Finite Group Databasebeta

← C2×#76720 #11430220

Subgroups — C2×#76720 #11430220

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#938C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5222C211yesmaximal, characteristic, complemented
6C2×#5222C211yesmaximal, characteristic, complemented
7C2×#5220C211yesmaximal, characteristic, complemented
8C2×#4959C211yesmaximal, characteristic, complemented
9C2×#4956C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4944C211yesmaximal, characteristic, complemented
12C2×#4951C211yesmaximal, characteristic, complemented
13C2×#4943C211yesmaximal, characteristic, complemented
14#76720C2116yesmaximal, direct product factor
15C2×#4664C211yesmaximal, characteristic, complemented
16C2×#4657C211yesmaximal, characteristic, complemented
17C2×#2699—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#939—28no—
38C2×#939C2218yescomplemented
39C2×#938—28no—
40C2×#938C2218yescomplemented
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C3×#392C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51#5223C2218yescomplemented
52#5222C2218yescomplemented
53#5222C2218yescomplemented
54#5220C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4956C2218yescomplemented
65#4951C2218yescomplemented
66#4944C2218yescomplemented
67#4943C2218yescomplemented
68#4664C2218yescomplemented
69#4657C2218yescomplemented
70C22×#121—31no—
71C22×#121—31no—
72#2699—316no—
73C2×#398—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#392—31no—
78C2×#392D311yescharacteristic, complemented
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#381—31no—
85C2×#381—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—42no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C22×C3×D4C2314yes—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—24no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67D418yescomplemented
115C22×#67C2314yes—
116C22×#67C2314yes—
117C22×#67C2314yes—
118C23×Dic3—24no—
119C23×Dic3—24no—
120C23×Dic3—42no—
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2314yes—
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C22×C4×D3—24no—
130C22×C4×D3—24no—
131C22×C4×D3—42no—
132C22×C4×D3C2314yes—
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4—42no—
135C2×C3×C22⋊C4—42no—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C22⋊C4C2314yes—
138C2×C3×C22⋊C4C2314yes—
139C2×#217—24no—
140C2×#217—24no—
141C2×#217—24no—
142C2×#217—24no—
143C2×#217—42no—
144C2×#217—42no—
145C2×#217—42no—
146C2×#217—42no—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155#939—232no—
156#938—232no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—42no—
159C2×(C2×D3)⋊C4—42no—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×C4⋊Dic3—24no—
164C2×C4⋊Dic3C2314yes—
165C2×Dic3⋊C4—24no—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3—42no—
172C2×C4×Dic3C2314yes—
173C3×#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4C2×D311yescharacteristic
185C23×D4C2×D311yescharacteristic
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4—31no—
189C2×#121—38no—
190C2×#121—38no—
191C2×#121—68no—
192C2×#121—68no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#398—38no—
213#394—38no—
214#394—38no—
215#394—38no—
216#392—38no—
217#392C2×D318yescomplemented
218#390—38no—
219#388—38no—
220#388—38no—
221#386—38no—
222#386—38no—
223#381—38no—
224#381—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95C2×D311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3C2×D414yes—
254C24×C3C2412yes—
255C24×C3C2412yes—
256C24×C3C2412yes—
257C24×C3C2411yescharacteristic
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3C2×D414yes—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—416no—
276C2×C3×D4—416no—
277C2×C3×D4—416no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4#4114yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—416no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—416no—
304C2×#67—416no—
305C2×#67C2×D4116yescomplemented
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—28no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—28no—
327C22×Dic3—44no—
328C22×Dic3—416no—
329C22×Dic3C2×D414yes—
330C22×Dic3#4114yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—44no—
341C2×C4×D3—416no—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—44no—
344C3×C22⋊C4—44no—
345#217—28no—
346#217—28no—
347#217—28no—
348#217—28no—
349#217—44no—
350#217—44no—
351#217—44no—
352#217—44no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356C4⋊Dic3—28no—
357Dic3⋊C4—28no—
358Dic3⋊C4—44no—
359Dic3⋊C4—44no—
360C4×Dic3—44no—
361C25—31no—
362C25C22×D311yescharacteristic
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—38no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—64no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4C22×D314yes—
387C22×D4C22×D314yes—
388C22×D4C22×D314yes—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—34no—
397C23×C4—34no—
398C23×C4—64no—
399C23×C4—64no—
400C23×C4—64no—
401C23×C4—64no—
402C23×C4—122no—
403C23×C4—122no—
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#121—632no—
409#121—632no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—122no—
417C2×C4⋊C4—122no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C42—34no—
447C2×C42—122no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95C22×D314yes—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3C22×D414yes—
498C23×C3C22×D412yes—
499C23×C3C2×#4112yes—
500C23×C3C2×#4112yes—
501C23×C3H(5,𝔽2)12yes—
502C23×C3H(5,𝔽2)12yes—
503C23×C3H(5,𝔽2)12yes—
504C23×C3H(5,𝔽2)12yes—
505C23×C3C2511yescharacteristic
506C22×D3—28no—
507C22×D3—28no—
508C22×D3—28no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C22×D3C22×D414yes—
520C3×D4—416no—
521C3×D4—416no—
522C3×D4—416no—
523C2×C3×C4—28no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—44no—
536C2×C3×C4—44no—
537C2×C3×C4—44no—
538C2×C3×C4C2×#4114yes—
539#67—416no—
540#67—416no—
541#67—416no—
542C2×Dic3—28no—
543C2×Dic3—28no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—416no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3C22×D414yes—
570C2×Dic3C2×#4114yes—
571C4×D3—416no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—34no—
593C24—32no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24D3×D414yes—
601C24C23×D312yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—316no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—416no—
616C2×D4—416no—
617C2×D4—416no—
618C2×D4—68no—
619C2×D4—68no—
620C2×D4—68no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—1216no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—1216no—
628C2×D4—1216no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—34no—
641C22×C4—34no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—68no—
650C22×C4—68no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—68no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—68no—
672C22×C4—124no—
673C22×C4—1216no—
674C22×C4—124no—
675C22×C4—1216no—
676C22×C4#23714yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—68no—
692C22⋊C4—68no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C42—124no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—416no—
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×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—88no—
723C22×C3—88no—
724C22×C3#53414yes—
725C22×C3#54014yes—
726C22×C3#54014yes—
727C22×C3#54614yes—
728C22×C3#54614yes—
729C22×C3#55514yes—
730C22×C3#56014yes—
731C22×C3C23×D411yescharacteristic
732C22×C3C22×#4111yescharacteristic
733C22×C3C22×#4111yescharacteristic
734C22×C3C2×H(5,𝔽2)11yescharacteristic
735C22×C3C2×H(5,𝔽2)11yescharacteristic
736C22×C3C2×H(5,𝔽2)11yescharacteristic
737C22×C3C2×H(5,𝔽2)11yescharacteristic
738C2×D3—24no—
739C2×D3—24no—
740C2×D3—24no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—416no—
744C2×D3—42no—
745C2×D3—42no—
746C3×C4—24no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750Dic3—24no—
751Dic3—24no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—28no—
764C23—28no—
765C23—28no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—34no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—68no—
806C23—68no—
807C23—68no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23C2×D3×D414yes—
813C23C2×D3×D412yes—
814C23C2×#23712yes—
815C23#100412yes—
816C23#100412yes—
817C23#100412yes—
818C23#100412yes—
819C23D3×#4112yes—
820C23C24×D311yescharacteristic
821D4—416no—
822D4—416no—
823D4—416no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—28no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—34no—
840C2×C4—34no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—68no—
849C2×C4—68no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—1216no—
866C2×C4—1216no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4C2×#23714yes—
873C2×C3—44no—
874C2×C3—82no—
875C2×C3—82no—
876C2×C3#269918yescomplemented
877C2×C3C2×#53411yescharacteristic
878C2×C3C2×#54011yescharacteristic
879C2×C3C2×#54011yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#54611yescharacteristic
882C2×C3C2×#55511yescharacteristic
883C2×C3C2×#56011yescharacteristic
884D3—44no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—416no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—64no—
908C22—64no—
909C22—64no—
910C22—88no—
911C22—88no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—1216no—
916C22—122no—
917C22#558914yes—
918C22#559114yes—
919C22#559514yes—
920C22#561014yes—
921C22#561514yes—
922C22#561614yes—
923C22#571914yes—
924C22C22×D3×D411yescharacteristic
925C22C22×#23711yescharacteristic
926C22C2×#100411yescharacteristic
927C22C2×#100411yescharacteristic
928C22C2×#100411yescharacteristic
929C22C2×#100411yescharacteristic
930C22C2×D3×#4111yescharacteristic
931C4—24no—
932C4—42no—
933C4—42no—
934C4—42no—
935C4—64no—
936C4—64no—
937C4—122no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#269911yescharacteristic, complemented, Sylow
943C2—44no—
944C2—82no—
945C2—82no—
946C2—124no—
947C2#7672018yesdirect product factor
948C2C2×#558911yescharacteristic
949C2C2×#559111yescharacteristic
950C2C2×#559511yescharacteristic
951C2C2×#561511yescharacteristic
952C2C2×#561611yescharacteristic
953C2C2×#561011yescharacteristic
954C2C2×#571911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2699
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C22×#939C2semidirect
3. C2×C3×#392C2semidirect
4. C2×#5223C2semidirect
5. C2×#5222C2semidirect
6. C2×#5222C2semidirect
7. C2×#5220C2semidirect
8. C2×#4959C2semidirect
9. C2×#4956C2semidirect
10. C2×#4957C2semidirect
11. C2×#4944C2semidirect
12. C2×#4951C2semidirect
13. C2×#4943C2semidirect
14. #76720C2direct (N × H)
15. C2×#4664C2semidirect
16. C2×#4657C2semidirect
38. C2×#939C22semidirect
40. C2×#938C22semidirect
49. C3×#392C22semidirect
51. #5223C22semidirect
52. #5222C22semidirect
53. #5222C22semidirect
54. #5220C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4956C22semidirect
65. #4951C22semidirect
66. #4944C22semidirect
67. #4943C22semidirect
68. #4664C22semidirect
69. #4657C22semidirect
78. C2×#392D3semidirect
114. C22×#67D4semidirect
217. #392C2×D3semidirect
305. C2×#67C2×D4semidirect
876. C2×C3#2699semidirect
942. C3C2×#2699semidirect
947. C2#76720direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9382
C22×#9392
C2×C3×#3922
C2×#52232
C2×#52222
C2×#52202
C2×#49592
C2×#49562
C2×#49572
C2×#49442
C2×#49512
C2×#49432
#767202
C2×#46642
C2×#46572
C2×#26993