Finite Group Databasebeta

← C2×#76834 #11430787

Subgroups — C2×#76834 #11430787

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#944C211yesmaximal, characteristic, complemented
2C22×#885C211yesmaximal, characteristic
3C2×C3×#393C211yesmaximal, characteristic, complemented
4C2×#5231C211yesmaximal, characteristic, complemented
5C2×#4959C211yesmaximal, characteristic
6C2×#4959C211yesmaximal, characteristic
7C2×#4948C211yesmaximal, characteristic, complemented
8C2×#4944C211yesmaximal, characteristic, complemented
9C2×#4944C211yesmaximal, characteristic, complemented
10#76834C2116yesmaximal, direct product factor
11C2×#4676C211yesmaximal, characteristic, complemented
12C2×#4646C211yesmaximal, characteristic, complemented
13C2×#4670C211yesmaximal, characteristic, complemented
14C2×#4669C211yesmaximal, characteristic, complemented
15C2×#4654C211yesmaximal, characteristic, complemented
16C2×#4652C211yesmaximal, characteristic, complemented
17C2×#2731—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C2×#944—28no—
28C2×#944C2218yescomplemented
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#885—28no—
46C2×#885C2218yes—
47C3×#393C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51#5231C2218yescomplemented
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4959C2218yes—
60#4959C2218yes—
61#4948C2218yescomplemented
62#4944C2218yescomplemented
63#4944C2218yescomplemented
64#4676C2218yescomplemented
65#4670C2218yescomplemented
66#4669C2218yescomplemented
67#4654C2218yescomplemented
68#4652C2218yescomplemented
69#4646C2218yescomplemented
70C22×C4⋊Q8—31no—
71C22×#124—31no—
72#2731—316no—
73C2×#396—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#393—31no—
78C2×#393D311yescharacteristic, complemented
79C2×#391—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#387—31no—
85C2×#387—31no—
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C22×C3×Q8—24no—
89C22×C3×Q8—42no—
90C22×C3×Q8—42no—
91C22×C3×Q8C2314yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—24no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67C2314yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C22×Dic6—42no—
110C22×Dic6—42no—
111C22×Dic6D418yes—
112C22×Dic6C2314yes—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—42no—
115C2×C3×C22⋊C4—42no—
116C2×C3×C22⋊C4C2314yes—
117C2×C3×C22⋊C4C2314yes—
118C2×C3×C22⋊C4C2314yes—
119C2×#217—24no—
120C2×#217—24no—
121C2×#217—24no—
122C2×#217C2314yes—
123C2×#217C2314yes—
124C2×#217C2314yes—
125#944—232no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—42no—
131C2×(C2×D3)⋊C4—42no—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×C4⋊Dic3—24no—
139C2×C4⋊Dic3C2314yes—
140C2×Dic3⋊C4—24no—
141C2×Dic3⋊C4—24no—
142C2×Dic3⋊C4—24no—
143C2×Dic3⋊C4—24no—
144C2×Dic3⋊C4—24no—
145C2×Dic3⋊C4—42no—
146C2×Dic3⋊C4C2314yes—
147C2×Dic3⋊C4C2314yes—
148C2×Dic3⋊C4C2314yes—
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×Dic3⋊C4C2314yes—
152C2×C4×Dic3—24no—
153C2×C4×Dic3—24no—
154C2×C4×Dic3—42no—
155C2×C4×Dic3C2314yes—
156C2×C4×Dic3C2314yes—
157C2×C4×Dic3C2314yes—
158#885—232no—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C23×Q8—31no—
170C23×Q8C2×D311yescharacteristic
171C23×D4—31no—
172C2×C4⋊Q8—38no—
173C2×C4⋊Q8—68no—
174C2×#124—38no—
175C2×#124—68no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C22⋊C4C2×D311yescharacteristic
194C22×C22⋊C4C2×D311yescharacteristic
195C22×C42—31no—
196C22×C42—31no—
197C22×C42—31no—
198#396—38no—
199#396—38no—
200#394—38no—
201#394—38no—
202#393—38no—
203#393C2×D318yescomplemented
204#391—38no—
205#388—38no—
206#388—38no—
207#388—38no—
208#388—38no—
209#387—38no—
210#387—38no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3C2412yes—
229C24×C3C2411yescharacteristic
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3C2412yes—
238C2×C3×Q8—28no—
239C2×C3×Q8—44no—
240C2×C3×Q8—44no—
241C2×C3×Q8—416no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4C2×D414yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C2×#67—28no—
267C2×#67—44no—
268C2×#67—44no—
269C2×#67—416no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3C2×D414yes—
288C22×Dic3C2×D414yes—
289C22×Dic3#4114yes—
290C22×Dic3#4114yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C2×Dic6—416no—
299C2×Dic6—44no—
300C2×Dic6—44no—
301C2×Dic6C2×D4116yes—
302C3×C22⋊C4—28no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305#217—28no—
306#217—28no—
307#217—28no—
308(C2×D3)⋊C4—28no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—28no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—44no—
313(C2×D3)⋊C4—44no—
314C4⋊Dic3—28no—
315Dic3⋊C4—28no—
316Dic3⋊C4—28no—
317Dic3⋊C4—28no—
318Dic3⋊C4—28no—
319Dic3⋊C4—28no—
320Dic3⋊C4—44no—
321C4×Dic3—28no—
322C4×Dic3—28no—
323C4×Dic3—44no—
324C25—31no—
325C25C22×D311yescharacteristic
326C22×Q8—24no—
327C22×Q8—38no—
328C22×Q8—34no—
329C22×Q8—42no—
330C22×Q8—42no—
331C22×Q8—122no—
332C22×Q8—122no—
333C22×Q8C22×D314yes—
334C22×D4—34no—
335C22×D4—64no—
336C22×D4—122no—
337C22×D4—122no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C4⋊Q8—632no—
352#124—632no—
353C2×C4⋊C4—34no—
354C2×C4⋊C4—34no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—34no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4—64no—
365C2×C4⋊C4—64no—
366C2×C4⋊C4—122no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—34no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—122no—
387C2×C22⋊C4—122no—
388C2×C22⋊C4C22×D314yes—
389C2×C22⋊C4C22×D314yes—
390C2×C22⋊C4C22×D314yes—
391C2×C42—34no—
392C2×C42—34no—
393C2×C42—34no—
394C2×C42—64no—
395C2×C42—64no—
396C2×C42—122no—
397#95—34no—
398#95—34no—
399#95—34no—
400#95—34no—
401#95—34no—
402#95—34no—
403#95—34no—
404#95C22×D314yes—
405#95C22×D314yes—
406#95C22×D314yes—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—44no—
415C23×C3—44no—
416C23×C3—44no—
417C23×C3—44no—
418C23×C3—44no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3C22×D412yes—
422C23×C3C2×#4112yes—
423C23×C3C2×#4112yes—
424C23×C3H(5,𝔽2)12yes—
425C23×C3H(5,𝔽2)12yes—
426C23×C32−1+412yes—
427C23×C32−1+412yes—
428C23×C3C2511yescharacteristic
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—44no—
437C22×D3—44no—
438C22×D3—44no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C3×Q8—416no—
444C2×C3×C4—28no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4C22×D414yes—
468#67—416no—
469C2×Dic3—28no—
470C2×Dic3—28no—
471C2×Dic3—28no—
472C2×Dic3—28no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—44no—
491C2×Dic3—44no—
492C2×Dic3—44no—
493C2×Dic3C22×D414yes—
494C2×Dic3C22×D414yes—
495C2×Dic3C2×#4114yes—
496C2×Dic3C2×#4114yes—
497Dic6—416no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—32no—
506C24—62no—
507C24—62no—
508C24—62no—
509C24—62no—
510C24—62no—
511C24—62no—
512C24—62no—
513C24C23×D312yes—
514C24C23×D311yescharacteristic
515C2×Q8—28no—
516C2×Q8—316no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—416no—
520C2×Q8—124no—
521C2×Q8—124no—
522C2×Q8—1216no—
523C2×D4—68no—
524C2×D4—124no—
525C2×D4—124no—
526C2×D4—1216no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—34no—
547C22×C4—34no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4D3×D414yes—
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D312yes—
576C22×C4C23×D312yes—
577C22×C4C23×D312yes—
578C22×C4C23×D312yes—
579C4⋊C4—68no—
580C4⋊C4—68no—
581C4⋊C4—68no—
582C4⋊C4—68no—
583C4⋊C4—68no—
584C4⋊C4—68no—
585C4⋊C4—124no—
586C22⋊C4—28no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—68no—
590C22⋊C4—68no—
591C22⋊C4—68no—
592C22⋊C4—68no—
593C22⋊C4—68no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C42—68no—
599C42—68no—
600C42—124no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—88no—
609C22×C3#53414yes—
610C22×C3#54214yes—
611C22×C3#54214yes—
612C22×C3#54814yes—
613C22×C3#54814yes—
614C22×C3#55514yes—
615C22×C3#56314yes—
616C22×C3C23×D411yescharacteristic
617C22×C3C22×#4111yescharacteristic
618C22×C3C22×#4111yescharacteristic
619C22×C3C2×H(5,𝔽2)11yescharacteristic
620C22×C3C2×H(5,𝔽2)11yescharacteristic
621C22×C3C2×2−1+411yescharacteristic
622C22×C3C2×2−1+411yescharacteristic
623C2×D3—42no—
624C2×D3—42no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—88no—
631C3×C4—24no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637Dic3—24no—
638Dic3—24no—
639Dic3—24no—
640Dic3—24no—
641Dic3—42no—
642Dic3—42no—
643Dic3—42no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—62no—
665C23—124no—
666C23—124no—
667C23—124no—
668C23—124no—
669C23—124no—
670C23—124no—
671C23—124no—
672C23C2×D3×D412yes—
673C23#100412yes—
674C23#100412yes—
675C23#100712yes—
676C23D3×#4112yes—
677C23D3×#4112yes—
678C23#101012yes—
679C23C24×D311yescharacteristic
680Q8—416no—
681Q8—1216no—
682D4—1216no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—34no—
702C2×C4—34no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—68no—
711C2×C4—68no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—68no—
721C2×C4—68no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—124no—
732C2×C4—124no—
733C2×C4—124no—
734C2×C4C2×D3×D414yes—
735C2×C3—82no—
736C2×C3#273118yescomplemented
737C2×C3C2×#53411yescharacteristic
738C2×C3C2×#54211yescharacteristic
739C2×C3C2×#54211yescharacteristic
740C2×C3C2×#54811yescharacteristic
741C2×C3C2×#54811yescharacteristic
742C2×C3C2×#55511yescharacteristic
743C2×C3C2×#56311yescharacteristic
744D3—82no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—88no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—248no—
761C22#558914yes—
762C22#563314yes—
763C22#564014yes—
764C22#564614yes—
765C22#566914yes—
766C22#567014yes—
767C22#567714yes—
768C22C22×D3×D411yescharacteristic
769C22C2×#100411yescharacteristic
770C22C2×#100411yescharacteristic
771C22C2×#100711yescharacteristic
772C22C2×D3×#4111yescharacteristic
773C22C2×D3×#4111yescharacteristic
774C22C2×#101011yescharacteristic
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—64no—
782C4—64no—
783C4—64no—
784C4—64no—
785C4—122no—
786C4—122no—
787C4—122no—
788C3C2×#273111yescharacteristic, complemented, Sylow
789C2—82no—
790C2—242no—
791C2#7683418yesdirect product factor
792C2C2×#558911yescharacteristic
793C2C2×#564011yescharacteristic
794C2C2×#564611yescharacteristic
795C2C2×#563311yescharacteristic
796C2C2×#566911yescharacteristic
797C2C2×#567011yescharacteristic
798C2C2×#567711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#393C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#393D3
hypocenterC3C2×#2731
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#944C2semidirect
3. C2×C3×#393C2semidirect
4. C2×#5231C2semidirect
7. C2×#4948C2semidirect
8. C2×#4944C2semidirect
9. C2×#4944C2semidirect
10. #76834C2direct (N × H)
11. C2×#4676C2semidirect
12. C2×#4646C2semidirect
13. C2×#4670C2semidirect
14. C2×#4669C2semidirect
15. C2×#4654C2semidirect
16. C2×#4652C2semidirect
28. C2×#944C22semidirect
47. C3×#393C22semidirect
51. #5231C22semidirect
61. #4948C22semidirect
62. #4944C22semidirect
63. #4944C22semidirect
64. #4676C22semidirect
65. #4670C22semidirect
66. #4669C22semidirect
67. #4654C22semidirect
68. #4652C22semidirect
69. #4646C22semidirect
78. C2×#393D3semidirect
203. #393C2×D3semidirect
736. C2×C3#2731semidirect
788. C3C2×#2731semidirect
791. C2#76834direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9442
C22×#8852
C2×C3×#3932
C2×#52312
C2×#49592
C2×#49482
C2×#49442
#768342
C2×#46762
C2×#46462
C2×#46702
C2×#46692
C2×#46542
C2×#46522
C2×#27313