Finite Group Databasebeta

← C2×#76728 #11430474

Subgroups — C2×#76728 #11430474

Order 768.

3434 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic, complemented
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5221C211yesmaximal, characteristic, complemented
7C2×#5221C211yesmaximal, characteristic, complemented
8C2×#5220C211yesmaximal, characteristic, complemented
9C2×#4952C211yesmaximal, characteristic, complemented
10C2×#4961C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4950C211yesmaximal, characteristic, complemented
14#76728C2116yesmaximal, direct product factor
15C2×#4670C211yesmaximal, characteristic, complemented
16C2×#4655C211yesmaximal, characteristic, complemented
17C2×#2714—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C2×#939—28no—
37C2×#939C2218yescomplemented
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×C4×Dic3C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#879—28no—
50C2×#879C2218yescomplemented
51C3×#392C2218yescomplemented
52C2×C3×#95C2211yescharacteristic
53#5223C2218yescomplemented
54#5223C2218yescomplemented
55#5221C2218yescomplemented
56#5221C2218yescomplemented
57#5220C2218yescomplemented
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4961C2218yescomplemented
64#4961C2218yescomplemented
65#4957C2218yescomplemented
66#4952C2218yescomplemented
67#4950C2218yescomplemented
68#4670C2218yescomplemented
69#4655C2218yescomplemented
70C22×#126—31no—
71C22×#121—31no—
72#2714—316no—
73C2×#397—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392D311yescharacteristic, complemented
79C2×#390—31no—
80C2×#390—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#387—31no—
84C2×#386—31no—
85C2×#385—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
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×#67—42no—
115C22×#67C2314yes—
116C22×#67C2314yes—
117C22×#67C2314yes—
118C23×Dic3—24no—
119C23×Dic3—42no—
120C23×Dic3—42no—
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2314yes—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—24no—
131C2×C3×C22⋊C4—42no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217—24no—
138C2×#217—42no—
139C2×#217—42no—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217—42no—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151#939—232no—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×C4⋊Dic3—24no—
161C2×C4⋊Dic3—42no—
162C2×C4⋊Dic3—42no—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2314yes—
165C2×C4⋊Dic3C2314yes—
166C2×Dic3⋊C4—24no—
167C2×Dic3⋊C4D418yescomplemented
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—24no—
171C2×C4×Dic3—42no—
172C2×C4×Dic3C2314yes—
173C2×C4×Dic3C2314yes—
174#879—232no—
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—
188C2×#126—38no—
189C2×#126—68no—
190C2×#121—38no—
191C2×#121—68no—
192C22×C4⋊C4—31no—
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⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C22×C42—31no—
214#397—38no—
215#394—38no—
216#394—38no—
217#392—38no—
218#392—38no—
219#392C2×D318yescomplemented
220#390—38no—
221#390—38no—
222#390—38no—
223#388—38no—
224#387—38no—
225#386—38no—
226#385—38no—
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×C3#4114yes—
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×D3—22no—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
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×C4C2×D414yes—
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—44no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—416no—
304C2×#67—416no—
305C2×#67—416no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
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—28no—
326C22×Dic3—44no—
327C22×Dic3—44no—
328C22×Dic3—416no—
329C22×Dic3C2×D414yes—
330C22×Dic3C2×D414yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—44no—
341#217—28no—
342#217—28no—
343#217—28no—
344#217—44no—
345#217—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353C4⋊Dic3—28no—
354C4⋊Dic3—44no—
355C4⋊Dic3—44no—
356Dic3⋊C4—28no—
357Dic3⋊C4C2×D4116yescomplemented
358C4×Dic3—28no—
359C4×Dic3—44no—
360C25—31no—
361C25C22×D311yescharacteristic
362C25C22×D311yescharacteristic
363C25C22×D311yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4C22×D314yes—
386C22×D4C22×D314yes—
387C22×D4C22×D314yes—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—34no—
396C23×C4—64no—
397C23×C4—122no—
398C23×C4—122no—
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#126—632no—
404#121—632no—
405C2×C4⋊C4—38no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4—64no—
413C2×C4⋊C4—122no—
414C2×C4⋊C4—122no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
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—42no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—122no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4C22×D314yes—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C42—34no—
446C2×C42—34no—
447C2×C42—64no—
448C2×C42—122no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95C22×D314yes—
455C23×C3—28no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—22no—
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—44no—
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×C3C22×D412yes—
497C23×C3C2×#4114yes—
498C23×C3C2×#4112yes—
499C23×C3C2×#4112yes—
500C23×C3H(5,𝔽2)12yes—
501C23×C3H(5,𝔽2)12yes—
502C23×C3H(5,𝔽2)12yes—
503C23×C3H(5,𝔽2)12yes—
504C23×C3C2511yescharacteristic
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C3×D4—416no—
520C3×D4—416no—
521C3×D4—416no—
522C2×C3×C4—28no—
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—44no—
535C2×C3×C4—44no—
536C2×C3×C4C22×D414yes—
537C2×C3×C4C2×#4114yes—
538#67—416no—
539#67—416no—
540#67—416no—
541C2×Dic3—28no—
542C2×Dic3—28no—
543C2×Dic3—22no—
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—416no—
563C2×Dic3—44no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3C22×D414yes—
569C2×Dic3C22×D414yes—
570C24—22no—
571C24—22no—
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—32no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24#23714yes—
599C24C23×D312yes—
600C24C23×D312yes—
601C24C23×D312yes—
602C24C23×D311yescharacteristic
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—416no—
614C2×D4—416no—
615C2×D4—68no—
616C2×D4—68no—
617C2×D4—68no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—1216no—
625C2×D4—1216no—
626C2×D4—1216no—
627C22×C4—22no—
628C22×C4—22no—
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—34no—
638C22×C4—34no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—68no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—124no—
667C22×C4—124no—
668C22×C4—1216no—
669C22×C4D3×D414yes—
670C22×C4#23714yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—316no—
676C4⋊C4—68no—
677C4⋊C4—68no—
678C4⋊C4—124no—
679C4⋊C4—124no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—44no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—124no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C42—68no—
696C42—124no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—416no—
704C22×C3—42no—
705C22×C3—42no—
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—88no—
720C22×C3—88no—
721C22×C3#53514yes—
722C22×C3#53814yes—
723C22×C3#53814yes—
724C22×C3#54614yes—
725C22×C3#55014yes—
726C22×C3#55314yes—
727C22×C3#56014yes—
728C22×C3C23×D411yescharacteristic
729C22×C3C22×#4111yescharacteristic
730C22×C3C22×#4111yescharacteristic
731C22×C3C2×H(5,𝔽2)11yescharacteristic
732C22×C3C2×H(5,𝔽2)11yescharacteristic
733C22×C3C2×H(5,𝔽2)11yescharacteristic
734C22×C3C2×H(5,𝔽2)11yescharacteristic
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—42no—
746C3×C4—42no—
747Dic3—24no—
748Dic3—24no—
749Dic3—42no—
750Dic3—42no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—28no—
761C23—28no—
762C23—28no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
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—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23C2×D3×D412yes—
810C23C2×#23714yes—
811C23C2×#23712yes—
812C23C2×#23712yes—
813C23#100412yes—
814C23#100412yes—
815C23#100412yes—
816C23#100912yes—
817C23C24×D311yescharacteristic
818D4—416no—
819D4—416no—
820D4—416no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—34no—
837C2×C4—34no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—68no—
845C2×C4—68no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
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—1216no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—124no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4C2×D3×D414yes—
868C2×C4C2×#23714yes—
869C2×C3—44no—
870C2×C3—82no—
871C2×C3—82no—
872C2×C3#271418yescomplemented
873C2×C3C2×#53511yescharacteristic
874C2×C3C2×#53811yescharacteristic
875C2×C3C2×#53811yescharacteristic
876C2×C3C2×#54611yescharacteristic
877C2×C3C2×#55011yescharacteristic
878C2×C3C2×#55311yescharacteristic
879C2×C3C2×#56011yescharacteristic
880D3—82no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—416no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—88no—
904C22—88no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—248no—
913C22#559114yes—
914C22#559314yes—
915C22#559314yes—
916C22#560714yes—
917C22#561814yes—
918C22#562014yes—
919C22#571814yes—
920C22C22×D3×D411yescharacteristic
921C22C22×#23711yescharacteristic
922C22C22×#23711yescharacteristic
923C22C2×#100411yescharacteristic
924C22C2×#100411yescharacteristic
925C22C2×#100411yescharacteristic
926C22C2×#100911yescharacteristic
927C4—24no—
928C4—24no—
929C4—42no—
930C4—42no—
931C4—64no—
932C4—64no—
933C4—122no—
934C4—122no—
935C4—122no—
936C4—122no—
937C4—122no—
938C3C2×#271411yescharacteristic, complemented, Sylow
939C2—44no—
940C2—82no—
941C2—82no—
942C2—242no—
943C2#7672818yesdirect product factor
944C2C2×#559311yescharacteristic
945C2C2×#559311yescharacteristic
946C2C2×#559111yescharacteristic
947C2C2×#561811yescharacteristic
948C2C2×#560711yescharacteristic
949C2C2×#562011yescharacteristic
950C2C2×#571811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2714
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#939C2semidirect
2. C22×#879C2semidirect
3. C2×C3×#392C2semidirect
4. C2×#5223C2semidirect
5. C2×#5223C2semidirect
6. C2×#5221C2semidirect
7. C2×#5221C2semidirect
8. C2×#5220C2semidirect
9. C2×#4952C2semidirect
10. C2×#4961C2semidirect
11. C2×#4961C2semidirect
12. C2×#4957C2semidirect
13. C2×#4950C2semidirect
14. #76728C2direct (N × H)
15. C2×#4670C2semidirect
16. C2×#4655C2semidirect
37. C2×#939C22semidirect
50. C2×#879C22semidirect
51. C3×#392C22semidirect
53. #5223C22semidirect
54. #5223C22semidirect
55. #5221C22semidirect
56. #5221C22semidirect
57. #5220C22semidirect
63. #4961C22semidirect
64. #4961C22semidirect
65. #4957C22semidirect
66. #4952C22semidirect
67. #4950C22semidirect
68. #4670C22semidirect
69. #4655C22semidirect
78. C2×#392D3semidirect
167. C2×Dic3⋊C4D4semidirect
219. #392C2×D3semidirect
357. Dic3⋊C4C2×D4semidirect
872. C2×C3#2714semidirect
938. C3C2×#2714semidirect
943. C2#76728direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#8792
C2×C3×#3922
C2×#52232
C2×#52212
C2×#52202
C2×#49522
C2×#49612
C2×#49572
C2×#49502
#767282
C2×#46702
C2×#46552
C2×#27143