Finite Group Databasebeta

← #10720173

Subgroups — #10720173

Order 768.

2634 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#886C211yesmaximal, characteristic
2C22×#877C211yesmaximal, characteristic, complemented
3C2×#5213C211yesmaximal, characteristic
4C22×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#4958C211yesmaximal, characteristic
6C3×C22⋊#95C211yesmaximal, characteristic, complemented
7#71544C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69411C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11#69407C212yesmaximal, complemented
12#14135—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×C4×Dic3C2212yes—
28C2×#886—24no—
29C2×#886—24no—
30C2×#886C418yescomplemented
31C2×#877—24no—
32C2×#877—24no—
33C2×#877—24no—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36#5213—24no—
37C2×C3⋊#95—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44#4958—24no—
45C22×#123—31no—
46C22×#117—31no—
47C2×#386—31no—
48C2×#386—31no—
49C22×#95—31no—
50#1441—32no—
51#1439—32no—
52#1437—32no—
53#1436—32no—
54C22⋊#95—31no—
55C22⋊#95D311yescharacteristic, complemented
56C25×C3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C23×C3×C4—22no—
59C23×C3×C4—24no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—42no—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2312yes—
67C22×#67—22no—
68C22×#67—22no—
69C22×#67—22no—
70C22×#67—22no—
71C22×#67—22no—
72C22×#67—22no—
73C22×#67C2×C414yes—
74C23×Dic3—22no—
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—24no—
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—42no—
83C23×Dic3C2×C414yes—
84C23×Dic3D414yes—
85C23×Dic3D414yes—
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4C2×C414yes—
96C2×C3×C22⋊C4D414yes—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217D414yes—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4C2×C414yescomplemented
111C2×(C2×D3)⋊C4C2×C414yescomplemented
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3C2×C414yescomplemented
117C2×C4⋊Dic3C2×C414yescomplemented
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—24no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3—24no—
123C2×C4×Dic3—24no—
124#886—232no—
125#877—232no—
126C3×#95—24no—
127C3×#95—42no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—42no—
134C23×D4—31no—
135C24×C4—31no—
136C24×C4—31no—
137C24×C4C2×D311yescharacteristic
138C2×#123—38no—
139C2×#123—64no—
140C2×#123—64no—
141C2×#117—64no—
142C2×#117—64no—
143C2×#117—64no—
144C22×C4⋊C4—31no—
145C22×C4⋊C4—31no—
146C22×C4⋊C4—32no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4C2×D311yescharacteristic
153C22×C22⋊C4C2×D311yescharacteristic
154C22×C42—32no—
155#386—64no—
156#386—64no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—64no—
164C2×#95C2×D312yes—
165C2×#95C2×D312yes—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3C22×C412yes—
171C24×C3C2×D412yes—
172C24×C3C2×D412yes—
173C24×C3C2×D412yes—
174C24×C3C2×D412yes—
175C24×C3#4112yes—
176C24×C3#4112yes—
177C24×C3C2411yescharacteristic
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3C22×C412yes—
189C22×C3×C4—28no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—48no—
211C22×C3×C4—48no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C22×C412yes—
216C22×C3×C4C2×D414yes—
217C22×C3×C4#4114yes—
218C2×#67—28no—
219C2×#67—28no—
220C2×#67—28no—
221C2×#67—44no—
222C2×#67—44no—
223C2×#67—44no—
224C2×#67—44no—
225C22×Dic3—28no—
226C22×Dic3—28no—
227C22×Dic3—28no—
228C22×Dic3—28no—
229C22×Dic3—28no—
230C22×Dic3—28no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—28no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—48no—
259C22×Dic3—48no—
260C22×Dic3—44no—
261C22×Dic3—44no—
262C22×Dic3C22⋊C4116yescomplemented
263C22×Dic3C22×C412yes—
264C22×Dic3C22×C412yes—
265C22×Dic3C22×C412yes—
266C22×Dic3C2×D414yes—
267C22×Dic3C2×D412yes—
268C22×Dic3C2×D412yes—
269C22×Dic3C2×D412yes—
270C22×Dic3C2×D412yes—
271C22×Dic3#4114yes—
272C3×C22⋊C4—28no—
273C3×C22⋊C4—28no—
274#217—28no—
275(C2×D3)⋊C4—28no—
276(C2×D3)⋊C4—28no—
277(C2×D3)⋊C4—48no—
278(C2×D3)⋊C4—48no—
279C4⋊Dic3—28no—
280C4⋊Dic3—28no—
281Dic3⋊C4—216no—
282C4×Dic3—216no—
283C25—31no—
284C25C22×D311yescharacteristic
285C22×D4—34no—
286C22×D4—62no—
287C22×D4—62no—
288C22×D4—62no—
289C22×D4—62no—
290C22×D4—62no—
291C22×D4—62no—
292C23×C4—22no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—34no—
297C23×C4—34no—
298C23×C4—34no—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—32no—
302C23×C4—32no—
303C23×C4—31no—
304C23×C4—42no—
305C23×C4—64no—
306C23×C4—62no—
307C23×C4—62no—
308C23×C4—62no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—62no—
313C23×C4—122no—
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D312yes—
317C23×C4C22×D312yes—
318#123—632no—
319#117—632no—
320C2×C4⋊C4—34no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—64no—
323C2×C4⋊C4—64no—
324C2×C4⋊C4—62no—
325C2×C4⋊C4—62no—
326C2×C4⋊C4—62no—
327C2×C4⋊C4—62no—
328C2×C4⋊C4—64no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—34no—
334C2×C22⋊C4—34no—
335C2×C22⋊C4—34no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4—62no—
341C2×C22⋊C4—62no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—122no—
347C2×C22⋊C4—122no—
348C2×C22⋊C4C4×D314yes—
349C2×C22⋊C4D1214yes—
350C2×C42—64no—
351C2×C42—64no—
352C2×C42—64no—
353#95—24no—
354#95—42no—
355#95—64no—
356#95—64no—
357#95—64no—
358#95—64no—
359#95—64no—
360#95—122no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3C2×C22⋊C414yes—
378C23×C3C4×D414yes—
379C23×C3C4×D414yes—
380C23×C3#12014yes—
381C23×C3#12114yes—
382C23×C3#12114yes—
383C23×C3#12314yes—
384C23×C3C23×C411yescharacteristic
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4112yes—
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4112yes—
393C23×C3H(5,𝔽2)12yes—
394C23×C32−1+412yes—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—42no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—416no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—42no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443#67—416no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—232no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—24no—
465C2×Dic3—24no—
466C2×Dic3—416no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—42no—
477C2×Dic3—42no—
478C2×Dic3—42no—
479C2×Dic3C2×C22⋊C414yes—
480C2×Dic3C2×C22⋊C414yes—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—32no—
486C24—61no—
487C24—61no—
488C24—61no—
489C24—61no—
490C24—61no—
491C24—62no—
492C24—62no—
493C24—61no—
494C24—62no—
495C24—62no—
496C24C2×C4×D312yes—
497C24C2×D1212yes—
498C24#23512yes—
499C24D3×D412yes—
500C24D3×D412yes—
501C24D3×D412yes—
502C24#23912yes—
503C24C23×D311yescharacteristic
504C2×D4—68no—
505C2×D4—68no—
506C2×D4—68no—
507C2×D4—124no—
508C2×D4—124no—
509C2×D4—124no—
510C2×D4—124no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—316no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—68no—
547C22×C4—68no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—68no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—68no—
561C22×C4—61no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—61no—
565C22×C4—62no—
566C22×C4—61no—
567C22×C4—62no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—61no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—128no—
580C22×C4—128no—
581C22×C4—124no—
582C22×C4—124no—
583C22×C4C2×C4×D312yes—
584C22×C4C2×C4×D312yes—
585C22×C4C2×D1214yes—
586C22×C4#23714yes—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—616no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—68no—
593C22⋊C4—68no—
594C22⋊C4—68no—
595C22⋊C4—128no—
596C22⋊C4—128no—
597C42—616no—
598C22×C3—24no—
599C22×C3—28no—
600C22×C3—28no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—28no—
606C22×C3—28no—
607C22×C3—24no—
608C22×C3#38618yes—
609C22×C3C22×C22⋊C411yescharacteristic
610C22×C3C2×C4×D411yescharacteristic
611C22×C3C2×C4×D411yescharacteristic
612C22×C3C4×#4112yes—
613C22×C3#52012yes—
614C22×C3C2×#12011yescharacteristic
615C22×C3C2×#12111yescharacteristic
616C22×C3C2×#12111yescharacteristic
617C22×C3C2×#12311yescharacteristic
618C22×C3#52511yescharacteristic
619C22×C3#52511yescharacteristic
620C22×C3#53212yes—
621C22×C3#53511yescharacteristic
622C22×C3#53611yescharacteristic
623C22×C3#53712yes—
624C22×C3#54612yes—
625C22×C3#54612yes—
626C22×C3#54712yes—
627C22×C3#54712yes—
628C22×C3#55112yes—
629C22×C3#55112yes—
630C22×C3#55212yes—
631C22×C3#55212yes—
632C2×D3—42no—
633C2×D3—44no—
634C2×D3—44no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—82no—
642C2×D3—82no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—44no—
646C3×C4—42no—
647Dic3—24no—
648Dic3—24no—
649Dic3—44no—
650Dic3—44no—
651Dic3—42no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—64no—
672C23—64no—
673C23—122no—
674C23—122no—
675C23—121no—
676C23—122no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—122no—
681C23—121no—
682C23—121no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—121no—
687C23—122no—
688C23—121no—
689C23—122no—
690C23—122no—
691C23C4×D1214yes—
692C23D3×C22⋊C414yes—
693C23#88214yes—
694C23#88414yes—
695C23#89314yes—
696C23#89414yes—
697C23#89514yes—
698C23C22×C4×D311yescharacteristic
699C23C22×D1211yescharacteristic
700C23C2×#23511yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703C23C2×D3×D411yescharacteristic
704C23C2×#23712yes—
705C23#100412yes—
706C23C2×#23911yescharacteristic
707C23D3×#4112yes—
708C23#101012yes—
709D4—1216no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—34no—
721C2×C4—34no—
722C2×C4—416no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—632no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—64no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—64no—
759C2×C4—1216no—
760C2×C4—122no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—122no—
765C2×C4—121no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C3—28no—
773C2×C3C2×#38611yescharacteristic
774C2×C3#229711yescharacteristic
775C2×C3#231111yescharacteristic
776C2×C3#235912yes—
777C2×C3#235912yes—
778C2×C3#241111yescharacteristic
779C2×C3#241111yescharacteristic
780C2×C3#241311yescharacteristic
781C2×C3#241311yescharacteristic
782C2×C3#243012yes—
783C2×C3#249812yes—
784D3—82no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—122no—
796C22—124no—
797C22—122no—
798C22—122no—
799C22—124no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—242no—
805C22—242no—
806C22#466518yes—
807C22C2×C4×D1211yescharacteristic
808C22C2×D3×C22⋊C411yescharacteristic
809C22C2×#88211yescharacteristic
810C22C2×#88411yescharacteristic
811C22#549512yes—
812C22C2×#89311yescharacteristic
813C22C2×#89411yescharacteristic
814C22C2×#89511yescharacteristic
815C22#553112yes—
816C22C4×#23712yes—
817C22#554612yes—
818C22#555412yes—
819C22#555512yes—
820C22#558611yescharacteristic
821C22#559112yes—
822C22#559211yescharacteristic
823C22#559612yes—
824C22#559712yes—
825C22#563712yes—
826C22#564212yes—
827C22#564811yescharacteristic
828C22#565512yes—
829C22#565611yescharacteristic
830C4—44no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—64no—
835C4—64no—
836C4—124no—
837C4—122no—
838C4—124no—
839C3#1413511yescharacteristic, complemented, Sylow
840C2—28no—
841C2—242no—
842C2C2×#466511yescharacteristic
843C2#7346412yes—
844C2#7382511yescharacteristic
845C2#7392612yes—
846C2#7406411yescharacteristic
847C2#7439512yes—
848C2#7440711yescharacteristic
849C2#7460211yescharacteristic
850C2#7465811yescharacteristic
851C2#7466211yescharacteristic
852C2#7469912yes—
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14135
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#877C2semidirect
4. C22×C3⋊#95C2semidirect
6. C3×C22⋊#95C2semidirect
7. #71544C2semidirect
8. #69428C2semidirect
9. #69411C2semidirect
10. #69408C2semidirect
11. #69407C2semidirect
30. C2×#886C4semidirect
55. C22⋊#95D3semidirect
110. C2×(C2×D3)⋊C4C2×C4semidirect
111. C2×(C2×D3)⋊C4C2×C4semidirect
116. C2×C4⋊Dic3C2×C4semidirect
117. C2×C4⋊Dic3C2×C4semidirect
262. C22×Dic3C22⋊C4semidirect
839. C3#14135semidirect

Maximal subgroups

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

subgroupindex
C22×#8862
C22×#8772
C2×#52132
C22×C3⋊#952
C2×#49582
C3×C22⋊#952
#715442
#694282
#694112
#694082
#694072
#141353