Finite Group Databasebeta

← #11919008

Subgroups — #11919008

Order 1152.

2981 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596669C212yesmaximal, complemented
2C2×#64113C211yesmaximal, characteristic, complemented
3C2×C3×#904C211yesmaximal, characteristic, complemented
4C2×C3×#901C211yesmaximal, characteristic, complemented
5#10594795C212yesmaximal, complemented
6#10594692C212yesmaximal, complemented
7#10594691C212yesmaximal, complemented
8#10594680C212yesmaximal, complemented
9#10594679C214yesmaximal, complemented
10#10594678C212yesmaximal, complemented
11#10594677C214yesmaximal, complemented
12#10594676C214yesmaximal, complemented
13D3×#904C214yesmaximal, complemented
14#87187—31nomaximal
15#87163—31nomaximal
16C2×#3828C2212yescomplemented
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2212yescomplemented
19#64330—24no—
20#64308C2214yescomplemented
21#64307—22no—
22#64307C2214yescomplemented
23#64306—24no—
24D3×#235—24no—
25D3×#235C2218yescomplemented
26#64298C2214yescomplemented
27#64297—22no—
28#64297C2214yescomplemented
29C22×C32×C8C2211yescharacteristic, complemented
30C2×#3746C2211yescharacteristic, complemented
31#64113C2212yescomplemented
32#64113C2212yescomplemented
33#64113C2212yescomplemented
34#64113C2212yescomplemented
35C2×#3745C2211yescharacteristic, complemented
36C2×#3744C2212yescomplemented
37C2×C3×#208C2211yescharacteristic, complemented
38C2×C3×Dic12C2211yescharacteristic, complemented
39C3×#904C2212yescomplemented
40C3×#904C2212yescomplemented
41C3×#904C2212yescomplemented
42C3×#904C2212yescomplemented
43C2×C3×D24C2211yescharacteristic, complemented
44C2×C3×#204C2212yescomplemented
45C3×#901C2212yescomplemented
46C3×#901C2212yescomplemented
47C3×#901C2212yescomplemented
48C3×#901C2212yescomplemented
49C2×C3×ΓL(1,𝔽25)C2212yescomplemented
50C2×C3×D3×C8C2212yescomplemented
51#63833C2214yescomplemented
52#63831C2214yescomplemented
53#63830C2214yescomplemented
54#63829C2218yescomplemented
55#63825C2214yescomplemented
56#63808C2214yescomplemented
57#63807C2214yescomplemented
58#63806C2218yescomplemented
59#63801C2218yescomplemented
60#63800C2218yescomplemented
61D3×Dic12C2214yescomplemented
62#63795C2218yescomplemented
63#63794C2218yescomplemented
64D3×D24C2214yescomplemented
65D3×#204C2218yescomplemented
66#5964—32no—
67#5964—32no—
68C2×C3×#135—31no—
69C2×C3×#131—31no—
70#5822—32no—
71#5771—32no—
72#5770—34no—
73#5769—32no—
74#5768—34no—
75D3×#135—34no—
76#5766—32no—
77#5762—34no—
78#5757—32no—
79#5753—32no—
80#5753—32no—
81#5752—32no—
82#5752—32no—
83#5751—34no—
84#5751—34no—
85#5748—32no—
86#5748—34no—
87C2×#904—31no—
88C2×#904—31no—
89C2×#904—34no—
90C2×#904—61no—
91C2×#904D311yescharacteristic, complemented
92C2×#901D311yescharacteristic, complemented
93C22×C32×C4C2311yescharacteristic
94C2×#638—22no—
95#3828—22no—
96#3828—22no—
97#3828C2314yes—
98#3828C2314yes—
99C2×C4⋊(C3⋊D3)C2312yes—
100C2×C4×C3⋊D3—22no—
101C2×#634C2312yes—
102C2×C3×#67—22no—
103C2×C3×#67D412yes—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235D412yes—
107C3×#235D412yes—
108C3×#235C2312yes—
109C3×#235C2312yes—
110C3×#235C2314yes—
111C3×#235C2314yes—
112C2×C3×D12D411yescharacteristic
113C2×C3×D12C2312yes—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3C2312yes—
116C2×C3×Dic6D411yescharacteristic
117C2×C3×Dic6C2312yes—
118#3811—28no—
119D3×#67—28no—
120D3×#67—28no—
121#3805—28no—
122#3804—28no—
123#3804—28no—
124#3802—24no—
125D3×D12—24no—
126D3×D12C2318yes—
127C4×D32—28no—
128#3799—24no—
129#3799C2318yes—
130#3798—28no—
131#3797—24no—
132#3796—24no—
133#3796—24no—
134#3795—24no—
135#3795C2318yes—
136D3×Dic6—24no—
137D3×Dic6C2318yes—
138C2×C32×C8C2311yescharacteristic
139C2×C32×C8C2311yescharacteristic
140C2×C32×C8C2311yescharacteristic
141C2×C32×C8C2311yescharacteristic
142C2×C32×C8C2311yescharacteristic
143C2×C32×C8C2311yescharacteristic
144#3746C2312yes—
145#3746C2312yes—
146#3745C2312yes—
147#3745C2312yes—
148#3744C2314yes—
149#3744C2314yes—
150C3×#208C2312yes—
151C3×#208C2312yes—
152C2×C3×C3⋊C8C2312yes—
153C3×Dic12C2312yes—
154C3×Dic12C2312yes—
155C3×D24C2312yes—
156C3×D24C2312yes—
157C3×#204C2314yes—
158C3×#204C2314yes—
159C3×ΓL(1,𝔽25)C2314yes—
160C3×ΓL(1,𝔽25)C2314yes—
161C3×D3×C8C2314yes—
162C3×D3×C8C2314yes—
163#3719C2318yes—
164#3717C2318yes—
165#3716C2318yes—
166#3714C2318yes—
167#3584—91noSylow
168C2×C3×#41—31no—
169C2×C3×#41—32no—
170#1010—34no—
171#1010—34no—
172#1010—34no—
173#1010—62no—
174#1009—34no—
175#1009—34no—
176#1009—34no—
177#1009—62no—
178D3×#41—38no—
179D3×#41—64no—
180D3×#41—64no—
181D3×#41—64no—
182#1007—34no—
183#1007—62no—
184#1004—34no—
185#1004—62no—
186#1004—64no—
187#1004—64no—
188C2×#235—32no—
189C2×#235—32no—
190C2×#235—38no—
191C2×#235—62no—
192C2×#235—64no—
193C2×#235C2×D311yescharacteristic
194C2×#235C2×D312yescomplemented
195C3×#135—32no—
196C3×#135—32no—
197C3×#135—32no—
198C3×#135—32no—
199C2×C3×Q16—31no—
200C2×C3×SD16—32no—
201C2×C3×D8—31no—
202C3×#131—32no—
203C3×#131—32no—
204C3×#131—32no—
205C3×#131—32no—
206C2×C3×M16—31no—
207C2×C3×M16—32no—
208C22×C3×C8—21no—
209C22×C3×C8—32no—
210C22×C3×C8C2×D311yescharacteristic, complemented
211C22×C3×C8C2×D311yescharacteristic, complemented
212#951—34no—
213#950—38no—
214#949—34no—
215#942—34no—
216#932—34no—
217C2×#208C2×D311yescharacteristic, complemented
218#919—34no—
219#918—38no—
220D3×Q16—34no—
221#916—38no—
222#915—38no—
223#914—38no—
224D3×SD16—38no—
225#912—34no—
226#911—38no—
227D3×D8—34no—
228#909—34no—
229#909—34no—
230#909—38no—
231#909—38no—
232#908—34no—
233#908—34no—
234#908—38no—
235#908—38no—
236C2×Dic12—31no—
237C2×Dic12—31no—
238C2×Dic12—34no—
239C2×Dic12—61no—
240C2×Dic12C2×D311yescharacteristic, complemented
241#904—38no—
242#904—32no—
243#904—32no—
244#904—32no—
245#904—32no—
246#904—32no—
247#904—32no—
248#904—32no—
249#904—32no—
250#904—34no—
251#904—34no—
252#904—38no—
253#904—62no—
254#904—62no—
255#904—62no—
256#904—62no—
257#904C2×D312yescomplemented
258#904C2×D312yescomplemented
259#904C2×D312yescomplemented
260#904C2×D312yescomplemented
261C2×D24—31no—
262C2×D24—31no—
263C2×D24—34no—
264C2×D24—61no—
265C2×D24C2×D311yescharacteristic, complemented
266C2×#204—32no—
267C2×#204—32no—
268C2×#204—38no—
269C2×#204—62no—
270C2×#204C2×D312yescomplemented
271#901C2×D312yescomplemented
272#901C2×D312yescomplemented
273#901C2×D312yescomplemented
274#901C2×D312yescomplemented
275C2×ΓL(1,𝔽25)C2×D312yescomplemented
276C2×D3×C8C2×D312yescomplemented
277C23×C32C2×D411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3C2×D412yes—
281C2×D32—28no—
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2×D411yescharacteristic
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2411yescharacteristic
286C2×C32×C4C2411yescharacteristic
287C2×C32×C4C2411yescharacteristic
288#638—24no—
289#638—24no—
290C2×C3⋊Dic3—22no—
291C4⋊(C3⋊D3)—22no—
292C4⋊(C3⋊D3)C2414yes—
293C4×C3⋊D3—24no—
294C4×C3⋊D3—24no—
295#634—22no—
296#634C2414yes—
297C3×#67—24no—
298C3×#67—24no—
299C3×#67C2×D414yes—
300C3×#67C2×D414yes—
301C2×C3×Dic3—22no—
302C2×C3×Dic3C2×D412yes—
303C3×D12—22no—
304C3×D12C2×D412yes—
305C3×D12C2×D412yes—
306C3×D12C2414yes—
307C3×C4×D3—24no—
308C3×C4×D3—24no—
309C3×C4×D3C2×D414yes—
310C3×C4×D3C2414yes—
311C3×Dic6—22no—
312C3×Dic6C2×D412yes—
313C3×Dic6C2×D412yes—
314C3×Dic6C2414yes—
315#627—28no—
316#626—28no—
317#626—28no—
318#625—28no—
319#624—28no—
320D3×Dic3—28no—
321D3×Dic3—28no—
322C32×C8C2411yescharacteristic
323C32×C8C2411yescharacteristic
324C32×C8C2411yescharacteristic
325C32×C8C2411yescharacteristic
326C3×C3⋊C8C2414yes—
327#585—92no—
328#578—92no—
329#578—92no—
330#577—94no—
331#577—94no—
332#576—92no—
333#576—92no—
334#575—94no—
335#575—92no—
336C2×#135—31no—
337C2×#135—94no—
338C2×#135—91no—
339C2×#131—31no—
340C3×#41—32no—
341C3×#41—32no—
342C3×#41—32no—
343C3×#41—32no—
344C3×#41—34no—
345C3×#41—34no—
346C3×#41—62no—
347C3×#41—62no—
348C2×C3×Q8—31no—
349C2×C3×Q8—32no—
350C2×C3×D4—32no—
351C2×C3×D4—31no—
352C2×C3×D4—32no—
353C2×C3×D4—62no—
354C22×C3×C4—21no—
355C22×C3×C4—32no—
356C22×C3×C4—62no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—22no—
360C2×#67—68no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—68no—
364C2×#67—122no—
365C2×#67D1212yes—
366#239—38no—
367#239—64no—
368#239—64no—
369#239—64no—
370D3×Q8—38no—
371D3×Q8—64no—
372D3×Q8—64no—
373D3×Q8—64no—
374#237—38no—
375#237—64no—
376#237—64no—
377#237—68no—
378#237—68no—
379#237—68no—
380#237—68no—
381#237—64no—
382D3×D4—38no—
383D3×D4—64no—
384D3×D4—64no—
385D3×D4—68no—
386D3×D4—68no—
387D3×D4—68no—
388D3×D4—68no—
389D3×D4—64no—
390#235—22no—
391#235—22no—
392#235—34no—
393#235—34no—
394#235—34no—
395#235—34no—
396#235—38no—
397#235—38no—
398#235—64no—
399#235—64no—
400#235—68no—
401#235—68no—
402#235—62no—
403#235—62no—
404#235—62no—
405#235—62no—
406#235—68no—
407#235—64no—
408#235—68no—
409#235—64no—
410#235—122no—
411#235—122no—
412#235D1212yes—
413#235D1212yes—
414#235C22×D312yes—
415#235C22×D312yes—
416#235C22×D314yes—
417#235C22×D314yes—
418C2×D12—32no—
419C2×D12—32no—
420C2×D12—38no—
421C2×D12—62no—
422C2×D12—64no—
423C2×D12D1211yescharacteristic
424C2×D12C22×D312yes—
425C2×C4×D3—22no—
426C2×C4×D3—68no—
427C2×C4×D3—62no—
428C2×C4×D3—62no—
429C2×C4×D3—68no—
430C2×C4×D3—122no—
431C2×C4×D3C22×D312yes—
432C2×Dic6—32no—
433C2×Dic6—32no—
434C2×Dic6—38no—
435C2×Dic6—62no—
436C2×Dic6—64no—
437C2×Dic6D1211yescharacteristic
438C2×Dic6C22×D312yes—
439C3×Q16—32no—
440C3×Q16—32no—
441C3×SD16—34no—
442C3×SD16—34no—
443C3×D8—32no—
444C3×D8—32no—
445C3×M16—32no—
446C3×M16—32no—
447C3×M16—34no—
448C3×M16—34no—
449C2×C3×C8—21no—
450C2×C3×C8—21no—
451C2×C3×C8—21no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—21no—
455C2×C3×C8—32no—
456C2×C3×C8—34no—
457C2×C3×C8—34no—
458C2×C3×C8C22×D311yescharacteristic
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C2×C3×C8C22×D311yescharacteristic
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C2×C3×C8C22×D311yescharacteristic
468C2×C3×C8C22×D311yescharacteristic
469C2×C3×C8C22×D311yescharacteristic
470#216—38no—
471#215—38no—
472#214—38no—
473#213—38no—
474#208C22×D312yes—
475#208C22×D312yes—
476C2×C3⋊C8C22×D312yes—
477Dic12—38no—
478Dic12—32no—
479Dic12—32no—
480Dic12—32no—
481Dic12—32no—
482Dic12—62no—
483Dic12—62no—
484Dic12C22×D312yes—
485Dic12C22×D312yes—
486D24—38no—
487D24—32no—
488D24—32no—
489D24—32no—
490D24—32no—
491D24—62no—
492D24—62no—
493D24C22×D312yes—
494D24C22×D312yes—
495#204—38no—
496#204—38no—
497#204—34no—
498#204—34no—
499#204—34no—
500#204—34no—
501#204—64no—
502#204—64no—
503#204C22×D314yes—
504#204C22×D314yes—
505ΓL(1,𝔽25)C22×D314yes—
506ΓL(1,𝔽25)C22×D314yes—
507D3×C8C22×D314yes—
508D3×C8C22×D314yes—
509C22×C32—41no—
510C22×C32C22×D411yescharacteristic
511C22×C32C22×D411yescharacteristic
512C22×C32C22×D411yescharacteristic
513C2×C3⋊D3—24no—
514C2×C3⋊D3—82no—
515C2×C3×D3—24no—
516C2×C3×D3—42no—
517C2×C3×D3—82no—
518C2×C3×D3C22×D414yes—
519D32—88no—
520C32×C4C22×D411yescharacteristic
521C32×C4C22×D411yescharacteristic
522C32×C4C22×D411yescharacteristic
523C32×C4C2511yescharacteristic
524C3⋊Dic3—24no—
525C3×Dic3—24no—
526C3×Dic3C22×D414yes—
5272−1+4—94no—
5282−1+4—94no—
5292−1+4—182no—
530H(5,𝔽2)—94no—
531H(5,𝔽2)—94no—
532H(5,𝔽2)—184no—
533H(5,𝔽2)—182no—
534C2×#41—31no—
535C2×#41—32no—
536C2×#41—98no—
537C2×#41—92no—
538C2×#41—184no—
539C2×#41—184no—
540#137—98no—
541#137—98no—
542#137—94no—
543#137—94no—
544AGL(1,ℤ/8)—98no—
545AGL(1,ℤ/8)—98no—
546AGL(1,ℤ/8)—94no—
547AGL(1,ℤ/8)—94no—
548#135—32no—
549#135—32no—
550#135—32no—
551#135—32no—
552#135—94no—
553#135—98no—
554#135—94no—
555#135—98no—
556#135—92no—
557#135—92no—
558#135—92no—
559#135—92no—
560C2×Q16—31no—
561C2×Q16—94no—
562C2×Q16—91no—
563C2×SD16—32no—
564C2×SD16—98no—
565C2×SD16—92no—
566C2×D8—31no—
567C2×D8—94no—
568C2×D8—91no—
569#131—32no—
570#131—32no—
571#131—32no—
572#131—32no—
573C2×M16—31no—
574C2×M16—32no—
575C22×C8—32no—
576C22×C8D3211yescharacteristic, complemented
577C23×C3—21no—
578C23×C3—32no—
579C23×C3—62no—
580C23×C3C2×D1211yescharacteristic
581C23×C3D3×D411yescharacteristic
582C22×D3—22no—
583C22×D3—68no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—68no—
587C22×D3—122no—
588C22×D3C2×D1212yes—
589C3×Q8—32no—
590C3×Q8—32no—
591C3×Q8—34no—
592C3×Q8—62no—
593C3×D4—34no—
594C3×D4—34no—
595C3×D4—32no—
596C3×D4—32no—
597C3×D4—34no—
598C3×D4—64no—
599C3×D4—64no—
600C3×D4—62no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—32no—
608C2×C3×C4—34no—
609C2×C3×C4—34no—
610C2×C3×C4—62no—
611C2×C3×C4—64no—
612C2×C3×C4—64no—
613C2×C3×C4C2×D1211yescharacteristic
614C2×C3×C4C2×D1211yescharacteristic
615C2×C3×C4C2×D1211yescharacteristic
616C2×C3×C4D3×D411yescharacteristic
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D411yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C23×D311yescharacteristic
625#67—24no—
626#67—24no—
627#67—68no—
628#67—68no—
629#67—64no—
630#67—64no—
631#67—64no—
632#67—64no—
633#67—68no—
634#67—68no—
635#67—124no—
636#67—124no—
637#67C2×D1214yes—
638#67C2×D1214yes—
639C2×Dic3—22no—
640C2×Dic3—68no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—68no—
644C2×Dic3—122no—
645C2×Dic3C2×D1212yes—
646D12—22no—
647D12—34no—
648D12—34no—
649D12—64no—
650D12—68no—
651D12—68no—
652D12—62no—
653D12—62no—
654D12—122no—
655D12C2×D1212yes—
656D12C2×D1212yes—
657D12C23×D314yes—
658C4×D3—24no—
659C4×D3—24no—
660C4×D3—68no—
661C4×D3—68no—
662C4×D3—68no—
663C4×D3—64no—
664C4×D3—64no—
665C4×D3—64no—
666C4×D3—64no—
667C4×D3—68no—
668C4×D3—124no—
669C4×D3—124no—
670C4×D3C2×D1214yes—
671C4×D3C23×D314yes—
672Dic6—22no—
673Dic6—34no—
674Dic6—34no—
675Dic6—64no—
676Dic6—68no—
677Dic6—62no—
678Dic6—62no—
679Dic6—68no—
680Dic6—122no—
681Dic6C2×D1212yes—
682Dic6C2×D1212yes—
683Dic6C23×D314yes—
684C3×C8—21no—
685C3×C8—21no—
686C3×C8—21no—
687C3×C8—21no—
688C3×C8—34no—
689C3×C8C23×D311yescharacteristic
690C3×C8C23×D311yescharacteristic
691C3×C8C23×D311yescharacteristic
692C3×C8C23×D311yescharacteristic
693C3×C8C23×D311yescharacteristic
694C3×C8C23×D311yescharacteristic
695C3×C8C23×D311yescharacteristic
696C3×C8C23×D311yescharacteristic
697C3⋊C8C23×D314yes—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—21no—
701C2×C32C23×D411yescharacteristic
702C3⋊D3—44no—
703C3×D3—24no—
704C3×D3—44no—
705#41—32no—
706#41—32no—
707#41—32no—
708#41—32no—
709#41—34no—
710#41—34no—
711#41—62no—
712#41—62no—
713#41—98no—
714#41—98no—
715#41—94no—
716#41—94no—
717#41—188no—
718#41—188no—
719#41—188no—
720#41—184no—
721#41—184no—
722#41—188no—
723#41—184no—
724#41—184no—
725#41—182no—
726#41—182no—
727C2×Q8—31no—
728C2×Q8—32no—
729C2×Q8—98no—
730C2×Q8—92no—
731C2×Q8—184no—
732C2×Q8—184no—
733C2×D4—32no—
734C2×D4—32no—
735C2×D4—31no—
736C2×D4—62no—
737C2×D4—98no—
738C2×D4—92no—
739C2×D4—184no—
740C2×D4—188no—
741C2×D4—184no—
742C2×D4—188no—
743C2×D4—188no—
744C2×D4—182no—
745C22×C4—32no—
746C22×C4—62no—
747C22×C4—188no—
748C22×C4—182no—
749C22×C4C2×D3211yescharacteristic
750Q16—32no—
751Q16—32no—
752Q16—98no—
753Q16—92no—
754Q16—92no—
755SD16—34no—
756SD16—34no—
757SD16—98no—
758SD16—98no—
759SD16—94no—
760SD16—94no—
761D8—32no—
762D8—32no—
763D8—98no—
764D8—92no—
765D8—92no—
766M16—32no—
767M16—32no—
768M16—34no—
769M16—34no—
770C2×C8—32no—
771C2×C8—34no—
772C2×C8—34no—
773C2×C8C2×D3211yescharacteristic
774C2×C8C2×D3211yescharacteristic
775C2×C8C2×D3211yescharacteristic
776C2×C8C2×D3211yescharacteristic
777C2×C8C2×D3211yescharacteristic
778C2×C8C2×D3211yescharacteristic
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—34no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—42no—
786C22×C3—64no—
787C22×C3—122no—
788C22×C3—242no—
789C22×C3C22×D1211yescharacteristic
790C22×C3C22×D1211yescharacteristic
791C22×C3C22×D1211yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C2×D3—24no—
796C2×D3—42no—
797C2×D3—64no—
798C2×D3—64no—
799C2×D3—82no—
800C2×D3—124no—
801C2×D3—248no—
802C2×D3—248no—
803C2×D3—242no—
804C2×D3—242no—
805C2×D3—244no—
806C2×D3C22×D1214yes—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—34no—
812C3×C4—64no—
813C3×C4C22×D1211yescharacteristic
814C3×C4C22×D1211yescharacteristic
815C3×C4C22×D1211yescharacteristic
816C3×C4C2×D3×D411yescharacteristic
817C3×C4C2×D3×D411yescharacteristic
818C3×C4C2×D3×D411yescharacteristic
819C3×C4C24×D311yescharacteristic
820C3×C4C24×D311yescharacteristic
821Dic3—24no—
822Dic3—64no—
823Dic3—64no—
824Dic3—124no—
825Dic3C22×D1214yes—
826C32#358411yescharacteristic, complemented, Sylow
827C23—32no—
828C23—62no—
829C23—188no—
830C23—182no—
831C23D3×D1211yescharacteristic
832Q8—32no—
833Q8—32no—
834Q8—34no—
835Q8—62no—
836Q8—94no—
837Q8—188no—
838Q8—182no—
839D4—34no—
840D4—34no—
841D4—32no—
842D4—32no—
843D4—34no—
844D4—64no—
845D4—64no—
846D4—62no—
847D4—94no—
848D4—188no—
849D4—188no—
850D4—188no—
851D4—184no—
852D4—184no—
853D4—182no—
854C2×C4—32no—
855C2×C4—34no—
856C2×C4—34no—
857C2×C4—62no—
858C2×C4—64no—
859C2×C4—64no—
860C2×C4—188no—
861C2×C4—188no—
862C2×C4—188no—
863C2×C4—182no—
864C2×C4—184no—
865C2×C4—184no—
866C2×C4D3×D1211yescharacteristic
867C2×C4D3×D1211yescharacteristic
868C2×C4D3×D1211yescharacteristic
869C2×C4C22×D3211yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C8—34no—
873C8C22×D3211yescharacteristic
874C8C22×D3211yescharacteristic
875C8C22×D3211yescharacteristic
876C8C22×D3211yescharacteristic
877C2×C3—22no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—41no—
886C2×C3—41no—
887C2×C3—64no—
888C2×C3—124no—
889C2×C3C23×D1211yescharacteristic
890C2×C3C22×D3×D411yescharacteristic
891D3—24no—
892D3—44no—
893D3—124no—
894D3—124no—
895D3—244no—
896C22—34no—
897C22—41no—
898C22—64no—
899C22—122no—
900C22—184no—
901C22—242no—
902C22—722no—
903C22—728no—
904C22C2×D3×D1211yescharacteristic
905C22C2×D3×D1211yescharacteristic
906C22C2×D3×D1211yescharacteristic
907C4—34no—
908C4—64no—
909C4—184no—
910C4C2×D3×D1211yescharacteristic
911C4C2×D3×D1211yescharacteristic
912C4C2×D3×D1211yescharacteristic
913C4C23×D3211yescharacteristic
914C3—21no—
915C3#8716311yescharacteristic, complemented
916C3#8718711yescharacteristic, complemented
917C2—21no—
918C2—21no—
919C2—21no—
920C2—64no—
921C2—124no—
922C2—364no—
923C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC2×C32C23×D4
hypercenterC22×C8D32
hypocenterC32#3584
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10596669C2semidirect
2. C2×#64113C2semidirect
3. C2×C3×#904C2semidirect
4. C2×C3×#901C2semidirect
5. #10594795C2semidirect
6. #10594692C2semidirect
7. #10594691C2semidirect
8. #10594680C2semidirect
9. #10594679C2semidirect
10. #10594678C2semidirect
11. #10594677C2semidirect
12. #10594676C2semidirect
13. D3×#904C2semidirect
16. C2×#3828C22semidirect
18. C2×C3×#235C22semidirect
20. #64308C22semidirect
22. #64307C22semidirect
25. D3×#235C22semidirect
26. #64298C22semidirect
28. #64297C22semidirect
29. C22×C32×C8C22semidirect
30. C2×#3746C22semidirect
31. #64113C22semidirect
32. #64113C22semidirect
33. #64113C22semidirect
34. #64113C22semidirect
35. C2×#3745C22semidirect
36. C2×#3744C22semidirect
37. C2×C3×#208C22semidirect
38. C2×C3×Dic12C22semidirect
39. C3×#904C22semidirect
40. C3×#904C22semidirect
41. C3×#904C22semidirect
42. C3×#904C22semidirect
43. C2×C3×D24C22semidirect
44. C2×C3×#204C22semidirect
45. C3×#901C22semidirect
46. C3×#901C22semidirect
47. C3×#901C22semidirect
48. C3×#901C22semidirect
49. C2×C3×ΓL(1,𝔽25)C22semidirect
50. C2×C3×D3×C8C22semidirect
51. #63833C22semidirect
52. #63831C22semidirect
53. #63830C22semidirect
54. #63829C22semidirect
55. #63825C22semidirect
56. #63808C22semidirect
57. #63807C22semidirect
58. #63806C22semidirect
59. #63801C22semidirect
60. #63800C22semidirect
61. D3×Dic12C22semidirect
62. #63795C22semidirect
63. #63794C22semidirect
64. D3×D24C22semidirect
65. D3×#204C22semidirect
91. C2×#904D3semidirect
92. C2×#901D3semidirect
194. C2×#235C2×D3semidirect
210. C22×C3×C8C2×D3semidirect
211. C22×C3×C8C2×D3semidirect
217. C2×#208C2×D3semidirect
240. C2×Dic12C2×D3semidirect
257. #904C2×D3semidirect
258. #904C2×D3semidirect
259. #904C2×D3semidirect
260. #904C2×D3semidirect
265. C2×D24C2×D3semidirect
270. C2×#204C2×D3semidirect
271. #901C2×D3semidirect
272. #901C2×D3semidirect
273. #901C2×D3semidirect
274. #901C2×D3semidirect
275. C2×ΓL(1,𝔽25)C2×D3semidirect
276. C2×D3×C8C2×D3semidirect
576. C22×C8D32semidirect
826. C32#3584semidirect
915. C3#87163semidirect
916. C3#87187semidirect

Maximal subgroups

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

subgroupindex
#105966692
C2×#641132
C2×C3×#9042
C2×C3×#9012
#105947952
#105946922
#105946912
#105946802
#105946792
#105946782
#105946772
#105946762
D3×#9042
#871873
#871633