Finite Group Databasebeta

← #11868121

Subgroups — #11868121

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C2×C3×#949C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10591681C214yesmaximal, complemented
6#10591678C214yesmaximal, complemented
7#10591143C211yesmaximal, characteristic, complemented
8#10591076C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#84002—31nomaximal
11#83943—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64157—22no—
16#64157C2214yescomplemented
17C2×#3748—22no—
18C2×#3748C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C3×#951C2212yescomplemented
21C3×#950—22no—
22C3×#949—22no—
23C3×#949C2214yes—
24C3×#949C2212yescomplemented
25C3×#942—21no—
26C2×C3×#215—21no—
27C3×#932—21no—
28C2×C3×#213—21no—
29C2×C3×#208C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C2×#3715C2212yescomplemented
32#63823—22no—
33#63823—22no—
34C2×#3713C2212yescomplemented
35#63578C2214yescomplemented
36#63560C2212yescomplemented
37#63558C2214yescomplemented
38#63558C2212yescomplemented
39C3×#575—31no—
40C2×C3×AGL(1,ℤ/8)—31no—
41#5822D311yescharacteristic, complemented
42C2×#949—31no—
43C2×#949D311yescharacteristic, complemented
44#5819—31no—
45#5819—31no—
46#5819—61no—
47C2×#932—31no—
48#5237—31no—
49C2×#833—31no—
50#5203—34no—
51#5200—34no—
52#5199—34no—
53#5199—34no—
54#5132—31no—
55C2×#823—31no—
56#5124—31no—
57#5124—31no—
58C23×C3×D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yes—
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4D411yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82#3748—21no—
83#3748—24no—
84#3748D412yes—
85#3748D412yes—
86#3748C2312yes—
87C2×C3⋊(C3⋊C8)—21no—
88C2×C3⋊(C3⋊C8)—24no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#216—22no—
91C3×#215—24no—
92C3×#215—22no—
93C3×#214—22no—
94C3×#213—24no—
95C3×#213—22no—
96C3×#208—21no—
97C3×#208—21no—
98C3×#208C2312yes—
99C3×#208C2312yes—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—21no—
102#3715—24no—
103#3713—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)—34no—
115C3×AGL(1,ℤ/8)—32no—
116C3×AGL(1,ℤ/8)—62no—
117C3×AGL(1,ℤ/8)—61no—
118C3×#135—62no—
119C2×C3×SD16—61no—
120C2×C3×D8—61no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123#951C2×D312yescomplemented
124#950—22no—
125#949—22no—
126#949—62no—
127#949—62no—
128#949C2×D314yes—
129#949C2×D312yescomplemented
130#948—34no—
131#948—34no—
132#948—64no—
133#948—62no—
134#948—62no—
135#948—64no—
136#942—21no—
137C2×#215—21no—
138C2×#215—32no—
139C2×#214—32no—
140#932—21no—
141#932—62no—
142#932—62no—
143C2×#213—21no—
144C2×#213—32no—
145C2×#213—32no—
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—31no—
149C2×#208—31no—
150C2×#208—61no—
151C2×#208—61no—
152C2×#208—62no—
153C2×#208—62no—
154C2×#208—64no—
155C2×#208C2×D311yescharacteristic
156C2×#208C2×D311yescharacteristic
157#836—32no—
158#833—32no—
159#833—34no—
160#824—32no—
161#823—34no—
162#823—32no—
163#822—34no—
164#822—34no—
165C23×C32—21no—
166C23×C32#4111yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C22×C3×D3—41no—
170C22×C3×D3—41no—
171C22×C3×D3—82no—
172C32×Q8—21no—
173C32×Q8C2×D412yes—
174C32×D4—22no—
175C32×D4—22no—
176C32×D4—21no—
177C32×D4C2×D412yes—
178C2×C32×C4—21no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4111yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C3×#67—41no—
188C3×#67—41no—
189C2×C3×Dic3—21no—
190C3×D12—21no—
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—21no—
194C3×D12—41no—
195C3×D12—41no—
196C3×C4×D3—41no—
197C3×C4×D3—41no—
198C3×Dic6—21no—
199C3×Dic6—21no—
200C3⋊(C3⋊C8)—22no—
201C3⋊(C3⋊C8)C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204#575—31no—
205C2×AGL(1,ℤ/8)—31no—
206C2×AGL(1,ℤ/8)—91no—
207#568—91no—
208#472—94no—
209#471—94no—
210#430—91no—
211#413—91no—
212C2×#100—91no—
213C24×C3—61no—
214C23×D3—21no—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—22no—
222C3×#41—22no—
223C3×#41—61no—
224C3×#41—61no—
225C3×#41—61no—
226C3×#41—61no—
227C3×#41#6712yes—
228C3×#41#6712yes—
229C3×#41C22×D312yes—
230C3×#41C22×D312yes—
231C2×C3×Q8—21no—
232C2×C3×Q8—31no—
233C2×C3×Q8#6711yescharacteristic
234C2×C3×Q8#6711yescharacteristic
235C2×C3×D4—22no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—31no—
240C2×C3×D4—32no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4—61no—
244C2×C3×D4—61no—
245C2×C3×D4—61no—
246C2×C3×D4—61no—
247C2×C3×D4#6711yescharacteristic
248C2×C3×D4#6711yescharacteristic
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—61no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—21no—
257#235—21no—
258#235—21no—
259#235—21no—
260#235—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12C22×D311yescharacteristic
267C2×D12C22×D312yes—
268C2×C4×D3—21no—
269C2×Dic6C22×D311yescharacteristic
270C3×Q16—62no—
271C3×SD16—64no—
272C3×SD16—62no—
273C3×SD16—62no—
274C3×D8—64no—
275C3×D8—62no—
276C3×M16—32no—
277C3×M16—32no—
278C3×M16—61no—
279C3×M16—61no—
280C2×C3×C8—61no—
281C2×C3×C8—61no—
282#216—22no—
283#215—24no—
284#215—22no—
285#215—64no—
286#214—22no—
287#214—64no—
288#213—24no—
289#213—22no—
290#213—64no—
291#213—64no—
292#208—21no—
293#208—21no—
294#208—32no—
295#208—32no—
296#208—32no—
297#208—32no—
298#208—32no—
299#208—32no—
300#208—62no—
301#208—62no—
302#208—62no—
303#208—64no—
304#208—64no—
305#208—62no—
306#208—68no—
307#208—61no—
308#208—61no—
309#208C22×D312yes—
310#208C22×D312yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—64no—
317C2×C3⋊C8—64no—
318C2×C3⋊C8—68no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—61no—
321C2×C3⋊C8—61no—
322C22×C32—22no—
323C22×C32—41no—
324C22×C32—81no—
325C22×C32#12111yescharacteristic
326C22×C32#12111yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C2×C3×D3—41no—
329C2×C3×D3—42no—
330C2×C3×D3—82no—
331C2×C3×D3—82no—
332C2×C3×D3—81no—
333C2×C3×D3—82no—
334C32×C4—22no—
335C32×C4#12111yescharacteristic
336C32×C4#12111yescharacteristic
337C32×C4C22×D411yescharacteristic
338C32×C4C22×D411yescharacteristic
339C3×Dic3—41no—
340C2×#41—31no—
341C2×#41D3211yescharacteristic
342C22×D4—31no—
343#137—32no—
344#137—61no—
345AGL(1,ℤ/8)—34no—
346AGL(1,ℤ/8)—32no—
347AGL(1,ℤ/8)—62no—
348AGL(1,ℤ/8)—61no—
349AGL(1,ℤ/8)—182no—
350AGL(1,ℤ/8)—182no—
351#135—62no—
352C2×SD16—61no—
353C2×SD16—92no—
354C2×D8—61no—
355C2×D8—92no—
356#131—94no—
357#131—182no—
358C2×M16—31no—
359C2×M16—31no—
360C2×M16—91no—
361C2×M16—91no—
362C2×M16—182no—
363#108—94no—
364#101—92no—
365#100—94no—
366#100—92no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—61no—
372C23×C3—62no—
373C23×C3—121no—
374C23×C3—121no—
375C23×C3—242no—
376C23×C3#23711yescharacteristic
377C23×C3#23711yescharacteristic
378C22×D3—21no—
379C22×D3—22no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—82no—
383C3×Q8—22no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—22no—
387C3×Q8—61no—
388C3×Q8—61no—
389C3×Q8C2×#6712yes—
390C3×Q8C2×#6712yes—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—21no—
399C3×D4—21no—
400C3×D4—22no—
401C3×D4—61no—
402C3×D4—62no—
403C3×D4—62no—
404C3×D4—61no—
405C3×D4—121no—
406C3×D4—121no—
407C3×D4—121no—
408C3×D4—121no—
409C3×D4C2×#6712yes—
410C3×D4C2×#6712yes—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—61no—
427C2×C3×C4—121no—
428C2×C3×C4—121no—
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4#23711yescharacteristic
434C2×C3×C4#23711yescharacteristic
435C2×C3×C4C2×#6711yescharacteristic
436C2×C3×C4C2×#6711yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C23×D311yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441#67—41no—
442#67—41no—
443C2×Dic3—21no—
444D12—21no—
445D12—22no—
446D12—22no—
447D12—21no—
448D12—41no—
449D12—41no—
450C4×D3—41no—
451C4×D3—41no—
452Dic6—21no—
453Dic6—21no—
454C3×C8—62no—
455C3×C8—62no—
456C3⋊C8—22no—
457C3⋊C8—22no—
458C3⋊C8—34no—
459C3⋊C8—34no—
460C3⋊C8—64no—
461C3⋊C8—64no—
462C3⋊C8—62no—
463C3⋊C8—62no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32—42no—
468C2×C32C2×#12111yescharacteristic
469C3×D3—81no—
470C3×D3—82no—
471C24—61no—
472#41—21no—
473#41—21no—
474#41—61no—
475#41—61no—
476#41—61no—
477#41—61no—
478#41#62512yes—
479#41C2×D3212yes—
480C2×Q8—31no—
481C2×Q8#62511yescharacteristic
482C2×D4—21no—
483C2×D4—31no—
484C2×D4—32no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4—61no—
489C2×D4—61no—
490C2×D4—61no—
491C2×D4#62511yescharacteristic
492C22×C4—21no—
493C22×C4—61no—
494C22×C4C2×D3211yescharacteristic
495Q16—62no—
496SD16—64no—
497SD16—62no—
498SD16—62no—
499SD16—184no—
500D8—64no—
501D8—62no—
502D8—184no—
503M16—32no—
504M16—32no—
505M16—61no—
506M16—61no—
507M16—92no—
508M16—92no—
509M16—92no—
510M16—184no—
511M16—181no—
512C2×C8—61no—
513C2×C8—61no—
514C2×C8—92no—
515C2×C8—184no—
516C2×C8—181no—
517C22×C3—24no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—82no—
529C22×C3—121no—
530C22×C3—122no—
531C22×C3—242no—
532C22×C3—241no—
533C22×C3—242no—
534C22×C3—242no—
535C22×C3#93911yescharacteristic
536C22×C3#93911yescharacteristic
537C22×C3#93911yescharacteristic
538C22×C3#93911yescharacteristic
539C22×C3C2×#23711yescharacteristic
540C22×C3C2×#23711yescharacteristic
541C2×D3—41no—
542C2×D3—42no—
543C2×D3—82no—
544C2×D3—82no—
545C2×D3—82no—
546C2×D3—81no—
547C3×C4—24no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—121no—
555C3×C4#93911yescharacteristic
556C3×C4#93911yescharacteristic
557C3×C4#93911yescharacteristic
558C3×C4#93911yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4C22×#6711yescharacteristic
562C3×C4C22×#6711yescharacteristic
563Dic3—41no—
564C32#306811yescharacteristic, complemented, Sylow
565C23—21no—
566C23—61no—
567C23—62no—
568C23—121no—
569C23—121no—
570C23—242no—
571C23#380511yescharacteristic
572Q8—21no—
573Q8—61no—
574Q8—61no—
575Q8C2×#62512yes—
576D4—22no—
577D4—22no—
578D4—21no—
579D4—62no—
580D4—61no—
581D4—61no—
582D4—62no—
583D4—121no—
584D4—121no—
585D4—121no—
586D4—121no—
587D4C2×#62512yes—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—61no—
592C2×C4—121no—
593C2×C4—121no—
594C2×C4#380511yescharacteristic
595C2×C4C2×#62511yescharacteristic
596C2×C4C2×#62511yescharacteristic
597C2×C4#381111yescharacteristic
598C2×C4#381111yescharacteristic
599C2×C4C22×D3211yescharacteristic
600C8—62no—
601C8—62no—
602C8—94no—
603C8—182no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—41no—
614C2×C3—44no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3—242no—
618C2×C3—241no—
619C2×C3C2×#93911yescharacteristic
620C2×C3C2×#93911yescharacteristic
621D3—81no—
622D3—82no—
623C22—22no—
624C22—41no—
625C22—81no—
626C22—121no—
627C22—122no—
628C22—242no—
629C22—241no—
630C22—242no—
631C22—242no—
632C22#6398011yescharacteristic
633C22#6398011yescharacteristic
634C22C2×#380511yescharacteristic
635C4—22no—
636C4—121no—
637C4#6398011yescharacteristic
638C4#6398011yescharacteristic
639C4C22×#62511yescharacteristic
640C4C2×#381111yescharacteristic
641C3—21no—
642C3#8394311yescharacteristic, complemented
643C3#8400211yescharacteristic, complemented
644C2—21no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—242no—
649C2—241no—
650C2C2×#6398011yescharacteristic
subgroupG/H
centerC2C2×#63980
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. #10596290C2semidirect
2. C3×#5822C2semidirect
3. C2×C3×#949C2semidirect
4. C2×#63823C2semidirect
5. #10591681C2semidirect
6. #10591678C2semidirect
7. #10591143C2semidirect
8. #10591076C2semidirect
9. C2×#63558C2semidirect
16. #64157C22semidirect
20. C3×#951C22semidirect
24. C3×#949C22semidirect
31. C2×#3715C22semidirect
34. C2×#3713C22semidirect
35. #63578C22semidirect
36. #63560C22semidirect
37. #63558C22semidirect
38. #63558C22semidirect
41. #5822D3semidirect
43. C2×#949D3semidirect
123. #951C2×D3semidirect
129. #949C2×D3semidirect
564. C32#3068semidirect
642. C3#83943semidirect
643. C3#84002semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58222
C2×C3×#9492
C2×#638232
#105916812
#105916782
#105911432
#105910762
C2×#635582
#840023
#839433