Finite Group Databasebeta

← #10722355

Subgroups — #10722355

Order 768.

3390 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C4C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4955C212yesmaximal
4C2×#4667C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71547C212yesmaximal, complemented
8#71546C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69427C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C212yesmaximal, complemented
12#14338—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic, complemented
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2211yescharacteristic
20C22×#217C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic, complemented
28C22×Dic3⋊C4C2212yescomplemented
29C2×D3×C22⋊C4—24no—
30C2×D3×C22⋊C4—24no—
31C2×D3×C22⋊C4C418yescomplemented
32C2×C3×#95C2211yescharacteristic, complemented
33C2×C3×#95C2212yescomplemented
34C2×C3⋊#95C2212yescomplemented
35C2×C3⋊#95C2211yescharacteristic, complemented
36C2×C3⋊#95C2212yescomplemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39#4987—24no—
40#4955—28no—
41#4667—24no—
42C23×C22⋊C4—31no—
43C2×#380—31no—
44C2×#380—31no—
45C2×#379—32no—
46#1439—31no—
47#1439—32no—
48#1439—31no—
49#1439—31no—
50#1439—32no—
51#1439D311yescharacteristic, complemented
52C22⋊#95—32no—
53C25×C3C2311yescharacteristic
54C24×D3—22no—
55C24×D3—22no—
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—42no—
59C24×D3—42no—
60C24×D3—42no—
61C24×D3—42no—
62C24×D3C2×C414yes—
63C24×D3D414yes—
64C24×D3Q814yes—
65C24×D3C2311yescharacteristic
66C24×D3C2311yescharacteristic
67C23×C3×C4C2312yes—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×Dic3C2312yes—
72C23×Dic3C2312yes—
73C23×Dic3C2311yescharacteristic
74C23×Dic3C2311yescharacteristic
75C22×C4×D3—22no—
76C22×C4×D3—22no—
77C22×C4×D3—42no—
78C22×C4×D3—42no—
79C22×C4×D3—42no—
80C22×C4×D3—42no—
81C22×C4×D3C2×C414yes—
82C22×C4×D3C2×C414yes—
83C22×C4×D3D414yes—
84C22×C4×D3D414yes—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—42no—
91C2×C3×C22⋊C4—42no—
92C2×C3×C22⋊C4C2×C414yes—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217—24no—
96C2×#217—42no—
97C2×#217—42no—
98C2×#217C2×C414yes—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4—42no—
114C2×(C2×D3)⋊C4—42no—
115C2×(C2×D3)⋊C4C2×C414yes—
116C2×(C2×D3)⋊C4C2×C414yes—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—42no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—42no—
121C2×Dic3⋊C4—42no—
122D3×C22⋊C4—232no—
123C3×#95—22no—
124C3×#95—42no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95—42no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C26—31no—
131C24×C4—31no—
132C24×C4—31no—
133C22×C4⋊C4—32no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4C2×D311yescharacteristic, complemented
136C22×C22⋊C4—31no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4—38no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—64no—
146C22×C22⋊C4—64no—
147C22×C22⋊C4C2×D311yescharacteristic
148C22×C22⋊C4C2×D312yes—
149#380—64no—
150#380—64no—
151#379—68no—
152C2×#95—32no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95C2×D311yescharacteristic, complemented
158C2×#95C2×D312yescomplemented
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3C22×C412yes—
168C24×C3C2×D412yes—
169C24×C3C2×Q812yes—
170C24×C3C2411yescharacteristic
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—21no—
176C23×D3—21no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—28no—
184C23×D3—28no—
185C23×D3—28no—
186C23×D3—28no—
187C23×D3—28no—
188C23×D3—28no—
189C23×D3—48no—
190C23×D3—48no—
191C23×D3—48no—
192C23×D3—48no—
193C23×D3—48no—
194C23×D3—48no—
195C23×D3—44no—
196C23×D3—44no—
197C23×D3—48no—
198C23×D3—44no—
199C23×D3—44no—
200C23×D3—48no—
201C23×D3—48no—
202C23×D3—48no—
203C23×D3—48no—
204C23×D3—48no—
205C23×D3C4⋊C4116yescomplemented
206C23×D3C22×C412yes—
207C23×D3C22×C412yes—
208C23×D3C2×D412yes—
209C23×D3C2×D412yes—
210C23×D3C2×D412yes—
211C23×D3C2×D412yes—
212C23×D3C2×Q812yes—
213C23×D3C2×Q812yes—
214C23×D3#4112yes—
215C23×D3#4112yes—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
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—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×C4C22×C412yes—
237C22×C3×C4C22×C412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3C22×C412yes—
261C22×Dic3C22×C412yes—
262C22×Dic3C2×D412yes—
263C22×Dic3C2×D412yes—
264C2×C4×D3—28no—
265C2×C4×D3—48no—
266C2×C4×D3—48no—
267C2×C4×D3—48no—
268C2×C4×D3—44no—
269C2×C4×D3—44no—
270C2×C4×D3—44no—
271C2×C4×D3—44no—
272C2×C4×D3—48no—
273C2×C4×D3C22⋊C4116yescomplemented
274C3×C4⋊C4—44no—
275C3×C22⋊C4—28no—
276C3×C22⋊C4—48no—
277#217—28no—
278#217—48no—
279(C2×D3)⋊C4—28no—
280(C2×D3)⋊C4—28no—
281(C2×D3)⋊C4—48no—
282(C2×D3)⋊C4—48no—
283(C2×D3)⋊C4—48no—
284(C2×D3)⋊C4—48no—
285C4⋊Dic3—44no—
286Dic3⋊C4—48no—
287C25—31no—
288C25—31no—
289C25—34no—
290C25—34no—
291C25—34no—
292C25—62no—
293C25—62no—
294C25—62no—
295C25—62no—
296C25—122no—
297C25—122no—
298C25—122no—
299C25—122no—
300C25C22×D311yescharacteristic
301C23×C4—31no—
302C23×C4—34no—
303C23×C4—34no—
304C23×C4—34no—
305C23×C4—31no—
306C23×C4—34no—
307C23×C4—32no—
308C23×C4—32no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—122no—
312C23×C4—122no—
313C23×C4—122no—
314C23×C4—122no—
315C23×C4C22×D312yes—
316C23×C4C22×D312yes—
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C2×C4⋊C4—22no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—64no—
322C2×C4⋊C4—62no—
323C2×C4⋊C4—122no—
324C2×C4⋊C4—122no—
325C2×C4⋊C4—122no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—34no—
330C2×C22⋊C4—34no—
331C2×C22⋊C4—34no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—632no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4—62no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—64no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—122no—
351C2×C22⋊C4—122no—
352C2×C22⋊C4—122no—
353C2×C22⋊C4—122no—
354C2×C22⋊C4—122no—
355C2×C22⋊C4—122no—
356C2×C22⋊C4C4×D314yes—
357#95—22no—
358#95—42no—
359#95—64no—
360#95—62no—
361#95—122no—
362#95—122no—
363#95—122no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3C2×C4⋊C414yes—
387C23×C3C23×C411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C22×D411yescharacteristic
390C23×C3C22×D411yescharacteristic
391C23×C3C22×Q811yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4111yescharacteristic
394C23×C3H(5,𝔽2)12yes—
395C23×C3H(5,𝔽2)12yes—
396C23×C3H(5,𝔽2)12yes—
397C23×C3H(5,𝔽2)12yes—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—232no—
427C22×D3—432no—
428C22×D3—416no—
429C22×D3—416no—
430C22×D3—432no—
431C22×D3—432no—
432C22×D3—416no—
433C22×D3—416no—
434C22×D3—416no—
435C22×D3—416no—
436C22×D3—432no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—42no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3C2×C22⋊C414yes—
448C22×D3C2×C4⋊C414yes—
449C22×D3C2×C4⋊C414yes—
450C22×D3#11714yes—
451C22×D3#12114yes—
452C22×D3#12114yes—
453C22×D3C22⋊Q814yes—
454C22×D3C22⋊Q814yes—
455C2×C3×C4—24no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—24no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4C2×C22⋊C414yes—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—42no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C2×Dic3C2×C22⋊C414yes—
503C4×D3—416no—
504C4×D3—416no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—32no—
514C24—32no—
515C24—32no—
516C24—32no—
517C24—32no—
518C24—32no—
519C24—32no—
520C24—32no—
521C24—32no—
522C24—32no—
523C24—316no—
524C24—68no—
525C24—68no—
526C24—68no—
527C24—68no—
528C24—68no—
529C24—68no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—61no—
535C24—61no—
536C24—62no—
537C24—62no—
538C24—61no—
539C24—61no—
540C24—62no—
541C24—62no—
542C24—128no—
543C24—128no—
544C24—128no—
545C24—128no—
546C24—128no—
547C24—128no—
548C24—124no—
549C24—128no—
550C24—124no—
551C24—128no—
552C24—128no—
553C24—124no—
554C24—124no—
555C24—128no—
556C24—128no—
557C24—128no—
558C24C2×C4×D312yes—
559C24D3×D412yes—
560C24D3×Q812yes—
561C24C23×D311yescharacteristic
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—316no—
586C22×C4—32no—
587C22×C4—68no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—124no—
609C22×C4—128no—
610C22×C4—124no—
611C22×C4—128no—
612C22×C4—128no—
613C22×C4—124no—
614C22×C4—124no—
615C22×C4—128no—
616C22×C4C2×C4×D312yes—
617C22×C4C2×C4×D312yes—
618C22×C4D3×D412yes—
619C22×C4D3×D412yes—
620C4⋊C4—44no—
621C4⋊C4—124no—
622C4⋊C4—128no—
623C22⋊C4—28no—
624C22⋊C4—48no—
625C22⋊C4—68no—
626C22⋊C4—68no—
627C22⋊C4—68no—
628C22⋊C4—128no—
629C22⋊C4—128no—
630C22⋊C4—128no—
631C22⋊C4—128no—
632C22⋊C4—128no—
633C22×C3—28no—
634C22×C3—24no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—44no—
644C22×C3C22×C22⋊C411yescharacteristic
645C22×C3C22×C4⋊C411yescharacteristic
646C22×C3C2×#11711yescharacteristic
647C22×C3#51812yes—
648C22×C3#51812yes—
649C22×C3C2×#12111yescharacteristic
650C22×C3C2×#12111yescharacteristic
651C22×C3C2×C22⋊Q811yescharacteristic
652C22×C3C2×C22⋊Q811yescharacteristic
653C22×C3#53411yescharacteristic
654C22×C3#53412yes—
655C22×C3#53411yescharacteristic
656C22×C3#53412yes—
657C22×C3#53412yes—
658C22×C3#53511yescharacteristic
659C22×C3#53511yescharacteristic
660C22×C3#53512yes—
661C22×C3#53812yes—
662C22×C3#53812yes—
663C22×C3#53812yes—
664C22×C3#53812yes—
665C22×C3#54312yes—
666C22×C3#54312yes—
667C2×D3—24no—
668C2×D3—24no—
669C2×D3—28no—
670C2×D3—28no—
671C2×D3—28no—
672C2×D3—24no—
673C2×D3—24no—
674C2×D3—24no—
675C2×D3—24no—
676C2×D3—28no—
677C2×D3—28no—
678C2×D3—24no—
679C2×D3—464no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—44no—
683C2×D3—44no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—44no—
689C2×D3#38018yes—
690C3×C4—24no—
691C3×C4—42no—
692C3×C4—82no—
693C3×C4—82no—
694Dic3—24no—
695Dic3—42no—
696Dic3—82no—
697Dic3—82no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—34no—
711C23—34no—
712C23—34no—
713C23—34no—
714C23—34no—
715C23—34no—
716C23—34no—
717C23—34no—
718C23—41no—
719C23—42no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—632no—
729C23—64no—
730C23—64no—
731C23—62no—
732C23—64no—
733C23—64no—
734C23—62no—
735C23—64no—
736C23—64no—
737C23—62no—
738C23—64no—
739C23—64no—
740C23—62no—
741C23—64no—
742C23—64no—
743C23—64no—
744C23—64no—
745C23—64no—
746C23—64no—
747C23—64no—
748C23—62no—
749C23—62no—
750C23—64no—
751C23—64no—
752C23—64no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—1232no—
758C23—1216no—
759C23—1232no—
760C23—1232no—
761C23—1216no—
762C23—1232no—
763C23—1216no—
764C23—1216no—
765C23—1216no—
766C23—1216no—
767C23—121no—
768C23—122no—
769C23—121no—
770C23—122no—
771C23—122no—
772C23—121no—
773C23—121no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23D3×C4⋊C414yes—
778C23C22×C4×D311yescharacteristic
779C23C2×D3×D411yescharacteristic
780C23C2×D3×D411yescharacteristic
781C23C2×D3×D411yescharacteristic
782C23#100412yes—
783C23#100412yes—
784C23C2×D3×Q811yescharacteristic
785C23D3×#4111yescharacteristic
786C23D3×#4111yescharacteristic
787C23#100912yes—
788C23#100912yes—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—34no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—62no—
814C2×C4—64no—
815C2×C4—62no—
816C2×C4—64no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—1216no—
820C2×C4—1216no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4D3×C22⋊C414yes—
839C2×C3—44no—
840C2×C3C2×#38011yescharacteristic
841C2×C3#230811yescharacteristic
842C2×C3#230911yescharacteristic
843C2×C3#231212yes—
844C2×C3#231512yes—
845C2×C3#261712yes—
846C2×C3#261711yescharacteristic
847C2×C3#261711yescharacteristic
848C2×C3#262611yescharacteristic
849C2×C3#262611yescharacteristic
850C2×C3#262612yes—
851D3—28no—
852D3—44no—
853C22—24no—
854C22—28no—
855C22—38no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—64no—
866C22—68no—
867C22—68no—
868C22—64no—
869C22—68no—
870C22—68no—
871C22—64no—
872C22—64no—
873C22—64no—
874C22—64no—
875C22—64no—
876C22—68no—
877C22—1264no—
878C22—122no—
879C22—124no—
880C22—124no—
881C22—122no—
882C22—124no—
883C22—122no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22C2×D3×C22⋊C411yescharacteristic
888C22C2×D3×C4⋊C411yescharacteristic
889C22D3×#11711yescharacteristic
890C22#554512yes—
891C22#554512yes—
892C22#558912yes—
893C22#558911yescharacteristic
894C22D3×#12111yescharacteristic
895C22D3×#12111yescharacteristic
896C22#560512yes—
897C22#560712yes—
898C22#561312yes—
899C22D3×C22⋊Q811yescharacteristic
900C22D3×C22⋊Q811yescharacteristic
901C22#563412yes—
902C22#563412yes—
903C22#565311yescharacteristic
904C22#565312yes—
905C22#565712yes—
906C22#567411yescharacteristic
907C22#567812yes—
908C22#570412yes—
909C22#571511yescharacteristic
910C4—24no—
911C4—42no—
912C4—64no—
913C4—82no—
914C4—82no—
915C4—122no—
916C4—242no—
917C4—242no—
918C3#1433811yescharacteristic, complemented, Sylow
919C2—44no—
920C2—68no—
921C2—124no—
922C2D3×#38011yescharacteristic
923C2#7459112yes—
924C2#7487411yescharacteristic
925C2#7582512yes—
926C2#7642811yescharacteristic
927C2#7676111yescharacteristic
928C2#7687111yescharacteristic
929C2#7712312yes—
930C2#7742412yes—
931C2#7768411yescharacteristic
932C2#7811011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC25×D3C22
hypercenter#1439D3
hypocenterC3#14338
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4987C2semidirect
4. C2×#4667C2semidirect
5. C3×#1439C2semidirect
6. #71570C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. #69428C2semidirect
10. #69427C2semidirect
11. (C2×D3)⋊#95C2semidirect
16. C22×C3×C4⋊C4C22semidirect
27. C22×C4⋊Dic3C22semidirect
28. C22×Dic3⋊C4C22semidirect
31. C2×D3×C22⋊C4C4semidirect
32. C2×C3×#95C22semidirect
33. C2×C3×#95C22semidirect
34. C2×C3⋊#95C22semidirect
35. C2×C3⋊#95C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
51. #1439D3semidirect
135. C22×C4⋊C4C2×D3semidirect
157. C2×#95C2×D3semidirect
158. C2×#95C2×D3semidirect
205. C23×D3C4⋊C4semidirect
273. C2×C4×D3C22⋊C4semidirect
918. C3#14338semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C42
C2×#49872
C2×#49552
C2×#46672
C3×#14392
#715702
#715472
#715462
#694282
#694272
(C2×D3)⋊#952
#143383