Finite Group Databasebeta

← #11233668

Subgroups — #11233668

Order 768.

4410 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5609C212yesmaximal, complemented
2C2×#5590C212yesmaximal, complemented
3C3×#2668C211yesmaximal, characteristic, complemented
4#82713C212yesmaximal, complemented
5#82604C212yesmaximal, complemented
6#78112C211yesmaximal, characteristic, complemented
7#78019C211yesmaximal, characteristic, complemented
8#77689C212yesmaximal, complemented
9#77513C212yesmaximal, complemented
10#77127C212yesmaximal, complemented
11#76895C212yesmaximal, complemented
12#76753C211yesmaximal, characteristic, complemented
13#76669C211yesmaximal, characteristic, complemented
14#74884C212yesmaximal, complemented
15#74884C212yesmaximal, complemented
16#74751C212yesmaximal, complemented
17#74667C212yesmaximal, complemented
18#73852C211yesmaximal, characteristic, complemented
19#73824C211yesmaximal, characteristic, complemented
20#45355—31nomaximal, Sylow
21C23×#67C2211yescharacteristic, complemented
22C23×#67C2212yescomplemented
23C22×D3×D4C2212yescomplemented
24C22×D3×D4C2211yescharacteristic, complemented
25C22×D3×D4C2212yescomplemented
26C22×D3×D4C2212yescomplemented
27C23×D12C2212yescomplemented
28C2×C3×#121C2212yescomplemented
29C2×C3×#120C2212yescomplemented
30C2×#953C2211yescharacteristic, complemented
31C2×#940C2212yes—
32C2×#939C2212yescomplemented
33C2×#939C2212yescomplemented
34C2×#937C2212yescomplemented
35C2×#937C2212yescomplemented
36C2×#937C2212yescomplemented
37C2×#937C2212yescomplemented
38C2×C4×#67C2212yescomplemented
39#5609—216no—
40#5590—216no—
41C2×#895C2212yescomplemented
42C2×#893C2212yescomplemented
43C2×#893C2211yescharacteristic, complemented
44C2×#884C2212yescomplemented
45C2×#884C2212yescomplemented
46C2×#884C2212yescomplemented
47C2×#884C2212yescomplemented
48C2×#882C2212yescomplemented
49C2×#882C2212yescomplemented
50C2×#882C2212yescomplemented
51C2×#882C2212yescomplemented
52C2×#882C2212yescomplemented
53C2×#882C2212yescomplemented
54C2×#882C2211yescharacteristic, complemented
55C2×#67⋊C4C2212yescomplemented
56C2×#67⋊C4C2212yescomplemented
57C2×#67⋊C4C2211yescharacteristic, complemented
58C3×#399C2211yescharacteristic, complemented
59C3×#397C2212yescomplemented
60C3×#394C2212yescomplemented
61C3×#392C2211yescharacteristic, complemented
62C3×#386C2212yescomplemented
63C3×#386C2212yescomplemented
64C3×#379C2211yescharacteristic, complemented
65#5223C2212yescomplemented
66#5223C2212yescomplemented
67#5222C2211yescharacteristic, complemented
68#5220C2212yescomplemented
69#5213C2212yescomplemented
70#5213C2212yescomplemented
71#4993C2212yescomplemented
72#4993C2211yescharacteristic, complemented
73#4992C2212yescomplemented
74#4991C2212yescomplemented
75#4960C2211yescharacteristic, complemented
76#4960C2212yescomplemented
77#4960C2212yescomplemented
78#4960C2211yescharacteristic, complemented
79#4960C2212yescomplemented
80#4960C2212yescomplemented
81#4959C2212yescomplemented
82#4958C2212yescomplemented
83#4958C2212yescomplemented
84#4958C2212yescomplemented
85#4957C2212yescomplemented
86#4957C2212yescomplemented
87#4956C2212yescomplemented
88#4956C2212yescomplemented
89#4956C2212yescomplemented
90#4955C2212yescomplemented
91#4955C2211yescharacteristic, complemented
92#4955C2212yescomplemented
93#4955C2212yescomplemented
94#4952C2212yescomplemented
95#4942C2211yescharacteristic, complemented
96#4675C2212yescomplemented
97#4672C2211yescharacteristic, complemented
98#4671C2212yescomplemented
99#4671C2211yescharacteristic, complemented
100#4671C2212yescomplemented
101#4667C2212yescomplemented
102#4667C2211yescharacteristic, complemented
103#4665C2212yescomplemented
104#4665C2212yescomplemented
105#4665C2212yescomplemented
106#4665C2212yescomplemented
107#4665C2212yescomplemented
108#4650C2212yescomplemented
109#4648C2211yescharacteristic, complemented
110C2×D42—32no—
111C2×D42—32no—
112#2668—31no—
113#2668—32no—
114#2668—32no—
115#2668—32no—
116#2668D311yescharacteristic, complemented
117#2535—32no—
118#2535—32no—
119#2408—32no—
120#2408—31no—
121#2408—31no—
122#2403—31no—
123#2403—32no—
124#2403—32no—
125#2403—31no—
126#2403—32no—
127#2397—31no—
128#2328—32no—
129C25×C3C2311yescharacteristic
130C24×D3C2312yes—
131C24×D3C2312yes—
132C24×D3C2312yes—
133C24×D3C2311yescharacteristic
134C22×C3×D4C2311yescharacteristic
135C22×C3×D4C2312yes—
136C22×C3×D4C2312yes—
137C22×C3×D4C2312yes—
138C23×C3×C4C2312yes—
139C22×#67—28no—
140C22×#67—28no—
141C22×#67—42no—
142C22×#67—44no—
143C22×#67—44no—
144C22×#67C2312yes—
145C22×#67C2312yes—
146C22×#67C2312yes—
147C22×#67C2312yes—
148C22×#67C2312yes—
149C22×#67C2312yes—
150C22×#67C2311yescharacteristic
151C22×#67C2312yes—
152C22×#67C2312yes—
153C22×#67C2312yes—
154C22×#67C2312yes—
155C23×Dic3C2311yescharacteristic
156C23×Dic3C2312yes—
157C2×D3×D4—28no—
158C2×D3×D4—28no—
159C2×D3×D4—28no—
160C2×D3×D4—28no—
161C2×D3×D4—28no—
162C2×D3×D4—42no—
163C2×D3×D4—44no—
164C2×D3×D4—44no—
165C2×D3×D4—44no—
166C2×D3×D4—44no—
167C2×D3×D4—44no—
168C22×D12—28no—
169C22×D12—44no—
170C22×D12—44no—
171C22×D12C2312yes—
172C22×D12C2312yes—
173C22×D12C2312yes—
174C22×D12C2312yes—
175C22×D12C2312yes—
176C22×D12C2311yescharacteristic
177C22×D12C2311yescharacteristic
178C22×D12C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2312yes—
182C22×C4×D3C2312yes—
183C3×#121—28no—
184C3×#120—28no—
185C2×C3×C4⋊C4C2312yes—
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C22⋊C4C2312yes—
188C2×C3×C22⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2311yescharacteristic
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2312yes—
196#953—42no—
197C2×#217C2312yes—
198C2×#217C2312yes—
199C2×#217C2311yescharacteristic
200C2×#217C2312yes—
201C2×#217C2312yes—
202#940D4116yescomplemented
203#939—28no—
204#939—28no—
205#937—28no—
206#937—28no—
207#937—28no—
208#937—44no—
209C4×#67—28no—
210C2×(C2×D3)⋊C4C2312yes—
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×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2312yes—
228C2×Dic3⋊C4C2312yes—
229C2×Dic3⋊C4C2312yes—
230C2×Dic3⋊C4C2312yes—
231C2×Dic3⋊C4C2311yescharacteristic
232C2×C4×Dic3C2311yescharacteristic
233C2×C4×Dic3C2312yes—
234#895—28no—
235#893—28no—
236#893—42no—
237#884—28no—
238#884—28no—
239#884—28no—
240#884—28no—
241#882—28no—
242#882—28no—
243#882—28no—
244#882—28no—
245#882—44no—
246#882—44no—
247#882—42no—
248#67⋊C4—28no—
249#67⋊C4—28no—
250#67⋊C4—42no—
251C3×#95C2311yescharacteristic
252C3×#95C2312yes—
253C3×#95C2311yescharacteristic
254C3×#95C2312yes—
255C3⋊#95C2312yes—
256C3⋊#95C2311yescharacteristic
257C3⋊#95C2312yes—
258C3⋊#95C2312yes—
259C3⋊#95C2312yes—
260C3⋊#95C2312yes—
261C3⋊#95C2312yes—
262C3⋊#95C2311yescharacteristic
263C23×D4—31no—
264C23×D4—32no—
265C23×D4—31no—
266C23×D4—32no—
267C23×D4—32no—
268C23×D4—32no—
269C23×D4—32no—
270D42—616no—
271D42—616no—
272C2×#127—32no—
273C2×#121—32no—
274C2×#121—32no—
275C2×#121—32no—
276C2×#121—32no—
277C2×#121—32no—
278C2×#121—32no—
279C2×#121—32no—
280C2×#121C2×D312yescomplemented
281C2×#120—32no—
282C2×#120—32no—
283C2×#120—32no—
284C2×#120—31no—
285C2×#120—32no—
286C2×#120—32no—
287C2×#120—32no—
288C2×#120—32no—
289C2×#120—32no—
290C2×#120—32no—
291C2×#120—32no—
292C2×#120—31no—
293C2×#120C2×D312yescomplemented
294C2×C4×D4—32no—
295C2×C4×D4—32no—
296C2×C4×D4—31no—
297C2×C4×D4—32no—
298C2×C4×D4—32no—
299C2×C4×D4—31no—
300#399—31no—
301#399—32no—
302#399C2×D311yescharacteristic, complemented
303#397—32no—
304#397—32no—
305#397—32no—
306#397C2×D312yescomplemented
307#394—31no—
308#394—32no—
309#394—32no—
310#394—31no—
311#394C2×D312yescomplemented
312#392—32no—
313#392—32no—
314#392—31no—
315#392—32no—
316#392—32no—
317#392—32no—
318#392—32no—
319#392—31no—
320#392—31no—
321#392—32no—
322#392—32no—
323#392C2×D311yescharacteristic, complemented
324#390—32no—
325#390—32no—
326#386—32no—
327#386—32no—
328#386—32no—
329#386—32no—
330#386—32no—
331#386—32no—
332#386—32no—
333#386—32no—
334#386—32no—
335#386—32no—
336#386—32no—
337#386—32no—
338#386—32no—
339#386—32no—
340#386C2×D312yescomplemented
341#386C2×D312yescomplemented
342#382—32no—
343#380—31no—
344#380—31no—
345#380—32no—
346#379—32no—
347#379—31no—
348#379—32no—
349#379—32no—
350#379C2×D311yescharacteristic, complemented
351#376—31no—
352C24×C3—24no—
353C24×C3—22no—
354C24×C3—41no—
355C24×C3—42no—
356C24×C3—41no—
357C24×C3C2412yes—
358C24×C3C2412yes—
359C24×C3C2411yescharacteristic
360C23×D3—24no—
361C23×D3—24no—
362C23×D3—24no—
363C23×D3—22no—
364C23×D3—24no—
365C23×D3—24no—
366C23×D3—24no—
367C23×D3—24no—
368C23×D3—24no—
369C23×D3—24no—
370C23×D3—24no—
371C23×D3—42no—
372C23×D3—42no—
373C23×D3—42no—
374C23×D3—42no—
375C23×D3—42no—
376C23×D3—42no—
377C23×D3—42no—
378C23×D3—42no—
379C23×D3—42no—
380C23×D3—42no—
381C23×D3—41no—
382C23×D3—42no—
383C23×D3—42no—
384C23×D3—41no—
385C23×D3—42no—
386C23×D3C2412yes—
387C23×D3C2412yes—
388C23×D3C2411yescharacteristic
389C23×D3C2412yes—
390C2×C3×D4—24no—
391C2×C3×D4—24no—
392C2×C3×D4—24no—
393C2×C3×D4—24no—
394C2×C3×D4—24no—
395C2×C3×D4—42no—
396C2×C3×D4—42no—
397C2×C3×D4—41no—
398C2×C3×D4—42no—
399C2×C3×D4—42no—
400C2×C3×D4C2×D418yescomplemented
401C22×C3×C4—24no—
402C22×C3×C4—42no—
403C22×C3×C4—42no—
404C22×C3×C4C2412yes—
405C22×C3×C4C2412yes—
406C22×C3×C4C2411yescharacteristic
407C22×C3×C4C2412yes—
408C22×C3×C4C2411yescharacteristic
409C22×C3×C4C2412yes—
410C2×#67—24no—
411C2×#67—24no—
412C2×#67—24no—
413C2×#67—24no—
414C2×#67—24no—
415C2×#67—24no—
416C2×#67—22no—
417C2×#67—24no—
418C2×#67—24no—
419C2×#67—24no—
420C2×#67—22no—
421C2×#67—24no—
422C2×#67—24no—
423C2×#67—24no—
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—41no—
430C2×#67—42no—
431C2×#67—42no—
432C2×#67—42no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C2×#67—42no—
439C2×#67—416no—
440C2×#67—432no—
441C2×#67C2×D418yescomplemented
442C2×#67C2×D418yescomplemented
443C2×#67C2×D418yescomplemented
444C2×#67C2×D418yescomplemented
445C22×Dic3—24no—
446C22×Dic3—24no—
447C22×Dic3—22no—
448C22×Dic3—42no—
449C22×Dic3—42no—
450C22×Dic3C2412yes—
451C22×Dic3C2412yes—
452C22×Dic3C2411yescharacteristic
453C22×Dic3C2411yescharacteristic
454C22×Dic3C2412yes—
455C22×Dic3C2411yescharacteristic
456D3×D4—432no—
457D3×D4—416no—
458D3×D4—432no—
459D3×D4—432no—
460C2×D12—24no—
461C2×D12—24no—
462C2×D12—24no—
463C2×D12—24no—
464C2×D12—24no—
465C2×D12—24no—
466C2×D12—24no—
467C2×D12—24no—
468C2×D12—24no—
469C2×D12—24no—
470C2×D12—24no—
471C2×D12—24no—
472C2×D12—24no—
473C2×D12—432no—
474C2×D12—41no—
475C2×D12—42no—
476C2×D12—42no—
477C2×D12—42no—
478C2×D12—42no—
479C2×D12—41no—
480C2×D12—42no—
481C2×D12—42no—
482C2×D12C2×D418yescomplemented
483C2×C4×D3—24no—
484C2×C4×D3—24no—
485C2×C4×D3—24no—
486C2×C4×D3—24no—
487C2×C4×D3—24no—
488C2×C4×D3—22no—
489C2×C4×D3—24no—
490C2×C4×D3—42no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C3×C4⋊C4—24no—
495C3×C4⋊C4—41no—
496C3×C22⋊C4—24no—
497C3×C22⋊C4—24no—
498C3×C22⋊C4—24no—
499C3×C22⋊C4—24no—
500C3×C22⋊C4—24no—
501C3×C22⋊C4—41no—
502C3×C22⋊C4—42no—
503C3×C22⋊C4—42no—
504C3×C22⋊C4—41no—
505#217—24no—
506#217—24no—
507#217—42no—
508#217—42no—
509#217—41no—
510(C2×D3)⋊C4—24no—
511(C2×D3)⋊C4—24no—
512(C2×D3)⋊C4—24no—
513(C2×D3)⋊C4—24no—
514(C2×D3)⋊C4—24no—
515(C2×D3)⋊C4—24no—
516(C2×D3)⋊C4—24no—
517(C2×D3)⋊C4—24no—
518(C2×D3)⋊C4—24no—
519(C2×D3)⋊C4—41no—
520(C2×D3)⋊C4—42no—
521(C2×D3)⋊C4—42no—
522(C2×D3)⋊C4—42no—
523(C2×D3)⋊C4—42no—
524(C2×D3)⋊C4—42no—
525(C2×D3)⋊C4—42no—
526(C2×D3)⋊C4—42no—
527(C2×D3)⋊C4—42no—
528Dic3⋊C4—24no—
529Dic3⋊C4—24no—
530Dic3⋊C4—24no—
531Dic3⋊C4—41no—
532C4×Dic3—22no—
533C4×Dic3C2×D418yescomplemented
534C25—31no—
535C25—32no—
536C25—32no—
537C25—32no—
538C25C22×D311yescharacteristic
539C22×D4—32no—
540C22×D4—32no—
541C22×D4—32no—
542C22×D4—32no—
543C22×D4—32no—
544C22×D4—31no—
545C22×D4—32no—
546C22×D4—32no—
547C22×D4—32no—
548C22×D4—32no—
549C22×D4—32no—
550C22×D4—32no—
551C22×D4—32no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—32no—
555C22×D4—32no—
556C22×D4—32no—
557C22×D4—32no—
558C22×D4—68no—
559C22×D4—68no—
560C22×D4—68no—
561C22×D4—68no—
562C22×D4—68no—
563C22×D4—68no—
564C22×D4—68no—
565C22×D4—68no—
566C22×D4—124no—
567C22×D4—124no—
568C22×D4—122no—
569C22×D4—124no—
570C22×D4—122no—
571C22×D4—124no—
572C22×D4—124no—
573C22×D4—124no—
574C22×D4—124no—
575C22×D4—124no—
576C22×D4—124no—
577C22×D4C22×D311yescharacteristic
578C22×D4C22×D312yes—
579C22×D4C22×D312yes—
580C22×D4C22×D312yes—
581C23×C4—31no—
582C23×C4—32no—
583C23×C4—31no—
584C23×C4—32no—
585C23×C4—32no—
586C23×C4—32no—
587C23×C4C22×D312yes—
588#127—316no—
589#121—28no—
590#121—68no—
591#121—68no—
592#121—68no—
593#121—68no—
594#121—68no—
595#121—68no—
596#121—68no—
597#120—28no—
598#120—68no—
599#120—68no—
600#120—68no—
601#120—68no—
602#120—68no—
603#120—68no—
604#120—68no—
605#120—124no—
606#120—124no—
607#120—122no—
608#120—124no—
609#120—122no—
610C4×D4—68no—
611C4×D4—68no—
612C4×D4—68no—
613C4×D4—68no—
614C4×D4—122no—
615C4×D4—122no—
616C2×C4⋊C4—32no—
617C2×C4⋊C4—32no—
618C2×C4⋊C4—32no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4C22×D312yes—
621C2×C4⋊C4C22×D311yescharacteristic
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—31no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—32no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—32no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4C22×D312yes—
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D312yes—
648C2×C22⋊C4C22×D312yes—
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D311yescharacteristic
651C2×C22⋊C4C22×D312yes—
652C2×C22⋊C4C22×D311yescharacteristic
653C2×C22⋊C4C22×D312yes—
654C2×C42—32no—
655C2×C42—31no—
656#95—31no—
657#95—32no—
658#95—32no—
659#95—31no—
660#95—32no—
661#95—32no—
662#95—32no—
663#95—32no—
664#95C22×D311yescharacteristic
665#95C22×D311yescharacteristic
666#95C22×D312yes—
667#95C22×D312yes—
668C23×C3—22no—
669C23×C3—22no—
670C23×C3—22no—
671C23×C3—21no—
672C23×C3—22no—
673C23×C3—22no—
674C23×C3—21no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—44no—
685C23×C3—48no—
686C23×C3—84no—
687C23×C3—82no—
688C23×C3—82no—
689C23×C3C22×D414yes—
690C23×C3C22×D414yes—
691C23×C3H(5,𝔽2)12yes—
692C23×C3C2511yescharacteristic
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—21no—
700C22×D3—22no—
701C22×D3—21no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—22no—
710C22×D3—22no—
711C22×D3—22no—
712C22×D3—22no—
713C22×D3—22no—
714C22×D3—22no—
715C22×D3—48no—
716C22×D3—48no—
717C22×D3—44no—
718C22×D3—48no—
719C22×D3—48no—
720C22×D3—48no—
721C22×D3—48no—
722C22×D3—48no—
723C22×D3—48no—
724C22×D3—48no—
725C22×D3—48no—
726C22×D3—84no—
727C22×D3—84no—
728C22×D3—84no—
729C22×D3—84no—
730C22×D3—84no—
731C22×D3—84no—
732C22×D3—84no—
733C22×D3—84no—
734C22×D3—84no—
735C22×D3—84no—
736C22×D3—82no—
737C22×D3—84no—
738C22×D3—84no—
739C22×D3—82no—
740C22×D3—84no—
741C22×D3C22×D414yes—
742C22×D3C22×D414yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D3H(5,𝔽2)14yes—
745C3×D4—48no—
746C3×D4—48no—
747C3×D4—44no—
748C3×D4—48no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—22no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—48no—
765C2×C3×C4C22×D414yes—
766#67—216no—
767#67—216no—
768#67—216no—
769#67—48no—
770#67—48no—
771#67—48no—
772#67—48no—
773#67—44no—
774#67—48no—
775#67—48no—
776#67—48no—
777C2×Dic3—22no—
778C2×Dic3—22no—
779C2×Dic3—22no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—48no—
791C2×Dic3—44no—
792C2×Dic3C22×D414yes—
793C2×Dic3C22×D414yes—
794C2×Dic3H(5,𝔽2)12yes—
795D12—216no—
796D12—48no—
797D12—44no—
798D12—48no—
799D12—48no—
800D12—44no—
801D12—48no—
802D12—48no—
803C4×D3—48no—
804C4×D3—48no—
805C4×D3—48no—
806C4×D3—44no—
807C24—24no—
808C24—22no—
809C24—32no—
810C24—32no—
811C24—31no—
812C24—32no—
813C24—41no—
814C24—42no—
815C24—41no—
816C24—64no—
817C24—64no—
818C24—64no—
819C24—64no—
820C24—64no—
821C24—64no—
822C24—64no—
823C24—64no—
824C24—64no—
825C24—64no—
826C24—62no—
827C24—122no—
828C24—122no—
829C24—121no—
830C24—122no—
831C24—122no—
832C24—122no—
833C24—122no—
834C24—122no—
835C24—122no—
836C24—122no—
837C24—122no—
838C24—122no—
839C24—121no—
840C24—122no—
841C24—122no—
842C24C23×D312yes—
843C24C23×D312yes—
844C24C23×D311yescharacteristic
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—38no—
851C2×D4—38no—
852C2×D4—38no—
853C2×D4—38no—
854C2×D4—38no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—41no—
859C2×D4—42no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—64no—
863C2×D4—64no—
864C2×D4—64no—
865C2×D4—64no—
866C2×D4—64no—
867C2×D4—64no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—64no—
871C2×D4—64no—
872C2×D4—64no—
873C2×D4—64no—
874C2×D4—64no—
875C2×D4—64no—
876C2×D4—64no—
877C2×D4—64no—
878C2×D4—64no—
879C2×D4—64no—
880C2×D4—64no—
881C2×D4—62no—
882C2×D4—64no—
883C2×D4—64no—
884C2×D4—64no—
885C2×D4—64no—
886C2×D4—64no—
887C2×D4—64no—
888C2×D4—64no—
889C2×D4—62no—
890C2×D4—64no—
891C2×D4—64no—
892C2×D4—121no—
893C2×D4—122no—
894C2×D4—122no—
895C2×D4—122no—
896C2×D4—122no—
897C2×D4—122no—
898C2×D4—121no—
899C2×D4—122no—
900C2×D4—1232no—
901C2×D4—121no—
902C2×D4—122no—
903C2×D4—122no—
904C2×D4—122no—
905C2×D4—122no—
906C2×D4—122no—
907C2×D4—122no—
908C2×D4—122no—
909C2×D4—122no—
910C2×D4—122no—
911C2×D4—1216no—
912C2×D4—1232no—
913C2×D4—1232no—
914C2×D4—1232no—
915C2×D4—1216no—
916C2×D4—1232no—
917C2×D4D3×D418yescomplemented
918C22×C4—24no—
919C22×C4—31no—
920C22×C4—32no—
921C22×C4—32no—
922C22×C4—32no—
923C22×C4—31no—
924C22×C4—31no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—64no—
928C22×C4—64no—
929C22×C4—64no—
930C22×C4—64no—
931C22×C4—62no—
932C22×C4—64no—
933C22×C4—64no—
934C22×C4—64no—
935C22×C4—62no—
936C22×C4—64no—
937C22×C4—122no—
938C22×C4—122no—
939C22×C4—122no—
940C22×C4—122no—
941C22×C4—122no—
942C22×C4—122no—
943C22×C4C23×D312yes—
944C22×C4C23×D312yes—
945C22×C4C23×D311yescharacteristic
946C22×C4C23×D312yes—
947C22×C4C23×D311yescharacteristic
948C22×C4C23×D312yes—
949C4⋊C4—24no—
950C4⋊C4—41no—
951C4⋊C4—64no—
952C4⋊C4—64no—
953C4⋊C4—64no—
954C4⋊C4—121no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—41no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—41no—
964C22⋊C4—64no—
965C22⋊C4—64no—
966C22⋊C4—64no—
967C22⋊C4—64no—
968C22⋊C4—64no—
969C22⋊C4—64no—
970C22⋊C4—64no—
971C22⋊C4—64no—
972C22⋊C4—64no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—121no—
976C22⋊C4—122no—
977C22⋊C4—122no—
978C22⋊C4—122no—
979C22⋊C4—122no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C22⋊C4—122no—
983C22⋊C4—122no—
984C22⋊C4—122no—
985C22⋊C4—122no—
986C22⋊C4—121no—
987C42—38no—
988C42—62no—
989C22×C3—24no—
990C22×C3—24no—
991C22×C3—24no—
992C22×C3—24no—
993C22×C3—24no—
994C22×C3—24no—
995C22×C3—24no—
996C22×C3—22no—
997C22×C3—41no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3—41no—
1007C22×C3—42no—
1008C22×C3—88no—
1009C22×C3C23×D412yes—
1010C22×C3C2×H(5,𝔽2)11yescharacteristic
1011C22×C3C2×H(5,𝔽2)11yescharacteristic
1012C22×C3C2×H(5,𝔽2)12yes—
1013C22×C3C2×H(5,𝔽2)11yescharacteristic
1014C2×D3—24no—
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—24no—
1019C2×D3—24no—
1020C2×D3—24no—
1021C2×D3—24no—
1022C2×D3—24no—
1023C2×D3—24no—
1024C2×D3—22no—
1025C2×D3—41no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—42no—
1030C2×D3—42no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—41no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C2×D3—42no—
1040C2×D3—816no—
1041C2×D3—816no—
1042C2×D3—816no—
1043C2×D3—88no—
1044C3×C4—24no—
1045C3×C4—42no—
1046C3×C4—41no—
1047C3×C4—42no—
1048C3×C4—42no—
1049C3×C4—41no—
1050Dic3—24no—
1051Dic3—41no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—41no—
1055Dic3D4214yes—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—34no—
1073C23—34no—
1074C23—34no—
1075C23—32no—
1076C23—44no—
1077C23—48no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—61no—
1084C23—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—62no—
1089C23—61no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—62no—
1099C23—62no—
1100C23—84no—
1101C23—82no—
1102C23—82no—
1103C23—128no—
1104C23—128no—
1105C23—128no—
1106C23—128no—
1107C23—128no—
1108C23—128no—
1109C23—128no—
1110C23—128no—
1111C23—128no—
1112C23—124no—
1113C23—128no—
1114C23—244no—
1115C23—242no—
1116C23—244no—
1117C23—244no—
1118C23—244no—
1119C23—244no—
1120C23—244no—
1121C23—244no—
1122C23—244no—
1123C23—244no—
1124C23—244no—
1125C23—242no—
1126C23—244no—
1127C23—244no—
1128C23—244no—
1129C23C2×D3×D414yes—
1130C23C2×D3×D414yes—
1131C23#100912yes—
1132C23C24×D311yescharacteristic
1133D4—48no—
1134D4—44no—
1135D4—48no—
1136D4—48no—
1137D4—616no—
1138D4—616no—
1139D4—616no—
1140D4—616no—
1141D4—128no—
1142D4—128no—
1143D4—128no—
1144D4—128no—
1145D4—124no—
1146D4—128no—
1147D4—124no—
1148D4—128no—
1149D4—128no—
1150D4—128no—
1151D4—128no—
1152D4—128no—
1153D4—128no—
1154D4—128no—
1155D4—124no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—34no—
1172C2×C4—32no—
1173C2×C4—34no—
1174C2×C4—48no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—61no—
1181C2×C4—62no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—61no—
1188C2×C4—128no—
1189C2×C4—128no—
1190C2×C4—124no—
1191C2×C4—124no—
1192C2×C4—128no—
1193C2×C4—128no—
1194C2×C4C2×D3×D414yes—
1195C2×C3—44no—
1196C2×C3—44no—
1197C2×C3—42no—
1198C2×C3C2×D4211yescharacteristic
1199C2×C3#348412yes—
1200C2×C3#348412yes—
1201C2×C3#353711yescharacteristic
1202C2×C3#353711yescharacteristic
1203D3—44no—
1204D3—44no—
1205D3—42no—
1206D3—44no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—22no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—41no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—41no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—64no—
1227C22—64no—
1228C22—64no—
1229C22—64no—
1230C22—64no—
1231C22—64no—
1232C22—64no—
1233C22—62no—
1234C22—64no—
1235C22—64no—
1236C22—64no—
1237C22—88no—
1238C22—121no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—121no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—2416no—
1254C22—248no—
1255C22—2416no—
1256C22—2416no—
1257C22C22×D3×D412yes—
1258C22C2×#100911yescharacteristic
1259C22D3×H(5,𝔽2)12yes—
1260C22D3×H(5,𝔽2)11yescharacteristic
1261C22D3×H(5,𝔽2)11yescharacteristic
1262C4—24no—
1263C4—34no—
1264C4—41no—
1265C4—42no—
1266C4—42no—
1267C4—41no—
1268C4—42no—
1269C4—64no—
1270C4—122no—
1271C4—121no—
1272C4—121no—
1273C4—122no—
1274C3#4535511yescharacteristic, complemented, Sylow
1275C2—44no—
1276C2—42no—
1277C2—44no—
1278C2—124no—
1279C2—122no—
1280C2—124no—
1281C2—124no—
1282C2#8630812yes—
1283C2#8639611yescharacteristic
1284C2D3×D4211yescharacteristic
1285C2#8666212yes—
1286C2#8707111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2668C2
hypercenter#2668D3
hypocenterC3#45355
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2668

Complements

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

NH ≅ G/Ntype
1. C2×#5609C2semidirect
2. C2×#5590C2semidirect
3. C3×#2668C2semidirect
4. #82713C2semidirect
5. #82604C2semidirect
6. #78112C2semidirect
7. #78019C2semidirect
8. #77689C2semidirect
9. #77513C2semidirect
10. #77127C2semidirect
11. #76895C2semidirect
12. #76753C2semidirect
13. #76669C2semidirect
14. #74884C2semidirect
15. #74884C2semidirect
16. #74751C2semidirect
17. #74667C2semidirect
18. #73852C2semidirect
19. #73824C2semidirect
21. C23×#67C22semidirect
22. C23×#67C22semidirect
23. C22×D3×D4C22semidirect
24. C22×D3×D4C22semidirect
25. C22×D3×D4C22semidirect
26. C22×D3×D4C22semidirect
27. C23×D12C22semidirect
28. C2×C3×#121C22semidirect
29. C2×C3×#120C22semidirect
30. C2×#953C22semidirect
32. C2×#939C22semidirect
33. C2×#939C22semidirect
34. C2×#937C22semidirect
35. C2×#937C22semidirect
36. C2×#937C22semidirect
37. C2×#937C22semidirect
38. C2×C4×#67C22semidirect
41. C2×#895C22semidirect
42. C2×#893C22semidirect
43. C2×#893C22semidirect
44. C2×#884C22semidirect
45. C2×#884C22semidirect
46. C2×#884C22semidirect
47. C2×#884C22semidirect
48. C2×#882C22semidirect
49. C2×#882C22semidirect
50. C2×#882C22semidirect
51. C2×#882C22semidirect
52. C2×#882C22semidirect
53. C2×#882C22semidirect
54. C2×#882C22semidirect
55. C2×#67⋊C4C22semidirect
56. C2×#67⋊C4C22semidirect
57. C2×#67⋊C4C22semidirect
58. C3×#399C22semidirect
59. C3×#397C22semidirect
60. C3×#394C22semidirect
61. C3×#392C22semidirect
62. C3×#386C22semidirect
63. C3×#386C22semidirect
64. C3×#379C22semidirect
65. #5223C22semidirect
66. #5223C22semidirect
67. #5222C22semidirect
68. #5220C22semidirect
69. #5213C22semidirect
70. #5213C22semidirect
71. #4993C22semidirect
72. #4993C22semidirect
73. #4992C22semidirect
74. #4991C22semidirect
75. #4960C22semidirect
76. #4960C22semidirect
77. #4960C22semidirect
78. #4960C22semidirect
79. #4960C22semidirect
80. #4960C22semidirect
81. #4959C22semidirect
82. #4958C22semidirect
83. #4958C22semidirect
84. #4958C22semidirect
85. #4957C22semidirect
86. #4957C22semidirect
87. #4956C22semidirect
88. #4956C22semidirect
89. #4956C22semidirect
90. #4955C22semidirect
91. #4955C22semidirect
92. #4955C22semidirect
93. #4955C22semidirect
94. #4952C22semidirect
95. #4942C22semidirect
96. #4675C22semidirect
97. #4672C22semidirect
98. #4671C22semidirect
99. #4671C22semidirect
100. #4671C22semidirect
101. #4667C22semidirect
102. #4667C22semidirect
103. #4665C22semidirect
104. #4665C22semidirect
105. #4665C22semidirect
106. #4665C22semidirect
107. #4665C22semidirect
108. #4650C22semidirect
109. #4648C22semidirect
116. #2668D3semidirect
202. #940D4semidirect
280. C2×#121C2×D3semidirect
293. C2×#120C2×D3semidirect
302. #399C2×D3semidirect
306. #397C2×D3semidirect
311. #394C2×D3semidirect
323. #392C2×D3semidirect
340. #386C2×D3semidirect
341. #386C2×D3semidirect
350. #379C2×D3semidirect
400. C2×C3×D4C2×D4semidirect
441. C2×#67C2×D4semidirect
442. C2×#67C2×D4semidirect
443. C2×#67C2×D4semidirect
444. C2×#67C2×D4semidirect
482. C2×D12C2×D4semidirect
533. C4×Dic3C2×D4semidirect
917. C2×D4D3×D4semidirect
1274. C3#45355semidirect

Maximal subgroups

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

subgroupindex
C2×#56092
C2×#55902
C3×#26682
#827132
#826042
#781122
#780192
#776892
#775132
#771272
#768952
#767532
#766692
#748842
#747512
#746672
#738522
#738242
#453553