Finite Group Databasebeta

← #11864994

Subgroups — #11864994

Order 1152.

1523 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3#10594786C212yesmaximal, complemented
4#10592936C211yesmaximal, characteristic, complemented
5#10591648C212yesmaximal, complemented
6#10591645C212yesmaximal, complemented
7#10591512C212yesmaximal, complemented
8#10591509C212yesmaximal, complemented
9C2×#63569C212yesmaximal, complemented
10#84121—31nomaximal
11#83322—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—22no—
14C3×#1009—22no—
15C3×D3×#41—24no—
16C3×#1007C2212yes—
17C3×#1004—22no—
18C3×#1004C2212yes—
19C2×C3×#235—22no—
20C2×C3×#235C2212yes—
21C2×C3×#235C2211yescharacteristic, complemented
22C2×#3748C2212yescomplemented
23C3×#947C2211yescharacteristic, complemented
24C3×#944C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C3×#939—22no—
27C3×#936C2211yescharacteristic, complemented
28C3×C4×#67—22no—
29C2×C3×C4×Dic3C2211yescharacteristic, complemented
30#63827—22no—
31#63827C2214yescomplemented
32#63823—22no—
33#63823C2214yescomplemented
34#63822—24no—
35#63663C2212yescomplemented
36#63660C2212yescomplemented
37#63569C2214yescomplemented
38#63569C2214yescomplemented
39C3×#585—31no—
40#5964D311yescharacteristic, complemented
41C3×#532—31no—
42#5832D311yescharacteristic, complemented
43#5822—32no—
44#5822—32no—
45#5246—32no—
46#5245—32no—
47#5242—32no—
48#5241—32no—
49#5237—31no—
50#5237—31no—
51#5237—61no—
52C2×#837—32no—
53#5095—32no—
54#5077—32no—
55#5062—32no—
56#5061—32no—
57C2×#805—32no—
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8C2311yescharacteristic
61C2×C32×D4D412yes—
62C2×C32×D4C2311yescharacteristic
63C22×C32×C4D412yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—24no—
66C2×C3×#67—22no—
67C2×C3×#67—22no—
68C2×C3×#67—21no—
69C22×C3×Dic3—21no—
70C3×#239—24no—
71C3×D3×Q8—24no—
72C3×#237—28no—
73C3×#237—24no—
74C3×D3×D4—28no—
75C3×D3×D4—24no—
76C3×#235—24no—
77C3×#235—24no—
78C3×#235—22no—
79C3×#235—24no—
80C3×#235—22no—
81C3×#235—22no—
82C3×#235—22no—
83C3×#235D414yescomplemented
84C3×#235C2314yes—
85C2×C3×D12—22no—
86C2×C3×D12D412yescomplemented
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—21no—
91C2×C3×Dic6—22no—
92C2×C3×Dic6D412yescomplemented
93C2×C3×Dic6C2311yescharacteristic
94#3748—22no—
95#3748C2314yes—
96C2×C3⋊(C3⋊C8)—22no—
97C3×#217—22no—
98C3×(C2×D3)⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103#3718—24no—
104#3715—24no—
105#3715—24no—
106#3713—24no—
107#3018—91noSylow
108C3×2−1+4—32no—
109C3×2−1+4—62no—
110C3×H(5,𝔽2)—32no—
111C3×H(5,𝔽2)—62no—
112C3×H(5,𝔽2)—62no—
113C2×C3×#41—21no—
114C2×C3×#41—32no—
115C2×C3×#41—31no—
116C2×C3×#41—64no—
117C2×C3×#41—62no—
118C2×C3×#41C2×D311yescharacteristic
119C2×C3×#41C2×D311yescharacteristic
120#1010—22no—
121#1009—22no—
122D3×#41—24no—
123#1007C2×D312yes—
124#1004—22no—
125#1004C2×D312yes—
126C2×#235—22no—
127C2×#235C2×D312yes—
128C2×#235C2×D311yescharacteristic, complemented
129C3×C4⋊Q8—31no—
130C3×#127—31no—
131C3×#124—31no—
132C3×#124—31no—
133C3×#121—62no—
134C3×C4×D4—62no—
135C2×C3×C42—31no—
136#951—34no—
137#951—62no—
138#950—64no—
139#950—64no—
140#949—34no—
141#949—62no—
142#947C2×D311yescharacteristic, complemented
143#944C2×D311yescharacteristic, complemented
144#942—34no—
145#942—62no—
146#940C2×D311yescharacteristic, complemented
147#939—22no—
148#936C2×D311yescharacteristic, complemented
149#932—34no—
150#932—62no—
151C4×#67—22no—
152C2×C4×Dic3C2×D311yescharacteristic, complemented
153C2×#208—32no—
154C2×#208—32no—
155C2×#208—62no—
156#837—34no—
157#837—34no—
158#836—32no—
159#836—32no—
160#836—62no—
161#833—32no—
162#833—32no—
163#833—62no—
164#805—34no—
165#805—34no—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—24no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C32×Q8—22no—
172C32×D4—24no—
173C32×D4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C3×#67—28no—
182C3×#67—24no—
183C3×#67—24no—
184C3×#67—44no—
185C3×#67—42no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—42no—
192C3×D12—24no—
193C3×D12—22no—
194C3×D12—22no—
195C3×D12C2×D414yes—
196C3×C4×D3—28no—
197C3×C4×D3—24no—
198C3×C4×D3—24no—
199C3×C4×D3—41no—
200C3×C4×D3—41no—
201C3×Dic6—24no—
202C3×Dic6—22no—
203C3×Dic6—22no—
204C3×Dic6C2×D414yes—
205C3⋊(C3⋊C8)—24no—
206#585—31no—
207#575—92no—
208#532—31no—
209#456—92no—
210#455—92no—
211#454—92no—
212#453—92no—
213C2×#104—92no—
214#413—91no—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—34no—
220C3×#41—34no—
221C3×#41—42no—
222C3×#41—42no—
223C3×#41—64no—
224C3×#41—64no—
225C3×#41—64no—
226C3×#41—68no—
227C3×#41—64no—
228C3×#41—62no—
229C3×#41—62no—
230C3×#41—64no—
231C3×#41—62no—
232C3×#41—62no—
233C2×C3×Q8—21no—
234C2×C3×Q8—32no—
235C2×C3×Q8—31no—
236C2×C3×Q8—62no—
237C2×C3×Q8—64no—
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×Q8C22×D311yescharacteristic
240C2×C3×D4—22no—
241C2×C3×D4—21no—
242C2×C3×D4—32no—
243C2×C3×D4—31no—
244C2×C3×D4—62no—
245C2×C3×D4—64no—
246C2×C3×D4—68no—
247C2×C3×D4—62no—
248C2×C3×D4—64no—
249C2×C3×D4—62no—
250C2×C3×D4—61no—
251C2×C3×D4#6712yes—
252C2×C3×D4#6712yes—
253C2×C3×D4C22×D311yescharacteristic
254C2×C3×D4C22×D311yescharacteristic
255C22×C3×C4—22no—
256C22×C3×C4—21no—
257C22×C3×C4—64no—
258C22×C3×C4—62no—
259C22×C3×C4—61no—
260C22×C3×C4—61no—
261C22×C3×C4#6712yes—
262C22×C3×C4#6712yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C2×#67—24no—
266C2×#67—22no—
267C2×#67—22no—
268C2×#67—21no—
269C22×Dic3—21no—
270#239—24no—
271D3×Q8—24no—
272#237—28no—
273#237—24no—
274D3×D4—28no—
275D3×D4—24no—
276#235—24no—
277#235—24no—
278#235—22no—
279#235—24no—
280#235—22no—
281#235—22no—
282#235—22no—
283#235#6714yescomplemented
284#235C22×D314yes—
285C2×D12—22no—
286C2×D12#6712yescomplemented
287C2×D12C22×D311yescharacteristic
288C2×C4×D3—24no—
289C2×C4×D3—22no—
290C2×C4×D3—21no—
291C2×Dic6—22no—
292C2×Dic6#6712yescomplemented
293C2×Dic6C22×D311yescharacteristic
294C3×C4⋊C4—62no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C42—31no—
298C3×C42—31no—
299C3×C42—61no—
300#217—22no—
301#216—64no—
302#216—64no—
303#215—64no—
304#215—64no—
305#214—64no—
306#214—64no—
307#213—64no—
308#213—64no—
309(C2×D3)⋊C4—22no—
310Dic3⋊C4—22no—
311C4×Dic3—21no—
312C4×Dic3C22×D311yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314#208—34no—
315#208—34no—
316#208—64no—
317#208—62no—
318#208—62no—
319#208—122no—
320C2×C3⋊C8—62no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8—122no—
323C22×C32—22no—
324C22×C32—41no—
325C22×C32—42no—
326C22×C32#12012yes—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—24no—
329C2×C3×D3—42no—
330C2×C3×D3—41no—
331C2×C3×D3—82no—
332C2×C3×D3—84no—
333C32×C4—22no—
334C32×C4#12011yescharacteristic
335C32×C4#12011yescharacteristic
336C32×C4C22×D412yes—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—41no—
340C3×Dic3—41no—
3412−1+4—32no—
3422−1+4—62no—
343H(5,𝔽2)—32no—
344H(5,𝔽2)—62no—
345H(5,𝔽2)—62no—
346C2×#41—32no—
347C2×#41—31no—
348C2×#41—64no—
349C2×#41—62no—
350C2×#41D3211yescharacteristic
351#137—94no—
352#137—182no—
353AGL(1,ℤ/8)—94no—
354AGL(1,ℤ/8)—182no—
355#135—184no—
356C2×M16—92no—
357C4⋊Q8—31no—
358#127—31no—
359#124—31no—
360#124—31no—
361#121—62no—
362C4×D4—62no—
363C2×C42—31no—
364#104—94no—
365#104—94no—
366#101—92no—
367#100—92no—
368C23×C3—21no—
369C23×C3—22no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3C2×#6712yes—
374C23×C3C2×#6712yes—
375C23×C3C2×#6711yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—24no—
378C22×D3—22no—
379C22×D3—21no—
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—34no—
383C3×Q8—42no—
384C3×Q8—64no—
385C3×Q8—62no—
386C3×Q8—62no—
387C3×D4—24no—
388C3×D4—24no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—34no—
392C3×D4—42no—
393C3×D4—44no—
394C3×D4—64no—
395C3×D4—68no—
396C3×D4—64no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4—62no—
400C3×D4—124no—
401C3×D4—122no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—68no—
414C2×C3×C4—64no—
415C2×C3×C4—62no—
416C2×C3×C4—61no—
417C2×C3×C4—64no—
418C2×C3×C4—64no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—122no—
422C2×C3×C4—121no—
423C2×C3×C4—121no—
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×D412yes—
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6712yes—
431C2×C3×C4C2×#6712yes—
432C2×C3×C4C23×D311yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434#67—28no—
435#67—24no—
436#67—24no—
437#67—44no—
438#67—42no—
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—42no—
445D12—24no—
446D12—22no—
447D12—22no—
448D12C2×#6714yes—
449C4×D3—28no—
450C4×D3—24no—
451C4×D3—24no—
452C4×D3—41no—
453C4×D3—41no—
454Dic6—24no—
455Dic6—22no—
456Dic6—22no—
457Dic6C2×#6714yes—
458C3⋊C8—64no—
459C3⋊C8—64no—
460C3⋊C8—124no—
461C2×C32—21no—
462C2×C32—22no—
463C2×C32—42no—
464C2×C32C2×#12011yescharacteristic
465C3×D3—44no—
466C3×D3—81no—
467#41—22no—
468#41—22no—
469#41—34no—
470#41—34no—
471#41—64no—
472#41—64no—
473#41—64no—
474#41—68no—
475#41—64no—
476#41—62no—
477#41—64no—
478#41—62no—
479#41—62no—
480#41—62no—
481C2×Q8—31no—
482C2×Q8—32no—
483C2×Q8—62no—
484C2×Q8—64no—
485C2×Q8C2×D3211yescharacteristic
486C2×D4—31no—
487C2×D4—32no—
488C2×D4—62no—
489C2×D4—64no—
490C2×D4—68no—
491C2×D4—62no—
492C2×D4—64no—
493C2×D4—62no—
494C2×D4—61no—
495C2×D4#62512yes—
496C2×D4C2×D3211yescharacteristic
497C22×C4—64no—
498C22×C4—62no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4#62512yes—
502C22×C4C2×D3211yescharacteristic
503Q16—184no—
504SD16—184no—
505SD16—184no—
506D8—184no—
507M16—94no—
508M16—182no—
509C2×C8—182no—
510C4⋊C4—62no—
511C22⋊C4—62no—
512C22⋊C4—62no—
513C42—31no—
514C42—31no—
515C42—61no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—42no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—64no—
526C22×C3—81no—
527C22×C3—82no—
528C22×C3—122no—
529C22×C3—121no—
530C22×C3—242no—
531C22×C3—244no—
532C22×C3#93712yes—
533C22×C3#95312yes—
534C22×C3C22×#6711yescharacteristic
535C22×C3C22×#6711yescharacteristic
536C2×D3—24no—
537C2×D3—42no—
538C2×D3—41no—
539C2×D3—82no—
540C2×D3—84no—
541C3×C4—22no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—42no—
547C3×C4—62no—
548C3×C4—64no—
549C3×C4—121no—
550C3×C4—121no—
551C3×C4#93711yescharacteristic
552C3×C4#93711yescharacteristic
553C3×C4#95311yescharacteristic
554C3×C4#95311yescharacteristic
555C3×C4C2×D3×D412yes—
556C3×C4C22×#6712yes—
557Dic3—22no—
558Dic3—24no—
559Dic3—41no—
560Dic3—41no—
561C32#301811yescharacteristic, complemented, Sylow
562C23—64no—
563C23—62no—
564C23—61no—
565C23C2×#62512yes—
566C23C2×#62511yescharacteristic
567Q8—22no—
568Q8—34no—
569Q8—64no—
570Q8—62no—
571Q8—62no—
572D4—24no—
573D4—22no—
574D4—34no—
575D4—64no—
576D4—68no—
577D4—64no—
578D4—64no—
579D4—62no—
580D4—62no—
581D4—124no—
582D4—122no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—68no—
586C2×C4—64no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—64no—
590C2×C4—64no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—122no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4C2×#62512yes—
597C2×C4C2×#62511yescharacteristic
598C2×C4D3×#6712yes—
599C2×C4D3×#6712yes—
600C2×C4C22×D3211yescharacteristic
601C8—184no—
602C2×C3—21no—
603C2×C3—22no—
604C2×C3—21no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—41no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3—42no—
611C2×C3—82no—
612C2×C3—124no—
613C2×C3—241no—
614C2×C3C2×#93711yescharacteristic
615C2×C3C2×#95311yescharacteristic
616D3—44no—
617D3—81no—
618C22—22no—
619C22—41no—
620C22—42no—
621C22—64no—
622C22—122no—
623C22—121no—
624C22—242no—
625C22—244no—
626C22#6397612yes—
627C22C22×#62511yescharacteristic
628C4—22no—
629C4—62no—
630C4—64no—
631C4—121no—
632C4—121no—
633C4#6397611yescharacteristic
634C4#6397611yescharacteristic
635C4C2×D3×#6712yes—
636C3—21no—
637C3#8332211yescharacteristic, complemented
638C3#8412111yescharacteristic, complemented
639C2—21no—
640C2—22no—
641C2—42no—
642C2—124no—
643C2—241no—
644C2C2×#6397611yescharacteristic
subgroupG/H
centerC4#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3018
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C3×#5832C2semidirect
3. #10594786C2semidirect
4. #10592936C2semidirect
5. #10591648C2semidirect
6. #10591645C2semidirect
7. #10591512C2semidirect
8. #10591509C2semidirect
9. C2×#63569C2semidirect
21. C2×C3×#235C22semidirect
22. C2×#3748C22semidirect
23. C3×#947C22semidirect
24. C3×#944C22semidirect
25. C3×#940C22semidirect
27. C3×#936C22semidirect
29. C2×C3×C4×Dic3C22semidirect
31. #63827C22semidirect
33. #63823C22semidirect
35. #63663C22semidirect
36. #63660C22semidirect
37. #63569C22semidirect
38. #63569C22semidirect
40. #5964D3semidirect
42. #5832D3semidirect
83. C3×#235D4semidirect
86. C2×C3×D12D4semidirect
92. C2×C3×Dic6D4semidirect
128. C2×#235C2×D3semidirect
142. #947C2×D3semidirect
143. #944C2×D3semidirect
146. #940C2×D3semidirect
148. #936C2×D3semidirect
152. C2×C4×Dic3C2×D3semidirect
283. #235#67semidirect
286. C2×D12#67semidirect
292. C2×Dic6#67semidirect
561. C32#3018semidirect
637. C3#83322semidirect
638. C3#84121semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C3×#58322
#105947862
#105929362
#105916482
#105916452
#105915122
#105915092
C2×#635692
#841213
#833223