Finite Group Databasebeta

← #11003113

Subgroups — #11003113

Order 768.

1662 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2626C211yesmaximal, characteristic
2#82811C211yesmaximal, characteristic, complemented
3#82745C211yesmaximal, characteristic, complemented
4#82117C211yesmaximal, characteristic
5C2×#4951C211yesmaximal, characteristic
6#78079C212yesmaximal, complemented
7#78069C212yesmaximal, complemented
8#77391C212yesmaximal, complemented
9#77385C212yesmaximal, complemented
10#77366C212yesmaximal, complemented
11#77365C212yesmaximal, complemented
12#76850C212yesmaximal, complemented
13#76830C212yesmaximal, complemented
14#74464C212yesmaximal, complemented
15#74441C212yesmaximal, complemented
16#73998C211yesmaximal, characteristic, complemented
17#73874C211yesmaximal, characteristic, complemented
18#73831C212yesmaximal
19#73830C212yesmaximal
20#36760—31nomaximal, Sylow
21C2×C3×C22⋊Q8C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C2×#944C2211yescharacteristic, complemented
26C22×C4⋊Dic3C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#890C2211yescharacteristic, complemented
30C2×#889C2212yescomplemented
31C2×#879C2212yes—
32C2×#879C2212yes—
33C3×#399C2212yes—
34C3×#396C2212yes—
35C3×#396C2212yes—
36C3×#393C2212yes—
37C3×#385C2212yes—
38C3×#380C2211yescharacteristic
39C3×#379C2212yes—
40#5247C2212yes—
41#5229C2212yescomplemented
42#5229C2211yescharacteristic, complemented
43#5212C2211yescharacteristic
44#5210C2212yes—
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47#4986C2212yescomplemented
48#4984C2211yescharacteristic, complemented
49#4984C2212yescomplemented
50#4982C2212yescomplemented
51#4982C2212yescomplemented
52#4981C2212yescomplemented
53#4980C2212yescomplemented
54#4980C2212yescomplemented
55#4980C2212yescomplemented
56#4978C2212yescomplemented
57#4977C2211yescharacteristic, complemented
58#4977C2212yescomplemented
59#4976C2212yescomplemented
60#4976C2212yescomplemented
61#4976C2212yescomplemented
62#4975C2211yescharacteristic, complemented
63#4973C2211yescharacteristic, complemented
64#4972C2211yescharacteristic, complemented
65#4972C2212yescomplemented
66#4953C2212yes—
67#4953C2212yes—
68#4952C2212yes—
69#4952C2212yes—
70#4952C2212yes—
71#4952C2212yes—
72#4951C2212yes—
73#4951C2212yes—
74#4951C2212yes—
75#4951C2212yes—
76#4951C2212yes—
77#4951C2212yes—
78#4950C2212yes—
79#4950C2212yes—
80#4949C2212yes—
81#4948C2212yes—
82#4948C2212yes—
83#4948C2212yes—
84#4948C2212yes—
85#4947C2212yes—
86#4946C2212yes—
87#4946C2212yes—
88#4945C2212yes—
89#4945C2212yes—
90#4944C2212yes—
91#4944C2212yes—
92#4942C2212yes—
93#4942C2212yes—
94Dic3×C22⋊C4C2212yes—
95Dic3×C22⋊C4C2212yes—
96#4660C2212yescomplemented
97#4660C2212yescomplemented
98#4659C2212yescomplemented
99#4657C2212yescomplemented
100#4655C2212yescomplemented
101#4655C2212yescomplemented
102#4654C2212yescomplemented
103#4654C2212yescomplemented
104#4653C2212yescomplemented
105#4653C2212yescomplemented
106#4647C2212yescomplemented
107#4646C2212yescomplemented
108#2857—31no—
109#2851—31no—
110#2798—32no—
111#2783—32no—
112#2772—32no—
113#2754—32no—
114#2725—32no—
115#2725—32no—
116#2721—32no—
117#2716—32no—
118#2626—31no—
119#2626D311yescharacteristic
120#2505—32no—
121#2480—32no—
122#2480—32no—
123#2473—32no—
124#2329—31no—
125#2329—31no—
126C2×#388—31no—
127C25×C3C2311yescharacteristic
128C22×C3×Q8C2311yescharacteristic
129C23×C3×C4C2311yescharacteristic
130C23×C3×C4C2311yescharacteristic
131C23×Dic3C2311yescharacteristic
132C23×Dic3C2311yescharacteristic
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C22×Dic6C2311yescharacteristic
136C3×C22⋊Q8—24no—
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C22⋊C4C2312yes—
146C2×C3×C22⋊C4C2312yes—
147C2×C3×C22⋊C4C2312yes—
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C22⋊C4C2312yes—
151C2×C3×C22⋊C4C2312yes—
152C2×#217—42no—
153C2×#217—42no—
154C2×#217C2312yes—
155C2×#217C2312yes—
156C2×#217C2312yes—
157C2×#217C2312yes—
158C2×#217C2312yes—
159C2×#217C2312yes—
160C2×#217C2312yes—
161C2×#217C2312yes—
162C2×#217C2312yes—
163C2×#217C2312yes—
164#944—42no—
165C2×C4⋊Dic3—42no—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2312yes—
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×C4⋊Dic3C2312yes—
175#924—24no—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2312yes—
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2312yes—
183C2×Dic3⋊C4C2312yes—
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×C4×Dic3—42no—
188C2×C4×Dic3C2311yescharacteristic
189C2×C4×Dic3C2311yescharacteristic
190C2×C4×Dic3C2312yes—
191C2×C4×Dic3C2312yes—
192C2×C4×Dic3C2312yes—
193C2×C4×Dic3C2311yescharacteristic
194C2×C4×Dic3C2312yes—
195C2×C4×Dic3C2311yescharacteristic
196#890—42no—
197#889—44no—
198#879—44no—
199#879—44no—
200C3×#95C2312yes—
201C3×#95C2312yes—
202C3×#95C2312yes—
203C3⋊#95C2312yes—
204C3⋊#95C2312yes—
205C3⋊#95C2312yes—
206C3⋊#95C2312yes—
207C3⋊#95C2312yes—
208C3⋊#95C2312yes—
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—
225C3⋊#95C2312yes—
226C2×C4⋊Q8—31no—
227C2×#126—32no—
228C2×#126—32no—
229C2×#125—31no—
230C2×#125—32no—
231C2×C22⋊Q8—31no—
232C2×C22⋊Q8C2×D311yescharacteristic
233C22×C4⋊C4—31no—
234C22×C22⋊C4—31no—
235C22×C22⋊C4—31no—
236C22×C22⋊C4C2×D311yescharacteristic
237C22×C42—31no—
238#400—32no—
239#400—32no—
240#400—32no—
241#400—32no—
242#399—32no—
243#399C2×D312yes—
244#398—32no—
245#398—32no—
246#398—32no—
247#398—32no—
248#397—32no—
249#397—32no—
250#397—32no—
251#397—32no—
252#397—32no—
253#397—32no—
254#396—32no—
255#396—32no—
256#396—32no—
257#396—32no—
258#396C2×D312yes—
259#396C2×D312yes—
260#393—32no—
261#393C2×D312yes—
262#391—32no—
263#391—31no—
264#391—31no—
265#391—32no—
266#389—32no—
267#389—32no—
268#389—31no—
269#389—31no—
270#389—32no—
271#389—32no—
272#389—32no—
273#389—32no—
274#388—32no—
275#388—32no—
276#388—32no—
277#388—32no—
278#388—32no—
279#388—32no—
280#388—32no—
281#388—32no—
282#388—32no—
283#388—32no—
284#387—32no—
285#387—32no—
286#387—32no—
287#387—32no—
288#387—32no—
289#387—32no—
290#387—32no—
291#387—32no—
292#387—32no—
293#387—32no—
294#385—32no—
295#385—32no—
296#385—32no—
297#385—32no—
298#385—32no—
299#385C2×D312yes—
300#384—31no—
301#382—31no—
302#382—32no—
303#380—31no—
304#380—32no—
305#380—32no—
306#380C2×D311yescharacteristic
307#379—32no—
308#379C2×D312yes—
309C4×C22⋊C4—32no—
310C4×C22⋊C4—32no—
311C2×#95—31no—
312C2×#95—31no—
313C24×C3—22no—
314C24×C3—22no—
315C24×C3—22no—
316C24×C3—41no—
317C24×C3—41no—
318C24×C3—41no—
319C24×C3—41no—
320C24×C3C2412yes—
321C24×C3C2411yescharacteristic
322C2×C3×Q8—22no—
323C2×C3×Q8—41no—
324C2×C3×Q8—41no—
325C22×C3×C4—22no—
326C22×C3×C4—41no—
327C22×C3×C4—41no—
328C22×C3×C4—41no—
329C22×C3×C4—41no—
330C22×C3×C4#4114yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2412yes—
333C22×C3×C4C2412yes—
334C22×C3×C4C2412yes—
335C22×C3×C4C2412yes—
336C22×C3×C4C2411yescharacteristic
337C22×C3×C4C2411yescharacteristic
338C22×Dic3—22no—
339C22×Dic3—22no—
340C22×Dic3—22no—
341C22×Dic3—22no—
342C22×Dic3—22no—
343C22×Dic3—22no—
344C22×Dic3—41no—
345C22×Dic3—41no—
346C22×Dic3—41no—
347C22×Dic3—41no—
348C22×Dic3—41no—
349C22×Dic3—41no—
350C22×Dic3C2411yescharacteristic
351C22×Dic3C2412yes—
352C22×Dic3C2411yescharacteristic
353C22×Dic3C2412yes—
354C22×Dic3C2412yes—
355C22×Dic3C2412yes—
356C22×Dic3C2412yes—
357C22×Dic3C2412yes—
358C22×Dic3C2411yescharacteristic
359C22×Dic3C2411yescharacteristic
360C2×Dic6—22no—
361C2×Dic6—41no—
362C2×Dic6—41no—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—24no—
365C3×C4⋊C4—42no—
366C3×C4⋊C4—41no—
367C3×C4⋊C4—41no—
368C3×C4⋊C4—42no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—42no—
374C3×C22⋊C4—42no—
375C3×C22⋊C4—42no—
376C3×C22⋊C4—42no—
377#217—24no—
378#217—24no—
379#217—24no—
380#217—24no—
381#217—42no—
382#217—42no—
383#217—42no—
384#217—42no—
385#217—42no—
386#217—42no—
387C4⋊Dic3—22no—
388C4⋊Dic3—24no—
389C4⋊Dic3—24no—
390C4⋊Dic3—42no—
391C4⋊Dic3—41no—
392C4⋊Dic3—42no—
393C4⋊Dic3—42no—
394C4⋊Dic3—42no—
395C4⋊Dic3—41no—
396Dic3⋊C4—24no—
397Dic3⋊C4—24no—
398Dic3⋊C4—24no—
399Dic3⋊C4—24no—
400Dic3⋊C4—42no—
401Dic3⋊C4—42no—
402Dic3⋊C4—42no—
403Dic3⋊C4—42no—
404Dic3⋊C4—42no—
405Dic3⋊C4—42no—
406Dic3⋊C4—42no—
407C4×Dic3—22no—
408C4×Dic3—22no—
409C4×Dic3—42no—
410C4×Dic3—42no—
411C4×Dic3—42no—
412C4×Dic3—41no—
413C4×Dic3—41no—
414C4×Dic3—42no—
415C25C22×D311yescharacteristic
416C22×Q8—31no—
417C22×Q8C22×D311yescharacteristic
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C4⋊Q8—122no—
425#126—124no—
426#126—124no—
427#125—122no—
428#125—124no—
429C22⋊Q8—24no—
430C22⋊Q8—64no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—32no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—32no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—32no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—32no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—32no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—122no—
452C2×C4⋊C4C22×D311yescharacteristic
453C2×C4⋊C4C22×D312yes—
454C2×C4⋊C4C22×D311yescharacteristic
455C2×C4⋊C4C22×D312yes—
456C2×C4⋊C4C22×D311yescharacteristic
457C2×C4⋊C4C22×D312yes—
458C2×C22⋊C4—24no—
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—122no—
470C2×C22⋊C4—122no—
471C2×C22⋊C4C22×D312yes—
472C2×C22⋊C4C22×D312yes—
473C2×C22⋊C4C22×D312yes—
474C2×C22⋊C4C22×D312yes—
475C2×C22⋊C4C22×D312yes—
476C2×C22⋊C4C22×D312yes—
477C2×C22⋊C4C22×D312yes—
478C2×C22⋊C4C22×D312yes—
479C2×C42—31no—
480C2×C42—31no—
481C2×C42—32no—
482C2×C42—32no—
483C2×C42—32no—
484C2×C42—32no—
485C2×C42—31no—
486C2×C42—31no—
487C2×C42—122no—
488#95—32no—
489#95—32no—
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—32no—
506#95—32no—
507#95—32no—
508#95—32no—
509#95—32no—
510#95—32no—
511#95C22×D312yes—
512#95C22×D312yes—
513#95C22×D312yes—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—44no—
526C23×C3—44no—
527C23×C3—44no—
528C23×C3—82no—
529C23×C3—82no—
530C23×C3—82no—
531C23×C3—82no—
532C23×C3C2×#4112yes—
533C23×C32−1+412yes—
534C23×C32−1+412yes—
535C23×C3C2511yescharacteristic
536C3×Q8—82no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
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—44no—
557C2×C3×C4—44no—
558C2×C3×C4C2×#4112yes—
559C2×C3×C4C2×#4112yes—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—21no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—21no—
579C2×Dic3—22no—
580C2×Dic3—21no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—21no—
588C2×Dic3—44no—
589C2×Dic3—44no—
590C2×Dic3—82no—
591C2×Dic3—82no—
592C2×Dic3H(5,𝔽2)12yes—
593C2×Dic3H(5,𝔽2)12yes—
594Dic6—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C23×D312yes—
603C24C23×D311yescharacteristic
604C2×Q8—22no—
605C2×Q8—41no—
606C2×Q8—41no—
607C2×Q8—62no—
608C2×Q8—121no—
609C2×Q8—121no—
610C22×C4—22no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—32no—
615C22×C4—31no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—121no—
632C22×C4—121no—
633C22×C4—121no—
634C22×C4—121no—
635C22×C4—121no—
636C22×C4—121no—
637C22×C4#23714yes—
638C22×C4C23×D312yes—
639C22×C4C23×D312yes—
640C22×C4C23×D312yes—
641C22×C4C23×D312yes—
642C22×C4C23×D312yes—
643C22×C4C23×D311yescharacteristic
644C22×C4C23×D311yescharacteristic
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—41no—
648C4⋊C4—42no—
649C4⋊C4—41no—
650C4⋊C4—42no—
651C4⋊C4—64no—
652C4⋊C4—64no—
653C4⋊C4—64no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—64no—
657C4⋊C4—62no—
658C4⋊C4—122no—
659C4⋊C4—122no—
660C4⋊C4—122no—
661C4⋊C4—122no—
662C4⋊C4—121no—
663C4⋊C4—122no—
664C4⋊C4—122no—
665C4⋊C4—122no—
666C4⋊C4—122no—
667C4⋊C4—122no—
668C4⋊C4—121no—
669C4⋊C4—122no—
670C4⋊C4—122no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C22⋊C4—122no—
688C22⋊C4—122no—
689C42—62no—
690C42—62no—
691C42—121no—
692C42—121no—
693C42—122no—
694C42—122no—
695C42—122no—
696C42—122no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—88no—
711C22×C3#54114yes—
712C22×C3C22×#4111yescharacteristic
713C22×C3C2×H(5,𝔽2)11yescharacteristic
714C22×C3C2×H(5,𝔽2)11yescharacteristic
715C22×C3C2×2−1+411yescharacteristic
716C22×C3C2×2−1+411yescharacteristic
717C22×C3#58511yescharacteristic
718C22×C3#58511yescharacteristic
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726Dic3—22no—
727Dic3—22no—
728Dic3—42no—
729Dic3—42no—
730Dic3—42no—
731Dic3—41no—
732Dic3—41no—
733Dic3—42no—
734Dic3—42no—
735Dic3—42no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—82no—
751C23—82no—
752C23—82no—
753C23—82no—
754C23C2×#23712yes—
755C23#100712yes—
756C23#101012yes—
757C23C24×D311yescharacteristic
758Q8—82no—
759Q8—242no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
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—32no—
780C2×C4—32no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—62no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—124no—
812C2×C4—124no—
813C2×C4—242no—
814C2×C4—242no—
815C2×C4C2×#23712yes—
816C2×C4C2×#23712yes—
817C2×C3—24no—
818C2×C3—82no—
819C2×C3C2×#54111yescharacteristic
820C2×C3#350511yescharacteristic
821C2×C3#350611yescharacteristic
822C2×C3#353511yescharacteristic
823C2×C3#353611yescharacteristic
824C2×C3#356111yescharacteristic
825C2×C3#356411yescharacteristic
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—88no—
840C22#562514yes—
841C22C22×#23711yescharacteristic
842C22C2×#100711yescharacteristic
843C22C2×#101011yescharacteristic
844C22D3×H(5,𝔽2)11yescharacteristic
845C22D3×H(5,𝔽2)11yescharacteristic
846C22#596611yescharacteristic
847C22#596611yescharacteristic
848C4—22no—
849C4—22no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—62no—
856C4—62no—
857C4—122no—
858C4—122no—
859C4—122no—
860C4—122no—
861C4—121no—
862C4—122no—
863C4—121no—
864C4—122no—
865C3#3676011yescharacteristic, complemented, Sylow
866C2—24no—
867C2—82no—
868C2C2×#562511yescharacteristic
869C2#8629911yescharacteristic
870C2#8631811yescharacteristic
871C2#8639511yescharacteristic
872C2#8640811yescharacteristic
873C2#8657611yescharacteristic
874C2#8658011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2626C2
prime radicalC25×C3C23
hypercenter#2626D3
hypocenterC3#36760
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #82811C2semidirect
3. #82745C2semidirect
6. #78079C2semidirect
7. #78069C2semidirect
8. #77391C2semidirect
9. #77385C2semidirect
10. #77366C2semidirect
11. #77365C2semidirect
12. #76850C2semidirect
13. #76830C2semidirect
14. #74464C2semidirect
15. #74441C2semidirect
16. #73998C2semidirect
17. #73874C2semidirect
25. C2×#944C22semidirect
29. C2×#890C22semidirect
30. C2×#889C22semidirect
41. #5229C22semidirect
42. #5229C22semidirect
47. #4986C22semidirect
48. #4984C22semidirect
49. #4984C22semidirect
50. #4982C22semidirect
51. #4982C22semidirect
52. #4981C22semidirect
53. #4980C22semidirect
54. #4980C22semidirect
55. #4980C22semidirect
56. #4978C22semidirect
57. #4977C22semidirect
58. #4977C22semidirect
59. #4976C22semidirect
60. #4976C22semidirect
61. #4976C22semidirect
62. #4975C22semidirect
63. #4973C22semidirect
64. #4972C22semidirect
65. #4972C22semidirect
96. #4660C22semidirect
97. #4660C22semidirect
98. #4659C22semidirect
99. #4657C22semidirect
100. #4655C22semidirect
101. #4655C22semidirect
102. #4654C22semidirect
103. #4654C22semidirect
104. #4653C22semidirect
105. #4653C22semidirect
106. #4647C22semidirect
107. #4646C22semidirect
865. C3#36760semidirect

Maximal subgroups

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

subgroupindex
C3×#26262
#828112
#827452
#821172
C2×#49512
#780792
#780692
#773912
#773852
#773662
#773652
#768502
#768302
#744642
#744412
#739982
#738742
#738312
#738302
#367603