Finite Group Databasebeta

← #10716867

Subgroups — #10716867

Order 768.

2702 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D12C211yesmaximal, characteristic
2C22×#872C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×#95C211yesmaximal, characteristic, complemented
7C4×C3⋊#95C211yesmaximal, characteristic, complemented
8#69429C212yesmaximal, complemented
9#69428C212yesmaximal, complemented
10#69426C212yesmaximal
11#69411C212yesmaximal, complemented
12#13839—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×C4×D12—24no—
30C2×C4×D12—24no—
31C2×C4×D12C418yescomplemented
32C2×#872—24no—
33C2×#872—24no—
34C2×#872—24no—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C4×(C2×D3)⋊C4—24no—
43C4×(C2×D3)⋊C4—24no—
44C4×(C2×D3)⋊C4—24no—
45C22×C4×D4—31no—
46C22×#117—31no—
47C2×C4×C22⋊C4—31no—
48C2×C4×C22⋊C4—31no—
49C2×C4×C22⋊C4—31no—
50#1441—32no—
51#1440—32no—
52#1439—32no—
53#1438—32no—
54C4×#95—31no—
55C4×#95D311yescharacteristic, complemented
56C24×D3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2312yes—
65C23×Dic3C2312yes—
66C23×Dic3C2311yescharacteristic
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—24no—
70C22×D12—24no—
71C22×D12C2×C414yes—
72C22×C4×D3—22no—
73C22×C4×D3—22no—
74C22×C4×D3—22no—
75C22×C4×D3—22no—
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3C2×C414yes—
83C22×C4×D3C2×C414yes—
84C22×C4×D3D414yes—
85C22×C4×D3D414yes—
86C2×C3×C42—22no—
87C2×C3×C42—22no—
88C2×C3×C42—22no—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×C3×C42—22no—
93C2×C3×C42C2×C414yes—
94C2×C3×C42D414yescomplemented
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4C2×C414yes—
112C2×(C2×D3)⋊C4C2×C414yes—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3C2×C414yes—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—22no—
124C2×C4×Dic3D414yescomplemented
125C4×D12—232no—
126#872—232no—
127C3×#95—24no—
128C3×#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—24no—
134C23×D4—31no—
135C24×C4—31no—
136C24×C4—31no—
137C2×C4×D4—38no—
138C2×C4×D4—64no—
139C2×C4×D4—64no—
140C2×#117—64no—
141C2×#117—64no—
142C2×#117—64no—
143C22×C4⋊C4—31no—
144C22×C4⋊C4—32no—
145C22×C22⋊C4—31no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C42—31no—
152C22×C42—31no—
153C22×C42C2×D311yescharacteristic
154C22×C42C2×D311yescharacteristic
155C22×C42C2×D311yescharacteristic
156C4×C22⋊C4—64no—
157C4×C22⋊C4—64no—
158C4×C22⋊C4—64no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95C2×D312yes—
165C2×#95C2×D312yes—
166C24×C3C2411yescharacteristic
167C23×D3—21no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—21no—
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—21no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3C22×C412yes—
185C23×D3C22×C412yes—
186C23×D3C2×D412yes—
187C23×D3C2×D412yes—
188C23×D3#4114yes—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
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×C4C22×C412yes—
209C22×C3×C4C22×C412yes—
210C22×C3×C4C22×C412yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4#4114yes—
217C22×C3×C4#4114yes—
218C22×C3×C4#4112yes—
219C22×C3×C4#4112yes—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3C22×C412yes—
243C22×Dic3C22×C412yes—
244C22×Dic3C2×D414yes—
245C22×Dic3C2×D412yes—
246C22×Dic3C2×D412yes—
247C22×Dic3#4114yes—
248C2×D12—216no—
249C2×D12—216no—
250C2×D12—28no—
251C2×D12—28no—
252C2×D12—28no—
253C2×C4×D3—28no—
254C2×C4×D3—28no—
255C2×C4×D3—28no—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C2×C4×D3—28no—
259C2×C4×D3—28no—
260C2×C4×D3—28no—
261C2×C4×D3—28no—
262C2×C4×D3—44no—
263C2×C4×D3—44no—
264C2×C4×D3—44no—
265C2×C4×D3—44no—
266C2×C4×D3C22⋊C4116yescomplemented
267C3×C42—28no—
268C3×C42—28no—
269C3×C42—44no—
270(C2×D3)⋊C4—216no—
271(C2×D3)⋊C4—216no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4—216no—
274(C2×D3)⋊C4—28no—
275(C2×D3)⋊C4—28no—
276C4⋊Dic3—28no—
277Dic3⋊C4—216no—
278C4×Dic3—28no—
279C4×Dic3—44no—
280C25—31no—
281C25—31no—
282C22×D4—34no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—64no—
286C22×D4—64no—
287C23×C4—31no—
288C23×C4—34no—
289C23×C4—34no—
290C23×C4—34no—
291C23×C4—32no—
292C23×C4—32no—
293C23×C4—31no—
294C23×C4—34no—
295C23×C4—62no—
296C23×C4—62no—
297C23×C4—62no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—62no—
301C23×C4—62no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—62no—
305C23×C4C22×D311yescharacteristic
306C23×C4C22×D312yes—
307C23×C4C22×D312yes—
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C4×D4—632no—
311#117—632no—
312C2×C4⋊C4—34no—
313C2×C4⋊C4—64no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—64no—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—34no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—34no—
344C2×C42—62no—
345C2×C42—62no—
346C2×C42—62no—
347C2×C42—62no—
348C2×C42—62no—
349C2×C42C4×D314yes—
350C2×C42D1214yescomplemented
351#95—24no—
352#95—24no—
353#95—64no—
354#95—64no—
355#95—64no—
356#95—64no—
357#95—64no—
358C23×C3C23×C411yescharacteristic
359C23×C3C22×D411yescharacteristic
360C23×C3C22×D411yescharacteristic
361C23×C3C22×D411yescharacteristic
362C23×C3C22×D411yescharacteristic
363C23×C3C2×#4112yes—
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4112yes—
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4112yes—
368C23×C3C2×#4112yes—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—41no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3C2×C22⋊C414yes—
414C22×D3#11714yescomplemented
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
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—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4C2×C22⋊C414yes—
439C2×C3×C4#11714yescomplemented
440C2×C3×C4C4×D414yes—
441C2×C3×C4C4×D414yes—
442C2×C3×C4#12014yes—
443C2×C3×C4#12114yes—
444C2×C3×C4#12114yes—
445C2×C3×C4#12314yes—
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—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—41no—
462C2×Dic3—42no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3C2×C22⋊C414yes—
474D12—232no—
475C4×D3—232no—
476C4×D3—416no—
477C24—32no—
478C24—32no—
479C24—32no—
480C24—32no—
481C24—34no—
482C24—61no—
483C24—61no—
484C24—62no—
485C24—62no—
486C24—61no—
487C24—61no—
488C24—62no—
489C24—62no—
490C24—61no—
491C24—61no—
492C24—61no—
493C24—61no—
494C24—61no—
495C24—61no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24C23×D311yescharacteristic
500C2×D4—68no—
501C2×D4—68no—
502C2×D4—616no—
503C2×D4—616no—
504C2×D4—68no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—316no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—34no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—68no—
536C22×C4—68no—
537C22×C4—68no—
538C22×C4—68no—
539C22×C4—68no—
540C22×C4—68no—
541C22×C4—61no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—68no—
560C22×C4—68no—
561C22×C4—68no—
562C22×C4—124no—
563C22×C4—124no—
564C22×C4—124no—
565C22×C4—124no—
566C22×C4C2×C4×D312yes—
567C22×C4C2×C4×D312yes—
568C22×C4C2×C4×D312yes—
569C22×C4C2×D1214yes—
570C22×C4C2×D1212yes—
571C22×C4#23514yes—
572C22×C4#23514yes—
573C22×C4#23512yes—
574C22×C4D3×D412yes—
575C22×C4D3×D412yes—
576C22×C4D3×D412yes—
577C22×C4#23912yes—
578C4⋊C4—68no—
579C4⋊C4—616no—
580C22⋊C4—68no—
581C22⋊C4—68no—
582C22⋊C4—616no—
583C22⋊C4—616no—
584C22⋊C4—616no—
585C22⋊C4—616no—
586C42—28no—
587C42—28no—
588C42—44no—
589C42—68no—
590C42—124no—
591C22×C3C22×C22⋊C411yescharacteristic
592C22×C3C2×#11711yescharacteristic
593C22×C3C2×#11711yescharacteristic
594C22×C3C2×C4×D411yescharacteristic
595C22×C3C2×C4×D411yescharacteristic
596C22×C3C4×#4111yescharacteristic
597C22×C3C4×#4111yescharacteristic
598C22×C3C2×#12011yescharacteristic
599C22×C3C2×#12111yescharacteristic
600C22×C3C2×#12111yescharacteristic
601C22×C3C2×#12311yescharacteristic
602C22×C3#52512yes—
603C22×C3#52512yes—
604C22×C3#52512yes—
605C22×C3#52512yes—
606C22×C3#52512yes—
607C22×C3#52912yes—
608C22×C3#52912yes—
609C22×C3#52912yes—
610C22×C3#52912yes—
611C22×C3#53212yes—
612C22×C3#53212yes—
613C22×C3#53212yes—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—44no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C3×C4—24no—
637C3×C4—44no—
638C3×C4—44no—
639C3×C4—42no—
640C3×C4#38618yes—
641Dic3—24no—
642Dic3—44no—
643Dic3—44no—
644Dic3—42no—
645C23—34no—
646C23—34no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—62no—
663C23—64no—
664C23—64no—
665C23—64no—
666C23—64no—
667C23—64no—
668C23—64no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—64no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23C22×C4×D311yescharacteristic
692C23C22×D1211yescharacteristic
693C23C2×#23512yes—
694C23C2×#23511yescharacteristic
695C23C2×#23512yes—
696C23C2×D3×D411yescharacteristic
697C23C2×D3×D411yescharacteristic
698C23C2×D3×D411yescharacteristic
699C23C2×#23911yescharacteristic
700C23D3×#4112yes—
701C23D3×#4112yes—
702D4—632no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—34no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—632no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—64no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—122no—
749C2×C4—121no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—1216no—
756C2×C4#87214yescomplemented
757C2×C4C4×D1214yes—
758C2×C4D3×C22⋊C414yes—
759C2×C4#88214yes—
760C2×C4#88414yes—
761C2×C4#89314yes—
762C2×C4#89414yes—
763C2×C4#89514yes—
764C2×C3#228011yescharacteristic
765C2×C3C2×#38611yescharacteristic
766C2×C3#229011yescharacteristic
767C2×C3#229011yescharacteristic
768C2×C3#229311yescharacteristic
769C2×C3#229311yescharacteristic
770C2×C3#229711yescharacteristic
771C2×C3#238812yes—
772C2×C3#239212yes—
773C2×C3#239212yes—
774C2×C3#239512yes—
775D3—44no—
776D3—44no—
777C22—64no—
778C22—64no—
779C22—64no—
780C22—64no—
781C22—64no—
782C22—64no—
783C22—122no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—124no—
792C22—124no—
793C22—124no—
794C22—124no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22C2×#87211yescharacteristic
800C22C2×C4×D1211yescharacteristic
801C22C4×#23511yescharacteristic
802C22#547712yes—
803C22#547912yes—
804C22C2×D3×C22⋊C411yescharacteristic
805C22C2×#88211yescharacteristic
806C22C2×#88411yescharacteristic
807C22C2×#89311yescharacteristic
808C22C2×#89411yescharacteristic
809C22C2×#89511yescharacteristic
810C22D3×#11711yescharacteristic
811C22#552211yescharacteristic
812C22#552412yes—
813C22#552812yes—
814C22#554712yes—
815C22#554712yes—
816C22#554712yes—
817C22#554712yes—
818C22#554812yes—
819C22#554812yes—
820C22#558012yes—
821C22#558012yes—
822C4—24no—
823C4—42no—
824C4—44no—
825C4—44no—
826C4—64no—
827C4—124no—
828C4—124no—
829C4—122no—
830C4#466518yes—
831C3#1383911yescharacteristic, complemented, Sylow
832C2—124no—
833C2—124no—
834C2#7329911yescharacteristic
835C2C2×#466511yescharacteristic
836C2#7341411yescharacteristic
837C2#7356111yescharacteristic
838C2#7356311yescharacteristic
839C2#7358012yes—
840C2#7358112yes—
841C2#7361711yescharacteristic
842C2#7375411yescharacteristic
843C2#7377612yes—
844C2#7377712yes—
subgroupG/H
centerC23×C4C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×C4×#95C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC4×#95D3
hypocenterC3#13839
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C22×#872C2semidirect
3. C2×C4×(C2×D3)⋊C4C2semidirect
4. C2×C4×(C2×D3)⋊C4C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
6. C3×C4×#95C2semidirect
7. C4×C3⋊#95C2semidirect
8. #69429C2semidirect
9. #69428C2semidirect
11. #69411C2semidirect
31. C2×C4×D12C4semidirect
55. C4×#95D3semidirect
94. C2×C3×C42D4semidirect
124. C2×C4×Dic3D4semidirect
266. C2×C4×D3C22⋊C4semidirect
350. C2×C42D12semidirect
414. C22×D3#117semidirect
439. C2×C3×C4#117semidirect
756. C2×C4#872semidirect
831. C3#13839semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D122
C22×#8722
C2×C4×(C2×D3)⋊C42
C3×C4×#952
C4×C3⋊#952
#694292
#694282
#694262
#694112
#138393