Finite Group Databasebeta

← #10731726

Subgroups — #10731726

Order 768.

3458 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#930C211yesmaximal, characteristic, complemented
2C22×C4×#67C211yesmaximal, characteristic, complemented
3C22×#895C211yesmaximal, characteristic, complemented
4C2×C3×#380C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4988C211yesmaximal, characteristic, complemented
7C2×#4960C212yesmaximal, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69426C212yesmaximal, complemented
12#15123—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×#67C2212yes—
16C23×D12C2211yescharacteristic
17C23×D12C2212yes—
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×#217C2211yescharacteristic
23C2×#930—24no—
24C2×#930—24no—
25C2×#930—24no—
26C2×C4×#67—24no—
27C2×C4×#67—24no—
28C2×C4×#67—24no—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×(C2×D3)⋊C4C2212yes—
34C22×(C2×D3)⋊C4C2212yes—
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#895—24no—
39C2×#895—24no—
40C2×#895—24no—
41C3×#380—24no—
42C2×C3×#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46#4988—24no—
47#4987—24no—
48#4960—28no—
49C22×#121—31no—
50C22×#121—31no—
51C22×C4×D4—31no—
52C2×#392—32no—
53C2×#390—31no—
54C2×#380—31no—
55C2×#380D311yescharacteristic, complemented
56#1439—32no—
57#1438—32no—
58#1438—32no—
59C4⋊#95—31no—
60C25×C3C2311yescharacteristic
61C24×D3C2312yes—
62C24×D3C2311yescharacteristic
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4D414yescomplemented
70C23×C3×C4C2312yes—
71C23×C3×C4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C22×#67—22no—
75C22×#67—22no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—24no—
79C22×#67—24no—
80C22×#67—24no—
81C22×#67—24no—
82C22×#67—22no—
83C22×#67—24no—
84C22×#67—22no—
85C22×#67—42no—
86C22×#67—42no—
87C22×#67D414yescomplemented
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2312yes—
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×D12—24no—
93C22×D12—24no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—24no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—24no—
102C22×D12—24no—
103C22×D12—42no—
104C22×D12—42no—
105C22×D12D414yescomplemented
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3D414yescomplemented
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4D414yescomplemented
119C2×C3×C22⋊C4—24no—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—42no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125#930—232no—
126C4×#67—232no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—24no—
136C2×(C2×D3)⋊C4—24no—
137C2×(C2×D3)⋊C4—24no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—42no—
143C2×(C2×D3)⋊C4—42no—
144C2×(C2×D3)⋊C4—42no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3D414yescomplemented
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3D414yescomplemented
154#895—232no—
155C3×#95—24no—
156C3⋊#95—24no—
157C3⋊#95—24no—
158C3⋊#95—42no—
159C23×D4—31no—
160C23×D4—32no—
161C23×D4—31no—
162C23×D4—32no—
163C24×C4—31no—
164C24×C4C2×D311yescharacteristic
165C2×#121—64no—
166C2×#121—64no—
167C2×#121—64no—
168C2×#121—64no—
169C2×#121—64no—
170C2×#121—64no—
171C2×C4×D4—64no—
172C2×C4×D4—64no—
173C2×C4×D4—64no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4C2×D311yescharacteristic
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C22⋊C4—31no—
179C22×C22⋊C4—32no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—32no—
182C22×C22⋊C4—32no—
183C22×C22⋊C4—32no—
184C22×C22⋊C4—32no—
185C22×C22⋊C4C2×D312yes—
186C22×C42—31no—
187#392—68no—
188#390—64no—
189#380—24no—
190#380—64no—
191C2×#95—32no—
192C2×#95—32no—
193C2×#95—32no—
194C2×#95C2×D312yes—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3C2×D412yes—
208C24×C3C2×D412yes—
209C24×C3#4112yes—
210C24×C3C2411yescharacteristic
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3C2×D414yes—
238C23×D3C2×D412yes—
239C23×D3C2×D412yes—
240C23×D3#4112yes—
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—28no—
254C22×C3×C4—28no—
255C22×C3×C4—28no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—44no—
264C22×C3×C4—44no—
265C22×C3×C4—44no—
266C22×C3×C4—44no—
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4#4112yes—
276C2×#67—28no—
277C2×#67—28no—
278C2×#67—28no—
279C2×#67—28no—
280C2×#67—28no—
281C2×#67—28no—
282C2×#67—216no—
283C2×#67—28no—
284C2×#67—48no—
285C2×#67—48no—
286C2×#67—48no—
287C2×#67—48no—
288C2×#67—48no—
289C2×#67—48no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—22no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—22no—
306C22×Dic3—21no—
307C22×Dic3—22no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—22no—
311C22×Dic3—21no—
312C22×Dic3C2×D414yes—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3#4112yes—
318C2×D12—216no—
319C2×D12—28no—
320C2×D12—28no—
321C2×D12—28no—
322C2×D12—48no—
323C2×D12—48no—
324C2×D12—48no—
325C2×D12—48no—
326C2×D12—48no—
327C2×D12—48no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—44no—
332C2×C4×D3—28no—
333C2×C4×D3—28no—
334C2×C4×D3—28no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4—44no—
341C3×C22⋊C4—48no—
342#217—28no—
343(C2×D3)⋊C4—216no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—216no—
346(C2×D3)⋊C4—48no—
347(C2×D3)⋊C4—48no—
348(C2×D3)⋊C4—48no—
349C4⋊Dic3—28no—
350Dic3⋊C4—28no—
351C4×Dic3—28no—
352C25—31no—
353C25—32no—
354C25C22×D311yescharacteristic
355C22×D4—34no—
356C22×D4—34no—
357C22×D4—64no—
358C22×D4—64no—
359C22×D4—64no—
360C22×D4—64no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—64no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—62no—
368C22×D4—64no—
369C22×D4—64no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—64no—
378C22×D4—62no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—32no—
393C23×C4—34no—
394C23×C4—62no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4D1214yescomplemented
401C23×C4C22×D312yes—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D312yes—
404C23×C4C22×D311yescharacteristic
405#121—632no—
406#121—632no—
407C4×D4—632no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4#6714yescomplemented
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—64no—
425C2×C22⋊C4—64no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—64no—
428C2×C22⋊C4—64no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—64no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4—64no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C42—34no—
445C2×C42—62no—
446C2×C42—62no—
447#95—24no—
448#95—64no—
449#95—64no—
450#95—122no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3#12114yescomplemented
486C23×C3C22×D411yescharacteristic
487C23×C3C22×D411yescharacteristic
488C23×C3C22×D411yescharacteristic
489C23×C3C22×D411yescharacteristic
490C23×C3C22×D411yescharacteristic
491C23×C3C22×D411yescharacteristic
492C23×C3C22×D411yescharacteristic
493C23×C3C2×#4111yescharacteristic
494C23×C3C2×#4111yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3H(5,𝔽2)11yescharacteristic
498C23×C3H(5,𝔽2)11yescharacteristic
499C23×C3H(5,𝔽2)11yescharacteristic
500C23×C32−1+411yescharacteristic
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—24no—
520C22×D3—24no—
521C22×D3—24no—
522C22×D3—24no—
523C22×D3—24no—
524C22×D3—24no—
525C22×D3—24no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—42no—
564C22×D3—42no—
565C22×D3—42no—
566C22×D3—42no—
567C22×D3—42no—
568C22×D3—42no—
569C22×D3—42no—
570C22×D3#12114yescomplemented
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—24no—
574C2×C3×C4—22no—
575C2×C3×C4—24no—
576C2×C3×C4—24no—
577C2×C3×C4—41no—
578C2×C3×C4—42no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—416no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4#12014yes—
594C2×C3×C4#12014yes—
595C2×C3×C4#12014yes—
596C2×C3×C4#12114yes—
597C2×C3×C4#12114yes—
598C2×C3×C4#12114yes—
599C2×C3×C4#12714yes—
600#67—232no—
601#67—432no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—24no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—24no—
616C2×Dic3—24no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—42no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—42no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—42no—
628C2×Dic3—42no—
629C2×Dic3#12114yescomplemented
630D12—432no—
631D12—416no—
632C4×D3—416no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—32no—
646C24—32no—
647C24—32no—
648C24—34no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—62no—
662C24—62no—
663C24—62no—
664C24—62no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—62no—
669C24—62no—
670C24—62no—
671C24—62no—
672C24—62no—
673C24—62no—
674C24—62no—
675C24C2×D1212yes—
676C24D3×D412yes—
677C24#23912yes—
678C24C23×D311yescharacteristic
679C2×D4—616no—
680C2×D4—68no—
681C2×D4—68no—
682C2×D4—68no—
683C2×D4—68no—
684C2×D4—68no—
685C2×D4—68no—
686C2×D4—68no—
687C2×D4—616no—
688C2×D4—68no—
689C2×D4—68no—
690C2×D4—68no—
691C2×D4—128no—
692C2×D4—128no—
693C2×D4—128no—
694C2×D4—128no—
695C2×D4—128no—
696C2×D4—128no—
697C2×D4—128no—
698C2×D4—128no—
699C2×D4—128no—
700C2×D4—128no—
701C2×D4—128no—
702C2×D4—128no—
703C2×D4—124no—
704C2×D4—124no—
705C2×D4—124no—
706C2×D4—124no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—34no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—62no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—62no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—62no—
753C22×C4—61no—
754C22×C4—62no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—62no—
758C22×C4—61no—
759C22×C4—62no—
760C22×C4—61no—
761C22×C4—68no—
762C22×C4—68no—
763C22×C4—68no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4C2×D1212yes—
769C22×C4C2×D1212yes—
770C22×C4#23512yes—
771C22×C4D3×D412yes—
772C22×C4D3×D412yes—
773C22×C4D3×D412yes—
774C22×C4D3×D412yes—
775C22×C4C2×#6714yes—
776C22×C4C2×#6712yes—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—68no—
780C4⋊C4—68no—
781C22⋊C4—48no—
782C22⋊C4—68no—
783C22⋊C4—616no—
784C22⋊C4—616no—
785C22⋊C4—68no—
786C22⋊C4—128no—
787C22⋊C4—128no—
788C22⋊C4—128no—
789C42—68no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3C2×#12011yescharacteristic
806C22×C3C2×#12011yescharacteristic
807C22×C3C2×#12011yescharacteristic
808C22×C3C2×#12111yescharacteristic
809C22×C3C2×#12111yescharacteristic
810C22×C3C2×#12111yescharacteristic
811C22×C3C2×#12111yescharacteristic
812C22×C3C2×#12111yescharacteristic
813C22×C3C2×#12111yescharacteristic
814C22×C3#52511yescharacteristic
815C22×C3#52511yescharacteristic
816C22×C3#52511yescharacteristic
817C22×C3C2×#12711yescharacteristic
818C22×C3#53511yescharacteristic
819C22×C3#53511yescharacteristic
820C22×C3#53511yescharacteristic
821C22×C3#53711yescharacteristic
822C22×C3#53711yescharacteristic
823C22×C3#53711yescharacteristic
824C22×C3D4211yescharacteristic
825C22×C3D4211yescharacteristic
826C22×C3D4211yescharacteristic
827C22×C3#54611yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#54611yescharacteristic
830C22×C3#54611yescharacteristic
831C22×C3#54711yescharacteristic
832C22×C3#54711yescharacteristic
833C22×C3#54811yescharacteristic
834C22×C3#54811yescharacteristic
835C22×C3#55011yescharacteristic
836C22×C3#55011yescharacteristic
837C22×C3#55311yescharacteristic
838C22×C3#55311yescharacteristic
839C22×C3#55511yescharacteristic
840C2×D3—24no—
841C2×D3—24no—
842C2×D3—24no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—44no—
856C2×D3—44no—
857C2×D3—44no—
858C2×D3—44no—
859C2×D3—44no—
860C2×D3—44no—
861C2×D3—44no—
862C2×D3—82no—
863C2×D3—82no—
864C2×D3—82no—
865C2×D3—82no—
866C2×D3—82no—
867C2×D3—82no—
868C2×D3—82no—
869C2×D3—82no—
870C3×C4—42no—
871C3×C4—44no—
872C3×C4—82no—
873C3×C4#39218yescomplemented
874Dic3—24no—
875Dic3—42no—
876Dic3—42no—
877Dic3—44no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—34no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—64no—
932C23—64no—
933C23—64no—
934C23—64no—
935C23—64no—
936C23—64no—
937C23—64no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—122no—
955C23—122no—
956C23—122no—
957C23—122no—
958C23—122no—
959C23—122no—
960C23—122no—
961C23—122no—
962C23—122no—
963C23—122no—
964C23—122no—
965C23—122no—
966C23—122no—
967C23—122no—
968C23—122no—
969C23—122no—
970C23—122no—
971C23—122no—
972C23—122no—
973C23—122no—
974C23—122no—
975C23—122no—
976C23—122no—
977C23—122no—
978C23—122no—
979C23—122no—
980C23—122no—
981C23—122no—
982C23#89514yescomplemented
983C23C22×D1211yescharacteristic
984C23C2×#23511yescharacteristic
985C23C2×D3×D411yescharacteristic
986C23C2×D3×D411yescharacteristic
987C23C2×D3×D411yescharacteristic
988C23C2×D3×D411yescharacteristic
989C23C2×D3×D411yescharacteristic
990C23#100411yescharacteristic
991C23C2×#23911yescharacteristic
992C23#100711yescharacteristic
993C23D3×#4111yescharacteristic
994C23D3×#4111yescharacteristic
995C23#100911yescharacteristic
996C23#100911yescharacteristic
997C23C22×#6711yescharacteristic
998D4—632no—
999D4—1232no—
1000D4—1232no—
1001D4—1216no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—34no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—416no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—64no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—64no—
1038C2×C4—62no—
1039C2×C4—64no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—122no—
1043C2×C4—121no—
1044C2×C4—122no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—122no—
1050C2×C4—121no—
1051C2×C4—122no—
1052C2×C4—1216no—
1053C2×C4#88214yes—
1054C2×C4#88214yes—
1055C2×C4#88414yes—
1056C2×C4#88414yes—
1057C2×C4#93014yes—
1058C2×C4#93714yes—
1059C2×C4#94014yes—
1060C2×C3—44no—
1061C2×C3C2×#39211yescharacteristic
1062C2×C3#240711yescharacteristic
1063C2×C3#240711yescharacteristic
1064C2×C3#240811yescharacteristic
1065C2×C3#240811yescharacteristic
1066C2×C3#241411yescharacteristic
1067C2×C3#241411yescharacteristic
1068C2×C3#241611yescharacteristic
1069C2×C3#241611yescharacteristic
1070C2×C3#253511yescharacteristic
1071C2×C3#253711yescharacteristic
1072C2×C3#254011yescharacteristic
1073C2×C3#254111yescharacteristic
1074C2×C3#261511yescharacteristic
1075C2×C3#284711yescharacteristic
1076D3—44no—
1077D3—84no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—64no—
1094C22—64no—
1095C22—64no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—124no—
1109C22—124no—
1110C22—124no—
1111C22—124no—
1112C22—124no—
1113C22—124no—
1114C22—124no—
1115C22—242no—
1116C22—242no—
1117C22—242no—
1118C22—242no—
1119C22—242no—
1120C22—242no—
1121C22—242no—
1122C22—242no—
1123C22C2×#88211yescharacteristic
1124C22C2×#88211yescharacteristic
1125C22C2×#88411yescharacteristic
1126C22C2×#88411yescharacteristic
1127C22C2×#89511yescharacteristic
1128C22#550711yescharacteristic
1129C22#551011yescharacteristic
1130C22#551411yescharacteristic
1131C22#552411yescharacteristic
1132C22#552511yescharacteristic
1133C22#553011yescharacteristic
1134C22#553211yescharacteristic
1135C22#559911yescharacteristic
1136C22D3×#12111yescharacteristic
1137C22D3×#12111yescharacteristic
1138C22#560711yescharacteristic
1139C22#560711yescharacteristic
1140C22#560911yescharacteristic
1141C22#560911yescharacteristic
1142C22#561211yescharacteristic
1143C22#562711yescharacteristic
1144C22#562711yescharacteristic
1145C22#562911yescharacteristic
1146C22#562911yescharacteristic
1147C22#563011yescharacteristic
1148C22#563011yescharacteristic
1149C22#563111yescharacteristic
1150C22#563311yescharacteristic
1151C22C2×#93011yescharacteristic
1152C22C2×#93711yescharacteristic
1153C22D4×#6711yescharacteristic
1154C22C2×#94011yescharacteristic
1155C22#581711yescharacteristic
1156C22#582911yescharacteristic
1157C22#583411yescharacteristic
1158C4—42no—
1159C4—44no—
1160C4—64no—
1161C4—82no—
1162C4—124no—
1163C4—122no—
1164C4—122no—
1165C4#496018yescomplemented
1166C3#1512311yescharacteristic, complemented, Sylow
1167C2—44no—
1168C2—124no—
1169C2—244no—
1170C2#7388711yescharacteristic
1171C2#7393311yescharacteristic
1172C2#7393511yescharacteristic
1173C2#7401511yescharacteristic
1174C2#7401611yescharacteristic
1175C2#7401911yescharacteristic
1176C2#7403011yescharacteristic
1177C2#7404811yescharacteristic
1178C2C2×#496011yescharacteristic
1179C2#8219311yescharacteristic
1180C2#8227611yescharacteristic
1181C2#8264011yescharacteristic
1182C2#8266911yescharacteristic
1183C2#8277911yescharacteristic
1184C2#8281211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
hypercenterC2×#380D3
hypocenterC3#15123
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#930C2semidirect
2. C22×C4×#67C2semidirect
3. C22×#895C2semidirect
4. C2×C3×#380C2semidirect
5. C2×#4987C2semidirect
6. C2×#4988C2semidirect
7. C2×#4960C2semidirect
8. #71563C2semidirect
9. #71550C2semidirect
10. #69428C2semidirect
11. #69426C2semidirect
55. C2×#380D3semidirect
69. C23×C3×C4D4semidirect
87. C22×#67D4semidirect
105. C22×D12D4semidirect
112. C22×C4×D3D4semidirect
118. C2×C3×C4⋊C4D4semidirect
147. C2×C4⋊Dic3D4semidirect
153. C2×C4×Dic3D4semidirect
400. C23×C4D12semidirect
419. C2×C4⋊C4#67semidirect
485. C23×C3#121semidirect
570. C22×D3#121semidirect
629. C2×Dic3#121semidirect
873. C3×C4#392semidirect
982. C23#895semidirect
1165. C4#4960semidirect
1166. C3#15123semidirect

Maximal subgroups

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

subgroupindex
C22×#9302
C22×C4×#672
C22×#8952
C2×C3×#3802
C2×#49872
C2×#49882
C2×#49602
#715632
#715502
#694282
#694262
#151233