Finite Group Databasebeta

← #10732195

Subgroups — #10732195

Order 768.

2770 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C22×C4×#67C211yesmaximal, characteristic
4C2×#5229C211yesmaximal, characteristic, complemented
5C2×#5212C211yesmaximal, characteristic, complemented
6C2×#4987C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71568C212yesmaximal, complemented
9#71563C211yesmaximal, characteristic, complemented
10#71550C212yesmaximal
11#71547C212yesmaximal, complemented
12#15177—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C2×C3×C22⋊Q8—24no—
18C2×C3×C22⋊Q8—24no—
19C2×C3×C22⋊Q8—24no—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×#217C2211yescharacteristic
24C22×#217C2212yes—
25C2×#946—24no—
26C2×#946—24no—
27C2×#946—24no—
28C2×C4×#67—24no—
29C2×C4×#67—24no—
30C2×C4×#67—24no—
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2212yes—
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2212yes—
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39#5229—24no—
40#5212—24no—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46C2×C3⋊#95C2212yes—
47#4987—24no—
48C22×C22⋊Q8—31no—
49C22×C22⋊Q8D311yescharacteristic, complemented
50C22×C4×D4—31no—
51C2×#391—31no—
52C2×#380—31no—
53C2×#380—31no—
54#1444—32no—
55#1439—32no—
56#1439—32no—
57#1438—32no—
58C4⋊#95—31no—
59C25×C3C2311yescharacteristic
60C24×D3C2311yescharacteristic
61C22×C3×Q8—22no—
62C22×C3×Q8—22no—
63C22×C3×Q8—22no—
64C22×C3×Q8—22no—
65C22×C3×Q8—22no—
66C22×C3×Q8—22no—
67C22×C3×Q8D414yescomplemented
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4D414yes—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2312yes—
77C23×C3×C4C2312yes—
78C23×C3×C4C2311yescharacteristic
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67Q814yescomplemented
86C23×Dic3C2312yes—
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2312yes—
90C23×Dic3C2311yescharacteristic
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3D414yes—
98C3×C22⋊Q8—232no—
99C2×C3×C4⋊C4—24no—
100C2×C3×C4⋊C4—24no—
101C2×C3×C4⋊C4—24no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4D414yescomplemented
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—24no—
112C2×#217—24no—
113C2×#217—42no—
114#946—232no—
115C4×#67—232no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—42no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3D414yescomplemented
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—24no—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3D414yes—
140C3⋊#95—24no—
141C3⋊#95—24no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—24no—
145C3⋊#95—42no—
146C23×Q8C2×D311yescharacteristic
147C23×D4—31no—
148C24×C4—31no—
149C24×C4C2×D311yescharacteristic
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—64no—
154C2×C22⋊Q8—64no—
155C2×C22⋊Q8—64no—
156C2×C4×D4—64no—
157C2×C4×D4—64no—
158C2×C4×D4—64no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—32no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4C2×D312yes—
164C22×C4⋊C4C2×D311yescharacteristic
165C22×C22⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—32no—
168C22×C22⋊C4—32no—
169C22×C22⋊C4—32no—
170C22×C22⋊C4C2×D312yes—
171C22×C42—31no—
172#391—64no—
173#380—64no—
174#380—64no—
175C2×#95—32no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C2×#95—32no—
180C2×#95—32no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3C2×D412yes—
194C24×C3C2×Q812yes—
195C24×C3#4112yes—
196C24×C3C2411yescharacteristic
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3C2×D412yes—
210C23×D3C2×Q812yes—
211C23×D3#4112yes—
212C2×C3×Q8—28no—
213C2×C3×Q8—28no—
214C2×C3×Q8—28no—
215C2×C3×Q8—44no—
216C2×C3×Q8—44no—
217C2×C3×Q8—44no—
218C2×C3×Q8—44no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—28no—
238C22×C3×C4—28no—
239C22×C3×C4—28no—
240C22×C3×C4—44no—
241C22×C3×C4—44no—
242C22×C3×C4—44no—
243C22×C3×C4—44no—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4#4112yes—
254C2×#67—28no—
255C2×#67—28no—
256C2×#67—28no—
257C2×#67—28no—
258C2×#67—28no—
259C2×#67—28no—
260C2×#67—28no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—22no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—22no—
282C22×Dic3—21no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3C2×D412yes—
291C22×Dic3C2×D414yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×Q812yes—
295C22×Dic3#4112yes—
296C2×C4×D3—28no—
297C2×C4×D3—28no—
298C2×C4×D3—28no—
299C2×C4×D3—44no—
300C2×C4×D3—44no—
301C2×C4×D3—44no—
302C2×C4×D3—44no—
303C3×C4⋊C4—216no—
304C3×C4⋊C4—28no—
305C3×C22⋊C4—216no—
306#217—28no—
307#217—48no—
308(C2×D3)⋊C4—28no—
309(C2×D3)⋊C4—216no—
310(C2×D3)⋊C4—48no—
311C4⋊Dic3—28no—
312C4⋊Dic3—44no—
313Dic3⋊C4—28no—
314Dic3⋊C4—216no—
315C4×Dic3—28no—
316C25—31no—
317C25C22×D311yescharacteristic
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8#6714yescomplemented
325C22×D4—34no—
326C22×D4—62no—
327C22×D4—62no—
328C22×D4—62no—
329C22×D4—62no—
330C22×D4—62no—
331C22×D4—62no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—31no—
339C23×C4—32no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—34no—
343C23×C4—32no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—62no—
349C23×C4—62no—
350C23×C4#6714yes—
351C23×C4C22×D312yes—
352C23×C4C22×D312yes—
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C22⋊Q8—232no—
356C22⋊Q8—632no—
357C4×D4—632no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—34no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—64no—
367C2×C4⋊C4—64no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4#6714yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—64no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—122no—
393C2×C22⋊C4—122no—
394C2×C42—34no—
395C2×C42—62no—
396C2×C42—62no—
397#95—64no—
398#95—64no—
399#95—64no—
400#95—64no—
401#95—64no—
402#95—122no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3C22⋊Q814yescomplemented
438C23×C3C22×D411yescharacteristic
439C23×C3C22×D411yescharacteristic
440C23×C3C22×D411yescharacteristic
441C23×C3C22×D411yescharacteristic
442C23×C3C22×D411yescharacteristic
443C23×C3C22×D411yescharacteristic
444C23×C3C22×Q811yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3H(5,𝔽2)11yescharacteristic
450C23×C32−1+411yescharacteristic
451C23×C32−1+411yescharacteristic
452C23×C32−1+411yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3C22⋊Q814yescomplemented
488C3×Q8—416no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—41no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—416no—
511C2×C3×C4#12014yes—
512C2×C3×C4#12014yes—
513C2×C3×C4#12014yes—
514C2×C3×C4#12114yes—
515C2×C3×C4#12114yes—
516C2×C3×C4#12114yes—
517C2×C3×C4#12714yes—
518#67—232no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—24no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—42no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—42no—
544C2×Dic3—42no—
545C2×Dic3—42no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3—42no—
550C2×Dic3—42no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3C22⋊Q814yescomplemented
554C4×D3—416no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—32no—
568C24—32no—
569C24—32no—
570C24—61no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—61no—
575C24—61no—
576C24—61no—
577C24—61no—
578C24—61no—
579C24—61no—
580C24—61no—
581C24—61no—
582C24D3×Q812yes—
583C24#23912yes—
584C24C2×#6712yes—
585C24C23×D311yescharacteristic
586C2×Q8—28no—
587C2×Q8—28no—
588C2×Q8—28no—
589C2×Q8—44no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×D4—68no—
594C2×D4—68no—
595C2×D4—68no—
596C2×D4—68no—
597C2×D4—68no—
598C2×D4—68no—
599C2×D4—68no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—34no—
626C22×C4—32no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—62no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—62no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—62no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—62no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—68no—
654C22×C4—68no—
655C22×C4—68no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—124no—
664C22×C4—124no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4D3×D412yes—
668C22×C4D3×D412yes—
669C22×C4D3×D412yes—
670C22×C4#23712yes—
671C22×C4C2×#6714yes—
672C22×C4C2×#6714yes—
673C22×C4C2×#6712yes—
674C22×C4C2×#6712yes—
675C22×C4C2×#6712yes—
676C22×C4C2×#6712yes—
677C4⋊C4—216no—
678C4⋊C4—28no—
679C4⋊C4—68no—
680C4⋊C4—616no—
681C4⋊C4—68no—
682C4⋊C4—124no—
683C22⋊C4—216no—
684C22⋊C4—68no—
685C22⋊C4—616no—
686C22⋊C4—68no—
687C22⋊C4—128no—
688C22⋊C4—128no—
689C42—68no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—24no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3C2×#12011yescharacteristic
706C22×C3C2×#12011yescharacteristic
707C22×C3C2×#12011yescharacteristic
708C22×C3C2×#12111yescharacteristic
709C22×C3C2×#12111yescharacteristic
710C22×C3C2×#12111yescharacteristic
711C22×C3C2×C22⋊Q811yescharacteristic
712C22×C3C2×C22⋊Q811yescharacteristic
713C22×C3C2×C22⋊Q811yescharacteristic
714C22×C3#52511yescharacteristic
715C22×C3#52511yescharacteristic
716C22×C3#52511yescharacteristic
717C22×C3C2×#12711yescharacteristic
718C22×C3#53611yescharacteristic
719C22×C3#53611yescharacteristic
720C22×C3#53611yescharacteristic
721C22×C3#53711yescharacteristic
722C22×C3#53711yescharacteristic
723C22×C3#53711yescharacteristic
724C22×C3#54611yescharacteristic
725C22×C3#54611yescharacteristic
726C22×C3#54711yescharacteristic
727C22×C3#54711yescharacteristic
728C22×C3#54811yescharacteristic
729C22×C3#54811yescharacteristic
730C22×C3#54811yescharacteristic
731C22×C3#54811yescharacteristic
732C22×C3D4×Q811yescharacteristic
733C22×C3D4×Q811yescharacteristic
734C22×C3D4×Q811yescharacteristic
735C22×C3#55011yescharacteristic
736C22×C3#55211yescharacteristic
737C22×C3#55211yescharacteristic
738C22×C3#55411yescharacteristic
739C22×C3#55611yescharacteristic
740C2×D3—24no—
741C2×D3—24no—
742C2×D3—24no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—42no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C3×C4—42no—
756C3×C4—44no—
757C3×C4—44no—
758C3×C4#39218yes—
759Dic3—24no—
760Dic3—42no—
761Dic3—42no—
762Dic3—44no—
763Dic3—82no—
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—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—34no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—121no—
818C23—121no—
819C23—121no—
820C23—121no—
821C23—121no—
822C23—121no—
823C23—121no—
824C23—121no—
825C23—121no—
826C23—121no—
827C23—121no—
828C23—121no—
829C23—121no—
830C23—121no—
831C23—121no—
832C23—121no—
833C23#94614yescomplemented
834C23C2×D3×D411yescharacteristic
835C23C2×D3×D411yescharacteristic
836C23C2×D3×D411yescharacteristic
837C23C2×#23711yescharacteristic
838C23C2×D3×Q811yescharacteristic
839C23C2×#23911yescharacteristic
840C23#100711yescharacteristic
841C23#100711yescharacteristic
842C23D3×#4111yescharacteristic
843C23D3×#4111yescharacteristic
844C23#100911yescharacteristic
845C23#101011yescharacteristic
846C23C22×#6711yescharacteristic
847C23C22×#6711yescharacteristic
848C23C22×#6711yescharacteristic
849Q8—416no—
850D4—632no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—34no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—416no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—64no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—64no—
888C2×C4—64no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4—121no—
893C2×C4—122no—
894C2×C4—121no—
895C2×C4—122no—
896C2×C4—121no—
897C2×C4—122no—
898C2×C4—121no—
899C2×C4—122no—
900C2×C4—121no—
901C2×C4—1216no—
902C2×C4—122no—
903C2×C4—122no—
904C2×C4—122no—
905C2×C4—122no—
906C2×C4—122no—
907C2×C4—122no—
908C2×C4—122no—
909C2×C4#93714yes—
910C2×C4#93714yes—
911C2×C4#93814yes—
912C2×C4#93914yes—
913C2×C4#93914yes—
914C2×C4#94014yes—
915C2×C4#95314yes—
916C2×C3—44no—
917C2×C3C2×#39211yescharacteristic
918C2×C3#240711yescharacteristic
919C2×C3#240711yescharacteristic
920C2×C3#240911yescharacteristic
921C2×C3#240911yescharacteristic
922C2×C3#241511yescharacteristic
923C2×C3#241511yescharacteristic
924C2×C3#241711yescharacteristic
925C2×C3#241711yescharacteristic
926C2×C3#253611yescharacteristic
927C2×C3#253811yescharacteristic
928C2×C3#254011yescharacteristic
929C2×C3#254211yescharacteristic
930C2×C3#261611yescharacteristic
931C2×C3#284811yescharacteristic
932D3—44no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—64no—
949C22—64no—
950C22—64no—
951C22—122no—
952C22—122no—
953C22—122no—
954C22—122no—
955C22—122no—
956C22—122no—
957C22—122no—
958C22—122no—
959C22—122no—
960C22—122no—
961C22—122no—
962C22—122no—
963C22D3×C22⋊Q811yescharacteristic
964C22D3×C22⋊Q811yescharacteristic
965C22#562711yescharacteristic
966C22#562711yescharacteristic
967C22#562811yescharacteristic
968C22#562811yescharacteristic
969C22#562911yescharacteristic
970C22#562911yescharacteristic
971C22#563011yescharacteristic
972C22#563111yescharacteristic
973C22#563211yescharacteristic
974C22#563311yescharacteristic
975C22#563511yescharacteristic
976C22#563911yescharacteristic
977C22#564111yescharacteristic
978C22#564211yescharacteristic
979C22C2×#93711yescharacteristic
980C22C2×#93711yescharacteristic
981C22C2×#93811yescharacteristic
982C22C2×#93911yescharacteristic
983C22C2×#93911yescharacteristic
984C22C2×#94011yescharacteristic
985C22C2×#94611yescharacteristic
986C22Q8×#6711yescharacteristic
987C22Q8×#6711yescharacteristic
988C22#581611yescharacteristic
989C22#581711yescharacteristic
990C22#581711yescharacteristic
991C22#582411yescharacteristic
992C22#582811yescharacteristic
993C22#582911yescharacteristic
994C22#583111yescharacteristic
995C22#583311yescharacteristic
996C22#583411yescharacteristic
997C22C2×#95311yescharacteristic
998C4—42no—
999C4—44no—
1000C4—44no—
1001C4—64no—
1002C4—122no—
1003C4—124no—
1004C4—122no—
1005C4—242no—
1006C4#522318yes—
1007C3#1517711yescharacteristic, complemented, Sylow
1008C2—44no—
1009C2—124no—
1010C2#8275111yescharacteristic
1011C2#8275211yescharacteristic
1012C2#8277711yescharacteristic
1013C2#8277811yescharacteristic
1014C2#8277911yescharacteristic
1015C2#8278011yescharacteristic
1016C2#8281211yescharacteristic
1017C2#8281311yescharacteristic
1018C2#8281411yescharacteristic
1019C2#8281511yescharacteristic
1020C2#8282011yescharacteristic
1021C2#8283411yescharacteristic
1022C2C2×#522311yescharacteristic
1023C2#8406811yescharacteristic
1024C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#15177
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#946C2semidirect
4. C2×#5229C2semidirect
5. C2×#5212C2semidirect
6. C2×#4987C2semidirect
7. #71570C2semidirect
8. #71568C2semidirect
9. #71563C2semidirect
11. #71547C2semidirect
49. C22×C22⋊Q8D3semidirect
67. C22×C3×Q8D4semidirect
85. C22×#67Q8semidirect
104. C2×C3×C4⋊C4D4semidirect
130. C2×C4⋊Dic3D4semidirect
324. C22×Q8#67semidirect
375. C2×C4⋊C4#67semidirect
437. C23×C3C22⋊Q8semidirect
487. C22×D3C22⋊Q8semidirect
553. C2×Dic3C22⋊Q8semidirect
833. C23#946semidirect
1007. C3#15177semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9462
C22×C4×#672
C2×#52292
C2×#52122
C2×#49872
#715702
#715682
#715632
#715502
#715472
#151773