Finite Group Databasebeta

← C2×#76133 #11430749

Subgroups — C2×#76133 #11430749

Order 768.

2678 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C22×#888C211yesmaximal, characteristic, complemented
3C2×C3×#389C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic
5C2×#4989C211yesmaximal, characteristic
6C2×#4982C211yesmaximal, characteristic, complemented
7C2×#4982C211yesmaximal, characteristic, complemented
8C2×#4979C211yesmaximal, characteristic, complemented
9C2×#4990C211yesmaximal, characteristic
10C2×#4929C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic
12#76133C2116yesmaximal, direct product factor
13C2×#4673C211yesmaximal, characteristic
14C2×#4668C211yesmaximal, characteristic
15C2×#4658C211yesmaximal, characteristic, complemented
16C2×#4652C211yesmaximal, characteristic, complemented
17C2×#2729—31nomaximal, Sylow
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C2×#896—28no—
42C2×#896C2218yes—
43C2×#888—28no—
44C2×#888C2218yescomplemented
45C3×#389C2218yescomplemented
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#4994C2218yes—
59#4990C2218yes—
60#4989C2218yes—
61#4982C2218yescomplemented
62#4982C2218yescomplemented
63#4979C2218yescomplemented
64#4940C2218yes—
65#4929C2218yescomplemented
66#4673C2218yes—
67#4668C2218yes—
68#4658C2218yescomplemented
69#4652C2218yescomplemented
70C22×C4⋊Q8—31no—
71C22×C22⋊Q8—31no—
72#2729—316no—
73C2×#400—31no—
74C2×#398—31no—
75C2×#398—31no—
76C2×#396—31no—
77C2×#395—31no—
78C2×#393—31no—
79C2×#391—31no—
80C2×#389D311yescharacteristic, complemented
81C2×#388—31no—
82C2×#388—31no—
83C2×#387—31no—
84C2×#385—31no—
85C2×#385—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—42no—
103C22×C4×D3—42no—
104C22×C4×D3C2314yes—
105C22×Dic6—24no—
106C22×Dic6—42no—
107C22×Dic6—42no—
108C22×Dic6—42no—
109C22×Dic6—42no—
110C22×Dic6D418yes—
111C22×Dic6C2314yes—
112C22×Dic6C2314yes—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4—24no—
115C2×C3×C4⋊C4—24no—
116C2×C3×C4⋊C4—42no—
117C2×C3×C4⋊C4C2314yes—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C42—42no—
122C2×C3×C42C2314yes—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—42no—
127C2×(C2×D3)⋊C4—42no—
128C2×(C2×D3)⋊C4Q818yescomplemented
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×C4⋊Dic3—24no—
136C2×C4⋊Dic3—42no—
137C2×C4⋊Dic3C2314yes—
138C2×C4⋊Dic3C2314yes—
139C2×Dic3⋊C4—24no—
140C2×Dic3⋊C4—24no—
141C2×Dic3⋊C4—24no—
142C2×Dic3⋊C4—24no—
143C2×Dic3⋊C4—24no—
144C2×Dic3⋊C4—42no—
145C2×Dic3⋊C4C2314yes—
146C2×Dic3⋊C4C2314yes—
147C2×Dic3⋊C4C2314yes—
148C2×Dic3⋊C4C2314yes—
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×C4×Dic3—24no—
152C2×C4×Dic3C2314yes—
153#896—232no—
154#888—232no—
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—
168C23×Q8—31no—
169C24×C4—31no—
170C2×C4⋊Q8—38no—
171C2×C4⋊Q8—68no—
172C2×C22⋊Q8—38no—
173C2×C22⋊Q8—68no—
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⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183C22×C4⋊C4C2×D311yescharacteristic
184C22×C4⋊C4C2×D311yescharacteristic
185C22×C4⋊C4C2×D311yescharacteristic
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×C42—31no—
193C22×C42C2×D311yescharacteristic
194#400—38no—
195#398—38no—
196#398—38no—
197#396—38no—
198#395—38no—
199#393—38no—
200#391—38no—
201#389C2×D318yescomplemented
202#388—38no—
203#388—38no—
204#387—38no—
205#385—38no—
206#385—38no—
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×#95—31no—
216C2×#95—31no—
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3C2411yescharacteristic
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3C2×Q814yes—
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×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3C2×D414yes—
275C22×Dic3C2×D414yes—
276C22×Dic3C2×Q814yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C22×Dic3C2412yes—
283C22×Dic3C2412yes—
284C2×C4×D3—28no—
285C2×C4×D3—44no—
286C2×C4×D3—44no—
287C2×C4×D3—416no—
288C2×Dic6—28no—
289C2×Dic6—416no—
290C2×Dic6—44no—
291C2×Dic6—44no—
292C2×Dic6—44no—
293C2×Dic6—44no—
294C2×Dic6—416no—
295C2×Dic6C2×D4116yes—
296C3×C4⋊C4—28no—
297C3×C4⋊C4—28no—
298C3×C4⋊C4—28no—
299C3×C4⋊C4—44no—
300C3×C42—44no—
301(C2×D3)⋊C4—28no—
302(C2×D3)⋊C4—28no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—44no—
305(C2×D3)⋊C4—44no—
306(C2×D3)⋊C4C2×Q8116yescomplemented
307C4⋊Dic3—28no—
308C4⋊Dic3—44no—
309Dic3⋊C4—28no—
310Dic3⋊C4—28no—
311Dic3⋊C4—28no—
312Dic3⋊C4—28no—
313Dic3⋊C4—28no—
314Dic3⋊C4—44no—
315C4×Dic3—28no—
316C25—31no—
317C22×Q8—38no—
318C22×Q8—34no—
319C22×Q8—34no—
320C22×Q8—64no—
321C22×Q8—122no—
322C22×Q8—122no—
323C22×Q8—122no—
324C22×Q8—122no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—34no—
333C23×C4—64no—
334C23×C4—122no—
335C23×C4—122no—
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C23×C4C22×D311yescharacteristic
342C23×C4C22×D311yescharacteristic
343C4⋊Q8—632no—
344C22⋊Q8—632no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—34no—
349C2×C4⋊C4—34no—
350C2×C4⋊C4—34no—
351C2×C4⋊C4—34no—
352C2×C4⋊C4—34no—
353C2×C4⋊C4—34no—
354C2×C4⋊C4—34no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—64no—
359C2×C4⋊C4—64no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—122no—
364C2×C4⋊C4—122no—
365C2×C4⋊C4C22×D314yes—
366C2×C4⋊C4C22×D314yes—
367C2×C4⋊C4C22×D314yes—
368C2×C4⋊C4C22×D314yes—
369C2×C22⋊C4—38no—
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—64no—
377C2×C22⋊C4—64no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4—122no—
380C2×C22⋊C4—122no—
381C2×C42—34no—
382C2×C42—42no—
383C2×C42—64no—
384C2×C42C22×D314yes—
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#95—34no—
395#95C22×D314yes—
396#95C22×D314yes—
397C23×C3C22×D412yes—
398C23×C3C22×Q812yes—
399C23×C3C2×#4112yes—
400C23×C3H(5,𝔽2)12yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C32−1+412yes—
403C23×C32−1+412yes—
404C23×C3C2511yescharacteristic
405C22×D3—28no—
406C22×D3—28no—
407C22×D3—28no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—44no—
417C22×D3—44no—
418C22×D3C22×Q814yes—
419C2×C3×C4—28no—
420C2×C3×C4—28no—
421C2×C3×C4—28no—
422C2×C3×C4—22no—
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—44no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4C22×D414yes—
445C2×C3×C4C22×Q814yes—
446C2×C3×C4C2×#4114yes—
447C2×Dic3—28no—
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—22no—
467C2×Dic3—22no—
468C2×Dic3—44no—
469C2×Dic3—44no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3C22×D414yes—
473C2×Dic3C22×D414yes—
474C2×Dic3C22×Q814yes—
475C4×D3—416no—
476Dic6—416no—
477Dic6—416no—
478C24—34no—
479C24—32no—
480C24—62no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24C23×D311yescharacteristic
487C2×Q8—316no—
488C2×Q8—68no—
489C2×Q8—124no—
490C2×Q8—124no—
491C2×Q8—1216no—
492C2×Q8—124no—
493C2×Q8—124no—
494C2×Q8—1216no—
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—22no—
512C22×C4—22no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—34no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—68no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—124no—
543C22×C4—124no—
544C22×C4—1216no—
545C22×C4#23514yes—
546C22×C4D3×D414yes—
547C22×C4D3×Q814yes—
548C22×C4C23×D312yes—
549C22×C4C23×D312yes—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D312yes—
553C22×C4C23×D312yes—
554C22×C4C23×D312yes—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—44no—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—68no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—124no—
566C4⋊C4—124no—
567C22⋊C4—316no—
568C22⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—124no—
572C22⋊C4—124no—
573C42—44no—
574C42—68no—
575C22×C3#53414yes—
576C22×C3#54214yes—
577C22×C3#54414yes—
578C22×C3#54814yes—
579C22×C3D4×Q814yes—
580C22×C3#55414yes—
581C22×C3#56314yes—
582C22×C3C23×D411yescharacteristic
583C22×C3C23×Q811yescharacteristic
584C22×C3C22×#4111yescharacteristic
585C22×C3C2×H(5,𝔽2)11yescharacteristic
586C22×C3C2×H(5,𝔽2)11yescharacteristic
587C22×C3C2×2−1+411yescharacteristic
588C22×C3C2×2−1+411yescharacteristic
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—416no—
596C2×D3—42no—
597C3×C4—24no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—42no—
604Dic3—24no—
605Dic3—24no—
606Dic3—24no—
607Dic3—42no—
608Dic3—42no—
609Dic3—42no—
610Dic3—42no—
611C23—34no—
612C23—68no—
613C23—62no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—68no—
620C23—68no—
621C23—124no—
622C23—124no—
623C23—124no—
624C23—124no—
625C23C2×#23512yes—
626C23C2×D3×D412yes—
627C23#100412yes—
628C23C2×D3×Q812yes—
629C23#100712yes—
630C23#100912yes—
631C23#101012yes—
632C23C24×D311yescharacteristic
633Q8—1216no—
634Q8—1216no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
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—34no—
657C2×C4—34no—
658C2×C4—34no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—68no—
670C2×C4—68no—
671C2×C4—68no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—1216no—
685C2×C4—124no—
686C2×C4—124no—
687C2×C4—124no—
688C2×C4—124no—
689C2×C4C2×#23514yes—
690C2×C4C2×D3×D414yes—
691C2×C4C2×D3×Q814yes—
692C2×C3#272918yescomplemented
693C2×C3C2×#53411yescharacteristic
694C2×C3C2×#54211yescharacteristic
695C2×C3C2×#54411yescharacteristic
696C2×C3C2×#54811yescharacteristic
697C2×C3C2×D4×Q811yescharacteristic
698C2×C3C2×#55411yescharacteristic
699C2×C3C2×#56311yescharacteristic
700D3—44no—
701C22—64no—
702C22—64no—
703C22—64no—
704C22—122no—
705C22—1216no—
706C22—122no—
707C22—122no—
708C22—122no—
709C22#551114yes—
710C22#555214yes—
711C22#558214yes—
712C22#560514yes—
713C22#564614yes—
714C22#568914yes—
715C22#572714yes—
716C22C22×#23511yescharacteristic
717C22C22×D3×D411yescharacteristic
718C22C2×#100411yescharacteristic
719C22C22×D3×Q811yescharacteristic
720C22C2×#100711yescharacteristic
721C22C2×#100911yescharacteristic
722C22C2×#101011yescharacteristic
723C4—24no—
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—64no—
731C4—64no—
732C4—64no—
733C4—122no—
734C4—122no—
735C4—122no—
736C4—122no—
737C3C2×#272911yescharacteristic, complemented, Sylow
738C2—124no—
739C2#7613318yesdirect product factor
740C2C2×#551111yescharacteristic
741C2C2×#555211yescharacteristic
742C2C2×#558211yescharacteristic
743C2C2×#560511yescharacteristic
744C2C2×#564611yescharacteristic
745C2C2×#568911yescharacteristic
746C2C2×#572711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#389C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#389D3
hypocenterC3C2×#2729
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#888C2semidirect
3. C2×C3×#389C2semidirect
6. C2×#4982C2semidirect
7. C2×#4982C2semidirect
8. C2×#4979C2semidirect
10. C2×#4929C2semidirect
12. #76133C2direct (N × H)
15. C2×#4658C2semidirect
16. C2×#4652C2semidirect
44. C2×#888C22semidirect
45. C3×#389C22semidirect
61. #4982C22semidirect
62. #4982C22semidirect
63. #4979C22semidirect
65. #4929C22semidirect
68. #4658C22semidirect
69. #4652C22semidirect
80. C2×#389D3semidirect
128. C2×(C2×D3)⋊C4Q8semidirect
201. #389C2×D3semidirect
306. (C2×D3)⋊C4C2×Q8semidirect
692. C2×C3#2729semidirect
737. C3C2×#2729semidirect
739. C2#76133direct (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×#8882
C2×C3×#3892
C2×#49942
C2×#49892
C2×#49822
C2×#49792
C2×#49902
C2×#49292
C2×#49402
#761332
C2×#46732
C2×#46682
C2×#46582
C2×#46522
C2×#27293