Finite Group Databasebeta

← C2×#75448 #11001087

Subgroups — C2×#75448 #11001087

Order 768.

3246 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C22×C42×D3C211yesmaximal, characteristic
3C2×C3×#387C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic
5C2×#4976C211yesmaximal, characteristic, complemented
6C2×#4978C211yesmaximal, characteristic, complemented
7C2×#4933C211yesmaximal, characteristic, complemented
8#75448C2116yesmaximal, direct product factor
9C2×#4668C211yesmaximal, characteristic
10C2×#4664C211yesmaximal, characteristic
11C2×#4664C211yesmaximal, characteristic
12C2×#4667C211yesmaximal, characteristic
13C2×#4646C211yesmaximal, characteristic, complemented
14C2×#4646C211yesmaximal, characteristic, complemented
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4653C211yesmaximal, characteristic, complemented
17C2×#2855—31nomaximal, Sylow
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C2×#896—28no—
40C2×#896C2218yes—
41C2×C42×D3—28no—
42C2×C42×D3C2218yes—
43C3×#387C2218yescomplemented
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4989C2218yes—
59#4978C2218yescomplemented
60#4976C2218yescomplemented
61#4933C2218yescomplemented
62#4668C2218yes—
63#4667C2218yes—
64#4664C2218yes—
65#4664C2218yes—
66#4653C2218yescomplemented
67#4647C2218yescomplemented
68#4646C2218yescomplemented
69#4646C2218yescomplemented
70C22×C22⋊Q8—31no—
71C23×C42—31no—
72#2855—316no—
73C2×#391—31no—
74C2×#391—31no—
75C2×#389—31no—
76C2×#389—31no—
77C2×#387—31no—
78C2×#387—31no—
79C2×#387—31no—
80C2×#387D311yescharacteristic, complemented
81C2×#385—31no—
82C2×#385—31no—
83C2×#381—31no—
84C2×#381—31no—
85C2×#380—31no—
86C24×D3C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×C4×D3—24no—
102C22×C4×D3—24no—
103C22×C4×D3—24no—
104C22×C4×D3—24no—
105C22×C4×D3—24no—
106C22×C4×D3—24no—
107C22×C4×D3—24no—
108C22×C4×D3D418yes—
109C22×C4×D3Q818yescomplemented
110C22×C4×D3C2314yes—
111C22×C4×D3C2314yes—
112C22×C4×D3C2314yes—
113C22×Dic6—24no—
114C22×Dic6—24no—
115C22×Dic6—24no—
116C22×Dic6C2314yes—
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C42—24no—
122C2×C3×C42C2314yes—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×C4⋊Dic3—24no—
132C2×C4⋊Dic3C2314yes—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—24no—
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—24no—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—24no—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×Dic3⋊C4C2314yes—
142C2×Dic3⋊C4C2314yes—
143C2×Dic3⋊C4C2314yes—
144C2×Dic3⋊C4C2314yes—
145C2×C4×Dic3—24no—
146C2×C4×Dic3—24no—
147C2×C4×Dic3—24no—
148C2×C4×Dic3C2314yes—
149C2×C4×Dic3C2314yes—
150C2×C4×Dic3C2314yes—
151#896—232no—
152C42×D3—232no—
153C3×#95C2314yes—
154C3×#95C2314yes—
155C3×#95C2314yes—
156C3×#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C23×Q8—31no—
168C24×C4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C2×C22⋊Q8—38no—
172C2×C22⋊Q8—68no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C4⋊C4C2×D311yescharacteristic
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C42—31no—
187C22×C42—31no—
188C22×C42—31no—
189C22×C42—38no—
190C22×C42—68no—
191C22×C42C2×D311yescharacteristic
192#391—38no—
193#391—38no—
194#389—38no—
195#389—38no—
196#387—38no—
197#387—38no—
198#387—38no—
199#387C2×D318yescomplemented
200#385—38no—
201#385—38no—
202#381—38no—
203#381—38no—
204#380—38no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3C2411yescharacteristic
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3—22no—
224C23×D3C2×D414yes—
225C23×D3C2×Q814yes—
226C23×D3#4114yes—
227C23×D3C2412yes—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×Q814yes—
248C22×C3×C4#4114yes—
249C22×C3×C4C2412yes—
250C22×C3×C4C2412yes—
251C22×C3×C4C2412yes—
252C22×C3×C4C2412yes—
253C22×C3×C4C2412yes—
254C22×C3×C4C2412yes—
255C22×C3×C4C2412yes—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3C2×D414yes—
273C22×Dic3C2×Q814yes—
274C22×Dic3#4114yes—
275C22×Dic3#4114yes—
276C22×Dic3#4114yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C22×Dic3C2412yes—
283C22×Dic3C2412yes—
284C2×C4×D3—232no—
285C2×C4×D3—232no—
286C2×C4×D3—28no—
287C2×C4×D3—28no—
288C2×C4×D3—28no—
289C2×C4×D3—28no—
290C2×C4×D3—232no—
291C2×C4×D3—28no—
292C2×C4×D3—28no—
293C2×C4×D3—28no—
294C2×C4×D3C2×D4116yes—
295C2×C4×D3C2×Q8116yescomplemented
296C2×Dic6—28no—
297C2×Dic6—28no—
298C2×Dic6—28no—
299C2×Dic6—416no—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—28no—
302C3×C42—28no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—28no—
307C4⋊Dic3—28no—
308Dic3⋊C4—28no—
309Dic3⋊C4—28no—
310Dic3⋊C4—28no—
311Dic3⋊C4—28no—
312Dic3⋊C4—28no—
313Dic3⋊C4—28no—
314C4×Dic3—28no—
315C4×Dic3—28no—
316C4×Dic3—28no—
317C25—31no—
318C22×Q8—34no—
319C22×Q8—64no—
320C22×Q8—64no—
321C22×Q8—64no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—38no—
326C23×C4—38no—
327C23×C4—34no—
328C23×C4—34no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—34no—
334C23×C4—64no—
335C23×C4—64no—
336C23×C4—64no—
337C23×C4—64no—
338C23×C4—64no—
339C23×C4—64no—
340C23×C4—64no—
341C23×C4C22×D311yescharacteristic
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C22⋊Q8—632no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—34no—
352C2×C4⋊C4—34no—
353C2×C4⋊C4—34no—
354C2×C4⋊C4—34no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—34no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—64no—
359C2×C4⋊C4—64no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4—64no—
365C2×C4⋊C4C22×D314yes—
366C2×C4⋊C4C22×D314yes—
367C2×C22⋊C4—34no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—34no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—64no—
375C2×C42—24no—
376C2×C42—34no—
377C2×C42—34no—
378C2×C42—34no—
379C2×C42—632no—
380C2×C42—64no—
381C2×C42—64no—
382C2×C42—64no—
383C2×C42C22×D314yes—
384#95—34no—
385#95—34no—
386#95—34no—
387#95—34no—
388#95—34no—
389#95—34no—
390#95—34no—
391#95—34no—
392#95—34no—
393#95—34no—
394#95C22×D314yes—
395#95C22×D314yes—
396#95C22×D314yes—
397#95C22×D314yes—
398C23×C3C22×D412yes—
399C23×C3C22×Q812yes—
400C23×C3C2×#4112yes—
401C23×C3C2×#4112yes—
402C23×C3C2×#4112yes—
403C23×C3C2×#4112yes—
404C23×C3C2×#4112yes—
405C23×C3C2511yescharacteristic
406C22×D3—28no—
407C22×D3—28no—
408C22×D3—28no—
409C22×D3—28no—
410C22×D3—28no—
411C22×D3—28no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3C22⋊Q8116yes—
417C22×D3C22×D414yes—
418C22×D3C22×Q814yes—
419C22×D3C2×#4114yes—
420C2×C3×C4—28no—
421C2×C3×C4—28no—
422C2×C3×C4—28no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4C22×D414yes—
446C2×C3×C4C22×Q814yes—
447C2×C3×C4C2×#4114yes—
448C2×Dic3—28no—
449C2×Dic3—28no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—44no—
467C2×Dic3—44no—
468C2×Dic3—44no—
469C2×Dic3—44no—
470C2×Dic3#123116yes—
471C2×Dic3C22×D414yes—
472C2×Dic3C22×Q814yes—
473C2×Dic3C2×#4114yes—
474C2×Dic3C2×#4114yes—
475C2×Dic3C2×#4114yes—
476C4×D3—232no—
477C4×D3—232no—
478C4×D3—232no—
479Dic6—416no—
480C24—34no—
481C24—34no—
482C24—34no—
483C24—32no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24C23×D311yescharacteristic
489C2×Q8—68no—
490C2×Q8—68no—
491C2×Q8—68no—
492C2×Q8—1216no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—34no—
512C22×C4—34no—
513C22×C4—34no—
514C22×C4—32no—
515C22×C4—34no—
516C22×C4—34no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—316no—
520C22×C4—316no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—632no—
526C22×C4—68no—
527C22×C4—68no—
528C22×C4—68no—
529C22×C4—68no—
530C22×C4—68no—
531C22×C4—68no—
532C22×C4—632no—
533C22×C4—632no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—68no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4#23514yes—
552C22×C4D3×D414yes—
553C22×C4D3×Q814yes—
554C22×C4C23×D312yes—
555C22×C4C23×D312yes—
556C22×C4C23×D312yes—
557C22×C4C23×D312yes—
558C22×C4C23×D312yes—
559C22×C4C23×D312yes—
560C22×C4C23×D312yes—
561C4⋊C4—28no—
562C4⋊C4—28no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—68no—
569C4⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—68no—
574C42—28no—
575C42—68no—
576C42—68no—
577C42—68no—
578C22×C3C2×C22⋊Q814yes—
579C22×C3C2×#12314yes—
580C22×C3#52514yes—
581C22×C3#52914yes—
582C22×C3#52914yes—
583C22×C3#53314yes—
584C22×C3#53314yes—
585C22×C3C23×D411yescharacteristic
586C22×C3C23×Q811yescharacteristic
587C22×C3C22×#4111yescharacteristic
588C22×C3C22×#4111yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C22×#4111yescharacteristic
591C22×C3C22×#4111yescharacteristic
592C2×D3—232no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3C2×C22⋊Q818yes—
600C3×C4—24no—
601C3×C4—24no—
602C3×C4—24no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607Dic3—24no—
608Dic3—24no—
609Dic3—42no—
610Dic3—42no—
611Dic3—42no—
612Dic3—42no—
613Dic3C2×#12318yes—
614C23—34no—
615C23—34no—
616C23—34no—
617C23—316no—
618C23—68no—
619C23—68no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—68no—
625C23—68no—
626C23—68no—
627C23—68no—
628C23C2×#23512yes—
629C23C2×D3×D412yes—
630C23C2×D3×Q812yes—
631C23D3×#4112yes—
632C23D3×#4112yes—
633C23D3×#4112yes—
634C23D3×#4112yes—
635C23C24×D311yescharacteristic
636Q8—1216no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—316no—
659C2×C4—34no—
660C2×C4—34no—
661C2×C4—34no—
662C2×C4—34no—
663C2×C4—34no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—632no—
669C2×C4—632no—
670C2×C4—632no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—68no—
676C2×C4—68no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—124no—
690C2×C4—124no—
691C2×C4—124no—
692C2×C4—124no—
693C2×C4C2×#23514yes—
694C2×C4C2×D3×D414yes—
695C2×C4C2×D3×Q814yes—
696C2×C3#285518yescomplemented
697C2×C3C22×C22⋊Q811yescharacteristic
698C2×C3C22×#12311yescharacteristic
699C2×C3C2×#52511yescharacteristic
700C2×C3C2×#52911yescharacteristic
701C2×C3C2×#52911yescharacteristic
702C2×C3C2×#53311yescharacteristic
703C2×C3C2×#53311yescharacteristic
704D3—28no—
705C22—38no—
706C22—64no—
707C22—64no—
708C22—64no—
709C22—64no—
710C22—632no—
711C22—64no—
712C22—64no—
713C22#552814yes—
714C22#554714yes—
715C22#557814yes—
716C22D3×C22⋊Q814yes—
717C22D3×#12314yes—
718C22#568814yes—
719C22#570614yes—
720C22C22×#23511yescharacteristic
721C22C22×D3×D411yescharacteristic
722C22C22×D3×Q811yescharacteristic
723C22C2×D3×#4111yescharacteristic
724C22C2×D3×#4111yescharacteristic
725C22C2×D3×#4111yescharacteristic
726C22C2×D3×#4111yescharacteristic
727C4—24no—
728C4—24no—
729C4—24no—
730C4—38no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—64no—
736C4—64no—
737C4—122no—
738C4—122no—
739C4—122no—
740C4—122no—
741C3C2×#285511yescharacteristic, complemented, Sylow
742C2—68no—
743C2#7544818yesdirect product factor
744C2C2×#552811yescharacteristic
745C2C2×#554711yescharacteristic
746C2C2×#557811yescharacteristic
747C2C2×D3×C22⋊Q811yescharacteristic
748C2C2×D3×#12311yescharacteristic
749C2C2×#568811yescharacteristic
750C2C2×#570611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#387C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#387D3
hypocenterC3C2×#2855
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C2×C3×#387C2semidirect
5. C2×#4976C2semidirect
6. C2×#4978C2semidirect
7. C2×#4933C2semidirect
8. #75448C2direct (N × H)
13. C2×#4646C2semidirect
14. C2×#4646C2semidirect
15. C2×#4647C2semidirect
16. C2×#4653C2semidirect
43. C3×#387C22semidirect
59. #4978C22semidirect
60. #4976C22semidirect
61. #4933C22semidirect
66. #4653C22semidirect
67. #4647C22semidirect
68. #4646C22semidirect
69. #4646C22semidirect
80. C2×#387D3semidirect
109. C22×C4×D3Q8semidirect
199. #387C2×D3semidirect
295. C2×C4×D3C2×Q8semidirect
696. C2×C3#2855semidirect
741. C3C2×#2855semidirect
743. C2#75448direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8962
C22×C42×D32
C2×C3×#3872
C2×#49892
C2×#49762
C2×#49782
C2×#49332
#754482
C2×#46682
C2×#46642
C2×#46672
C2×#46462
C2×#46472
C2×#46532
C2×#28553