Finite Group Databasebeta

← #13178776

Subgroups — #13178776

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64367C211yesmaximal, characteristic, complemented
2#11724619C211yesmaximal, characteristic, complemented
3C3×#64159C211yesmaximal, characteristic, complemented
4C3×#64158C211yesmaximal, characteristic, complemented
5#11723712C212yesmaximal, complemented
6#11723708C212yesmaximal, complemented
7#11723707C212yesmaximal, complemented
8#11723703C212yesmaximal, complemented
9#11723663C211yesmaximal, characteristic, complemented
10C2×#88811C211yesmaximal, characteristic, complemented
11#11723657C211yesmaximal, characteristic, complemented
12#10595462—31nomaximal
13#10595457—31nomaximal
14#10595455—31nomaximal
15C33×#41C2211yescharacteristic, complemented
16C3×Q8×C3⋊D3C2212yescomplemented
17C3×#3830—22no—
18C3×#3830C2212yescomplemented
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C3×#3828C2211yescharacteristic
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#634—21no—
24C2×C3×#634C2211yescharacteristic, complemented
25#89049—22no—
26C4⋊#1113—21no—
27C4⋊#1113C2212yes—
28#89041—21no—
29#89041C2212yes—
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#88812C2212yescomplemented
39#88811C2212yescomplemented
40#88811C2212yescomplemented
41#88811C2212yescomplemented
42#88809C2212yescomplemented
43#88808C2212yescomplemented
44#64367D311yescharacteristic, complemented
45C3×#1010—31no—
46C3×#1010—31no—
47C3×#1010—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#63951—32no—
60#63948—32no—
61#63946—32no—
62#63940—32no—
63D3×#215—32no—
64D3×#215—32no—
65#63936—32no—
66#63935—32no—
67#63933—32no—
68#63927—32no—
69#63925—32no—
70#63925—32no—
71#63833—31no—
72C2×#3717—31no—
73#63831—31no—
74C2×#3716—31no—
75#63827—31no—
76C2×#3715—31no—
77#63817—31no—
78#63815—31no—
79#63814—31no—
80C22×C3×C3⋊D3—21no—
81C2×#1113—22no—
82C33×Q8C2311yescharacteristic
83C33×D4—21no—
84C33×D4C2311yescharacteristic
85C2×C33×C4—21no—
86C2×C33×C4C2311yescharacteristic
87C3×#638—21no—
88C3×#638—22no—
89C3×#638D412yes—
90C2×C3×C3⋊Dic3—21no—
91C2×C3×C3⋊Dic3—22no—
92C3×C4⋊(C3⋊D3)—21no—
93C3×C4⋊(C3⋊D3)D411yescharacteristic
94C3×C4⋊(C3⋊D3)C2312yes—
95C3×C4⋊(C3⋊D3)C2311yescharacteristic
96C3×C4×C3⋊D3—22no—
97C3×C4×C3⋊D3—21no—
98C3×C4×C3⋊D3C2312yes—
99C3×#634—21no—
100C3×#634—22no—
101C3×#634D411yescharacteristic
102C3×#634C2311yescharacteristic
103C3×#634C2312yes—
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#5837—91no—
111#5775—91no—
112#5770—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
120Q8×C3⋊D3C2×D312yescomplemented
121#3830—22no—
122#3830C2×D312yescomplemented
123#3828—21no—
124#3828C2×D311yescharacteristic
125#3828C2×D311yescharacteristic
126C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
127C2×#634—21no—
128C2×#634C2×D311yescharacteristic, complemented
129C3×D3×Q8—32no—
130C3×D3×Q8—32no—
131C3×D3×Q8—62no—
132C3×#237—32no—
133C3×#237—32no—
134C3×#237—62no—
135C3×#237—62no—
136C3×#237—62no—
137C3×#237—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—61no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—61no—
153C2×C3×Dic6—61no—
154C2×C3×Dic6—61no—
155C2×C3×Dic6—62no—
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#3719—32no—
204#3719—32no—
205#3718—32no—
206#3717—32no—
207#3717—32no—
208#3717—32no—
209#3716—32no—
210#3716—32no—
211#3716—32no—
212#3715—32no—
213#3715—32no—
214#3715—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—21no—
225C2×C3×C3⋊D3—81no—
226C2×C3×C3⋊D3C2×D412yes—
227#1113—82no—
228C33×C4—21no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C3×C3⋊Dic3—22no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C3×2−1+4—91no—
235#1010—31no—
236#1010—31no—
237#1010—61no—
238#1009—91no—
239#1009—91no—
240#1004—91no—
241C3×AGL(1,ℤ/8)—91no—
242C3×#135—91no—
243#951—91no—
244#950—31no—
245#950—31no—
246#950—61no—
247#950—92no—
248#949—31no—
249#949—31no—
250#949—61no—
251#949—92no—
252#948—91no—
253#942—91no—
254#942—92no—
255C2×#215—91no—
256C2×#215—92no—
257C2×#214—91no—
258#918—92no—
259#916—92no—
260#915—92no—
261D3×SD16—92no—
262D3×SD16—92no—
263#912—92no—
264#911—92no—
265#911—92no—
266#909—91no—
267#907—91no—
268C2×#204—91no—
269#901—91no—
270C22×C3⋊D3—21no—
271C22×C3×D3—61no—
272C22×C3×D3—61no—
273C22×C3×D3—121no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—62no—
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8—41no—
281C32×Q8C22×D311yescharacteristic
282C32×Q8C22×D311yescharacteristic
283C32×Q8C22×D311yescharacteristic
284C32×D4—21no—
285C32×D4—22no—
286C32×D4—21no—
287C32×D4—21no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4—21no—
291C32×D4—41no—
292C32×D4—41no—
293C32×D4—41no—
294C32×D4—42no—
295C32×D4C22×D311yescharacteristic
296C32×D4C22×D311yescharacteristic
297C32×D4C22×D311yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4—22no—
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4—21no—
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4—41no—
306C2×C32×C4—41no—
307C2×C32×C4—41no—
308C2×C32×C4—42no—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312#638—22no—
313#638—21no—
314#638#6712yes—
315C2×C3⋊Dic3—21no—
316C2×C3⋊Dic3—22no—
317C4⋊(C3⋊D3)—21no—
318C4⋊(C3⋊D3)#6711yescharacteristic
319C4⋊(C3⋊D3)C22×D312yes—
320C4⋊(C3⋊D3)C22×D311yescharacteristic
321C4×C3⋊D3—22no—
322C4×C3⋊D3—21no—
323C4×C3⋊D3C22×D312yes—
324#634—21no—
325#634—22no—
326#634#6711yescharacteristic
327#634C22×D312yes—
328#634C22×D311yescharacteristic
329C3×#67—32no—
330C3×#67—32no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—62no—
334C3×#67—64no—
335C3×#67—61no—
336C3×#67—61no—
337C3×#67—121no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—62no—
340C2×C3×Dic3—64no—
341C2×C3×Dic3—62no—
342C2×C3×Dic3—61no—
343C2×C3×Dic3—61no—
344C3×D12—31no—
345C3×D12—31no—
346C3×D12—32no—
347C3×D12—31no—
348C3×D12—32no—
349C3×D12—31no—
350C3×D12—61no—
351C3×D12—62no—
352C3×D12—61no—
353C3×D12—61no—
354C3×D12—61no—
355C3×D12—121no—
356C3×C4×D3—32no—
357C3×C4×D3—32no—
358C3×C4×D3—62no—
359C3×C4×D3—62no—
360C3×C4×D3—62no—
361C3×C4×D3—64no—
362C3×C4×D3—61no—
363C3×C4×D3—61no—
364C3×C4×D3—121no—
365C3×Dic6—31no—
366C3×Dic6—31no—
367C3×Dic6—32no—
368C3×Dic6—32no—
369C3×Dic6—31no—
370C3×Dic6—31no—
371C3×Dic6—61no—
372C3×Dic6—62no—
373C3×Dic6—61no—
374C3×Dic6—62no—
375C3×Dic6—62no—
376C3×Dic6—62no—
377C3×Dic6—64no—
378C3×Dic6—61no—
379C3×Dic6—61no—
380#626—62no—
381#626—62no—
382#626—62no—
383#626—62no—
384#625—62no—
385#625—62no—
386#624—62no—
387D3×Dic3—62no—
388D3×Dic3—62no—
389C3⋊(C3⋊C8)C22×D311yescharacteristic
390C3⋊(C3⋊C8)C22×D312yes—
391C3⋊(C3⋊C8)C22×D311yescharacteristic
392C3×C3⋊C8—31no—
393C3×C3⋊C8—32no—
394C3×C3⋊C8—31no—
395C3×C3⋊C8—32no—
396C3×C3⋊C8—31no—
397C3×C3⋊C8—31no—
398C3×C3⋊C8—61no—
399C3×C3⋊C8—61no—
400C3×C3⋊C8—62no—
401#577—271noSylow
402C2×C33—21no—
403C2×C33—41no—
404C2×C33C22×D411yescharacteristic
405C3×C3⋊D3—22no—
406C3×C3⋊D3—41no—
407C3×C3⋊D3—42no—
408C3×#41—21no—
409C3×#41—21no—
410C3×#41—21no—
411C3×#41—41no—
412C3×#41—91no—
413C3×#41—92no—
414C3×#41—91no—
415C3×#41—181no—
416C3×#41—182no—
417C3×#41D3211yescharacteristic, complemented
418C3×#41D3211yescharacteristic, complemented
419C3×#41D3211yescharacteristic, complemented
420C2×C3×Q8—92no—
421C2×C3×Q8—91no—
422C2×C3×Q8—181no—
423C2×C3×D4—91no—
424C2×#67—182no—
425#239—92no—
426#239—181no—
427D3×Q8—32no—
428D3×Q8—32no—
429D3×Q8—62no—
430#237—32no—
431#237—32no—
432#237—62no—
433#237—62no—
434#237—62no—
435#237—64no—
436#237—92no—
437#237—181no—
438D3×D4—92no—
439D3×D4—92no—
440D3×D4—181no—
441D3×D4—181no—
442D3×D4—182no—
443D3×D4—182no—
444#235—31no—
445#235—31no—
446#235—31no—
447#235—31no—
448#235—61no—
449#235—61no—
450#235—61no—
451#235—61no—
452#235—62no—
453#235—92no—
454#235—181no—
455C2×D12—31no—
456C2×D12—31no—
457C2×D12—61no—
458C2×D12—92no—
459C2×D12—181no—
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—61no—
463C2×Dic6—61no—
464C2×Dic6—61no—
465C2×Dic6—62no—
466C3×Q16—91no—
467C3×SD16—91no—
468C3×SD16—92no—
469C3×SD16—91no—
470C3×D8—91no—
471C3×D8—92no—
472C3×M16—91no—
473C2×C3×C8—91no—
474#216—31no—
475#216—31no—
476#216—61no—
477#216—92no—
478#216—92no—
479#215—31no—
480#215—32no—
481#215—31no—
482#215—32no—
483#215—62no—
484#215—61no—
485#215—92no—
486#215—92no—
487#215—92no—
488#214—31no—
489#214—31no—
490#214—61no—
491#214—92no—
492#214—92no—
493#214—92no—
494#213—31no—
495#213—32no—
496#213—32no—
497#213—31no—
498#213—62no—
499#213—61no—
500#208—31no—
501#208—31no—
502#208—61no—
503#208—92no—
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—61no—
507C2×C3⋊C8—92no—
508Dic12—92no—
509#204—92no—
510#204—92no—
511#204—92no—
512ΓL(1,𝔽25)—92no—
513ΓL(1,𝔽25)—92no—
514D3×C8—92no—
515D3×C8—92no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—21no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—42no—
527C22×C32D3×D411yescharacteristic
528C22×C32D3×D411yescharacteristic
529C22×C32C2×#6711yescharacteristic
530C2×C3⋊D3—22no—
531C2×C3⋊D3—21no—
532C2×C3⋊D3—81no—
533C2×C3⋊D3C2×#6712yes—
534C2×C3×D3—32no—
535C2×C3×D3—32no—
536C2×C3×D3—62no—
537C2×C3×D3—62no—
538C2×C3×D3—61no—
539C2×C3×D3—62no—
540C2×C3×D3—61no—
541C2×C3×D3—121no—
542C2×C3×D3—122no—
543C2×C3×D3—241no—
544C2×C3×D3—241no—
545C2×C3×D3—242no—
546D32—242no—
547D32—242no—
548D32—242no—
549C32×C4—21no—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—41no—
560C32×C4—41no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—42no—
564C32×C4D3×D411yescharacteristic
565C32×C4D3×D411yescharacteristic
566C32×C4C2×#6711yescharacteristic
567C32×C4C23×D311yescharacteristic
568C32×C4C23×D311yescharacteristic
569C32×C4C23×D311yescharacteristic
570C3⋊Dic3—22no—
571C3⋊Dic3—21no—
572C3⋊Dic3C2×#6712yes—
573C3×Dic3—32no—
574C3×Dic3—32no—
575C3×Dic3—62no—
576C3×Dic3—64no—
577C3×Dic3—61no—
578C3×Dic3—62no—
579C3×Dic3—62no—
580C3×Dic3—61no—
581C3×Dic3—121no—
5822−1+4—91no—
583H(5,𝔽2)—271no—
584#137—271no—
585#137—272no—
586AGL(1,ℤ/8)—91no—
587AGL(1,ℤ/8)—272no—
588#135—91no—
589#135—272no—
590C2×SD16—271no—
591C2×SD16—272no—
592#131—271no—
593C33#57711yescharacteristic, complemented, Sylow
594C23×C3—181no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—121no—
598C22×D3—182no—
599C22×D3—182no—
600C22×D3—182no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—41no—
605C3×Q8—91no—
606C3×Q8—92no—
607C3×Q8—91no—
608C3×Q8—182no—
609C3×Q8—181no—
610C3×Q8C2×D3211yescharacteristic
611C3×Q8C2×D3211yescharacteristic
612C3×Q8C2×D3211yescharacteristic
613C3×D4—22no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—41no—
621C3×D4—41no—
622C3×D4—42no—
623C3×D4—41no—
624C3×D4—92no—
625C3×D4—91no—
626C3×D4—92no—
627C3×D4—91no—
628C3×D4—182no—
629C3×D4—181no—
630C3×D4—181no—
631C3×D4C2×D3211yescharacteristic
632C3×D4C2×D3211yescharacteristic
633C3×D4C2×D3211yescharacteristic
634C2×C3×C4—22no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—42no—
644C2×C3×C4—41no—
645C2×C3×C4—92no—
646C2×C3×C4—182no—
647C2×C3×C4—182no—
648C2×C3×C4—181no—
649C2×C3×C4—181no—
650C2×C3×C4C2×D3211yescharacteristic
651C2×C3×C4C2×D3211yescharacteristic
652C2×C3×C4C2×D3211yescharacteristic
653#67—32no—
654#67—32no—
655#67—62no—
656#67—62no—
657#67—62no—
658#67—64no—
659#67—61no—
660#67—61no—
661#67—121no—
662#67—182no—
663#67—182no—
664#67—182no—
665#67—182no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—64no—
669C2×Dic3—62no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—182no—
673D12—32no—
674D12—31no—
675D12—32no—
676D12—31no—
677D12—31no—
678D12—31no—
679D12—61no—
680D12—62no—
681D12—61no—
682D12—61no—
683D12—61no—
684D12—121no—
685D12—182no—
686D12—182no—
687C4×D3—32no—
688C4×D3—32no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—62no—
692C4×D3—64no—
693C4×D3—61no—
694C4×D3—61no—
695C4×D3—121no—
696C4×D3—182no—
697C4×D3—182no—
698Dic6—31no—
699Dic6—31no—
700Dic6—32no—
701Dic6—32no—
702Dic6—31no—
703Dic6—31no—
704Dic6—61no—
705Dic6—62no—
706Dic6—61no—
707Dic6—62no—
708Dic6—62no—
709Dic6—62no—
710Dic6—64no—
711Dic6—61no—
712Dic6—61no—
713C3×C8—91no—
714C3×C8—92no—
715C3×C8—91no—
716C3⋊C8—31no—
717C3⋊C8—32no—
718C3⋊C8—31no—
719C3⋊C8—31no—
720C3⋊C8—31no—
721C3⋊C8—32no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—62no—
725C2×C32—21no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—41no—
732C2×C32—41no—
733C2×C32—41no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—42no—
737C2×C32—41no—
738C2×C32—41no—
739C2×C32—81no—
740C2×C32—81no—
741C2×C32—81no—
742C2×C32—82no—
743C2×C32C2×D3×D411yescharacteristic
744C2×C32C2×D3×D411yescharacteristic
745C2×C32C22×#6711yescharacteristic
746C3⋊D3—22no—
747C3⋊D3—41no—
748C3⋊D3—42no—
749C3×D3—62no—
750C3×D3—62no—
751C3×D3—122no—
752C3×D3—122no—
753C3×D3—121no—
754C3×D3—121no—
755C3×D3—122no—
756C3×D3—241no—
757C3×D3—242no—
758#41—91no—
759#41—92no—
760#41—91no—
761#41—181no—
762#41—182no—
763#41—272no—
764#41—541no—
765#41#111311yescharacteristic, complemented
766C2×Q8—92no—
767C2×Q8—91no—
768C2×Q8—181no—
769C2×D4—91no—
770C2×D4—272no—
771C2×D4—541no—
772C2×D4—542no—
773Q16—91no—
774Q16—272no—
775SD16—91no—
776SD16—92no—
777SD16—91no—
778SD16—272no—
779SD16—272no—
780SD16—272no—
781D8—91no—
782D8—92no—
783M16—91no—
784M16—272no—
785C2×C8—91no—
786C2×C8—272no—
787C22×C3—22no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—42no—
797C22×C3—41no—
798C22×C3—92no—
799C22×C3—182no—
800C22×C3—181no—
801C22×C3—721no—
802C22×C3D3×#6711yescharacteristic
803C22×C3D3×#6711yescharacteristic
804C22×C3#381111yescharacteristic
805C2×D3—32no—
806C2×D3—32no—
807C2×D3—62no—
808C2×D3—61no—
809C2×D3—62no—
810C2×D3—61no—
811C2×D3—62no—
812C2×D3—121no—
813C2×D3—122no—
814C2×D3—241no—
815C2×D3—241no—
816C2×D3—242no—
817C2×D3—722no—
818C2×D3—722no—
819C2×D3—722no—
820C3×C4—22no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—42no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—92no—
836C3×C4—181no—
837C3×C4—182no—
838C3×C4D3×#6711yescharacteristic
839C3×C4D3×#6711yescharacteristic
840C3×C4#381111yescharacteristic
841C3×C4C22×D3211yescharacteristic
842C3×C4C22×D3211yescharacteristic
843C3×C4C22×D3211yescharacteristic
844Dic3—32no—
845Dic3—32no—
846Dic3—62no—
847Dic3—64no—
848Dic3—62no—
849Dic3—62no—
850Dic3—61no—
851Dic3—61no—
852Dic3—121no—
853C32—21no—
854C32—21no—
855C32—21no—
856C32—41no—
857C32#577011yescharacteristic, complemented
858C32#577511yescharacteristic, complemented
859C32#583711yescharacteristic, complemented
860C23—181no—
861C23—542no—
862Q8—91no—
863Q8—91no—
864Q8—92no—
865Q8—182no—
866Q8—181no—
867Q8C2×#111311yescharacteristic
868D4—21no—
869D4—92no—
870D4—92no—
871D4—91no—
872D4—91no—
873D4—182no—
874D4—181no—
875D4—181no—
876D4—542no—
877D4—542no—
878D4C2×#111311yescharacteristic
879C2×C4—21no—
880C2×C4—92no—
881C2×C4—182no—
882C2×C4—182no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—542no—
886C2×C4C2×#111311yescharacteristic
887C8—91no—
888C8—91no—
889C8—92no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—41no—
897C2×C3—41no—
898C2×C3—41no—
899C2×C3—42no—
900C2×C3—41no—
901C2×C3—41no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—81no—
905C2×C3—81no—
906C2×C3—81no—
907C2×C3—82no—
908C2×C3—182no—
909C2×C3—361no—
910C2×C3—362no—
911C2×C3C2×D3×#6711yescharacteristic
912C2×C3C2×D3×#6711yescharacteristic
913C2×C3C2×#381111yescharacteristic
914D3—62no—
915D3—62no—
916D3—122no—
917D3—122no—
918D3—121no—
919D3—122no—
920D3—121no—
921D3—242no—
922D3—241no—
923C22—21no—
924C22—92no—
925C22—181no—
926C22—182no—
927C22—721no—
928C22—2162no—
929C22#8904911yescharacteristic
930C4—21no—
931C4—92no—
932C4—182no—
933C4—181no—
934C4#8904911yescharacteristic
935C4C22×#111311yescharacteristic
936C3—21no—
937C3—21no—
938C3—21no—
939C3—41no—
940C3#1059545511yescharacteristic, complemented
941C3#1059545711yescharacteristic, complemented
942C3#1059546211yescharacteristic, complemented
943C2—21no—
944C2—41no—
945C2—182no—
946C2—362no—
947C2—361no—
948C2C2×#8904911yescharacteristic
subgroupG/H
centerC2C2×#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC33×#41C22
socleC2×C33C22×D4
hypercenter#41#1113
hypocenterC33#577
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×#64367C2semidirect
2. #11724619C2semidirect
3. C3×#64159C2semidirect
4. C3×#64158C2semidirect
5. #11723712C2semidirect
6. #11723708C2semidirect
7. #11723707C2semidirect
8. #11723703C2semidirect
9. #11723663C2semidirect
10. C2×#88811C2semidirect
11. #11723657C2semidirect
15. C33×#41C22semidirect
16. C3×Q8×C3⋊D3C22semidirect
18. C3×#3830C22semidirect
24. C2×C3×#634C22semidirect
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. #88812C22semidirect
39. #88811C22semidirect
40. #88811C22semidirect
41. #88811C22semidirect
42. #88809C22semidirect
43. #88808C22semidirect
44. #64367D3semidirect
51. #64159D3semidirect
52. #64158D3semidirect
117. C32×#41C2×D3semidirect
118. C32×#41C2×D3semidirect
119. C32×#41C2×D3semidirect
120. Q8×C3⋊D3C2×D3semidirect
122. #3830C2×D3semidirect
128. C2×#634C2×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
417. C3×#41D32semidirect
418. C3×#41D32semidirect
419. C3×#41D32semidirect
593. C33#577semidirect
765. #41#1113semidirect
857. C32#5770semidirect
858. C32#5775semidirect
859. C32#5837semidirect
940. C3#10595455semidirect
941. C3#10595457semidirect
942. C3#10595462semidirect

Maximal subgroups

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

subgroupindex
C3×#643672
#117246192
C3×#641592
C3×#641582
#117237122
#117237082
#117237072
#117237032
#117236632
C2×#888112
#117236572
#105954623
#105954573
#105954553