no—
140#936—61no—
141#935—62no—
142C2×#214—24no—
143C2×#214—32no—
144C2×#214C2×D314yescomplemented
145#929—62no—
146#926—31no—
147#926—31no—
148#926—61no—
149#924—34no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C22×C3⋊C8C2×D311yescharacteristic, complemented
154#835—32no—
155#832—34no—
156#832—34no—
157#832—32no—
158#832—64no—
159#830—34no—
160#821—32no—
161(C2×D3)⋊C8—34no—
162#816—32no—
163C23×C32—22no—
164C23×C32—24no—
165C23×C32—82no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—28no—
169C22×C3×D3—84no—
170C22×C3×D3C2×D412yes—
171C32×D4—24no—
172C32×D4—22no—
173C32×D4C2×D414yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C3×#67—28no—
180C3×#67—28no—
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—28no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—42no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×D12—21no—
190C3×D12C2×D412yes—
191C3×C4×D3—24no—
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—22no—
195C3×Dic6—21no—
196C3×Dic6—22no—
197C3×Dic6—22no—
198C3×Dic6—42no—
199C3×Dic6C2×D412yes—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C2×H(5,𝔽2)—31no—
203C2×#137—91no—
204C22×SD16—31no—
205#536—91no—
206#452—94no—
207#450—94no—
208#418—91no—
209#416—91no—
210#408—91no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—41no—
214C24×C3—62no—
215C23×D3—22no—
216C3×#41—34no—
217C3×#41—64no—
218C3×#41—68no—
219C3×#41—64no—
220C3×#41—62no—
221C3×#41—62no—
222C3×#41—62no—
223C2×C3×Q8—31no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—61no—
227C2×C3×Q8—62no—
228C2×C3×Q8—62no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—32no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—41no—
239C2×C3×D4—42no—
240C2×C3×D4—62no—
241C2×C3×D4—64no—
242C2×C3×D4—68no—
243C2×C3×D4—62no—
244C2×C3×D4—616no—
245C2×C3×D4—61no—
246C2×C3×D4—64no—
247C2×C3×D4#6714yes—
248C2×C3×D4#6714yes—
249C2×C3×D4C22×D312yes—
250C2×C3×D4C22×D312yes—
251C22×C3×C4—21no—
252C22×C3×C4—32no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—216no—
259C2×#67—21no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67#6712yes—
263C22×Dic3—22no—
264C22×Dic3—21no—
265#237—28no—
266#237—24no—
267#237—24no—
268D3×D4—28no—
269D3×D4—24no—
270D3×D4—24no—
271#235—22no—
272#235—22no—
273#235—22no—
274#235#6714yes—
275C2×D12#6711yescharacteristic
276C2×D12C22×D311yescharacteristic
277C2×C4×D3—21no—
278C2×C4×D3C22×D312yes—
279C2×Dic6—22no—
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6#6711yescharacteristic
283C2×Dic6C22×D312yes—
284C2×Dic6C22×D311yescharacteristic
285C3×SD16—68no—
286C2×C3×C8—32no—
287C2×C3×C8—62no—
288#217—64no—
289#217—61no—
290#217—61no—
291#217—121no—
292#216—64no—
293#216—64no—
294#215—64no—
295#214—28no—
296#214—64no—
297(C2×D3)⋊C4—64no—
298C4⋊Dic3—32no—
299C4⋊Dic3—32no—
300C4⋊Dic3—62no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—121no—
306#208—62no—
307#208—62no—
308#208—122no—
309C2×C3⋊C8—22no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8C22×D312yes—
314C22×C32—22no—
315C22×C32—24no—
316C22×C32—44no—
317C22×C32—84no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—42no—
324C2×C3×D3—88no—
325C32×C4#12012yes—
326C32×C4C22×D411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3⋊Dic3—42no—
329C3×Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332H(5,𝔽2)—64no—
333H(5,𝔽2)—64no—
334C2×#41—31no—
335C2×#41—32no—
336C2×#41—31no—
337C2×#41—61no—
338C22×Q8—31no—
339C22×D4—32no—
340C22×D4—61no—
341C22×D4—62no—
342C22×D4D3211yescharacteristic
343#137—184no—
344C2×Q16—92no—
345C2×SD16—34no—
346C2×SD16—64no—
347C2×SD16—92no—
348C2×M16—91no—
349C22×C8—31no—
350C4⋊Q8—181no—
351#124—181no—
352#123—182no—
353C22⋊Q8—94no—
354#117—91no—
355#103—92no—
356#102—92no—
357#102—94no—
358C22⋊C8—94no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—42no—
366C23×C3—44no—
367C23×C3—68no—
368C23×C3—61no—
369C23×C3—82no—
370C23×C3—82no—
371C23×C3—84no—
372C23×C3—244no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C22×D3—21no—
376C22×D3—28no—
377C22×D3—84no—
378C22×D3C2×#6712yes—
379C3×Q8—32no—
380C3×Q8—62no—
381C3×Q8—61no—
382C3×Q8—62no—
383C3×Q8—62no—
384C3×Q8—122no—
385C3×D4—24no—
386C3×D4—24no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—24no—
390C3×D4—32no—
391C3×D4—42no—
392C3×D4—44no—
393C3×D4—68no—
394C3×D4—68no—
395C3×D4—64no—
396C3×D4—64no—
397C3×D4—62no—
398C3×D4—61no—
399C3×D4C2×#6714yes—
400C3×D4C2×#6714yes—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—32no—
406C2×C3×C4—68no—
407C2×C3×C4—61no—
408C2×C3×C4—64no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—122no—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6712yes—
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—28no—
422#67—28no—
423#67—24no—
424#67—24no—
425C2×Dic3—28no—
426C2×Dic3—21no—
427C2×Dic3—22no—
428C2×Dic3—42no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—122no—
432C2×Dic3C2×#6712yes—
433D12—22no—
434D12—21no—
435D12C2×#6712yes—
436C4×D3—24no—
437C4×D3—22no—
438C4×D3—22no—
439Dic6—22no—
440Dic6—21no—
441Dic6—22no—
442Dic6—22no—
443Dic6—42no—
444Dic6C2×#6712yes—
445C3×C8—62no—
446C3⋊C8—22no—
447C3⋊C8—62no—
448C3⋊C8—62no—
449C3⋊C8—122no—
450C2×C32—22no—
451C2×C32—44no—
452C2×C32C2×#12011yescharacteristic
453C2×C32#57712yes—
454C3×D3—42no—
455C3×D3—42no—
456C24—21no—
457C24—62no—
458#41—34no—
459#41—64no—
460#41—68no—
461#41—64no—
462#41—62no—
463#41—62no—
464#41—62no—
465C2×Q8—31no—
466C2×Q8—31no—
467C2×Q8—32no—
468C2×Q8—61no—
469C2×Q8—62no—
470C2×Q8—62no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—32no—
474C2×D4—31no—
475C2×D4—31no—
476C2×D4—62no—
477C2×D4—64no—
478C2×D4—68no—
479C2×D4—62no—
480C2×D4—616no—
481C2×D4—61no—
482C2×D4—64no—
483C2×D4#62514yes—
484C2×D4C2×D3212yes—
485C22×C4—32no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4C2×D3211yescharacteristic
490Q16—184no—
491SD16—68no—
492SD16—184no—
493M16—182no—
494C2×C8—32no—
495C2×C8—62no—
496C2×C8—92no—
497C4⋊C4—92no—
498C4⋊C4—184no—
499C22⋊C4—184no—
500C22⋊C4—181no—
501C42—181no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—42no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—64no—
513C22×C3—62no—
514C22×C3—62no—
515C22×C3—84no—
516C22×C3—84no—
517C22×C3—84no—
518C22×C3—88no—
519C22×C3—122no—
520C22×C3—248no—
521C22×C3#93712yes—
522C22×C3#95312yes—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C22×#6711yescharacteristic
525C2×D3—24no—
526C2×D3—22no—
527C2×D3—22no—
528C2×D3—42no—
529C2×D3—88no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—62no—
534C3×C4—62no—
535C3×C4—122no—
536C3×C4#93712yes—
537C3×C4#95312yes—
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540C3×C4C22×#6711yescharacteristic
541C3×C4C22×#6711yescharacteristic
542Dic3—22no—
543Dic3—22no—
544Dic3—42no—
545Dic3—122no—
546Dic3—122no—
547Dic3—242no—
548C32#300911yescharacteristic, complemented, Sylow
549C23—22no—
550C23—24no—
551C23—32no—
552C23—68no—
553C23—61no—
554C23—82no—
555C23—244no—
556C23D3×#6711yescharacteristic
557Q8—32no—
558Q8—61no—
559Q8—62no—
560Q8—62no—
561Q8—62no—
562Q8—122no—
563D4—22no—
564D4—24no—
565D4—32no—
566D4—68no—
567D4—68no—
568D4—64no—
569D4—64no—
570D4—61no—
571D4—62no—
572D4C2×#62514yes—
573C2×C4—32no—
574C2×C4—68no—
575C2×C4—61no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—64no—
579C2×C4—62no—
580C2×C4—122no—
581C2×C4—182no—
582C2×C4C2×#62512yes—
583C2×C4D3×#6712yes—
584C2×C4D3×#6711yescharacteristic
585C2×C4C22×D3211yescharacteristic
586C8—62no—
587C8—182no—
588C2×C3—22no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—42no—
593C2×C3—44no—
594C2×C3—44no—
595C2×C3—84no—
596C2×C3—122no—
597C2×C3—122no—
598C2×C3#576212yes—
599C2×C3C2×#93711yescharacteristic
600C2×C3#583612yes—
601C2×C3C2×#95311yescharacteristic
602D3—42no—
603D3—42no—
604C22—22no—
605C22—24no—
606C22—44no—
607C22—64no—
608C22—62no—
609C22—62no—
610C22—84no—
611C22—122no—
612C22—248no—
613C22#6397612yes—
614C22C2×D3×#6711yescharacteristic
615C4—62no—
616C4—62no—
617C4—122no—
618C4—362no—
619C4#6397612yes—
620C4C22×#62511yescharacteristic
621C4C2×D3×#6711yescharacteristic
622C3—21no—
623C3#8385911yescharacteristic, complemented
624C3#8410511yescharacteristic, complemented
625C2—22no—
626C2—44no—
627C2—122no—
628C2—122no—
629C2#1059510512yes—
630C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#1004C2
hypercenterC22×D4D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. #10594855C2semidirect
4. C2×#63827C2semidirect
5. #10592914C2semidirect
6. #10591461C2semidirect
7. #10591458C2semidirect
8. #10591084C2semidirect
9. #10591070C2semidirect
22. C22×C3×Dic6C22semidirect
23. #64135C22semidirect
24. C2×#3748C22semidirect
26. C2×C3×#214C22semidirect
27. C22×C3×C3⋊C8C22semidirect
31. #63856C22semidirect
32. C2×#3718C22semidirect
34. C2×#3715C22semidirect
35. #63659C22semidirect
36. #63566C22semidirect
37. #63563C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
46. C22×#214D3semidirect
127. C22×Dic6C2×D3semidirect
144. C2×#214C2×D3semidirect
153. C22×C3⋊C8C2×D3semidirect
548. C32#3009semidirect
623. C3#83859semidirect
624. C3#84105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×C3×#2142
#105948552
C2×#638272
#105929142
#105914612
#105914582
#105910842
#105910702
#841053
#838593