Finite Group Databasebeta

← C2×#69428 #10716849

Subgroups — C2×#69428 #10716849

Order 768.

4926 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic
2C23×(C2×D3)⋊C4C211yesmaximal, characteristic
3C23×(C2×D3)⋊C4C211yesmaximal, characteristic
4C23×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C22×C3×#95C211yesmaximal, characteristic, complemented
6C22×C3⋊#95C211yesmaximal, characteristic, complemented
7C22×C3⋊#95C211yesmaximal, characteristic, complemented
8#69428C218yesmaximal, direct product factor
9C2×#1439—31nomaximal, Sylow
10C25×D3C2211yescharacteristic
11C24×C3×C4C2211yescharacteristic
12C24×C3×C4C2211yescharacteristic
13C24×C3×C4C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×(C2×D3)⋊C4—24no—
18C22×(C2×D3)⋊C4—24no—
19C22×(C2×D3)⋊C4—24no—
20C22×(C2×D3)⋊C4—24no—
21C22×(C2×D3)⋊C4—24no—
22C22×(C2×D3)⋊C4—24no—
23C22×(C2×D3)⋊C4—24no—
24C22×(C2×D3)⋊C4—24no—
25C22×(C2×D3)⋊C4C418yescomplemented
26C22×(C2×D3)⋊C4C2214yes—
27C22×(C2×D3)⋊C4C2214yes—
28C22×(C2×D3)⋊C4C2214yes—
29C22×Dic3⋊C4—24no—
30C22×Dic3⋊C4—24no—
31C22×Dic3⋊C4—24no—
32C22×Dic3⋊C4C2214yescomplemented
33C2×C3×#95—24no—
34C2×C3×#95C2214yescomplemented
35C2×C3⋊#95—24no—
36C2×C3⋊#95—24no—
37C2×C3⋊#95C2214yescomplemented
38C2×C3⋊#95C2214yescomplemented
39C23×C4⋊C4—31no—
40C23×C22⋊C4—31no—
41C23×C22⋊C4—31no—
42C23×C22⋊C4—31no—
43C22×#95—31no—
44C22×#95—31no—
45C22×#95D311yescharacteristic, complemented
46#1439—38no—
47C25×C3C2311yescharacteristic
48C24×D3—22no—
49C24×D3—22no—
50C24×D3—22no—
51C24×D3—22no—
52C24×D3—22no—
53C24×D3—22no—
54C24×D3—22no—
55C24×D3—22no—
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—22no—
59C24×D3—22no—
60C24×D3C2×C414yes—
61C24×D3D414yes—
62C24×D3Q814yes—
63C24×D3C2312yes—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
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×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4C2×C414yes—
83C23×C3×C4D414yes—
84C23×C3×C4D414yes—
85C23×C3×C4C2312yes—
86C23×C3×C4C2312yes—
87C23×C3×C4C2312yes—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3—22no—
101C23×Dic3—22no—
102C23×Dic3—22no—
103C23×Dic3—22no—
104C23×Dic3C2×C414yes—
105C23×Dic3D414yes—
106C23×Dic3D414yes—
107C23×Dic3D414yes—
108C23×Dic3D414yes—
109C23×Dic3C2312yes—
110C23×Dic3C2312yes—
111C23×Dic3C2312yes—
112C2×(C2×D3)⋊C4—232no—
113C2×(C2×D3)⋊C4—232no—
114C2×(C2×D3)⋊C4—28no—
115C2×(C2×D3)⋊C4—28no—
116C2×(C2×D3)⋊C4—28no—
117C2×(C2×D3)⋊C4—28no—
118C2×(C2×D3)⋊C4—232no—
119C2×(C2×D3)⋊C4—28no—
120C2×(C2×D3)⋊C4—28no—
121C2×(C2×D3)⋊C4—28no—
122C2×(C2×D3)⋊C4—28no—
123C2×(C2×D3)⋊C4C2×C4116yescomplemented
124C2×Dic3⋊C4—232no—
125C2×Dic3⋊C4—28no—
126C2×Dic3⋊C4—28no—
127C2×Dic3⋊C4—28no—
128C3×#95—28no—
129C3⋊#95—28no—
130C3⋊#95—28no—
131C26—31no—
132C24×C4—31no—
133C24×C4—31no—
134C24×C4—31no—
135C24×C4C2×D311yescharacteristic
136C24×C4C2×D311yescharacteristic
137C24×C4C2×D311yescharacteristic
138C22×C4⋊C4—34no—
139C22×C4⋊C4—64no—
140C22×C4⋊C4—64no—
141C22×C4⋊C4—64no—
142C22×C22⋊C4—38no—
143C22×C22⋊C4—34no—
144C22×C22⋊C4—34no—
145C22×C22⋊C4—34no—
146C22×C22⋊C4—64no—
147C22×C22⋊C4—64no—
148C22×C22⋊C4—64no—
149C22×C22⋊C4—64no—
150C22×C22⋊C4—64no—
151C22×C22⋊C4—64no—
152C22×C22⋊C4—64no—
153C22×C22⋊C4—64no—
154C2×#95—24no—
155C2×#95—34no—
156C2×#95—34no—
157C2×#95—64no—
158C2×#95—64no—
159C2×#95C2×D314yescomplemented
160C24×C3C22×C412yes—
161C24×C3C2×D412yes—
162C24×C3C2×D412yes—
163C24×C3C2×D412yes—
164C24×C3C2×D412yes—
165C24×C3C2×D412yes—
166C24×C3C2×D412yes—
167C24×C3C2×D412yes—
168C24×C3C2×Q812yes—
169C24×C3#4112yes—
170C24×C3#4112yes—
171C24×C3#4112yes—
172C24×C3#4112yes—
173C24×C3#4112yes—
174C24×C3#4112yes—
175C24×C3C2411yescharacteristic
176C23×D3—28no—
177C23×D3—28no—
178C23×D3—28no—
179C23×D3—28no—
180C23×D3—28no—
181C23×D3—28no—
182C23×D3—28no—
183C23×D3—28no—
184C23×D3—28no—
185C23×D3—28no—
186C23×D3—28no—
187C23×D3—28no—
188C23×D3—28no—
189C23×D3—28no—
190C23×D3—28no—
191C23×D3—28no—
192C23×D3—28no—
193C23×D3—28no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—44no—
207C23×D3—44no—
208C23×D3—44no—
209C23×D3—44no—
210C23×D3—44no—
211C23×D3—44no—
212C23×D3—44no—
213C23×D3—44no—
214C23×D3—44no—
215C23×D3—44no—
216C23×D3—44no—
217C23×D3—44no—
218C23×D3—44no—
219C23×D3—44no—
220C23×D3—44no—
221C23×D3—44no—
222C23×D3C4⋊C4116yescomplemented
223C23×D3C22×C414yes—
224C23×D3C2×D414yes—
225C23×D3C2×Q814yes—
226C22×C3×C4—28no—
227C22×C3×C4—28no—
228C22×C3×C4—28no—
229C22×C3×C4—28no—
230C22×C3×C4—28no—
231C22×C3×C4—28no—
232C22×C3×C4—28no—
233C22×C3×C4—28no—
234C22×C3×C4—28no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—44no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4—44no—
257C22×C3×C4—44no—
258C22×C3×C4—44no—
259C22×C3×C4—44no—
260C22×C3×C4—44no—
261C22×C3×C4—44no—
262C22×C3×C4—44no—
263C22×C3×C4—44no—
264C22×C3×C4—44no—
265C22×C3×C4C22×C414yes—
266C22×C3×C4C2×D414yes—
267C22×C3×C4C2×D414yes—
268C22×Dic3—28no—
269C22×Dic3—28no—
270C22×Dic3—28no—
271C22×Dic3—28no—
272C22×Dic3—28no—
273C22×Dic3—28no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—28no—
279C22×Dic3—28no—
280C22×Dic3—28no—
281C22×Dic3—28no—
282C22×Dic3—28no—
283C22×Dic3—28no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—44no—
297C22×Dic3—44no—
298C22×Dic3—44no—
299C22×Dic3—44no—
300C22×Dic3—44no—
301C22×Dic3—44no—
302C22×Dic3—44no—
303C22×Dic3—44no—
304C22×Dic3C22⋊C4116yescomplemented
305C22×Dic3C22×C414yes—
306C22×Dic3C2×D414yes—
307C22×Dic3C2×D414yes—
308C22×Dic3C2×D414yes—
309C22×Dic3C2×D414yes—
310(C2×D3)⋊C4—232no—
311(C2×D3)⋊C4—232no—
312(C2×D3)⋊C4—232no—
313Dic3⋊C4—232no—
314C25—34no—
315C25—34no—
316C25—34no—
317C25—32no—
318C25—62no—
319C25—62no—
320C25—62no—
321C25—62no—
322C25—62no—
323C25—62no—
324C25—62no—
325C25—62no—
326C25—62no—
327C25—62no—
328C25—62no—
329C25—62no—
330C25C22×D311yescharacteristic
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—34no—
350C23×C4—34no—
351C23×C4—34no—
352C23×C4—32no—
353C23×C4—34no—
354C23×C4—34no—
355C23×C4—32no—
356C23×C4—32no—
357C23×C4—62no—
358C23×C4—62no—
359C23×C4—62no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4—62no—
364C23×C4—62no—
365C23×C4—62no—
366C23×C4—62no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4C4×D314yes—
374C23×C4D1214yes—
375C23×C4#6714yes—
376C23×C4C22×D312yes—
377C23×C4C22×D312yes—
378C23×C4C22×D312yes—
379C2×C4⋊C4—68no—
380C2×C4⋊C4—68no—
381C2×C4⋊C4—632no—
382C2×C4⋊C4—68no—
383C2×C22⋊C4—316no—
384C2×C22⋊C4—632no—
385C2×C22⋊C4—68no—
386C2×C22⋊C4—68no—
387C2×C22⋊C4—68no—
388C2×C22⋊C4—68no—
389C2×C22⋊C4—68no—
390C2×C22⋊C4—68no—
391C2×C22⋊C4—632no—
392C2×C22⋊C4—632no—
393C2×C22⋊C4—68no—
394C2×C22⋊C4—68no—
395#95—28no—
396#95—68no—
397#95—68no—
398C23×C3C2×C22⋊C414yes—
399C23×C3C2×C4⋊C414yes—
400C23×C3#11714yes—
401C23×C3C4×D414yes—
402C23×C3C4×D414yes—
403C23×C3C4×D414yes—
404C23×C3C4×D414yes—
405C23×C3#12014yes—
406C23×C3#12014yes—
407C23×C3#12014yes—
408C23×C3#12114yes—
409C23×C3#12114yes—
410C23×C3#12114yes—
411C23×C3#12114yes—
412C23×C3#12114yes—
413C23×C3#12114yes—
414C23×C3#12114yes—
415C23×C3#12114yes—
416C23×C3C22⋊Q814yes—
417C23×C3C22⋊Q814yes—
418C23×C3C22⋊Q814yes—
419C23×C3C22⋊Q814yes—
420C23×C3C22⋊Q814yes—
421C23×C3C22⋊Q814yes—
422C23×C3#12314yes—
423C23×C3#12314yes—
424C23×C3#12314yes—
425C23×C3#12314yes—
426C23×C3#12314yes—
427C23×C3#12414yes—
428C23×C3#12414yes—
429C23×C3#12414yes—
430C23×C3#12614yes—
431C23×C3#12614yes—
432C23×C3#12714yes—
433C23×C3C23×C411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C22×D411yescharacteristic
436C23×C3C22×D411yescharacteristic
437C23×C3C22×D411yescharacteristic
438C23×C3C22×D411yescharacteristic
439C23×C3C22×D411yescharacteristic
440C23×C3C22×D411yescharacteristic
441C23×C3C22×Q811yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—24no—
466C22×D3—232no—
467C22×D3—232no—
468C22×D3—232no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3—42no—
474C22×D3—42no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—416no—
486C22×D3—416no—
487C22×D3—416no—
488C22×D3—416no—
489C22×D3—416no—
490C22×D3—416no—
491C22×D3—416no—
492C22×D3—416no—
493C22×D3—416no—
494C22×D3—416no—
495C22×D3—416no—
496C22×D3—416no—
497C22×D3C2×C4⋊C418yescomplemented
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—24no—
504C2×C3×C4—24no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—416no—
520C2×C3×C4—416no—
521C2×C3×C4—416no—
522C2×Dic3—24no—
523C2×Dic3—24no—
524C2×Dic3—24no—
525C2×Dic3—24no—
526C2×Dic3—24no—
527C2×Dic3—24no—
528C2×Dic3—232no—
529C2×Dic3—24no—
530C2×Dic3—24no—
531C2×Dic3—24no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—24no—
535C2×Dic3—42no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—416no—
544C2×Dic3—416no—
545C2×Dic3C2×C22⋊C418yescomplemented
546C24—316no—
547C24—34no—
548C24—34no—
549C24—34no—
550C24—68no—
551C24—68no—
552C24—68no—
553C24—68no—
554C24—68no—
555C24—68no—
556C24—68no—
557C24—68no—
558C24—68no—
559C24—68no—
560C24—68no—
561C24—68no—
562C24—68no—
563C24—68no—
564C24—68no—
565C24—68no—
566C24—68no—
567C24—68no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—62no—
578C24—62no—
579C24—62no—
580C24—124no—
581C24—124no—
582C24—124no—
583C24—124no—
584C24—124no—
585C24—124no—
586C24—124no—
587C24—124no—
588C24—124no—
589C24—124no—
590C24—124no—
591C24—124no—
592C24—124no—
593C24—124no—
594C24—124no—
595C24—124no—
596C24C2×C4×D312yes—
597C24C2×D1212yes—
598C24#23512yes—
599C24#23512yes—
600C24#23512yes—
601C24#23512yes—
602C24D3×D412yes—
603C24D3×D412yes—
604C24D3×D412yes—
605C24D3×D412yes—
606C24D3×D412yes—
607C24#23712yes—
608C24D3×Q812yes—
609C24#23912yes—
610C24C2×#6712yes—
611C24C23×D311yescharacteristic
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—316no—
640C22×C4—34no—
641C22×C4—34no—
642C22×C4—34no—
643C22×C4—34no—
644C22×C4—34no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—68no—
658C22×C4—68no—
659C22×C4—68no—
660C22×C4—68no—
661C22×C4—68no—
662C22×C4—68no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—68no—
668C22×C4—68no—
669C22×C4—68no—
670C22×C4—68no—
671C22×C4—68no—
672C22×C4—68no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—124no—
686C22×C4—124no—
687C22×C4—124no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4C2×C4×D314yes—
694C22×C4C2×D1214yes—
695C22×C4C2×#6714yes—
696C4⋊C4—632no—
697C22⋊C4—632no—
698C22⋊C4—632no—
699C22⋊C4—632no—
700C22×C3#38018yes—
701C22×C3#38518yes—
702C22×C3#38518yes—
703C22×C3#38618yes—
704C22×C3#38818yes—
705C22×C3#38818yes—
706C22×C3#39018yes—
707C22×C3#39218yes—
708C22×C3#39318yes—
709C22×C3#39418yes—
710C22×C3#39418yes—
711C22×C3#39618yes—
712C22×C3#39618yes—
713C22×C3#39718yes—
714C22×C3#39918yes—
715C22×C3C22×C22⋊C411yescharacteristic
716C22×C3C22×C4⋊C411yescharacteristic
717C22×C3C2×#11711yescharacteristic
718C22×C3C2×C4×D411yescharacteristic
719C22×C3C2×C4×D411yescharacteristic
720C22×C3C2×C4×D411yescharacteristic
721C22×C3C2×C4×D411yescharacteristic
722C22×C3C2×#12011yescharacteristic
723C22×C3C2×#12011yescharacteristic
724C22×C3C2×#12011yescharacteristic
725C22×C3C2×#12111yescharacteristic
726C22×C3C2×#12111yescharacteristic
727C22×C3C2×#12111yescharacteristic
728C22×C3C2×#12111yescharacteristic
729C22×C3C2×#12111yescharacteristic
730C22×C3C2×#12111yescharacteristic
731C22×C3C2×#12111yescharacteristic
732C22×C3C2×#12111yescharacteristic
733C22×C3C2×C22⋊Q811yescharacteristic
734C22×C3C2×C22⋊Q811yescharacteristic
735C22×C3C2×C22⋊Q811yescharacteristic
736C22×C3C2×C22⋊Q811yescharacteristic
737C22×C3C2×C22⋊Q811yescharacteristic
738C22×C3C2×C22⋊Q811yescharacteristic
739C22×C3C2×#12311yescharacteristic
740C22×C3C2×#12311yescharacteristic
741C22×C3C2×#12311yescharacteristic
742C22×C3C2×#12311yescharacteristic
743C22×C3C2×#12311yescharacteristic
744C22×C3C2×#12411yescharacteristic
745C22×C3C2×#12411yescharacteristic
746C22×C3C2×#12411yescharacteristic
747C22×C3C2×#12611yescharacteristic
748C22×C3C2×#12611yescharacteristic
749C22×C3C2×#12711yescharacteristic
750C2×D3—28no—
751C2×D3—28no—
752C2×D3—28no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—44no—
756C2×D3—44no—
757C2×D3—44no—
758C2×D3—44no—
759C2×D3—44no—
760C2×D3—44no—
761C2×D3—464no—
762C2×D3—44no—
763C2×D3—44no—
764C2×D3—44no—
765C2×D3—44no—
766C3×C4—44no—
767C3×C4—44no—
768C3×C4—44no—
769Dic3—28no—
770Dic3—44no—
771Dic3—44no—
772C23—38no—
773C23—632no—
774C23—632no—
775C23—64no—
776C23—64no—
777C23—64no—
778C23—64no—
779C23—64no—
780C23—64no—
781C23—64no—
782C23—64no—
783C23—632no—
784C23—64no—
785C23—64no—
786C23—64no—
787C23—64no—
788C23—64no—
789C23—64no—
790C23—64no—
791C23—64no—
792C23—64no—
793C23—64no—
794C23—1216no—
795C23—1216no—
796C23—1216no—
797C23—1216no—
798C23—1216no—
799C23—1216no—
800C23—1216no—
801C23—1216no—
802C23—1216no—
803C23—1216no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—1216no—
813C23—122no—
814C23—122no—
815C23—1216no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—122no—
820C23—122no—
821C23—122no—
822C23#87214yes—
823C23C4×D1214yes—
824C23#87514yes—
825C23#87614yes—
826C23D3×C22⋊C414yes—
827C23#67⋊C414yes—
828C23#88214yes—
829C23#88214yes—
830C23#88314yes—
831C23#88414yes—
832C23#88414yes—
833C23#88414yes—
834C23#88414yes—
835C23#88414yes—
836C23#88514yes—
837C23#88514yes—
838C23D3×C4⋊C414yes—
839C23#89314yes—
840C23#89414yes—
841C23#89414yes—
842C23#89414yes—
843C23#89514yes—
844C23#89614yes—
845C23#89614yes—
846C23#89614yes—
847C23#89614yes—
848C23#89714yes—
849C23#89814yes—
850C23C4×#6714yes—
851C23#92914yes—
852C23#93014yes—
853C23#93714yes—
854C23#93914yes—
855C23#94014yes—
856C23#94614yes—
857C23C22×C4×D311yescharacteristic
858C23C22×D1211yescharacteristic
859C23C2×#23511yescharacteristic
860C23C2×#23511yescharacteristic
861C23C2×#23511yescharacteristic
862C23C2×#23511yescharacteristic
863C23C2×D3×D411yescharacteristic
864C23C2×D3×D411yescharacteristic
865C23C2×D3×D411yescharacteristic
866C23C2×D3×D411yescharacteristic
867C23C2×D3×D411yescharacteristic
868C23C2×#23711yescharacteristic
869C23C2×D3×Q811yescharacteristic
870C23C2×#23911yescharacteristic
871C23C22×#6711yescharacteristic
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—38no—
882C2×C4—416no—
883C2×C4—416no—
884C2×C4—416no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—632no—
898C2×C4—64no—
899C2×C4—64no—
900C2×C4—64no—
901C2×C4—64no—
902C2×C4—64no—
903C2×C4—64no—
904C2×C4—64no—
905C2×C4—64no—
906C2×C4—64no—
907C2×C4—64no—
908C2×C4—64no—
909C2×C4—64no—
910C2×C4—1216no—
911C2×C4—1216no—
912C2×C4—122no—
913C2×C4—122no—
914C2×C4—122no—
915C2×C4—122no—
916C2×C4—122no—
917C2×C4—122no—
918C2×C4—122no—
919C2×C4—122no—
920C2×C3#1439116yescomplemented
921C2×C3C2×#38011yescharacteristic
922C2×C3C2×#38511yescharacteristic
923C2×C3C2×#38511yescharacteristic
924C2×C3C2×#38611yescharacteristic
925C2×C3C2×#38811yescharacteristic
926C2×C3C2×#38811yescharacteristic
927C2×C3C2×#39011yescharacteristic
928C2×C3C2×#39211yescharacteristic
929C2×C3C2×#39311yescharacteristic
930C2×C3C2×#39411yescharacteristic
931C2×C3C2×#39411yescharacteristic
932C2×C3C2×#39611yescharacteristic
933C2×C3C2×#39611yescharacteristic
934C2×C3C2×#39711yescharacteristic
935C2×C3C2×#39911yescharacteristic
936D3—48no—
937C22—68no—
938C22—68no—
939C22—68no—
940C22—124no—
941C22—124no—
942C22—1264no—
943C22—124no—
944C22—124no—
945C22—124no—
946C22—124no—
947C22—124no—
948C22—124no—
949C22—124no—
950C22—124no—
951C22—124no—
952C22—124no—
953C22#466518yes—
954C22#466718yes—
955C22#466818yes—
956C22#466918yes—
957C22#467218yes—
958C22#467318yes—
959C22#467518yes—
960C22#467618yes—
961C22#494018yes—
962C22#495718yes—
963C22#495918yes—
964C22#496018yes—
965C22#498918yes—
966C22#499318yes—
967C22#499418yes—
968C22C2×#87211yescharacteristic
969C22C2×C4×D1211yescharacteristic
970C22C2×#87511yescharacteristic
971C22C2×#87611yescharacteristic
972C22C2×D3×C22⋊C411yescharacteristic
973C22C2×#67⋊C411yescharacteristic
974C22C2×#88211yescharacteristic
975C22C2×#88211yescharacteristic
976C22C2×#88311yescharacteristic
977C22C2×#88411yescharacteristic
978C22C2×#88411yescharacteristic
979C22C2×#88411yescharacteristic
980C22C2×#88411yescharacteristic
981C22C2×#88411yescharacteristic
982C22C2×#88511yescharacteristic
983C22C2×#88511yescharacteristic
984C22C2×D3×C4⋊C411yescharacteristic
985C22C2×#89311yescharacteristic
986C22C2×#89411yescharacteristic
987C22C2×#89411yescharacteristic
988C22C2×#89411yescharacteristic
989C22C2×#89511yescharacteristic
990C22C2×#89611yescharacteristic
991C22C2×#89611yescharacteristic
992C22C2×#89611yescharacteristic
993C22C2×#89611yescharacteristic
994C22C2×#89711yescharacteristic
995C22C2×#89811yescharacteristic
996C22C2×C4×#6711yescharacteristic
997C22C2×#92911yescharacteristic
998C22C2×#93011yescharacteristic
999C22C2×#93711yescharacteristic
1000C22C2×#93911yescharacteristic
1001C22C2×#94011yescharacteristic
1002C22C2×#94611yescharacteristic
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4—68no—
1007C4—124no—
1008C4—124no—
1009C3C2×#143911yescharacteristic, complemented, Sylow
1010C2—128no—
1011C2#69428116yesdirect product factor
1012C2C2×#466911yescharacteristic
1013C2C2×#467211yescharacteristic
1014C2C2×#466711yescharacteristic
1015C2C2×#466811yescharacteristic
1016C2C2×#466511yescharacteristic
1017C2C2×#467311yescharacteristic
1018C2C2×#467611yescharacteristic
1019C2C2×#467511yescharacteristic
1020C2C2×#494011yescharacteristic
1021C2C2×#495711yescharacteristic
1022C2C2×#496011yescharacteristic
1023C2C2×#495911yescharacteristic
1024C2C2×#498911yescharacteristic
1025C2C2×#499411yescharacteristic
1026C2C2×#499311yescharacteristic
subgroupG/H
centerC25C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC22×C3×#95C2
socleC25×C3C23
prime radicalC25×D3C22
cosocleC24×C3C24
hypercenterC22×#95D3
hypocenterC3C2×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C23×Dic3⋊C4C2semidirect
5. C22×C3×#95C2semidirect
6. C22×C3⋊#95C2semidirect
7. C22×C3⋊#95C2semidirect
8. #69428C2direct (N × H)
25. C22×(C2×D3)⋊C4C4semidirect
32. C22×Dic3⋊C4C22semidirect
34. C2×C3×#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
45. C22×#95D3semidirect
123. C2×(C2×D3)⋊C4C2×C4semidirect
159. C2×#95C2×D3semidirect
222. C23×D3C4⋊C4semidirect
304. C22×Dic3C22⋊C4semidirect
497. C22×D3C2×C4⋊C4semidirect
545. C2×Dic3C2×C22⋊C4semidirect
920. C2×C3#1439semidirect
1009. C3C2×#1439semidirect
1011. C2#69428direct (N × H)

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C23×Dic3⋊C42
C22×C3×#952
C22×C3⋊#952
#694282
C2×#14393