Finite Group Databasebeta

← #11069249

Subgroups — #11069249

Order 768.

3888 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5590C212yesmaximal, complemented
2C2×#5589C212yesmaximal, complemented
3C3×#2679C211yesmaximal, characteristic, complemented
4#82605C212yesmaximal, complemented
5#82596C212yesmaximal, complemented
6#82588C212yesmaximal, complemented
7#82582C212yesmaximal, complemented
8#77136C212yesmaximal, complemented
9#77123C212yesmaximal, complemented
10#77108C212yesmaximal, complemented
11#76906C212yesmaximal, complemented
12#76900C212yesmaximal, complemented
13#76898C212yesmaximal, complemented
14#76476C211yesmaximal, characteristic, complemented
15#76466C211yesmaximal, characteristic, complemented
16#76464C211yesmaximal, characteristic, complemented
17D3×#390C211yesmaximal, characteristic, complemented
18#76379C211yesmaximal, characteristic, complemented
19#76291C211yesmaximal, characteristic, complemented
20#39358—31nomaximal, Sylow
21C23×#67C2212yescomplemented
22C23×#67C2212yescomplemented
23C22×D3×D4C2211yescharacteristic
24C22×D3×D4C2212yescomplemented
25C2×C3×#120C2212yescomplemented
26C2×C3×#120C2212yescomplemented
27C2×C3×#120C2212yescomplemented
28C2×#953C2212yescomplemented
29C2×#940C2212yes—
30C2×#940C2211yescharacteristic, complemented
31C2×#939C2212yes—
32C2×#939C2212yescomplemented
33C2×#939C2212yescomplemented
34C2×#938C2211yescharacteristic
35C2×#938C2212yescomplemented
36C2×#938C2211yescharacteristic, complemented
37C2×#937C2212yescomplemented
38C2×#937C2212yescomplemented
39C2×#937C2212yescomplemented
40C2×#935C2212yescomplemented
41C2×D4×Dic3C2211yescharacteristic, complemented
42#5590—216no—
43#5589—216no—
44C2×#895C2211yescharacteristic, complemented
45C2×D3×C4⋊C4C2211yescharacteristic, complemented
46C2×#886C2212yescomplemented
47C2×#884C2212yescomplemented
48C2×#884C2212yescomplemented
49C2×#884C2212yescomplemented
50C2×#884C2212yescomplemented
51C2×#883C2212yescomplemented
52C2×#883C2212yescomplemented
53C2×#882C2212yescomplemented
54C2×#882C2212yescomplemented
55C2×#882C2212yescomplemented
56C2×#67⋊C4C2212yescomplemented
57C2×#67⋊C4C2212yescomplemented
58C2×D3×C22⋊C4C2212yescomplemented
59C2×D3×C22⋊C4C2212yescomplemented
60C2×C42×D3C2211yescharacteristic, complemented
61C3×#394C2212yescomplemented
62C3×#394C2212yescomplemented
63C3×#394C2212yescomplemented
64C3×#390C2211yescharacteristic, complemented
65C3×#390C2211yescharacteristic, complemented
66C3×#390C2211yescharacteristic, complemented
67#5247C2212yescomplemented
68#5223C2212yescomplemented
69#5223C2212yescomplemented
70#5223C2212yescomplemented
71#5223C2212yescomplemented
72#5221C2211yescharacteristic, complemented
73#5220C2212yescomplemented
74#4994C2212yescomplemented
75#4991C2212yescomplemented
76#4989C2212yescomplemented
77#4988C2211yescharacteristic, complemented
78#4987C2211yescharacteristic, complemented
79#4975C2211yescharacteristic, complemented
80Dic3×C4⋊C4C2211yescharacteristic, complemented
81#4961C2212yescomplemented
82#4961C2212yescomplemented
83#4961C2212yescomplemented
84#4961C2212yescomplemented
85#4961C2212yescomplemented
86#4960C2212yescomplemented
87#4960C2212yescomplemented
88#4959C2212yescomplemented
89#4957C2212yescomplemented
90#4957C2212yescomplemented
91#4957C2212yescomplemented
92#4957C2212yescomplemented
93#4957C2212yescomplemented
94#4956C2212yescomplemented
95#4956C2212yescomplemented
96#4955C2212yescomplemented
97#4952C2212yescomplemented
98#4950C2212yescomplemented
99#4948C2212yescomplemented
100#4945C2212yescomplemented
101#4942C2212yescomplemented
102Dic3×C22⋊C4C2212yescomplemented
103#4939C2211yescharacteristic, complemented
104#4939C2211yescharacteristic, complemented
105#4928C2211yescharacteristic, complemented
106#4675C2212yescomplemented
107#4665C2212yescomplemented
108#4665C2212yescomplemented
109#4647C2212yescomplemented
110C2×D42—32no—
111C2×#534—32no—
112#2856—31no—
113#2682—31no—
114#2682—31no—
115#2679—31no—
116#2679D311yescharacteristic, complemented
117#2678—32no—
118#2678—32no—
119#2617—32no—
120#2445—32no—
121#2433—32no—
122#2422—32no—
123#2416—32no—
124#2410—32no—
125#2410—32no—
126#2408—32no—
127C4×#121—31no—
128C2×#390—31no—
129C25×C3C2312yes—
130C24×D3C2312yes—
131C24×D3C2312yes—
132C22×C3×D4C2312yes—
133C22×C3×D4C2312yes—
134C22×C3×D4C2311yescharacteristic
135C22×C3×D4C2312yes—
136C22×C3×D4C2311yescharacteristic
137C22×C3×D4C2311yescharacteristic
138C22×#67—28no—
139C22×#67—28no—
140C22×#67—28no—
141C22×#67—44no—
142C22×#67—44no—
143C22×#67—44no—
144C22×#67C2312yes—
145C22×#67C2312yes—
146C22×#67C2312yes—
147C22×#67C2312yes—
148C22×#67C2312yes—
149C22×#67C2312yes—
150C22×#67C2312yes—
151C22×#67C2312yes—
152C22×#67C2312yes—
153C22×#67C2312yes—
154C22×#67C2312yes—
155C23×Dic3C2312yes—
156C23×Dic3C2312yes—
157C2×D3×D4—28no—
158C2×D3×D4—28no—
159C2×D3×D4—42no—
160C2×D3×D4—42no—
161C2×D3×D4—44no—
162C2×D3×D4D418yescomplemented
163C22×D12C2312yes—
164C22×D12C2312yes—
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×C4×D3C2312yes—
168C22×C4×D3C2311yescharacteristic
169C22×C4×D3C2311yescharacteristic
170C22×C4×D3C2312yes—
171C22×C4×D3C2311yescharacteristic
172C3×#120—28no—
173C3×#120—28no—
174C3×#120—44no—
175C2×C3×C4⋊C4C2311yescharacteristic
176C2×C3×C4⋊C4C2311yescharacteristic
177C2×C3×C4⋊C4C2311yescharacteristic
178C2×C3×C22⋊C4C2312yes—
179C2×C3×C22⋊C4C2312yes—
180C2×C3×C22⋊C4C2312yes—
181C2×C3×C22⋊C4C2312yes—
182C2×C3×C22⋊C4C2312yes—
183C2×C3×C22⋊C4C2312yes—
184C2×C3×C22⋊C4C2312yes—
185C2×C3×C22⋊C4C2312yes—
186C2×C3×C22⋊C4C2312yes—
187C2×C3×C42C2311yescharacteristic
188#953—28no—
189C2×#217C2312yes—
190C2×#217C2312yes—
191C2×#217C2312yes—
192C2×#217C2312yes—
193C2×#217C2312yes—
194C2×#217C2312yes—
195C2×#217C2312yes—
196C2×#217C2312yes—
197C2×#217C2312yes—
198#940—28no—
199#940—42no—
200#939—28no—
201#939—28no—
202#939—44no—
203#938—28no—
204#938—42no—
205#938D418yescomplemented
206#937—28no—
207#937—28no—
208#937—28no—
209#935—28no—
210D4×Dic3—42no—
211C2×(C2×D3)⋊C4C2312yes—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yes—
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×C4⋊Dic3C2312yes—
225C2×C4⋊Dic3C2311yescharacteristic
226C2×C4⋊Dic3C2311yescharacteristic
227C2×C4⋊Dic3C2311yescharacteristic
228C2×C4⋊Dic3C2311yescharacteristic
229C2×Dic3⋊C4C2312yes—
230C2×Dic3⋊C4C2312yes—
231C2×Dic3⋊C4C2312yes—
232C2×Dic3⋊C4C2312yes—
233C2×Dic3⋊C4C2312yes—
234C2×C4×Dic3C2312yes—
235C2×C4×Dic3C2311yescharacteristic
236C2×C4×Dic3C2311yescharacteristic
237C2×C4×Dic3C2311yescharacteristic
238#895—42no—
239D3×C4⋊C4—42no—
240#886—28no—
241#884—28no—
242#884—28no—
243#884—28no—
244#884—28no—
245#883—28no—
246#883—28no—
247#882—28no—
248#882—28no—
249#882—44no—
250#67⋊C4—28no—
251#67⋊C4—28no—
252D3×C22⋊C4—28no—
253D3×C22⋊C4—44no—
254C42×D3—42no—
255C3×#95C2312yes—
256C3⋊#95C2312yes—
257C3⋊#95C2312yes—
258C3⋊#95C2312yes—
259C3⋊#95C2312yes—
260C3⋊#95C2312yes—
261C3⋊#95C2312yes—
262C23×D4—31no—
263C23×D4—32no—
264C23×D4—32no—
265C23×D4—32no—
266D42—616no—
267#534—616no—
268C2×#127—32no—
269C2×#127—31no—
270C2×#123—32no—
271C2×#123—32no—
272C2×#123—32no—
273C2×#123—32no—
274C2×#121—31no—
275C2×#121—32no—
276C2×#121—32no—
277C2×#121—32no—
278C2×#121—31no—
279C2×#121—32no—
280C2×#121—31no—
281C2×#121—32no—
282C2×#121—32no—
283C2×#121—32no—
284C2×#121—32no—
285C2×#120—32no—
286C2×#120—32no—
287C2×#120—32no—
288C2×#120—32no—
289C2×#120—32no—
290C2×#120—32no—
291C2×#120—32no—
292C2×#120C2×D312yescomplemented
293C2×#120C2×D312yescomplemented
294C2×#120C2×D312yescomplemented
295C2×C4×D4—31no—
296C2×C4×D4—32no—
297C2×C4×D4—32no—
298C22×C4⋊C4—31no—
299C22×C22⋊C4—32no—
300C22×C22⋊C4—32no—
301C22×C42—31no—
302#397—32no—
303#397—32no—
304#396—32no—
305#396—32no—
306#394—32no—
307#394—32no—
308#394—32no—
309#394—32no—
310#394—32no—
311#394—32no—
312#394—32no—
313#394C2×D312yescomplemented
314#394C2×D312yescomplemented
315#394C2×D312yescomplemented
316#392—32no—
317#392—32no—
318#392—32no—
319#392—32no—
320#392—32no—
321#392—32no—
322#390—31no—
323#390—31no—
324#390—32no—
325#390—32no—
326#390—32no—
327#390—32no—
328#390—32no—
329#390—31no—
330#390—31no—
331#390C2×D311yescharacteristic, complemented
332#390C2×D311yescharacteristic, complemented
333#390C2×D311yescharacteristic, complemented
334#389—31no—
335#389—32no—
336#388—32no—
337#386—32no—
338#386—32no—
339#386—32no—
340#386—32no—
341#386—32no—
342#385—32no—
343#385—32no—
344#384—31no—
345#380—31no—
346#380—32no—
347#379—32no—
348#379—32no—
349C4×C4⋊C4—31no—
350C4×C22⋊C4—32no—
351C24×C3—24no—
352C24×C3—24no—
353C24×C3—42no—
354C24×C3—42no—
355C24×C3—42no—
356C24×C3—42no—
357C24×C3—42no—
358C24×C3C2412yes—
359C24×C3C2412yes—
360C24×C3C2412yes—
361C23×D3—24no—
362C23×D3—24no—
363C23×D3—24no—
364C23×D3—24no—
365C23×D3—42no—
366C23×D3—42no—
367C23×D3—42no—
368C23×D3—42no—
369C23×D3—42no—
370C23×D3—42no—
371C23×D3—42no—
372C23×D3—42no—
373C23×D3—42no—
374C23×D3C2×D418yes—
375C23×D3C2412yes—
376C23×D3C2412yes—
377C23×D3C2411yescharacteristic
378C2×C3×D4—24no—
379C2×C3×D4—24no—
380C2×C3×D4—24no—
381C2×C3×D4—24no—
382C2×C3×D4—22no—
383C2×C3×D4—41no—
384C2×C3×D4—41no—
385C2×C3×D4—41no—
386C2×C3×D4—42no—
387C2×C3×D4—41no—
388C2×C3×D4—41no—
389C2×C3×D4—42no—
390C2×C3×D4—41no—
391C2×C3×D4—42no—
392C2×C3×D4—42no—
393C2×C3×D4—42no—
394C2×C3×D4C2×D414yes—
395C2×C3×D4C2×D414yescomplemented
396C22×C3×C4C2412yes—
397C22×C3×C4C2412yes—
398C22×C3×C4C2412yes—
399C22×C3×C4C2411yescharacteristic
400C22×C3×C4C2411yescharacteristic
401C22×C3×C4C2411yescharacteristic
402C2×#67—24no—
403C2×#67—24no—
404C2×#67—24no—
405C2×#67—24no—
406C2×#67—24no—
407C2×#67—24no—
408C2×#67—24no—
409C2×#67—24no—
410C2×#67—24no—
411C2×#67—24no—
412C2×#67—24no—
413C2×#67—24no—
414C2×#67—24no—
415C2×#67—24no—
416C2×#67—24no—
417C2×#67—24no—
418C2×#67—24no—
419C2×#67—24no—
420C2×#67—24no—
421C2×#67—24no—
422C2×#67—42no—
423C2×#67—42no—
424C2×#67—42no—
425C2×#67—42no—
426C2×#67—42no—
427C2×#67—42no—
428C2×#67—42no—
429C2×#67—42no—
430C2×#67—42no—
431C2×#67—42no—
432C2×#67—42no—
433C2×#67—432no—
434C2×#67—432no—
435C2×#67C2×D418yes—
436C2×#67C2×D418yescomplemented
437C22×Dic3—24no—
438C22×Dic3—24no—
439C22×Dic3—24no—
440C22×Dic3—24no—
441C22×Dic3—24no—
442C22×Dic3—42no—
443C22×Dic3C2412yes—
444C22×Dic3C2411yescharacteristic
445C22×Dic3C2412yes—
446C22×Dic3C2412yes—
447C22×Dic3C2411yescharacteristic
448C22×Dic3C2412yes—
449C22×Dic3C2411yescharacteristic
450D3×D4—416no—
451D3×D4—432no—
452C2×D12—24no—
453C2×D12—24no—
454C2×D12—24no—
455C2×D12—24no—
456C2×D12—22no—
457C2×D12—41no—
458C2×D12—41no—
459C2×D12—42no—
460C2×D12—41no—
461C2×D12—41no—
462C2×D12—42no—
463C2×D12C2×D414yes—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—24no—
467C2×C4×D3—22no—
468C2×C4×D3—22no—
469C2×C4×D3—24no—
470C2×C4×D3—24no—
471C2×C4×D3—41no—
472C2×C4×D3—41no—
473C2×C4×D3—41no—
474C2×C4×D3—42no—
475C2×C4×D3—42no—
476C2×C4×D3—42no—
477C2×C4×D3C2×D414yes—
478C2×C4×D3C2×D414yescomplemented
479C3×C4⋊C4—41no—
480C3×C4⋊C4—41no—
481C3×C4⋊C4—41no—
482C3×C22⋊C4—24no—
483C3×C22⋊C4—24no—
484C3×C22⋊C4—24no—
485C3×C22⋊C4—24no—
486C3×C22⋊C4—24no—
487C3×C22⋊C4—24no—
488C3×C22⋊C4—24no—
489C3×C22⋊C4—24no—
490C3×C22⋊C4—42no—
491C3×C42—41no—
492#217—24no—
493#217—24no—
494#217—24no—
495#217—24no—
496#217—42no—
497#217—42no—
498#217—42no—
499#217—42no—
500#217C2×D418yescomplemented
501(C2×D3)⋊C4—24no—
502(C2×D3)⋊C4—24no—
503(C2×D3)⋊C4—24no—
504(C2×D3)⋊C4—24no—
505(C2×D3)⋊C4—24no—
506(C2×D3)⋊C4—24no—
507(C2×D3)⋊C4—24no—
508(C2×D3)⋊C4—24no—
509(C2×D3)⋊C4—24no—
510(C2×D3)⋊C4—42no—
511(C2×D3)⋊C4—42no—
512(C2×D3)⋊C4—42no—
513(C2×D3)⋊C4—42no—
514C4⋊Dic3—24no—
515C4⋊Dic3—41no—
516C4⋊Dic3—41no—
517C4⋊Dic3—41no—
518C4⋊Dic3C2×D414yescomplemented
519Dic3⋊C4—24no—
520Dic3⋊C4—24no—
521Dic3⋊C4—24no—
522Dic3⋊C4—24no—
523Dic3⋊C4—24no—
524C4×Dic3—24no—
525C4×Dic3—22no—
526C4×Dic3—22no—
527C4×Dic3—41no—
528C25—32no—
529C25—32no—
530C25C22×D312yes—
531C22×D4—32no—
532C22×D4—32no—
533C22×D4—38no—
534C22×D4—32no—
535C22×D4—32no—
536C22×D4—32no—
537C22×D4—32no—
538C22×D4—32no—
539C22×D4—32no—
540C22×D4—32no—
541C22×D4—32no—
542C22×D4—32no—
543C22×D4—31no—
544C22×D4—32no—
545C22×D4—32no—
546C22×D4—31no—
547C22×D4—68no—
548C22×D4—68no—
549C22×D4—68no—
550C22×D4—68no—
551C22×D4—68no—
552C22×D4—122no—
553C22×D4—122no—
554C22×D4—124no—
555C22×D4—124no—
556C22×D4—124no—
557C22×D4—124no—
558C22×D4C22×D312yes—
559C22×D4C22×D312yes—
560C22×D4C22×D312yes—
561C22×D4C22×D311yescharacteristic
562C22×D4C22×D311yescharacteristic
563C22×D4C22×D311yescharacteristic
564C23×C4—31no—
565C23×C4—31no—
566C23×C4—32no—
567C23×C4—32no—
568C23×C4—31no—
569C23×C4—32no—
570C23×C4—32no—
571#127—68no—
572#127—122no—
573#123—68no—
574#123—68no—
575#123—68no—
576#123—68no—
577#121—38no—
578#121—68no—
579#121—68no—
580#121—68no—
581#121—68no—
582#121—68no—
583#121—68no—
584#121—68no—
585#121—122no—
586#121—124no—
587#121—122no—
588#120—28no—
589#120—28no—
590#120—44no—
591#120—68no—
592#120—68no—
593#120—68no—
594#120—68no—
595#120—68no—
596#120—68no—
597#120—124no—
598C4×D4—68no—
599C4×D4—68no—
600C4×D4—122no—
601C2×C4⋊C4—31no—
602C2×C4⋊C4—32no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—32no—
605C2×C4⋊C4—32no—
606C2×C4⋊C4—32no—
607C2×C4⋊C4—32no—
608C2×C4⋊C4—31no—
609C2×C4⋊C4—31no—
610C2×C4⋊C4—31no—
611C2×C4⋊C4—122no—
612C2×C4⋊C4C22×D311yescharacteristic
613C2×C4⋊C4C22×D311yescharacteristic
614C2×C4⋊C4C22×D311yescharacteristic
615C2×C22⋊C4—32no—
616C2×C22⋊C4—32no—
617C2×C22⋊C4—32no—
618C2×C22⋊C4—32no—
619C2×C22⋊C4—32no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—32no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—32no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—68no—
638C2×C22⋊C4—124no—
639C2×C22⋊C4C22×D312yes—
640C2×C22⋊C4C22×D312yes—
641C2×C22⋊C4C22×D312yes—
642C2×C22⋊C4C22×D312yes—
643C2×C22⋊C4C22×D312yes—
644C2×C22⋊C4C22×D312yes—
645C2×C22⋊C4C22×D312yes—
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D312yes—
648C2×C42—32no—
649C2×C42—31no—
650C2×C42—31no—
651C2×C42—31no—
652C2×C42—122no—
653C2×C42C22×D311yescharacteristic
654#95—32no—
655#95—32no—
656#95—32no—
657#95—32no—
658#95—32no—
659#95—32no—
660#95C22×D312yes—
661C23×C3—22no—
662C23×C3—22no—
663C23×C3—22no—
664C23×C3—22no—
665C23×C3—22no—
666C23×C3—22no—
667C23×C3—22no—
668C23×C3—22no—
669C23×C3—22no—
670C23×C3—22no—
671C23×C3—22no—
672C23×C3—22no—
673C23×C3—22no—
674C23×C3—22no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—48no—
681C23×C3—48no—
682C23×C3—84no—
683C23×C3—84no—
684C23×C3—84no—
685C23×C3—84no—
686C23×C3—84no—
687C23×C3C22×D414yes—
688C23×C3C22×D414yes—
689C23×C3C2511yescharacteristic
690C22×D3—21no—
691C22×D3—21no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—216no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—48no—
709C22×D3—48no—
710C22×D3—48no—
711C22×D3—48no—
712C22×D3—84no—
713C22×D3—84no—
714C22×D3—84no—
715C22×D3—84no—
716C22×D3—84no—
717C22×D3—84no—
718C22×D3—84no—
719C22×D3—84no—
720C22×D3—84no—
721C22×D3C22×D414yes—
722C22×D3C22×D412yes—
723C22×D3C22×D412yes—
724C22×D3H(5,𝔽2)12yes—
725C3×D4—44no—
726C3×D4—44no—
727C3×D4—48no—
728C3×D4—82no—
729C3×D4—84no—
730C3×D4—84no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—22no—
740C2×C3×C4—22no—
741C2×C3×C4—22no—
742C2×C3×C4—22no—
743C2×C3×C4—22no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4C22×D412yes—
747C2×C3×C4C22×D412yes—
748C2×C3×C4H(5,𝔽2)12yes—
749#67—216no—
750#67—216no—
751#67—48no—
752#67—48no—
753#67—48no—
754#67—48no—
755#67—48no—
756#67—48no—
757#67—48no—
758#67—84no—
759#67—84no—
760C2×Dic3—22no—
761C2×Dic3—21no—
762C2×Dic3—22no—
763C2×Dic3—21no—
764C2×Dic3—22no—
765C2×Dic3—22no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—21no—
769C2×Dic3—22no—
770C2×Dic3—22no—
771C2×Dic3—22no—
772C2×Dic3—22no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3—48no—
777C2×Dic3—48no—
778C2×Dic3C22×D412yes—
779C2×Dic3C22×D414yes—
780C2×Dic3C22×D412yes—
781C2×Dic3H(5,𝔽2)12yes—
782C2×Dic3H(5,𝔽2)12yes—
783D12—44no—
784D12—48no—
785D12—82no—
786D12—84no—
787C4×D3—28no—
788C4×D3—44no—
789C4×D3—48no—
790C4×D3—44no—
791C4×D3—84no—
792C24—24no—
793C24—24no—
794C24—31no—
795C24—32no—
796C24—38no—
797C24—32no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—64no—
804C24—64no—
805C24—64no—
806C24—64no—
807C24—122no—
808C24—122no—
809C24—122no—
810C24—122no—
811C24—122no—
812C24—122no—
813C24—122no—
814C24—122no—
815C24—122no—
816C24C23×D312yes—
817C24C23×D312yes—
818C24C23×D312yes—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—22no—
824C2×D4—38no—
825C2×D4—38no—
826C2×D4—34no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—42no—
831C2×D4—41no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—41no—
835C2×D4—42no—
836C2×D4—41no—
837C2×D4—42no—
838C2×D4—64no—
839C2×D4—64no—
840C2×D4—64no—
841C2×D4—64no—
842C2×D4—64no—
843C2×D4—64no—
844C2×D4—64no—
845C2×D4—64no—
846C2×D4—64no—
847C2×D4—64no—
848C2×D4—64no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—64no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—64no—
857C2×D4—64no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—121no—
864C2×D4—121no—
865C2×D4—122no—
866C2×D4—121no—
867C2×D4—121no—
868C2×D4—122no—
869C2×D4—1216no—
870C2×D4—122no—
871C2×D4—122no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—1232no—
882C2×D4—1232no—
883C2×D4—1232no—
884C2×D4D3×D414yes—
885C2×D4D3×D414yescomplemented
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—32no—
889C22×C4—34no—
890C22×C4—34no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—32no—
894C22×C4—32no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—64no—
898C22×C4—64no—
899C22×C4—62no—
900C22×C4—64no—
901C22×C4—64no—
902C22×C4—64no—
903C22×C4—64no—
904C22×C4—64no—
905C22×C4—64no—
906C22×C4—62no—
907C22×C4—121no—
908C22×C4—121no—
909C22×C4—122no—
910C22×C4—121no—
911C22×C4—122no—
912C22×C4—122no—
913C22×C4—122no—
914C22×C4C23×D312yes—
915C22×C4C23×D312yes—
916C22×C4C23×D312yes—
917C22×C4C23×D311yescharacteristic
918C22×C4C23×D311yescharacteristic
919C22×C4C23×D311yescharacteristic
920C4⋊C4—34no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—64no—
925C4⋊C4—64no—
926C4⋊C4—64no—
927C4⋊C4—64no—
928C4⋊C4—64no—
929C4⋊C4—64no—
930C4⋊C4—121no—
931C4⋊C4—121no—
932C4⋊C4—121no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—38no—
942C22⋊C4—42no—
943C22⋊C4—64no—
944C22⋊C4—64no—
945C22⋊C4—64no—
946C22⋊C4—64no—
947C22⋊C4—64no—
948C22⋊C4—64no—
949C22⋊C4—64no—
950C22⋊C4—64no—
951C22⋊C4—64no—
952C22⋊C4—64no—
953C22⋊C4—64no—
954C22⋊C4—64no—
955C22⋊C4—64no—
956C22⋊C4—122no—
957C22⋊C4—122no—
958C22⋊C4—122no—
959C22⋊C4—122no—
960C22⋊C4—122no—
961C22⋊C4—122no—
962C22⋊C4—122no—
963C22⋊C4—122no—
964C42—41no—
965C42—62no—
966C42—62no—
967C42—64no—
968C42—121no—
969C22×C3—24no—
970C22×C3—24no—
971C22×C3—24no—
972C22×C3—24no—
973C22×C3—24no—
974C22×C3—24no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—42no—
978C22×C3—42no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—42no—
989C22×C3—42no—
990C22×C3—816no—
991C22×C3C23×D411yescharacteristic
992C22×C3C23×D411yescharacteristic
993C22×C3C2×H(5,𝔽2)11yescharacteristic
994C22×C3C2×H(5,𝔽2)11yescharacteristic
995C22×C3C2×H(5,𝔽2)11yescharacteristic
996C22×C3C2×H(5,𝔽2)11yescharacteristic
997C22×C3#58511yescharacteristic
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—22no—
1003C2×D3—22no—
1004C2×D3—24no—
1005C2×D3—24no—
1006C2×D3—24no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—42no—
1010C2×D3—42no—
1011C2×D3—42no—
1012C2×D3—42no—
1013C2×D3—42no—
1014C2×D3—42no—
1015C2×D3—42no—
1016C2×D3—42no—
1017C2×D3—42no—
1018C2×D3—816no—
1019C2×D3—816no—
1020C2×D3D4214yes—
1021C3×C4—22no—
1022C3×C4—22no—
1023C3×C4—22no—
1024C3×C4—42no—
1025C3×C4—42no—
1026C3×C4—42no—
1027Dic3—24no—
1028Dic3—22no—
1029Dic3—42no—
1030Dic3—42no—
1031Dic3—42no—
1032Dic3—41no—
1033Dic3#53414yescomplemented
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—32no—
1054C23—32no—
1055C23—32no—
1056C23—34no—
1057C23—48no—
1058C23—48no—
1059C23—616no—
1060C23—61no—
1061C23—61no—
1062C23—61no—
1063C23—61no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—84no—
1078C23—84no—
1079C23—84no—
1080C23—84no—
1081C23—84no—
1082C23—128no—
1083C23—128no—
1084C23—128no—
1085C23—128no—
1086C23—244no—
1087C23—244no—
1088C23—244no—
1089C23—244no—
1090C23—244no—
1091C23—244no—
1092C23—244no—
1093C23—244no—
1094C23—244no—
1095C23C2×D3×D414yes—
1096C23C2×D3×D414yes—
1097C23C24×D311yescharacteristic
1098D4—44no—
1099D4—44no—
1100D4—48no—
1101D4—616no—
1102D4—616no—
1103D4—82no—
1104D4—84no—
1105D4—84no—
1106D4—124no—
1107D4—128no—
1108D4—128no—
1109D4—128no—
1110D4—128no—
1111D4—128no—
1112D4—128no—
1113D4—128no—
1114D4—128no—
1115D4—242no—
1116D4—244no—
1117D4—244no—
1118D4—244no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—32no—
1135C2×C4—32no—
1136C2×C4—32no—
1137C2×C4—32no—
1138C2×C4—34no—
1139C2×C4—68no—
1140C2×C4—62no—
1141C2×C4—61no—
1142C2×C4—62no—
1143C2×C4—61no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—124no—
1157C2×C4—124no—
1158C2×C4—128no—
1159C2×C4—128no—
1160C2×C4—128no—
1161C2×C4—244no—
1162C2×C4C2×D3×D412yes—
1163C2×C4C2×D3×D412yes—
1164C2×C4#100412yes—
1165C2×C3—44no—
1166C2×C3—44no—
1167C2×C3—82no—
1168C2×C3C2×#53411yescharacteristic
1169C2×C3C2×D4211yescharacteristic
1170C2×C3#349611yescharacteristic
1171C2×C3#349611yescharacteristic
1172C2×C3#349811yescharacteristic
1173C2×C3#353711yescharacteristic
1174C2×C3#355811yescharacteristic
1175D3—24no—
1176D3—44no—
1177D3—82no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—24no—
1184C22—34no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—62no—
1201C22—62no—
1202C22—62no—
1203C22—62no—
1204C22—62no—
1205C22—62no—
1206C22—64no—
1207C22—64no—
1208C22—64no—
1209C22—816no—
1210C22—122no—
1211C22—122no—
1212C22—122no—
1213C22—122no—
1214C22—122no—
1215C22—122no—
1216C22—122no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—122no—
1221C22—2416no—
1222C22—2416no—
1223C22C22×D3×D411yescharacteristic
1224C22C22×D3×D411yescharacteristic
1225C22C2×#100411yescharacteristic
1226C22D3×H(5,𝔽2)11yescharacteristic
1227C22D3×H(5,𝔽2)11yescharacteristic
1228C22D3×H(5,𝔽2)11yescharacteristic
1229C22#596611yescharacteristic
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—34no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—62no—
1238C4—64no—
1239C4—121no—
1240C4—122no—
1241C4—122no—
1242C4—122no—
1243C3#3935811yescharacteristic, complemented, Sylow
1244C2—44no—
1245C2—44no—
1246C2—64no—
1247C2—82no—
1248C2—124no—
1249C2—242no—
1250C2#8629811yescharacteristic
1251C2#8630111yescharacteristic
1252C2D3×#53411yescharacteristic
1253C2#8660811yescharacteristic
1254C2D3×D4211yescharacteristic
1255C2#8662111yescharacteristic
1256C2#8709211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2679C2
hypercenter#2679D3
hypocenterC3#39358
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. C2×#5590C2semidirect
2. C2×#5589C2semidirect
3. C3×#2679C2semidirect
4. #82605C2semidirect
5. #82596C2semidirect
6. #82588C2semidirect
7. #82582C2semidirect
8. #77136C2semidirect
9. #77123C2semidirect
10. #77108C2semidirect
11. #76906C2semidirect
12. #76900C2semidirect
13. #76898C2semidirect
14. #76476C2semidirect
15. #76466C2semidirect
16. #76464C2semidirect
17. D3×#390C2semidirect
18. #76379C2semidirect
19. #76291C2semidirect
21. C23×#67C22semidirect
22. C23×#67C22semidirect
24. C22×D3×D4C22semidirect
25. C2×C3×#120C22semidirect
26. C2×C3×#120C22semidirect
27. C2×C3×#120C22semidirect
28. C2×#953C22semidirect
30. C2×#940C22semidirect
32. C2×#939C22semidirect
33. C2×#939C22semidirect
35. C2×#938C22semidirect
36. C2×#938C22semidirect
37. C2×#937C22semidirect
38. C2×#937C22semidirect
39. C2×#937C22semidirect
40. C2×#935C22semidirect
41. C2×D4×Dic3C22semidirect
44. C2×#895C22semidirect
45. C2×D3×C4⋊C4C22semidirect
46. C2×#886C22semidirect
47. C2×#884C22semidirect
48. C2×#884C22semidirect
49. C2×#884C22semidirect
50. C2×#884C22semidirect
51. C2×#883C22semidirect
52. C2×#883C22semidirect
53. C2×#882C22semidirect
54. C2×#882C22semidirect
55. C2×#882C22semidirect
56. C2×#67⋊C4C22semidirect
57. C2×#67⋊C4C22semidirect
58. C2×D3×C22⋊C4C22semidirect
59. C2×D3×C22⋊C4C22semidirect
60. C2×C42×D3C22semidirect
61. C3×#394C22semidirect
62. C3×#394C22semidirect
63. C3×#394C22semidirect
64. C3×#390C22semidirect
65. C3×#390C22semidirect
66. C3×#390C22semidirect
67. #5247C22semidirect
68. #5223C22semidirect
69. #5223C22semidirect
70. #5223C22semidirect
71. #5223C22semidirect
72. #5221C22semidirect
73. #5220C22semidirect
74. #4994C22semidirect
75. #4991C22semidirect
76. #4989C22semidirect
77. #4988C22semidirect
78. #4987C22semidirect
79. #4975C22semidirect
80. Dic3×C4⋊C4C22semidirect
81. #4961C22semidirect
82. #4961C22semidirect
83. #4961C22semidirect
84. #4961C22semidirect
85. #4961C22semidirect
86. #4960C22semidirect
87. #4960C22semidirect
88. #4959C22semidirect
89. #4957C22semidirect
90. #4957C22semidirect
91. #4957C22semidirect
92. #4957C22semidirect
93. #4957C22semidirect
94. #4956C22semidirect
95. #4956C22semidirect
96. #4955C22semidirect
97. #4952C22semidirect
98. #4950C22semidirect
99. #4948C22semidirect
100. #4945C22semidirect
101. #4942C22semidirect
102. Dic3×C22⋊C4C22semidirect
103. #4939C22semidirect
104. #4939C22semidirect
105. #4928C22semidirect
106. #4675C22semidirect
107. #4665C22semidirect
108. #4665C22semidirect
109. #4647C22semidirect
116. #2679D3semidirect
162. C2×D3×D4D4semidirect
205. #938D4semidirect
292. C2×#120C2×D3semidirect
293. C2×#120C2×D3semidirect
294. C2×#120C2×D3semidirect
313. #394C2×D3semidirect
314. #394C2×D3semidirect
315. #394C2×D3semidirect
331. #390C2×D3semidirect
332. #390C2×D3semidirect
333. #390C2×D3semidirect
395. C2×C3×D4C2×D4semidirect
436. C2×#67C2×D4semidirect
478. C2×C4×D3C2×D4semidirect
500. #217C2×D4semidirect
518. C4⋊Dic3C2×D4semidirect
885. C2×D4D3×D4semidirect
1033. Dic3#534semidirect
1243. C3#39358semidirect

Maximal subgroups

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

subgroupindex
C2×#55902
C2×#55892
C3×#26792
#826052
#825962
#825882
#825822
#771362
#771232
#771082
#769062
#769002
#768982
#764762
#764662
#764642
D3×#3902
#763792
#762912
#393583