Finite Group Databasebeta

← #10732200

Subgroups — #10732200

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×#924C211yesmaximal, characteristic, complemented
2C22×C4×#67C211yesmaximal, characteristic
3C22×#897C211yesmaximal, characteristic, complemented
4C2×C3×#380C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4973C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal
9#71546C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69420C212yesmaximal, complemented
12#15177—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×#217C2211yescharacteristic
21C22×#217C2212yes—
22C2×C4×#67—24no—
23C2×C4×#67—24no—
24C2×C4×#67—24no—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×C4⋊Dic3C2212yes—
29C22×C4⋊Dic3C2211yescharacteristic
30C2×#924—24no—
31C2×#924—24no—
32C2×#924—24no—
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2212yes—
35C22×C4×Dic3C2211yescharacteristic
36C2×#897—24no—
37C2×#897—24no—
38C2×#897—24no—
39C3×#380—24no—
40C2×C3×#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46#4987—24no—
47#4973—24no—
48C22×C22⋊Q8—31no—
49C22×C22⋊Q8—31no—
50C22×C4×D4—31no—
51C2×#391—31no—
52C2×#380—31no—
53C2×#380D311yescharacteristic, complemented
54#1444—32no—
55#1439—32no—
56#1439—32no—
57#1438—32no—
58C4⋊#95—31no—
59C25×C3C2311yescharacteristic
60C24×D3C2311yescharacteristic
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4D414yes—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2312yes—
71C23×C3×C4C2311yescharacteristic
72C22×#67—22no—
73C22×#67—22no—
74C22×#67—22no—
75C22×#67—22no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67Q814yescomplemented
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2312yes—
83C23×Dic3C2311yescharacteristic
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3D414yes—
91C22×Dic6—22no—
92C22×Dic6—22no—
93C22×Dic6—22no—
94C22×Dic6—22no—
95C22×Dic6—22no—
96C22×Dic6—22no—
97C22×Dic6D414yescomplemented
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4D414yescomplemented
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—42no—
107C2×#217—24no—
108C2×#217—22no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—22no—
112C2×#217—22no—
113C4×#67—232no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—42no—
123C2×C4⋊Dic3—24no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3—24no—
127C2×C4⋊Dic3—24no—
128C2×C4⋊Dic3D414yescomplemented
129#924—232no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3—22no—
138C2×C4×Dic3D414yes—
139#897—232no—
140C3×#95—24no—
141C3⋊#95—24no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—24no—
145C3⋊#95—42no—
146C23×Q8—31no—
147C23×D4—31no—
148C24×C4—31no—
149C24×C4C2×D311yescharacteristic
150C2×C22⋊Q8—64no—
151C2×C22⋊Q8—64no—
152C2×C22⋊Q8—64no—
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—32no—
163C22×C4⋊C4C2×D311yescharacteristic
164C22×C4⋊C4C2×D311yescharacteristic
165C22×C22⋊C4—31no—
166C22×C22⋊C4—32no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—32no—
169C22×C22⋊C4—32no—
170C22×C22⋊C4C2×D312yes—
171C22×C42—31no—
172#391—64no—
173#380—24no—
174#380—64no—
175C2×#95—32no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C2×#95—32no—
180C2×#95C2×D312yes—
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—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—28no—
225C22×C3×C4—28no—
226C22×C3×C4—28no—
227C22×C3×C4—22no—
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—44no—
235C22×C3×C4—44no—
236C22×C3×C4—44no—
237C22×C3×C4—44no—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4#4112yes—
247C2×#67—28no—
248C2×#67—28no—
249C2×#67—28no—
250C2×#67—28no—
251C2×#67—28no—
252C2×#67—28no—
253C2×#67—28no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—22no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—22no—
278C22×Dic3—21no—
279C22×Dic3—22no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3C2×D412yes—
283C22×Dic3C2×D414yes—
284C22×Dic3C2×D412yes—
285C22×Dic3C2×D414yes—
286C22×Dic3C2×D412yes—
287C22×Dic3C2×Q812yes—
288C22×Dic3#4112yes—
289C2×C4×D3—28no—
290C2×C4×D3—28no—
291C2×C4×D3—28no—
292C2×C4×D3—44no—
293C2×C4×D3—44no—
294C2×C4×D3—44no—
295C2×C4×D3—44no—
296C2×Dic6—28no—
297C2×Dic6—28no—
298C2×Dic6—28no—
299C2×Dic6—44no—
300C2×Dic6—44no—
301C2×Dic6—44no—
302C2×Dic6—44no—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—44no—
305C3×C22⋊C4—48no—
306#217—216no—
307#217—28no—
308(C2×D3)⋊C4—216no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—48no—
311C4⋊Dic3—216no—
312C4⋊Dic3—28no—
313Dic3⋊C4—216no—
314Dic3⋊C4—28no—
315C4×Dic3—28no—
316C25—31no—
317C25C22×D311yescharacteristic
318C22×Q8—34no—
319C22×Q8—62no—
320C22×Q8—62no—
321C22×Q8—62no—
322C22×Q8—62no—
323C22×Q8—62no—
324C22×Q8—62no—
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—32no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—34no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—62no—
349C23×C4—62no—
350C23×C4D1214yes—
351C23×C4C22×D312yes—
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D312yes—
354C23×C4C22×D311yescharacteristic
355C22⋊Q8—632no—
356C22⋊Q8—632no—
357C4×D4—632no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
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—64no—
369C2×C4⋊C4—64no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—64no—
375C2×C4⋊C4#6714yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—42no—
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—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—64no—
393C2×C22⋊C4—122no—
394C2×C42—34no—
395C2×C42—62no—
396C2×C42—62no—
397#95—24no—
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
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—416no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4#12014yes—
511C2×C3×C4#12014yes—
512C2×C3×C4#12014yes—
513C2×C3×C4#12114yes—
514C2×C3×C4#12114yes—
515C2×C3×C4#12114yes—
516C2×C3×C4#12714yes—
517#67—232no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—24no—
526C2×Dic3—24no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—24no—
530C2×Dic3—24no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—24no—
535C2×Dic3—24no—
536C2×Dic3—42no—
537C2×Dic3—41no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—42no—
549C2×Dic3—41no—
550C2×Dic3—42no—
551C2×Dic3—42no—
552C2×Dic3C22⋊Q814yescomplemented
553C4×D3—416no—
554Dic6—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—
582C24C2×D1212yes—
583C24#23712yes—
584C24D3×Q812yes—
585C24C23×D311yescharacteristic
586C2×Q8—68no—
587C2×Q8—68no—
588C2×Q8—68no—
589C2×Q8—124no—
590C2×Q8—124no—
591C2×Q8—124no—
592C2×Q8—124no—
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—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—32no—
626C22×C4—34no—
627C22×C4—34no—
628C22×C4—32no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—62no—
639C22×C4—61no—
640C22×C4—62no—
641C22×C4—61no—
642C22×C4—62no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—62no—
647C22×C4—61no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—62no—
653C22×C4—61no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—62no—
660C22×C4—61no—
661C22×C4—68no—
662C22×C4—68no—
663C22×C4—68no—
664C22×C4—124no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4—124no—
668C22×C4C2×D1212yes—
669C22×C4C2×D1212yes—
670C22×C4#23512yes—
671C22×C4D3×D412yes—
672C22×C4D3×D412yes—
673C22×C4D3×D412yes—
674C22×C4D3×D412yes—
675C22×C4C2×#6714yes—
676C22×C4C2×#6712yes—
677C4⋊C4—28no—
678C4⋊C4—44no—
679C4⋊C4—68no—
680C4⋊C4—616no—
681C4⋊C4—616no—
682C4⋊C4—68no—
683C22⋊C4—48no—
684C22⋊C4—68no—
685C22⋊C4—616no—
686C22⋊C4—68no—
687C22⋊C4—616no—
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—82no—
758C3×C4#39218yes—
759Dic3—24no—
760Dic3—42no—
761Dic3—44no—
762Dic3—42no—
763Dic3—44no—
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#89714yescomplemented
834C23C22×D1211yescharacteristic
835C23C2×#23511yescharacteristic
836C23C2×D3×D411yescharacteristic
837C23C2×D3×D411yescharacteristic
838C23C2×D3×D411yescharacteristic
839C23C2×D3×D411yescharacteristic
840C23C2×#23711yescharacteristic
841C23#100411yescharacteristic
842C23C2×D3×Q811yescharacteristic
843C23#100711yescharacteristic
844C23D3×#4111yescharacteristic
845C23D3×#4111yescharacteristic
846C23#101011yescharacteristic
847C23#101011yescharacteristic
848C23C22×#6711yescharacteristic
849Q8—1216no—
850D4—632no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—34no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—416no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
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—64no—
884C2×C4—62no—
885C2×C4—64no—
886C2×C4—64no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—64no—
890C2×C4—62no—
891C2×C4—64no—
892C2×C4—122no—
893C2×C4—121no—
894C2×C4—122no—
895C2×C4—121no—
896C2×C4—122no—
897C2×C4—122no—
898C2×C4—121no—
899C2×C4—122no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—122no—
903C2×C4—121no—
904C2×C4—122no—
905C2×C4—122no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—1216no—
909C2×C4#88214yes—
910C2×C4#88214yes—
911C2×C4#88414yes—
912C2×C4#88414yes—
913C2×C4#93014yes—
914C2×C4#93714yes—
915C2×C4#94014yes—
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—
963C22C2×#88211yescharacteristic
964C22C2×#88211yescharacteristic
965C22C2×#88411yescharacteristic
966C22C2×#88411yescharacteristic
967C22C2×#89711yescharacteristic
968C22#551011yescharacteristic
969C22#551111yescharacteristic
970C22#551311yescharacteristic
971C22#552411yescharacteristic
972C22#552611yescharacteristic
973C22#552911yescharacteristic
974C22#553311yescharacteristic
975C22#559811yescharacteristic
976C22#559811yescharacteristic
977C22#559911yescharacteristic
978C22#560611yescharacteristic
979C22#560611yescharacteristic
980C22#560811yescharacteristic
981C22#560811yescharacteristic
982C22#561211yescharacteristic
983C22D3×C22⋊Q811yescharacteristic
984C22D3×C22⋊Q811yescharacteristic
985C22#562811yescharacteristic
986C22#562811yescharacteristic
987C22#563111yescharacteristic
988C22#563211yescharacteristic
989C22#563211yescharacteristic
990C22#563311yescharacteristic
991C22C2×#93011yescharacteristic
992C22C2×#93711yescharacteristic
993C22C2×#94011yescharacteristic
994C22#580611yescharacteristic
995C22Q8×#6711yescharacteristic
996C22#582411yescharacteristic
997C22#583111yescharacteristic
998C4—44no—
999C4—42no—
1000C4—64no—
1001C4—82no—
1002C4—124no—
1003C4—122no—
1004C4—124no—
1005C4—122no—
1006C4#496018yes—
1007C3#1517711yescharacteristic, complemented, Sylow
1008C2—44no—
1009C2—124no—
1010C2#7388811yescharacteristic
1011C2#7393411yescharacteristic
1012C2#7393611yescharacteristic
1013C2#7395011yescharacteristic
1014C2#7401511yescharacteristic
1015C2#7401711yescharacteristic
1016C2#7402011yescharacteristic
1017C2#7404911yescharacteristic
1018C2C2×#496011yescharacteristic
1019C2#8219411yescharacteristic
1020C2#8227711yescharacteristic
1021C2#8266811yescharacteristic
1022C2#8270111yescharacteristic
1023C2#8275111yescharacteristic
1024C2#8278011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC23×#67C22
hypercenterC2×#380D3
hypocenterC3#15177
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#924C2semidirect
3. C22×#897C2semidirect
4. C2×C3×#380C2semidirect
5. C2×#4987C2semidirect
6. C2×#4973C2semidirect
7. #71563C2semidirect
9. #71546C2semidirect
10. #69428C2semidirect
11. #69420C2semidirect
53. C2×#380D3semidirect
78. C22×#67Q8semidirect
97. C22×Dic6D4semidirect
103. C2×C3×C4⋊C4D4semidirect
128. C2×C4⋊Dic3D4semidirect
375. C2×C4⋊C4#67semidirect
437. C23×C3C22⋊Q8semidirect
487. C22×D3C22⋊Q8semidirect
552. C2×Dic3C22⋊Q8semidirect
833. C23#897semidirect
1007. C3#15177semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C22×C4×#672
C22×#8972
C2×C3×#3802
C2×#49872
C2×#49732
#715632
#715502
#715462
#694282
#694202
#151773