Finite Group Databasebeta

← #11235776

Subgroups — #11235776

Order 768.

1830 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2812C211yesmaximal, characteristic
2#82602C212yesmaximal, complemented
3#82580C212yesmaximal, complemented
4#77617C211yesmaximal, characteristic, complemented
5#77599C212yesmaximal, complemented
6#77537C211yesmaximal, characteristic, complemented
7#77519C212yesmaximal, complemented
8#77052C212yesmaximal, complemented
9#77052C212yesmaximal, complemented
10#77016C212yesmaximal, complemented
11#76950C212yesmaximal, complemented
12#76941C212yesmaximal, complemented
13#76932C212yesmaximal, complemented
14#76734C211yesmaximal, characteristic, complemented
15#76724C212yesmaximal, complemented
16#76692C211yesmaximal, characteristic, complemented
17#76678C212yesmaximal, complemented
18#73845C211yesmaximal, characteristic, complemented
19#73817C211yesmaximal, characteristic, complemented
20#45461—31nomaximal, Sylow
21C24×Dic3C2211yescharacteristic
22C2×C3×#120C2212yes—
23C2×#935C2212yes—
24C2×#935C2212yes—
25C2×D4×Dic3C2211yescharacteristic, complemented
26C2×#890C2211yescharacteristic, complemented
27C2×#879C2212yescomplemented
28C2×#877C2211yescharacteristic
29C2×#877C2211yescharacteristic
30C3×#397C2212yes—
31C3×#397C2211yescharacteristic
32C3×#394C2212yes—
33C3×#394C2212yes—
34C3×#394C2212yes—
35C3×#392C2212yes—
36C3×#392C2211yescharacteristic
37C3×#379C2211yescharacteristic
38#5247C2211yescharacteristic
39#5247C2212yes—
40#5222C2212yescomplemented
41#5222C2211yescharacteristic, complemented
42#5221C2212yes—
43#5221C2212yes—
44#5221C2212yes—
45#5220C2212yes—
46#5220C2212yes—
47#5220C2212yes—
48#5220C2212yes—
49#5220C2212yes—
50#5220C2212yes—
51#5220C2212yes—
52#4985C2212yescomplemented
53#4984C2212yescomplemented
54#4983C2211yescharacteristic, complemented
55#4978C2212yescomplemented
56#4978C2212yescomplemented
57#4976C2212yescomplemented
58#4953C2212yescomplemented
59#4951C2212yes—
60#4951C2212yes—
61#4951C2212yes—
62#4951C2212yes—
63#4951C2212yes—
64#4951C2212yes—
65#4951C2212yescomplemented
66#4951C2212yescomplemented
67#4949C2211yescharacteristic
68#4949C2212yes—
69#4949C2211yescharacteristic
70#4949C2212yescomplemented
71#4948C2212yes—
72#4948C2212yes—
73#4948C2212yes—
74#4948C2212yes—
75#4948C2212yescomplemented
76#4946C2212yes—
77#4946C2212yes—
78#4946C2212yes—
79#4946C2212yes—
80#4946C2212yescomplemented
81#4945C2212yescomplemented
82#4945C2212yescomplemented
83#4944C2212yescomplemented
84#4943C2212yes—
85#4943C2211yescharacteristic
86#4943C2211yescharacteristic
87#4943C2212yes—
88#4943C2212yescomplemented
89#4942C2212yes—
90#4942C2212yes—
91#4942C2212yescomplemented
92Dic3×C22⋊C4C2212yes—
93Dic3×C22⋊C4C2212yes—
94#4660C2212yescomplemented
95#4660C2212yescomplemented
96#4660C2212yescomplemented
97#4659C2211yescharacteristic, complemented
98#4659C2212yescomplemented
99#4659C2211yescharacteristic, complemented
100#4657C2212yescomplemented
101#4654C2212yescomplemented
102#4653C2212yescomplemented
103#4652C2212yescomplemented
104#4651C2211yescharacteristic, complemented
105#4649C2212yescomplemented
106#4648C2211yescharacteristic, complemented
107#4647C2212yescomplemented
108#2849—32no—
109#2842—31no—
110#2812D311yescharacteristic
111#2771—31no—
112#2752—31no—
113#2743—32no—
114#2743—32no—
115#2739—32no—
116#2705—32no—
117#2695—32no—
118#2611—31no—
119#2598—31no—
120#2573—32no—
121#2558—32no—
122#2526—32no—
123#2479—32no—
124#2457—32no—
125#2375—32no—
126#2280—31no—
127C25×C3C2311yescharacteristic
128C22×C3×D4C2312yes—
129C22×C3×D4C2312yes—
130C22×C3×D4C2312yes—
131C22×C3×D4C2311yescharacteristic
132C23×Dic3—24no—
133C23×Dic3—42no—
134C23×Dic3—42no—
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2312yes—
137C23×Dic3C2312yes—
138C23×Dic3C2311yescharacteristic
139C23×Dic3C2312yes—
140C3×#120—28no—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C22⋊C4C2312yes—
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C22⋊C4C2312yes—
146C2×C3×C22⋊C4C2312yes—
147C2×C3×C22⋊C4C2312yes—
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2311yescharacteristic
150C2×C3×C22⋊C4C2311yescharacteristic
151C2×C3×C22⋊C4C2312yes—
152C2×C3×C22⋊C4C2312yes—
153C2×#217C2312yes—
154C2×#217C2312yes—
155C2×#217C2312yes—
156C2×#217C2312yes—
157C2×#217C2312yes—
158C2×#217C2312yes—
159C2×#217C2312yes—
160C2×#217C2311yescharacteristic
161C2×#217C2311yescharacteristic
162C2×#217C2312yes—
163C2×#217C2312yes—
164C2×#217C2312yes—
165C2×#217C2312yes—
166C2×#217C2312yes—
167C2×#217C2312yes—
168C2×#217C2312yes—
169C2×#217C2312yes—
170#935—44no—
171#935—44no—
172D4×Dic3—42no—
173C2×C4⋊Dic3C2312yes—
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2312yes—
176C2×C4⋊Dic3C2311yescharacteristic
177C2×C4⋊Dic3C2311yescharacteristic
178C2×C4⋊Dic3C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2311yescharacteristic
183C2×Dic3⋊C4C2312yes—
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2311yescharacteristic
189C2×Dic3⋊C4C2312yes—
190C2×C4×Dic3C2311yescharacteristic
191C2×C4×Dic3C2311yescharacteristic
192C2×C4×Dic3C2312yes—
193C2×C4×Dic3C2312yes—
194C2×C4×Dic3C2312yes—
195C2×C4×Dic3C2312yes—
196#890—42no—
197#879—44no—
198#877—42no—
199#877—42no—
200C3×#95C2312yes—
201C3×#95C2311yescharacteristic
202C3×#95C2312yes—
203C3×#95C2311yescharacteristic
204C3⋊#95C2312yes—
205C3⋊#95C2312yes—
206C3⋊#95C2311yescharacteristic
207C3⋊#95C2312yes—
208C3⋊#95C2311yescharacteristic
209C3⋊#95C2312yes—
210C3⋊#95C2312yes—
211C3⋊#95C2312yes—
212C3⋊#95C2312yes—
213C3⋊#95C2312yes—
214C3⋊#95C2312yes—
215C3⋊#95C2312yes—
216C3⋊#95C2312yes—
217C3⋊#95C2312yes—
218C3⋊#95C2312yes—
219C3⋊#95C2312yes—
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C24×C4—31no—
226C2×#126—32no—
227C2×#125—31no—
228C2×#123—32no—
229C2×#123—32no—
230C2×#120C2×D312yes—
231C2×C4×D4—31no—
232C2×#117—31no—
233C2×#117—31no—
234#400—32no—
235#400—32no—
236#400—31no—
237#400—31no—
238#400—32no—
239#400—32no—
240#400—32no—
241#399—31no—
242#399—31no—
243#399—32no—
244#399—32no—
245#398—31no—
246#398—32no—
247#397—32no—
248#397C2×D312yes—
249#397C2×D311yescharacteristic
250#396—32no—
251#396—32no—
252#396—32no—
253#396—32no—
254#396—32no—
255#394—31no—
256#394—32no—
257#394C2×D312yes—
258#394C2×D312yes—
259#394C2×D312yes—
260#392C2×D311yescharacteristic
261#392C2×D312yes—
262#390—32no—
263#390—32no—
264#390—32no—
265#389—32no—
266#389—32no—
267#389—32no—
268#388—32no—
269#388—32no—
270#388—32no—
271#388—32no—
272#388—32no—
273#388—32no—
274#388—32no—
275#388—32no—
276#388—32no—
277#388—32no—
278#388—32no—
279#387—32no—
280#387—32no—
281#387—32no—
282#387—32no—
283#387—32no—
284#386—32no—
285#386—32no—
286#386—32no—
287#386—32no—
288#386—32no—
289#386—32no—
290#386—32no—
291#385—32no—
292#385—32no—
293#385—32no—
294#385—32no—
295#385—32no—
296#383—31no—
297#381—32no—
298#381—32no—
299#381—31no—
300#381—31no—
301#381—32no—
302#380—32no—
303#380—32no—
304#380—32no—
305#379—32no—
306#379—31no—
307#379C2×D311yescharacteristic
308C4×C4⋊C4—32no—
309C4×C22⋊C4—32no—
310C4×C22⋊C4—32no—
311#376—31no—
312C24×C3—42no—
313C24×C3—42no—
314C24×C3—41no—
315C24×C3—41no—
316C24×C3#4114yes—
317C24×C3C2412yes—
318C24×C3C2411yescharacteristic
319C24×C3C2412yes—
320C2×C3×D4—24no—
321C2×C3×D4—24no—
322C2×C3×D4—24no—
323C2×C3×D4—41no—
324C2×C3×D4—42no—
325C2×C3×D4—42no—
326C2×C3×D4—42no—
327C2×C3×D4—42no—
328C2×C3×D4—42no—
329C2×C3×D4—42no—
330C2×C3×D4—42no—
331C22×C3×C4C2412yes—
332C22×C3×C4C2412yes—
333C22×C3×C4C2411yescharacteristic
334C22×C3×C4C2411yescharacteristic
335C22×C3×C4C2412yes—
336C22×C3×C4C2412yes—
337C22×Dic3—22no—
338C22×Dic3—22no—
339C22×Dic3—22no—
340C22×Dic3—24no—
341C22×Dic3—24no—
342C22×Dic3—22no—
343C22×Dic3—24no—
344C22×Dic3—24no—
345C22×Dic3—42no—
346C22×Dic3—42no—
347C22×Dic3—41no—
348C22×Dic3—41no—
349C22×Dic3—42no—
350C22×Dic3—42no—
351C22×Dic3—42no—
352C22×Dic3—416no—
353C22×Dic3C2411yescharacteristic
354C22×Dic3C2412yes—
355C22×Dic3C2412yes—
356C22×Dic3C2411yescharacteristic
357C22×Dic3C2412yes—
358C22×Dic3C2412yes—
359C22×Dic3C2412yes—
360C22×Dic3C2412yes—
361C22×Dic3C2411yescharacteristic
362C22×Dic3C2411yescharacteristic
363C3×C4⋊C4—41no—
364C3×C4⋊C4—42no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—42no—
371C3×C22⋊C4—42no—
372C3×C22⋊C4—42no—
373C3×C22⋊C4—42no—
374C3×C22⋊C4—42no—
375#217—24no—
376#217—24no—
377#217—41no—
378#217—41no—
379#217—42no—
380#217—42no—
381#217—42no—
382#217—42no—
383#217—42no—
384#217—42no—
385#217—42no—
386#217—42no—
387#217—42no—
388#217—42no—
389#217—42no—
390#217—42no—
391#217—42no—
392C4⋊Dic3—42no—
393C4⋊Dic3—42no—
394C4⋊Dic3—41no—
395C4⋊Dic3—42no—
396C4⋊Dic3—42no—
397C4⋊Dic3—41no—
398Dic3⋊C4—24no—
399Dic3⋊C4—24no—
400Dic3⋊C4—24no—
401Dic3⋊C4—41no—
402Dic3⋊C4—41no—
403Dic3⋊C4—42no—
404Dic3⋊C4—42no—
405Dic3⋊C4—42no—
406Dic3⋊C4—42no—
407Dic3⋊C4—42no—
408Dic3⋊C4—42no—
409C4×Dic3—22no—
410C4×Dic3—22no—
411C4×Dic3—42no—
412C4×Dic3—42no—
413C4×Dic3—42no—
414C4×Dic3—42no—
415C25C22×D311yescharacteristic
416C22×D4C22×D312yes—
417C22×D4C22×D312yes—
418C22×D4C22×D312yes—
419C22×D4C22×D311yescharacteristic
420C23×C4—31no—
421C23×C4—32no—
422C23×C4—32no—
423C23×C4—31no—
424C23×C4—32no—
425C23×C4—64no—
426C23×C4—122no—
427C23×C4—122no—
428#126—124no—
429#125—122no—
430#123—124no—
431#123—124no—
432#120—28no—
433C4×D4—122no—
434#117—122no—
435#117—122no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—32no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—32no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—32no—
447C2×C4⋊C4—32no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4C22×D311yescharacteristic
454C2×C4⋊C4C22×D312yes—
455C2×C22⋊C4—32no—
456C2×C22⋊C4—32no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—32no—
460C2×C22⋊C4—32no—
461C2×C22⋊C4—32no—
462C2×C22⋊C4—32no—
463C2×C22⋊C4—32no—
464C2×C22⋊C4—32no—
465C2×C22⋊C4—32no—
466C2×C22⋊C4—32no—
467C2×C22⋊C4—32no—
468C2×C22⋊C4—32no—
469C2×C22⋊C4—32no—
470C2×C22⋊C4—32no—
471C2×C22⋊C4—32no—
472C2×C22⋊C4C22×D312yes—
473C2×C22⋊C4C22×D312yes—
474C2×C22⋊C4C22×D312yes—
475C2×C22⋊C4C22×D311yescharacteristic
476C2×C22⋊C4C22×D311yescharacteristic
477C2×C22⋊C4C22×D312yes—
478C2×C22⋊C4C22×D312yes—
479C2×C22⋊C4C22×D312yes—
480C2×C22⋊C4C22×D312yes—
481C2×C22⋊C4C22×D312yes—
482C2×C42—31no—
483C2×C42—31no—
484C2×C42—32no—
485C2×C42—32no—
486C2×C42—32no—
487C2×C42—32no—
488#95—32no—
489#95—31no—
490#95—32no—
491#95—32no—
492#95—32no—
493#95—32no—
494#95—32no—
495#95—32no—
496#95—32no—
497#95—32no—
498#95—32no—
499#95—32no—
500#95—32no—
501#95—32no—
502#95—32no—
503#95—32no—
504#95—32no—
505#95—31no—
506#95—32no—
507#95—32no—
508#95—32no—
509#95C22×D311yescharacteristic
510#95C22×D312yes—
511#95C22×D311yescharacteristic
512#95C22×D312yes—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—44no—
531C23×C3—48no—
532C23×C3—44no—
533C23×C3—48no—
534C23×C3—44no—
535C23×C3C2×#4112yes—
536C23×C3C2×#4114yes—
537C23×C3C2511yescharacteristic
538C3×D4—44no—
539C3×D4—84no—
540C3×D4—84no—
541C3×D4—84no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×Dic3—28no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—22no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—48no—
586C2×Dic3—48no—
587C2×Dic3—44no—
588C2×Dic3—84no—
589C2×Dic3H(5,𝔽2)12yes—
590C2×Dic3H(5,𝔽2)12yes—
591C24—41no—
592C24—41no—
593C24—42no—
594C24—42no—
595C24#23714yes—
596C24C23×D312yes—
597C24C23×D311yescharacteristic
598C24C23×D312yes—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—32no—
614C22×C4—32no—
615C22×C4—31no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—64no—
623C22×C4—64no—
624C22×C4—62no—
625C22×C4—64no—
626C22×C4—64no—
627C22×C4—62no—
628C22×C4—122no—
629C22×C4—122no—
630C22×C4—121no—
631C22×C4—121no—
632C22×C4—122no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—1216no—
636C22×C4C23×D312yes—
637C22×C4C23×D312yes—
638C22×C4C23×D311yescharacteristic
639C22×C4C23×D311yescharacteristic
640C22×C4C23×D312yes—
641C22×C4C23×D312yes—
642C4⋊C4—41no—
643C4⋊C4—42no—
644C4⋊C4—64no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—121no—
648C4⋊C4—121no—
649C4⋊C4—121no—
650C4⋊C4—122no—
651C4⋊C4—122no—
652C4⋊C4—121no—
653C4⋊C4—122no—
654C4⋊C4—122no—
655C4⋊C4—122no—
656C4⋊C4—122no—
657C4⋊C4—122no—
658C4⋊C4—122no—
659C4⋊C4—122no—
660C4⋊C4—122no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—64no—
672C22⋊C4—64no—
673C22⋊C4—121no—
674C22⋊C4—121no—
675C22⋊C4—122no—
676C22⋊C4—122no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—122no—
682C22⋊C4—122no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C22⋊C4—122no—
688C42—62no—
689C42—62no—
690C42—122no—
691C42—122no—
692C42—122no—
693C42—122no—
694C22×C3—22no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—416no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—41no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3C22×#4111yescharacteristic
715C22×C3C2×H(5,𝔽2)11yescharacteristic
716C22×C3C2×H(5,𝔽2)11yescharacteristic
717C22×C3#58512yes—
718C22×C3#58512yes—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—42no—
724C3×C4—41no—
725Dic3—22no—
726Dic3—22no—
727Dic3—42no—
728Dic3—41no—
729Dic3—42no—
730Dic3—42no—
731Dic3—42no—
732Dic3—42no—
733Dic3—42no—
734Dic3—41no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—44no—
753C23—48no—
754C23—48no—
755C23—44no—
756C23—44no—
757C23C2×#23712yes—
758C23C2×#23714yes—
759C23C24×D311yescharacteristic
760D4—44no—
761D4—84no—
762D4—84no—
763D4—84no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—68no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—62no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—128no—
810C2×C4—128no—
811C2×C4—124no—
812C2×C4—244no—
813C2×C3—42no—
814C2×C3—44no—
815C2×C3—82no—
816C2×C3#349011yescharacteristic
817C2×C3#349112yes—
818C2×C3#352911yescharacteristic
819C2×C3#353912yes—
820C2×C3#354011yescharacteristic
821C22—24no—
822C22—24no—
823C22—24no—
824C22—22no—
825C22—24no—
826C22—416no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22C22×#23711yescharacteristic
842C22D3×H(5,𝔽2)11yescharacteristic
843C22D3×H(5,𝔽2)11yescharacteristic
844C22#596612yes—
845C22#596612yes—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—62no—
853C4—62no—
854C4—122no—
855C4—122no—
856C4—122no—
857C4—121no—
858C4—122no—
859C4—122no—
860C4—121no—
861C4—122no—
862C3#4546111yescharacteristic, complemented, Sylow
863C2—42no—
864C2—44no—
865C2—82no—
866C2#8629712yes—
867C2#8630911yescharacteristic
868C2#8707212yes—
869C2#8707311yescharacteristic
870C2#8708511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC3×#2812C2
hypercenter#2812D3
hypocenterC3#45461
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2812

Complements

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

NH ≅ G/Ntype
2. #82602C2semidirect
3. #82580C2semidirect
4. #77617C2semidirect
5. #77599C2semidirect
6. #77537C2semidirect
7. #77519C2semidirect
8. #77052C2semidirect
9. #77052C2semidirect
10. #77016C2semidirect
11. #76950C2semidirect
12. #76941C2semidirect
13. #76932C2semidirect
14. #76734C2semidirect
15. #76724C2semidirect
16. #76692C2semidirect
17. #76678C2semidirect
18. #73845C2semidirect
19. #73817C2semidirect
25. C2×D4×Dic3C22semidirect
26. C2×#890C22semidirect
27. C2×#879C22semidirect
40. #5222C22semidirect
41. #5222C22semidirect
52. #4985C22semidirect
53. #4984C22semidirect
54. #4983C22semidirect
55. #4978C22semidirect
56. #4978C22semidirect
57. #4976C22semidirect
58. #4953C22semidirect
65. #4951C22semidirect
66. #4951C22semidirect
70. #4949C22semidirect
75. #4948C22semidirect
80. #4946C22semidirect
81. #4945C22semidirect
82. #4945C22semidirect
83. #4944C22semidirect
88. #4943C22semidirect
91. #4942C22semidirect
94. #4660C22semidirect
95. #4660C22semidirect
96. #4660C22semidirect
97. #4659C22semidirect
98. #4659C22semidirect
99. #4659C22semidirect
100. #4657C22semidirect
101. #4654C22semidirect
102. #4653C22semidirect
103. #4652C22semidirect
104. #4651C22semidirect
105. #4649C22semidirect
106. #4648C22semidirect
107. #4647C22semidirect
862. C3#45461semidirect

Maximal subgroups

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

subgroupindex
C3×#28122
#826022
#825802
#776172
#775992
#775372
#775192
#770522
#770162
#769502
#769412
#769322
#767342
#767242
#766922
#766782
#738452
#738172
#454613