Finite Group Databasebeta

← #13178775

Subgroups — #13178775

Order 1728.

1408 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64366C211yesmaximal, characteristic, complemented
2#11724619C211yesmaximal, characteristic, complemented
3C3×#64159C211yesmaximal, characteristic, complemented
4C3×#64158C211yesmaximal, characteristic, complemented
5#11723713C212yesmaximal, complemented
6#11723709C212yesmaximal, complemented
7#11723706C212yesmaximal, complemented
8#11723702C212yesmaximal, complemented
9#11723661C211yesmaximal, characteristic, complemented
10C2×#88810C211yesmaximal, characteristic, complemented
11#11723657C211yesmaximal, characteristic, complemented
12#10595461—31nomaximal
13#10595456—31nomaximal
14#10595454—31nomaximal
15C33×#41C2211yescharacteristic, complemented
16C3×#3832C2212yescomplemented
17C3×D4×C3⋊D3—22no—
18C3×D4×C3⋊D3C2212yescomplemented
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C3×#3828C2211yescharacteristic, complemented
22C2×C3×C4⋊(C3⋊D3)—21no—
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25#89049—22no—
26C4⋊#1113—21no—
27C4⋊#1113C2212yescomplemented
28#89041—21no—
29#89041C2212yescomplemented
30C3×#3756C2211yescharacteristic, complemented
31C3×#3755C2212yescomplemented
32C3×#3755C2211yescharacteristic, complemented
33C3×#3754C2211yescharacteristic, complemented
34C3×#3753C2212yescomplemented
35C3×#3753C2211yescharacteristic, complemented
36C3×#3748C2211yescharacteristic, complemented
37C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38#88811C2212yescomplemented
39#88810C2212yescomplemented
40#88810C2212yescomplemented
41#88810C2212yescomplemented
42#88809C2212yescomplemented
43#88808C2212yescomplemented
44#64366D311yescharacteristic, complemented
45C3×#1009—31no—
46C3×#1009—31no—
47C3×#1009—61no—
48#64308—31no—
49#64307—31no—
50#64307—31no—
51#64159D311yescharacteristic, complemented
52#64158D311yescharacteristic, complemented
53C3×#950—31no—
54C3×#950—31no—
55C3×#950—61no—
56C3×#949—31no—
57C3×#949—31no—
58C3×#949—61no—
59#63950—32no—
60#63949—32no—
61#63947—32no—
62#63941—32no—
63#63939—32no—
64#63939—32no—
65#63937—32no—
66#63934—32no—
67#63932—32no—
68#63926—32no—
69D3×#213—32no—
70D3×#213—32no—
71#63830—31no—
72#63825—31no—
73C2×#3714—31no—
74C2×#3714—31no—
75#63823—31no—
76C2×#3713—31no—
77#63817—31no—
78#63815—31no—
79#63814—31no—
80C22×C3×C3⋊D3—21no—
81C22×C3×C3⋊D3—21no—
82C22×C3×C3⋊D3—22no—
83C2×#1113—22no—
84C33×Q8C2311yescharacteristic
85C33×D4—21no—
86C33×D4C2311yescharacteristic
87C2×C33×C4—21no—
88C2×C33×C4C2311yescharacteristic
89C3×#638—21no—
90C3×#638—22no—
91C3×#638D412yes—
92C3×C4⋊(C3⋊D3)—22no—
93C3×C4⋊(C3⋊D3)—21no—
94C3×C4⋊(C3⋊D3)—21no—
95C3×C4⋊(C3⋊D3)D411yescharacteristic
96C3×C4⋊(C3⋊D3)C2312yes—
97C3×C4⋊(C3⋊D3)C2311yescharacteristic
98C3×C4⋊(C3⋊D3)C2312yes—
99C3×C4×C3⋊D3—21no—
100C3×C4×C3⋊D3—22no—
101C3×C4×C3⋊D3C2312yes—
102C3×#634D411yescharacteristic
103C3×#634C2311yescharacteristic
104#6295—22no—
105#6295—22no—
106#6294—22no—
107C3×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×C3⋊(C3⋊C8)C2312yes—
110#5835—91no—
111#5774—91no—
112#5769—91no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—41no—
117C32×#41C2×D311yescharacteristic, complemented
118C32×#41C2×D311yescharacteristic, complemented
119C32×#41C2×D311yescharacteristic, complemented
120#3832C2×D312yescomplemented
121D4×C3⋊D3—22no—
122D4×C3⋊D3C2×D312yescomplemented
123#3828—21no—
124#3828C2×D311yescharacteristic
125#3828C2×D311yescharacteristic, complemented
126C2×C4⋊(C3⋊D3)—21no—
127C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
129C3×#239—32no—
130C3×#239—32no—
131C3×#239—62no—
132C3×D3×D4—32no—
133C3×D3×D4—32no—
134C3×D3×D4—62no—
135C3×D3×D4—62no—
136C3×D3×D4—62no—
137C3×D3×D4—64no—
138C3×#235—31no—
139C3×#235—31no—
140C3×#235—31no—
141C3×#235—31no—
142C3×#235—61no—
143C3×#235—61no—
144C3×#235—61no—
145C3×#235—62no—
146C3×#235—61no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—61no—
152C2×C3×D12—61no—
153C2×C3×D12—61no—
154C2×C3×D12—62no—
155C2×C3×D12—61no—
156#3811—62no—
157D3×#67—62no—
158D3×#67—62no—
159#3802—32no—
160#3802—61no—
161D3×D12—32no—
162D3×D12—32no—
163D3×D12—61no—
164D3×D12—61no—
165#3799—32no—
166#3799—61no—
167#3796—32no—
168#3796—61no—
169#3795—32no—
170#3795—61no—
171#3756C2×D311yescharacteristic, complemented
172#3755C2×D312yescomplemented
173#3755C2×D311yescharacteristic, complemented
174#3754C2×D311yescharacteristic, complemented
175#3753C2×D312yescomplemented
176#3753C2×D311yescharacteristic, complemented
177#3748C2×D311yescharacteristic, complemented
178C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
179C3×#216—31no—
180C3×#216—31no—
181C3×#216—61no—
182C3×#215—32no—
183C3×#215—32no—
184C3×#215—31no—
185C3×#215—31no—
186C3×#215—62no—
187C3×#215—61no—
188C3×#214—31no—
189C3×#214—31no—
190C3×#214—61no—
191C3×#213—32no—
192C3×#213—32no—
193C3×#213—31no—
194C3×#213—31no—
195C3×#213—62no—
196C3×#213—61no—
197C3×#208—31no—
198C3×#208—31no—
199C3×#208—61no—
200C2×C3×C3⋊C8—31no—
201C2×C3×C3⋊C8—31no—
202C2×C3×C3⋊C8—61no—
203#3717—32no—
204#3716—32no—
205#3715—32no—
206#3714—32no—
207#3714—32no—
208#3714—32no—
209#3714—32no—
210#3714—32no—
211#3714—32no—
212#3713—32no—
213#3713—32no—
214#3713—32no—
215#3712—32no—
216#3711—32no—
217#3711—32no—
218#3710—32no—
219D3×C3⋊C8—32no—
220D3×C3⋊C8—32no—
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—22no—
224C2×C3×C3⋊D3—22no—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—82no—
227C2×C3×C3⋊D3—81no—
228C2×C3×C3⋊D3—81no—
229C2×C3×C3⋊D3C2×D412yes—
230#1113—82no—
231C33×C4—21no—
232C33×C4C2×D411yescharacteristic
233C33×C4C2411yescharacteristic
234C3×C3⋊Dic3—21no—
235C3×C3⋊Dic3C2×D412yes—
236C3×H(5,𝔽2)—91no—
237#1009—31no—
238#1009—31no—
239#1009—61no—
240#1009—91no—
241#1009—91no—
242#1004—91no—
243C3×AGL(1,ℤ/8)—91no—
244C3×#135—91no—
245#950—31no—
246#950—31no—
247#950—61no—
248#950—92no—
249#949—31no—
250#949—31no—
251#949—61no—
252#949—91no—
253#949—92no—
254#948—91no—
255#932—91no—
256#932—92no—
257C2×#213—91no—
258C2×#213—91no—
259C2×#213—92no—
260#919—92no—
261#916—92no—
262#914—92no—
263#914—92no—
264#914—92no—
265#911—92no—
266D3×D8—92no—
267D3×D8—92no—
268#908—91no—
269#907—91no—
270C2×D24—91no—
271#901—91no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3—21no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—64no—
278C22×C3×D3—62no—
279C22×C3×D3—61no—
280C22×C3×D3—61no—
281C22×C3×D3—61no—
282C22×C3×D3—61no—
283C22×C3×D3—121no—
284C2×D32—62no—
285C2×D32—62no—
286C2×D32—62no—
287C32×Q8—21no—
288C32×Q8—21no—
289C32×Q8—21no—
290C32×Q8—41no—
291C32×Q8C22×D311yescharacteristic
292C32×Q8C22×D311yescharacteristic
293C32×Q8C22×D311yescharacteristic
294C32×D4—21no—
295C32×D4—22no—
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—41no—
302C32×D4—41no—
303C32×D4—41no—
304C32×D4—42no—
305C32×D4C22×D311yescharacteristic
306C32×D4C22×D311yescharacteristic
307C32×D4C22×D311yescharacteristic
308C2×C32×C4—21no—
309C2×C32×C4—22no—
310C2×C32×C4—21no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—41no—
316C2×C32×C4—41no—
317C2×C32×C4—41no—
318C2×C32×C4—42no—
319C2×C32×C4C22×D311yescharacteristic
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C22×D311yescharacteristic
322#638—22no—
323#638—21no—
324#638#6712yes—
325C4⋊(C3⋊D3)—22no—
326C4⋊(C3⋊D3)—21no—
327C4⋊(C3⋊D3)—21no—
328C4⋊(C3⋊D3)#6711yescharacteristic
329C4⋊(C3⋊D3)C22×D312yes—
330C4⋊(C3⋊D3)C22×D312yes—
331C4⋊(C3⋊D3)C22×D311yescharacteristic
332C4×C3⋊D3—22no—
333C4×C3⋊D3—21no—
334C4×C3⋊D3C22×D312yes—
335#634#6711yescharacteristic
336#634C22×D311yescharacteristic
337C3×#67—32no—
338C3×#67—32no—
339C3×#67—62no—
340C3×#67—62no—
341C3×#67—62no—
342C3×#67—64no—
343C3×#67—61no—
344C3×#67—61no—
345C3×#67—121no—
346C3×D12—31no—
347C3×D12—31no—
348C3×D12—32no—
349C3×D12—32no—
350C3×D12—31no—
351C3×D12—32no—
352C3×D12—32no—
353C3×D12—31no—
354C3×D12—61no—
355C3×D12—62no—
356C3×D12—62no—
357C3×D12—61no—
358C3×D12—62no—
359C3×D12—62no—
360C3×D12—62no—
361C3×D12—64no—
362C3×D12—61no—
363C3×D12—61no—
364C3×D12—61no—
365C3×D12—61no—
366C3×D12—121no—
367C3×C4×D3—32no—
368C3×C4×D3—32no—
369C3×C4×D3—62no—
370C3×C4×D3—62no—
371C3×C4×D3—62no—
372C3×C4×D3—64no—
373C3×C4×D3—61no—
374C3×C4×D3—61no—
375C3×C4×D3—121no—
376C3×Dic6—31no—
377C3×Dic6—31no—
378C3×Dic6—31no—
379C3×Dic6—31no—
380C3×Dic6—61no—
381C3×Dic6—61no—
382#626—62no—
383#626—62no—
384#626—62no—
385#626—62no—
386#625—62no—
387#625—62no—
388#624—62no—
389D3×Dic3—62no—
390D3×Dic3—62no—
391C3⋊(C3⋊C8)C22×D311yescharacteristic
392C3⋊(C3⋊C8)C22×D312yes—
393C3⋊(C3⋊C8)C22×D311yescharacteristic
394C3×C3⋊C8—31no—
395C3×C3⋊C8—32no—
396C3×C3⋊C8—31no—
397C3×C3⋊C8—32no—
398C3×C3⋊C8—31no—
399C3×C3⋊C8—31no—
400C3×C3⋊C8—61no—
401C3×C3⋊C8—61no—
402C3×C3⋊C8—62no—
403#576—271noSylow
404C2×C33—21no—
405C2×C33—41no—
406C2×C33C22×D411yescharacteristic
407C3×C3⋊D3—22no—
408C3×C3⋊D3—42no—
409C3×C3⋊D3—41no—
410C3×C3⋊D3—42no—
411C3×#41—21no—
412C3×#41—21no—
413C3×#41—21no—
414C3×#41—41no—
415C3×#41—91no—
416C3×#41—92no—
417C3×#41—91no—
418C3×#41—181no—
419C3×#41D3211yescharacteristic, complemented
420C3×#41D3211yescharacteristic, complemented
421C3×#41D3211yescharacteristic, complemented
422C2×C3×D4—92no—
423C2×C3×D4—91no—
424C2×C3×D4—91no—
425C2×C3×D4—181no—
426C2×C3×D4—182no—
427C2×#67—182no—
428#239—32no—
429#239—32no—
430#239—62no—
431#239—92no—
432#239—181no—
433#237—92no—
434#237—181no—
435D3×D4—32no—
436D3×D4—32no—
437D3×D4—62no—
438D3×D4—62no—
439D3×D4—62no—
440D3×D4—64no—
441D3×D4—92no—
442D3×D4—92no—
443D3×D4—181no—
444D3×D4—181no—
445D3×D4—182no—
446D3×D4—182no—
447#235—31no—
448#235—31no—
449#235—31no—
450#235—31no—
451#235—61no—
452#235—61no—
453#235—61no—
454#235—61no—
455#235—62no—
456#235—92no—
457#235—181no—
458C2×D12—31no—
459C2×D12—31no—
460C2×D12—31no—
461C2×D12—31no—
462C2×D12—61no—
463C2×D12—61no—
464C2×D12—61no—
465C2×D12—61no—
466C2×D12—62no—
467C2×D12—92no—
468C2×D12—181no—
469C3×Q16—91no—
470C3×SD16—91no—
471C3×SD16—92no—
472C3×SD16—91no—
473C3×D8—91no—
474C3×D8—92no—
475C3×M16—91no—
476C2×C3×C8—91no—
477#216—31no—
478#216—31no—
479#216—61no—
480#215—31no—
481#215—32no—
482#215—32no—
483#215—31no—
484#215—62no—
485#215—61no—
486#215—92no—
487#214—31no—
488#214—31no—
489#214—61no—
490#214—92no—
491#213—31no—
492#213—32no—
493#213—31no—
494#213—32no—
495#213—62no—
496#213—61no—
497#213—92no—
498#213—92no—
499#213—92no—
500#213—92no—
501#213—92no—
502#213—92no—
503#208—31no—
504#208—31no—
505#208—61no—
506#208—92no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—31no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8—92no—
511D24—92no—
512D24—92no—
513D24—92no—
514#204—92no—
515ΓL(1,𝔽25)—92no—
516ΓL(1,𝔽25)—92no—
517D3×C8—92no—
518D3×C8—92no—
519C22×C32—21no—
520C22×C32—22no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—21no—
524C22×C32—21no—
525C22×C32—21no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—42no—
530C22×C32D3×D411yescharacteristic
531C22×C32D3×D411yescharacteristic
532C22×C32C2×#6711yescharacteristic
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—82no—
537C2×C3⋊D3—81no—
538C2×C3⋊D3—81no—
539C2×C3⋊D3C2×#6712yes—
540C2×C3×D3—32no—
541C2×C3×D3—32no—
542C2×C3×D3—62no—
543C2×C3×D3—64no—
544C2×C3×D3—62no—
545C2×C3×D3—61no—
546C2×C3×D3—62no—
547C2×C3×D3—62no—
548C2×C3×D3—62no—
549C2×C3×D3—61no—
550C2×C3×D3—121no—
551C2×C3×D3—122no—
552C2×C3×D3—242no—
553C2×C3×D3—242no—
554C2×C3×D3—241no—
555C2×C3×D3—241no—
556C2×C3×D3—241no—
557C2×C3×D3—241no—
558C2×C3×D3—242no—
559C2×C3×D3—244no—
560C2×C3×D3—242no—
561D32—242no—
562D32—242no—
563D32—242no—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—41no—
575C32×C4—41no—
576C32×C4—41no—
577C32×C4—41no—
578C32×C4—42no—
579C32×C4D3×D411yescharacteristic
580C32×C4D3×D411yescharacteristic
581C32×C4C2×#6711yescharacteristic
582C32×C4C23×D311yescharacteristic
583C32×C4C23×D311yescharacteristic
584C32×C4C23×D311yescharacteristic
585C3⋊Dic3—21no—
586C3⋊Dic3C2×#6712yes—
587C3×Dic3—32no—
588C3×Dic3—32no—
589C3×Dic3—62no—
590C3×Dic3—61no—
591C3×Dic3—61no—
592C3×Dic3—121no—
593H(5,𝔽2)—91no—
594H(5,𝔽2)—271no—
595AGL(1,ℤ/8)—91no—
596AGL(1,ℤ/8)—271no—
597AGL(1,ℤ/8)—272no—
598AGL(1,ℤ/8)—272no—
599#135—91no—
600#135—272no—
601C2×D8—271no—
602C2×D8—272no—
603#131—271no—
604C33#57611yescharacteristic, complemented, Sylow
605C23×C3—182no—
606C23×C3—181no—
607C23×C3—181no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—64no—
611C22×D3—62no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—121no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—41no—
624C3×Q8—91no—
625C3×Q8—91no—
626C3×Q8C2×D3211yescharacteristic
627C3×Q8C2×D3211yescharacteristic
628C3×Q8C2×D3211yescharacteristic
629C3×D4—22no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—42no—
639C3×D4—41no—
640C3×D4—92no—
641C3×D4—92no—
642C3×D4—91no—
643C3×D4—92no—
644C3×D4—91no—
645C3×D4—182no—
646C3×D4—182no—
647C3×D4—181no—
648C3×D4—181no—
649C3×D4—181no—
650C3×D4C2×D3211yescharacteristic
651C3×D4C2×D3211yescharacteristic
652C3×D4C2×D3211yescharacteristic
653C2×C3×C4—22no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—42no—
663C2×C3×C4—41no—
664C2×C3×C4—92no—
665C2×C3×C4—182no—
666C2×C3×C4—181no—
667C2×C3×C4C2×D3211yescharacteristic
668C2×C3×C4C2×D3211yescharacteristic
669C2×C3×C4C2×D3211yescharacteristic
670#67—32no—
671#67—32no—
672#67—62no—
673#67—62no—
674#67—62no—
675#67—64no—
676#67—61no—
677#67—61no—
678#67—121no—
679#67—182no—
680#67—182no—
681#67—182no—
682#67—182no—
683C2×Dic3—182no—
684D12—32no—
685D12—32no—
686D12—31no—
687D12—32no—
688D12—32no—
689D12—31no—
690D12—31no—
691D12—31no—
692D12—61no—
693D12—62no—
694D12—62no—
695D12—61no—
696D12—62no—
697D12—62no—
698D12—62no—
699D12—64no—
700D12—61no—
701D12—61no—
702D12—61no—
703D12—61no—
704D12—121no—
705D12—182no—
706D12—182no—
707C4×D3—32no—
708C4×D3—32no—
709C4×D3—62no—
710C4×D3—62no—
711C4×D3—62no—
712C4×D3—64no—
713C4×D3—61no—
714C4×D3—61no—
715C4×D3—121no—
716C4×D3—182no—
717C4×D3—182no—
718Dic6—31no—
719Dic6—31no—
720Dic6—31no—
721Dic6—31no—
722Dic6—61no—
723Dic6—61no—
724C3×C8—91no—
725C3×C8—92no—
726C3×C8—91no—
727C3⋊C8—31no—
728C3⋊C8—32no—
729C3⋊C8—31no—
730C3⋊C8—31no—
731C3⋊C8—31no—
732C3⋊C8—32no—
733C3⋊C8—61no—
734C3⋊C8—61no—
735C3⋊C8—62no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—41no—
743C2×C32—41no—
744C2×C32—41no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—42no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—81no—
751C2×C32—81no—
752C2×C32—81no—
753C2×C32—82no—
754C2×C32C2×D3×D411yescharacteristic
755C2×C32C2×D3×D411yescharacteristic
756C2×C32C22×#6711yescharacteristic
757C3⋊D3—22no—
758C3⋊D3—42no—
759C3⋊D3—41no—
760C3⋊D3—42no—
761C3×D3—62no—
762C3×D3—62no—
763C3×D3—122no—
764C3×D3—124no—
765C3×D3—122no—
766C3×D3—122no—
767C3×D3—121no—
768C3×D3—122no—
769C3×D3—121no—
770C3×D3—122no—
771C3×D3—241no—
772C3×D3—242no—
773#41—91no—
774#41—92no—
775#41—91no—
776#41—181no—
777#41—272no—
778#41—541no—
779#41#111311yescharacteristic, complemented
780C2×D4—92no—
781C2×D4—91no—
782C2×D4—91no—
783C2×D4—181no—
784C2×D4—182no—
785C2×D4—272no—
786C2×D4—541no—
787C2×D4—542no—
788Q16—91no—
789SD16—91no—
790SD16—92no—
791SD16—91no—
792SD16—272no—
793D8—91no—
794D8—92no—
795D8—272no—
796D8—272no—
797D8—272no—
798M16—91no—
799M16—272no—
800C2×C8—91no—
801C2×C8—272no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—42no—
812C22×C3—41no—
813C22×C3—92no—
814C22×C3—182no—
815C22×C3—181no—
816C22×C3—182no—
817C22×C3—721no—
818C22×C3—721no—
819C22×C3—722no—
820C22×C3D3×#6711yescharacteristic
821C22×C3D3×#6711yescharacteristic
822C22×C3#381111yescharacteristic
823C2×D3—32no—
824C2×D3—32no—
825C2×D3—62no—
826C2×D3—64no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—61no—
830C2×D3—62no—
831C2×D3—61no—
832C2×D3—62no—
833C2×D3—121no—
834C2×D3—122no—
835C2×D3—242no—
836C2×D3—242no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—242no—
842C2×D3—244no—
843C2×D3—242no—
844C2×D3—722no—
845C2×D3—722no—
846C2×D3—722no—
847C3×C4—22no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—42no—
860C3×C4—41no—
861C3×C4—41no—
862C3×C4—92no—
863C3×C4—181no—
864C3×C4D3×#6711yescharacteristic
865C3×C4D3×#6711yescharacteristic
866C3×C4#381111yescharacteristic
867C3×C4C22×D3211yescharacteristic
868C3×C4C22×D3211yescharacteristic
869C3×C4C22×D3211yescharacteristic
870Dic3—32no—
871Dic3—32no—
872Dic3—62no—
873Dic3—61no—
874Dic3—61no—
875Dic3—121no—
876C32—21no—
877C32—21no—
878C32—21no—
879C32—41no—
880C32#576911yescharacteristic, complemented
881C32#577411yescharacteristic, complemented
882C32#583511yescharacteristic, complemented
883C23—182no—
884C23—181no—
885C23—181no—
886C23—542no—
887Q8—91no—
888Q8—91no—
889Q8C2×#111311yescharacteristic
890D4—21no—
891D4—92no—
892D4—92no—
893D4—91no—
894D4—92no—
895D4—91no—
896D4—182no—
897D4—182no—
898D4—181no—
899D4—181no—
900D4—181no—
901D4—542no—
902D4—542no—
903D4C2×#111311yescharacteristic
904C2×C4—21no—
905C2×C4—92no—
906C2×C4—182no—
907C2×C4—181no—
908C2×C4—542no—
909C2×C4C2×#111311yescharacteristic
910C8—91no—
911C8—91no—
912C8—92no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—42no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—81no—
930C2×C3—82no—
931C2×C3—182no—
932C2×C3—361no—
933C2×C3—362no—
934C2×C3—362no—
935C2×C3C2×D3×#6711yescharacteristic
936C2×C3C2×D3×#6711yescharacteristic
937C2×C3C2×#381111yescharacteristic
938D3—62no—
939D3—62no—
940D3—122no—
941D3—124no—
942D3—122no—
943D3—122no—
944D3—122no—
945D3—121no—
946D3—122no—
947D3—121no—
948D3—242no—
949D3—241no—
950C22—21no—
951C22—92no—
952C22—182no—
953C22—181no—
954C22—182no—
955C22—721no—
956C22—721no—
957C22—722no—
958C22—2162no—
959C22#8904911yescharacteristic
960C4—21no—
961C4—92no—
962C4—181no—
963C4#8904911yescharacteristic
964C4C22×#111311yescharacteristic
965C3—21no—
966C3—21no—
967C3—21no—
968C3—41no—
969C3#1059545411yescharacteristic, complemented
970C3#1059545611yescharacteristic, complemented
971C3#1059546111yescharacteristic, complemented
972C2—21no—
973C2—41no—
974C2—182no—
975C2—362no—
976C2—362no—
977C2—361no—
978C2C2×#8904911yescharacteristic
subgroupG/H
centerC2C2×#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC33×#41C22
socleC2×C33C22×D4
hypercenter#41#1113
hypocenterC33#576
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#64366C2semidirect
2. #11724619C2semidirect
3. C3×#64159C2semidirect
4. C3×#64158C2semidirect
5. #11723713C2semidirect
6. #11723709C2semidirect
7. #11723706C2semidirect
8. #11723702C2semidirect
9. #11723661C2semidirect
10. C2×#88810C2semidirect
11. #11723657C2semidirect
15. C33×#41C22semidirect
16. C3×#3832C22semidirect
18. C3×D4×C3⋊D3C22semidirect
21. C3×#3828C22semidirect
23. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C4⋊#1113C22semidirect
29. #89041C22semidirect
30. C3×#3756C22semidirect
31. C3×#3755C22semidirect
32. C3×#3755C22semidirect
33. C3×#3754C22semidirect
34. C3×#3753C22semidirect
35. C3×#3753C22semidirect
36. C3×#3748C22semidirect
37. C2×C3×C3⋊(C3⋊C8)C22semidirect
38. #88811C22semidirect
39. #88810C22semidirect
40. #88810C22semidirect
41. #88810C22semidirect
42. #88809C22semidirect
43. #88808C22semidirect
44. #64366D3semidirect
51. #64159D3semidirect
52. #64158D3semidirect
117. C32×#41C2×D3semidirect
118. C32×#41C2×D3semidirect
119. C32×#41C2×D3semidirect
120. #3832C2×D3semidirect
122. D4×C3⋊D3C2×D3semidirect
125. #3828C2×D3semidirect
127. C2×C4⋊(C3⋊D3)C2×D3semidirect
128. C2×C4⋊(C3⋊D3)C2×D3semidirect
171. #3756C2×D3semidirect
172. #3755C2×D3semidirect
173. #3755C2×D3semidirect
174. #3754C2×D3semidirect
175. #3753C2×D3semidirect
176. #3753C2×D3semidirect
177. #3748C2×D3semidirect
178. C2×C3⋊(C3⋊C8)C2×D3semidirect
419. C3×#41D32semidirect
420. C3×#41D32semidirect
421. C3×#41D32semidirect
604. C33#576semidirect
779. #41#1113semidirect
880. C32#5769semidirect
881. C32#5774semidirect
882. C32#5835semidirect
969. C3#10595454semidirect
970. C3#10595456semidirect
971. C3#10595461semidirect

Maximal subgroups

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

subgroupindex
C3×#643662
#117246192
C3×#641592
C3×#641582
#117237132
#117237092
#117237062
#117237022
#117236612
C2×#888102
#117236572
#105954613
#105954563
#105954543