Finite Group Databasebeta

← #11868125

Subgroups — #11868125

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5#10592936C211yesmaximal, characteristic, complemented
6#10591642C214yesmaximal, complemented
7#10591505C214yesmaximal, complemented
8#10591141C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#84002—31nomaximal
11#83963—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#951—21no—
18C3×#950—22no—
19C3×#949—21no—
20C3×#949—22no—
21C3×#949—22no—
22C3×#942C2212yescomplemented
23C2×C3×#215C2212yescomplemented
24C3×#932C2212yescomplemented
25C2×C3×#213C2212yescomplemented
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×#3715—21no—
29#63823—22no—
30#63823C2214yes—
31C2×#3713—21no—
32#63815—22no—
33#63814C2214yescomplemented
34D3×#208—22no—
35#63663C2212yescomplemented
36#63660C2212yescomplemented
37#63577C2214yescomplemented
38#63558C2214yescomplemented
39C3×#575—31no—
40C2×C3×AGL(1,ℤ/8)—31no—
41#5822D311yescharacteristic, complemented
42C2×#949—31no—
43C2×#949D311yescharacteristic, complemented
44#5819—31no—
45C2×#932—31no—
46#5745—31no—
47#5237—31no—
48#5237—31no—
49#5237—61no—
50C2×#833—31no—
51#5203—34no—
52#5199—34no—
53#5177—34no—
54#5160—34no—
55C2×#823—31no—
56#5125—31no—
57#5124—31no—
58C23×C3×D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41—21no—
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235D412yes—
72C3×#235C2312yes—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12D411yescharacteristic
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—21no—
81C2×C3×Dic6D411yescharacteristic
82#3748—21no—
83#3748—21no—
84#3748C2312yes—
85#3748C2312yes—
86C2×C3⋊(C3⋊C8)—21no—
87C2×C3⋊(C3⋊C8)—21no—
88C3×#216—22no—
89C3×#215—22no—
90C3×#215—24no—
91C3×#214—22no—
92C3×#213—22no—
93C3×#213—24no—
94C3×#208—21no—
95C3×#208D412yes—
96C3×#208D412yes—
97C3×#208C2312yes—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8C2312yes—
100#3715—24no—
101#3713—24no—
102#3711—24no—
103D3×C3⋊C8—24no—
104#3068—91noSylow
105C2×C3×#41—21no—
106C2×C3×#41—31no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C22×C3×D4—31no—
110C2×#235C2×D311yescharacteristic
111C22×D12C2×D311yescharacteristic
112C3×#137—32no—
113C3×#137—61no—
114C3×AGL(1,ℤ/8)—32no—
115C3×AGL(1,ℤ/8)—62no—
116C3×AGL(1,ℤ/8)—62no—
117C3×AGL(1,ℤ/8)—61no—
118C3×#135—62no—
119C2×C3×SD16—32no—
120C2×C3×D8—32no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123#951—21no—
124#950—22no—
125#949—21no—
126#949—22no—
127#949—22no—
128#949—34no—
129#949—62no—
130#948—34no—
131#948—62no—
132#942C2×D312yescomplemented
133C2×#215—61no—
134C2×#215C2×D312yescomplemented
135C2×#214—61no—
136#932—34no—
137#932—62no—
138#932C2×D312yescomplemented
139C2×#213—61no—
140C2×#213—61no—
141C2×#213C2×D312yescomplemented
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C2×#208—61no—
148C2×#208—62no—
149C2×#208C2×D311yescharacteristic
150C2×#208C2×D311yescharacteristic
151#907—62no—
152D3×M16—62no—
153#901—34no—
154#836—32no—
155#836—32no—
156#836—62no—
157#833—32no—
158#833—32no—
159#833—34no—
160#833—62no—
161#823—34no—
162#822—34no—
163#819—34no—
164C23×C32—21no—
165C23×C32#4111yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—41no—
169C22×C3×D3—41no—
170C22×C3×D3—82no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×D4—21no—
174C32×D4—21no—
175C32×D4—41no—
176C32×D4—41no—
177C2×C32×C4—21no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4#4111yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C3×#67—22no—
187C3×#67—22no—
188C2×C3×Dic3—21no—
189C3×D12—21no—
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—41no—
193C3×D12—41no—
194C3×D12C2×D412yes—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199C3⋊(C3⋊C8)—22no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C3×C3⋊C8C2×D414yes—
203#575—31no—
204C2×AGL(1,ℤ/8)—31no—
205C2×AGL(1,ℤ/8)—91no—
206#568—91no—
207#472—94no—
208#471—94no—
209#430—91no—
210#413—91no—
211C2×#100—91no—
212C24×C3—61no—
213C23×D3—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—32no—
223C3×#41—32no—
224C3×#41—41no—
225C3×#41—41no—
226C3×#41—41no—
227C3×#41—41no—
228C3×#41—61no—
229C3×#41—61no—
230C2×C3×Q8—21no—
231C2×C3×Q8—31no—
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—31no—
239C2×C3×D4—32no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4—61no—
244C2×C3×D4—61no—
245C2×C3×D4—61no—
246C2×C3×D4C22×D311yescharacteristic
247C2×C3×D4C22×D311yescharacteristic
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67—21no—
256#235—21no—
257#235—21no—
258#235#6712yes—
259#235C22×D312yes—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12#6711yescharacteristic
266C2×D12C22×D312yes—
267C2×C4×D3—21no—
268C2×Dic6#6711yescharacteristic
269C3×Q16—62no—
270C3×SD16—64no—
271C3×SD16—62no—
272C3×SD16—62no—
273C3×D8—64no—
274C3×D8—62no—
275C3×M16—32no—
276C3×M16—32no—
277C3×M16—32no—
278C3×M16—61no—
279C2×C3×C8—32no—
280C2×C3×C8—61no—
281#216—22no—
282#215—22no—
283#215—24no—
284#215—64no—
285#214—22no—
286#214—64no—
287#213—22no—
288#213—24no—
289#213—64no—
290#213—64no—
291#208—21no—
292#208—32no—
293#208—32no—
294#208—32no—
295#208—32no—
296#208—62no—
297#208—62no—
298#208—61no—
299#208—61no—
300#208—61no—
301#208—61no—
302#208—64no—
303#208—121no—
304#208—121no—
305#208#6712yes—
306#208#6712yes—
307#208C22×D312yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—61no—
310C2×C3⋊C8—61no—
311C2×C3⋊C8—61no—
312C2×C3⋊C8—61no—
313C2×C3⋊C8—64no—
314C2×C3⋊C8—121no—
315C2×C3⋊C8—121no—
316C2×C3⋊C8C22×D312yes—
317ΓL(1,𝔽25)—64no—
318D3×C8—64no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—81no—
322C22×C32#12111yescharacteristic
323C22×C32#12111yescharacteristic
324C22×C32C2×#4111yescharacteristic
325C2×C3×D3—22no—
326C2×C3×D3—42no—
327C2×C3×D3—81no—
328C2×C3×D3—82no—
329C2×C3×D3—82no—
330C2×C3×D3—82no—
331C32×C4—41no—
332C32×C4#12111yescharacteristic
333C32×C4#12111yescharacteristic
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3×Dic3—22no—
337C2×#41—31no—
338C2×#41D3211yescharacteristic
339C22×D4—31no—
340#137—32no—
341#137—61no—
342AGL(1,ℤ/8)—32no—
343AGL(1,ℤ/8)—62no—
344AGL(1,ℤ/8)—62no—
345AGL(1,ℤ/8)—61no—
346AGL(1,ℤ/8)—94no—
347AGL(1,ℤ/8)—182no—
348#135—62no—
349C2×SD16—32no—
350C2×SD16—181no—
351C2×D8—32no—
352C2×D8—181no—
353#131—94no—
354#131—182no—
355C2×M16—31no—
356C2×M16—31no—
357C2×M16—91no—
358C2×M16—91no—
359C2×M16—182no—
360#108—94no—
361#101—92no—
362#100—94no—
363#100—92no—
364C23×C3—22no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—61no—
369C23×C3—62no—
370C23×C3—121no—
371C23×C3—121no—
372C23×C3—242no—
373C23×C3#23711yescharacteristic
374C23×C3#23711yescharacteristic
375C22×D3—21no—
376C22×D3—22no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—82no—
380C3×Q8—21no—
381C3×Q8—21no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—32no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8—61no—
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—21no—
392C3×D4—32no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—41no—
400C3×D4—41no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4—61no—
404C3×D4—62no—
405C3×D4—62no—
406C3×D4—121no—
407C3×D4—121no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—61no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4#23711yescharacteristic
431C2×C3×C4#23711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6711yescharacteristic
435C2×C3×C4C2×#6711yescharacteristic
436C2×C3×C4C23×D311yescharacteristic
437C2×C3×C4C23×D311yescharacteristic
438#67—22no—
439#67—22no—
440C2×Dic3—21no—
441D12—21no—
442D12—22no—
443D12—22no—
444D12—41no—
445D12—41no—
446D12C2×#6712yes—
447C4×D3—22no—
448C4×D3—22no—
449Dic6—21no—
450Dic6C2×#6712yes—
451C3×C8—34no—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—62no—
455C3⋊C8—62no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C3⋊C8—122no—
459C3⋊C8—122no—
460C3⋊C8C2×#6714yes—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—81no—
465C2×C32C2×#12111yescharacteristic
466C3×D3—42no—
467C3×D3—82no—
468C24—61no—
469#41—21no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—32no—
474#41—32no—
475#41—61no—
476#41—61no—
477C2×Q8—31no—
478C2×Q8C2×D3211yescharacteristic
479C2×D4—21no—
480C2×D4—32no—
481C2×D4—31no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4C2×D3211yescharacteristic
489C22×C4—21no—
490C22×C4—61no—
491C22×C4C2×D3211yescharacteristic
492Q16—62no—
493SD16—64no—
494SD16—62no—
495SD16—62no—
496SD16—184no—
497D8—64no—
498D8—62no—
499D8—184no—
500M16—32no—
501M16—32no—
502M16—32no—
503M16—61no—
504M16—92no—
505M16—92no—
506M16—184no—
507M16—181no—
508M16—181no—
509C2×C8—32no—
510C2×C8—61no—
511C2×C8—184no—
512C2×C8—181no—
513C2×C8—181no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—42no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—62no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—81no—
526C22×C3—82no—
527C22×C3—122no—
528C22×C3—241no—
529C22×C3—242no—
530C22×C3—242no—
531C22×C3—242no—
532C22×C3#93811yescharacteristic
533C22×C3#93811yescharacteristic
534C22×C3#93911yescharacteristic
535C22×C3#93911yescharacteristic
536C22×C3C2×#23711yescharacteristic
537C22×C3C2×#23711yescharacteristic
538C2×D3—22no—
539C2×D3—42no—
540C2×D3—81no—
541C2×D3—82no—
542C2×D3—82no—
543C2×D3—82no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—42no—
549C3×C4—41no—
550C3×C4—41no—
551C3×C4—62no—
552C3×C4#93811yescharacteristic
553C3×C4#93811yescharacteristic
554C3×C4#93911yescharacteristic
555C3×C4#93911yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C2×D3×D411yescharacteristic
558C3×C4C22×#6711yescharacteristic
559C3×C4C22×#6711yescharacteristic
560Dic3—22no—
561C32#306811yescharacteristic, complemented, Sylow
562C23—21no—
563C23—61no—
564C23—62no—
565C23—121no—
566C23—121no—
567C23—242no—
568C23#380511yescharacteristic
569Q8—21no—
570Q8—21no—
571Q8—32no—
572Q8—61no—
573D4—21no—
574D4—21no—
575D4—32no—
576D4—41no—
577D4—41no—
578D4—62no—
579D4—62no—
580D4—62no—
581D4—62no—
582D4—61no—
583D4—121no—
584D4—121no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—61no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4#380511yescharacteristic
592C2×C4D3×#6711yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C2×C4D3×#6711yescharacteristic
595C2×C4D3×#6711yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—34no—
598C8—62no—
599C8—182no—
600C8—182no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—41no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—82no—
612C2×C3—81no—
613C2×C3—81no—
614C2×C3—122no—
615C2×C3—242no—
616C2×C3C2×#93811yescharacteristic
617C2×C3C2×#93911yescharacteristic
618D3—42no—
619D3—82no—
620C22—41no—
621C22—41no—
622C22—62no—
623C22—81no—
624C22—122no—
625C22—241no—
626C22—242no—
627C22—242no—
628C22—242no—
629C22#6397011yescharacteristic
630C22#6397011yescharacteristic
631C22C2×#380511yescharacteristic
632C4—41no—
633C4—62no—
634C4#6397011yescharacteristic
635C4#6397011yescharacteristic
636C4C2×D3×#6711yescharacteristic
637C4C2×D3×#6711yescharacteristic
638C3—21no—
639C3#8396311yescharacteristic, complemented
640C3#8400211yescharacteristic, complemented
641C2—21no—
642C2—21no—
643C2—21no—
644C2—81no—
645C2—122no—
646C2—242no—
647C2C2×#6397011yescharacteristic
subgroupG/H
centerC2C2×#63970
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#121
hypercenterC2×#41D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5822C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63823C2semidirect
4. #10594776C2semidirect
5. #10592936C2semidirect
6. #10591642C2semidirect
7. #10591505C2semidirect
8. #10591141C2semidirect
9. C2×#63558C2semidirect
22. C3×#942C22semidirect
23. C2×C3×#215C22semidirect
24. C3×#932C22semidirect
25. C2×C3×#213C22semidirect
33. #63814C22semidirect
35. #63663C22semidirect
36. #63660C22semidirect
37. #63577C22semidirect
38. #63558C22semidirect
41. #5822D3semidirect
43. C2×#949D3semidirect
132. #942C2×D3semidirect
134. C2×#215C2×D3semidirect
138. #932C2×D3semidirect
141. C2×#213C2×D3semidirect
561. C32#3068semidirect
639. C3#83963semidirect
640. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C2×C3×#9492
C2×#638232
#105947762
#105929362
#105916422
#105915052
#105911412
C2×#635582
#840023
#839633