Finite Group Databasebeta

← #11868134

Subgroups — #11868134

Order 1152.

1025 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×#5748C211yesmaximal, characteristic, complemented
2C2×#63825C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5C2×#63650C211yesmaximal, characteristic, complemented
6C3×#5124C211yesmaximal, characteristic, complemented
7#10591076C211yesmaximal, characteristic, complemented
8#10590985C214yesmaximal, complemented
9#10590984C214yesmaximal, complemented
10#84002—31nomaximal
11#79261—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#909—21no—
20C3×#909C2212yescomplemented
21C3×#908—21no—
22C3×#908C2212yescomplemented
23C3×#904—22no—
24C2×#3717—21no—
25C2×#3717C2212yescomplemented
26#63825—22no—
27#63825—22no—
28#63825—22no—
29#63825C2214yes—
30C2×#3714—21no—
31C2×#3714C2212yescomplemented
32#63815—22no—
33#63814C2214yescomplemented
34D3×#208—22no—
35#63650C2214yescomplemented
36C3×#822C2214yescomplemented
37#63560C2212yescomplemented
38#63558C2212yescomplemented
39C3×#575—31no—
40C2×#949—31no—
41C2×#949—31no—
42#5819—31no—
43#5748D311yescharacteristic, complemented
44C2×#908—31no—
45C2×#908—31no—
46#5745—31no—
47C3×#430—31no—
48#5237—31no—
49#5203—34no—
50#5199—34no—
51#5132—31no—
52C2×#823—31no—
53C2×#823—31no—
54C2×#823—61no—
55#5124D311yescharacteristic, complemented
56#4898—34no—
57#4897—34no—
58C23×C3⋊D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C3×#67—21no—
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235D412yes—
75C3×#235C2312yes—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16C2312yes—
84C2×C32×C8—21no—
85#3748—21no—
86#3748C2312yes—
87C2×C3⋊(C3⋊C8)—21no—
88C3×#208—21no—
89C3×#208D412yes—
90C3×#208D412yes—
91C3×#208C2312yes—
92C2×C3×C3⋊C8—21no—
93C2×C3×C3⋊C8C2312yes—
94C3×Dic12—22no—
95C3×D24—22no—
96C3×#204—22no—
97C3×#204—22no—
98#3717—24no—
99#3717—24no—
100#3714—24no—
101#3714—24no—
102#3711—24no—
103D3×C3⋊C8—24no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C2×#235C2×D311yescharacteristic
108C2×#235C2×D311yescharacteristic
109C22×D12—31no—
110C22×D12—31no—
111C22×D12—61no—
112C3×#137—32no—
113C3×#137—61no—
114C3×AGL(1,ℤ/8)—32no—
115C3×AGL(1,ℤ/8)—61no—
116C3×#135—62no—
117C2×C3×M16—21no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C2×C3×M16C2×D311yescharacteristic
121C2×C3×M16C2×D311yescharacteristic
122#949—34no—
123#949—62no—
124#949—62no—
125#949—62no—
126#948—34no—
127#948—62no—
128C2×#215—32no—
129C2×#215—61no—
130C2×#213—32no—
131C2×#213—61no—
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C2×#208—62no—
136C2×#208C2×D311yescharacteristic
137C2×#208C2×D311yescharacteristic
138#909—21no—
139#909C2×D312yescomplemented
140#908—21no—
141#908—34no—
142#908—62no—
143#908—62no—
144#908—62no—
145#908C2×D312yescomplemented
146#907—62no—
147D3×M16—62no—
148#904—22no—
149C2×D24—32no—
150C2×D24—61no—
151C2×#204—32no—
152C2×#204—61no—
153#901—34no—
154C3×#108—34no—
155#836—32no—
156#833—32no—
157#824—32no—
158#823—32no—
159#823—34no—
160#823—34no—
161#823—64no—
162#822C2×D314yescomplemented
163C23×C32#4111yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—41no—
166C22×C3⋊D3—41no—
167C22×C3⋊D3—82no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4#4111yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—41no—
179C4⋊(C3⋊D3)—41no—
180C3×#67—22no—
181C3×#67—22no—
182C3×#67—41no—
183C3×#67—41no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—21no—
189C3×D12C2×D412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—41no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6C2×D412yes—
198C32×C8—22no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8C2×D414yes—
202#575—31no—
203C2×AGL(1,ℤ/8)—91no—
204C2×AGL(1,ℤ/8)—91no—
205#568—91no—
206#472—94no—
207#471—94no—
208#430—31no—
209#413—91no—
210C2×#100—91no—
211C23×D3—62no—
212C23×D3—61no—
213C23×D3—61no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41—61no—
221C3×#41—61no—
222C2×C3×Q8—31no—
223C2×C3×Q8—31no—
224C2×C3×D4—31no—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238#235—21no—
239#235—21no—
240#235—21no—
241#235#6712yes—
242#235C22×D312yes—
243C2×D12—32no—
244C2×D12—32no—
245C2×D12—62no—
246C2×D12—61no—
247C2×D12—61no—
248C2×D12—61no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—62no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—121no—
258C2×D12—121no—
259C2×D12—121no—
260C2×D12—121no—
261C2×D12#6711yescharacteristic
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×Dic6#6711yescharacteristic
266C2×Dic6C22×D311yescharacteristic
267C3×Q16—62no—
268C3×SD16—62no—
269C3×SD16—62no—
270C3×D8—62no—
271C3×M16—21no—
272C3×M16—21no—
273C3×M16—22no—
274C3×M16—32no—
275C3×M16—32no—
276C3×M16—32no—
277C3×M16—41no—
278C3×M16—61no—
279C3×M16C22×D312yes—
280C3×M16C22×D312yes—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—32no—
284C2×C3×C8—41no—
285C2×C3×C8—61no—
286#215—64no—
287#215—64no—
288#213—64no—
289#213—64no—
290#208—21no—
291#208—32no—
292#208—32no—
293#208—62no—
294#208—61no—
295#208—61no—
296#208—64no—
297#208—121no—
298#208D1212yes—
299#208D1212yes—
300#208C22×D312yes—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—64no—
305C2×C3⋊C8—121no—
306C2×C3⋊C8C22×D312yes—
307Dic12—22no—
308D24—22no—
309D24—64no—
310D24—64no—
311#204—22no—
312#204—22no—
313#204—64no—
314#204—64no—
315ΓL(1,𝔽25)—64no—
316D3×C8—64no—
317C22×C32—41no—
318C22×C32#12111yescharacteristic
319C22×C32#12111yescharacteristic
320C22×C32C2×#4111yescharacteristic
321C2×C3⋊D3—42no—
322C2×C3⋊D3—82no—
323C2×C3⋊D3—82no—
324C2×C3⋊D3—82no—
325C2×C3×D3—22no—
326C2×C3×D3—41no—
327C2×C3×D3—81no—
328C2×C3×D3—81no—
329C32×C4#12111yescharacteristic
330C32×C4#12111yescharacteristic
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3×Dic3—22no—
334C3×Dic3—41no—
335C2×#41—31no—
336C2×#41—31no—
337C22×D4—91no—
338#137—32no—
339#137—61no—
340AGL(1,ℤ/8)—32no—
341AGL(1,ℤ/8)—61no—
342AGL(1,ℤ/8)—94no—
343AGL(1,ℤ/8)—182no—
344AGL(1,ℤ/8)—182no—
345AGL(1,ℤ/8)—182no—
346#135—62no—
347C2×SD16—92no—
348C2×SD16—181no—
349C2×D8—92no—
350C2×D8—181no—
351#131—94no—
352#131—182no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—91no—
356C2×M16—182no—
357C2×M16D3211yescharacteristic
358#108—34no—
359#101—92no—
360#100—92no—
361#100—94no—
362C23×C3—21no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3#23711yescharacteristic
366C23×C3#23911yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—64no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—121no—
375C22×D3—121no—
376C22×D3—121no—
377C22×D3—121no—
378C22×D3—242no—
379C22×D3—242no—
380C22×D3—244no—
381C3×Q8—32no—
382C3×Q8—61no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—32no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C3×D4—61no—
390C3×D4—61no—
391C3×D4—121no—
392C3×D4—121no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4#23711yescharacteristic
412C2×C3×C4#23911yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—22no—
418#67—22no—
419#67—41no—
420#67—41no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423D12—21no—
424D12—21no—
425D12—21no—
426D12—62no—
427D12—62no—
428D12—62no—
429D12—62no—
430D12—122no—
431D12—122no—
432D12—122no—
433D12—122no—
434D12—121no—
435D12—121no—
436D12—121no—
437D12—121no—
438D12C2×#6712yes—
439C4×D3—22no—
440C4×D3—22no—
441C4×D3—41no—
442C4×D3—41no—
443Dic6—21no—
444Dic6—21no—
445Dic6—21no—
446Dic6C2×#6712yes—
447C3×C8—22no—
448C3×C8—22no—
449C3×C8—34no—
450C3×C8—42no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—122no—
456C3⋊C8C2×D1214yes—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32C2×#12111yescharacteristic
461C3⋊D3—82no—
462C3×D3—42no—
463C3×D3—81no—
464C24—181no—
465#41—32no—
466#41—32no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471#41—61no—
472#41—61no—
473C2×Q8—31no—
474C2×Q8—31no—
475C2×D4—31no—
476C2×D4—31no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—92no—
480C2×D4—181no—
481C2×D4—181no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4—181no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4C2×D3211yescharacteristic
488Q16—62no—
489SD16—62no—
490SD16—62no—
491SD16—184no—
492SD16—184no—
493D8—62no—
494D8—184no—
495D8—184no—
496M16—21no—
497M16—32no—
498M16—32no—
499M16—32no—
500M16—61no—
501M16—92no—
502M16—184no—
503M16—181no—
504M16C2×D3212yes—
505C2×C8—21no—
506C2×C8—32no—
507C2×C8—61no—
508C2×C8—184no—
509C2×C8—181no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—42no—
516C22×C3—62no—
517C22×C3—121no—
518C22×C3—241no—
519C22×C3—241no—
520C22×C3#89511yescharacteristic
521C22×C3#89511yescharacteristic
522C22×C3#93911yescharacteristic
523C22×C3#93911yescharacteristic
524C22×C3C2×#23711yescharacteristic
525C22×C3C2×#23911yescharacteristic
526C2×D3—22no—
527C2×D3—41no—
528C2×D3—81no—
529C2×D3—81no—
530C2×D3—124no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—244no—
536C2×D3—242no—
537C2×D3—242no—
538C2×D3—244no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—244no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—62no—
547C3×C4—121no—
548C3×C4#89511yescharacteristic
549C3×C4#89511yescharacteristic
550C3×C4#93911yescharacteristic
551C3×C4#93911yescharacteristic
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4C22×#6711yescharacteristic
556Dic3—22no—
557Dic3—41no—
558C32#306811yescharacteristic, complemented, Sylow
559C23—61no—
560C23—61no—
561C23—182no—
562C23—361no—
563C23—361no—
564C23—722no—
565C23#379611yescharacteristic
566Q8—32no—
567Q8—61no—
568Q8—61no—
569Q8—61no—
570D4—32no—
571D4—62no—
572D4—62no—
573D4—61no—
574D4—61no—
575D4—61no—
576D4—121no—
577D4—121no—
578D4—182no—
579D4—182no—
580D4—361no—
581D4—361no—
582C2×C4—61no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—61no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4#379611yescharacteristic
589C2×C4D3×D1211yescharacteristic
590C2×C4D3×D1211yescharacteristic
591C2×C4D3×#6711yescharacteristic
592C2×C4D3×#6711yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—22no—
595C8—34no—
596C8—62no—
597C8—182no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—41no—
607C2×C3—41no—
608C2×C3—122no—
609C2×C3—241no—
610C2×C3C2×#89511yescharacteristic
611C2×C3C2×#93911yescharacteristic
612D3—42no—
613D3—81no—
614D3—244no—
615D3—242no—
616D3—242no—
617C22—41no—
618C22—62no—
619C22—121no—
620C22—241no—
621C22—241no—
622C22—362no—
623C22—722no—
624C22—722no—
625C22—722no—
626C22#6388611yescharacteristic
627C22#6388611yescharacteristic
628C22C2×#379611yescharacteristic
629C4—62no—
630C4—121no—
631C4#6388611yescharacteristic
632C4#6388611yescharacteristic
633C4C2×D3×D1211yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3#7926111yescharacteristic, complemented
637C3#8400211yescharacteristic, complemented
638C2—21no—
639C2—21no—
640C2—21no—
641C2—122no—
642C2—241no—
643C2—722no—
644C2C2×#6388611yescharacteristic
subgroupG/H
centerC2C2×#63886
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×#121
hypercenterC2×M16D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5748C2semidirect
2. C2×#63825C2semidirect
3. C2×#63825C2semidirect
4. #10594776C2semidirect
5. C2×#63650C2semidirect
6. C3×#5124C2semidirect
7. #10591076C2semidirect
8. #10590985C2semidirect
9. #10590984C2semidirect
20. C3×#909C22semidirect
22. C3×#908C22semidirect
25. C2×#3717C22semidirect
31. C2×#3714C22semidirect
33. #63814C22semidirect
35. #63650C22semidirect
36. C3×#822C22semidirect
37. #63560C22semidirect
38. #63558C22semidirect
43. #5748D3semidirect
55. #5124D3semidirect
139. #909C2×D3semidirect
145. #908C2×D3semidirect
162. #822C2×D3semidirect
558. C32#3068semidirect
636. C3#79261semidirect
637. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×#638252
#105947762
C2×#636502
C3×#51242
#105910762
#105909852
#105909842
#840023
#792613