Finite Group Databasebeta

← #10795120

Subgroups — #10795120

Order 768.

1866 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic
2#73862C212yesmaximal, complemented
3C3×#1799C211yesmaximal, characteristic, complemented
4#71619C211yesmaximal, characteristic, complemented
5#70035C212yesmaximal
6Dic3×#99C212yesmaximal, complemented
7#69530C212yesmaximal, complemented
8#68969C212yesmaximal, complemented
9#68952C212yesmaximal, complemented
10#20722—31nomaximal, Sylow
11C22×D3×D4C2211yescharacteristic
12C23×C4×D3C411yescharacteristic, complemented
13C23×C4×D3C2211yescharacteristic
14C2×C3×C4×D4C2211yescharacteristic
15C2×D4×Dic3C2211yescharacteristic
16C2×C4×#67C411yescharacteristic, complemented
17C2×C4×#67C2211yescharacteristic
18C4×D3×D4—22no—
19C4×D3×D4—22no—
20C4×D3×D4—22no—
21C4×D3×D4—22no—
22C2×#893C411yescharacteristic, complemented
23C2×#892—22no—
24C2×D3×C4⋊C4C411yescharacteristic, complemented
25C2×#67⋊C4C411yescharacteristic, complemented
26C2×#67⋊C4C2211yescharacteristic
27C2×D3×C22⋊C4C411yescharacteristic, complemented
28C2×D3×C22⋊C4C2211yescharacteristic
29C2×C4×D12C411yescharacteristic, complemented
30C2×C42×D3C411yescharacteristic, complemented
31C2×C3×#99C2212yes—
32C3×#380C2212yescomplemented
33C2×#834C2212yes—
34#5212C2212yescomplemented
35#4987—22no—
36#4955C2214yes—
37C2×#806C2214yes—
38Dic3×C22⋊C4C2214yescomplemented
39#4666—22no—
40#4664—22no—
41C3×#342C2212yescomplemented
42#4527C2214yescomplemented
43#4526C2212yescomplemented
44C22×C4×D4—31no—
45#2280—32no—
46#1819—32no—
47#1799—32no—
48#1799—31no—
49#1799D311yescharacteristic, complemented
50#1781—32no—
51C4×#99—32no—
52C4×#99—32no—
53C24×D3C2×C411yescharacteristic
54C24×D3C2311yescharacteristic
55C22×C3×D4C2311yescharacteristic
56C23×C3×C4C2×C411yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C22×#67C2×C411yescharacteristic
59C22×#67C2311yescharacteristic
60C23×Dic3C2×C411yescharacteristic
61C23×Dic3C2311yescharacteristic
62C2×D3×D4—22no—
63C2×D3×D4—22no—
64C2×D3×D4—22no—
65C2×D3×D4—22no—
66C2×D3×D4—24no—
67C22×D12C2×C411yescharacteristic
68C22×C4×D3—21no—
69C22×C4×D3—21no—
70C22×C4×D3—21no—
71C22×C4×D3—21no—
72C22×C4×D3—44no—
73C22×C4×D3—44no—
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3C2×C411yescharacteristic
77C22×C4×D3C2×C411yescharacteristic
78C22×C4×D3C2×C411yescharacteristic
79C22×C4×D3C2×C411yescharacteristic
80C22×C4×D3C2×C411yescharacteristic
81C22×C4×D3C2×C411yescharacteristic
82C22×C4×D3C2×C411yescharacteristic
83C22×C4×D3D412yes—
84C22×C4×D3D412yes—
85C22×C4×D3D412yes—
86C22×C4×D3D412yes—
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4C2×C411yescharacteristic
91C2×C3×C22⋊C4C2×C411yescharacteristic
92C2×C3×C22⋊C4C2314yes—
93C2×C3×C22⋊C4C2311yescharacteristic
94C2×C3×C42C2×C411yescharacteristic
95C2×#217C2×C411yescharacteristic
96C2×#217C2314yes—
97C2×#217C2311yescharacteristic
98D4×Dic3—22no—
99D4×Dic3—22no—
100C4×#67—22no—
101C4×#67—22no—
102C4×#67—22no—
103C4×#67—22no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4C2×C411yescharacteristic
107C2×(C2×D3)⋊C4C2×C411yescharacteristic
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3C2×C411yescharacteristic
112C2×Dic3⋊C4C2×C411yescharacteristic
113C2×Dic3⋊C4C2×C411yescharacteristic
114C2×C4×Dic3—24no—
115C2×C4×Dic3C2×C411yescharacteristic
116C2×C4×Dic3C2×C411yescharacteristic
117C2×C4×Dic3C2×C411yescharacteristic
118#893—22no—
119#893—22no—
120#892—48no—
121D3×C4⋊C4—22no—
122D3×C4⋊C4—22no—
123#67⋊C4—22no—
124#67⋊C4—22no—
125#67⋊C4—22no—
126#67⋊C4—22no—
127D3×C22⋊C4—22no—
128D3×C22⋊C4—22no—
129D3×C22⋊C4—22no—
130D3×C22⋊C4—22no—
131C4×D12—22no—
132C4×D12—22no—
133C42×D3—21no—
134C42×D3—21no—
135C42×D3—21no—
136C42×D3—21no—
137C3×#99—24no—
138C3×#95—22no—
139#834—24no—
140C3⋊#95—22no—
141C3⋊#95—24no—
142#806—28no—
143C23×D4—31no—
144C24×C4—31no—
145C24×C4—31no—
146C2×C4×D4—31no—
147C2×C4×D4—31no—
148C2×C4×D4—31no—
149C2×C4×D4—31no—
150C2×C4×D4—31no—
151C2×C4×D4—31no—
152C2×C4×D4—31no—
153C2×C4×D4—62no—
154C2×C4×D4—62no—
155C2×C4×D4—62no—
156C2×C4×D4—62no—
157C2×C4×D4C2×D311yescharacteristic
158C2×#117—62no—
159C22×C4⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C42—31no—
163C2×#99—32no—
164C2×#99—34no—
165C2×#99C2×D312yes—
166#381—62no—
167#380—32no—
168#380—62no—
169#380C2×D312yescomplemented
170#379—34no—
171C4×C22⋊C4—34no—
172C4×C22⋊C4—62no—
173#342—32no—
174#342—34no—
175#342C2×D312yescomplemented
176C24×C3C22×C411yescharacteristic
177C24×C3C2411yescharacteristic
178C23×D3—22no—
179C23×D3—21no—
180C23×D3—21no—
181C23×D3—22no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—22no—
185C23×D3—42no—
186C23×D3—42no—
187C23×D3—42no—
188C23×D3—42no—
189C23×D3C22×C411yescharacteristic
190C23×D3C22×C411yescharacteristic
191C23×D3C22×C411yescharacteristic
192C23×D3C2×D412yes—
193C23×D3C2×D412yes—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4#4112yes—
197C2×C3×D4#4112yes—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—24no—
201C22×C3×C4—42no—
202C22×C3×C4—42no—
203C22×C3×C4C22×C411yescharacteristic
204C22×C3×C4C22×C411yescharacteristic
205C22×C3×C4C22×C411yescharacteristic
206C22×C3×C4C22×C411yescharacteristic
207C22×C3×C4C22×C411yescharacteristic
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C2×#67—22no—
211C2×#67—22no—
212C2×#67—21no—
213C2×#67—21no—
214C2×#67—22no—
215C2×#67—22no—
216C2×#67#4114yes—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—24no—
220C22×Dic3—42no—
221C22×Dic3—42no—
222C22×Dic3C22×C411yescharacteristic
223C22×Dic3C22×C411yescharacteristic
224C22×Dic3C22×C411yescharacteristic
225C22×Dic3C22×C411yescharacteristic
226C22×Dic3C22×C411yescharacteristic
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D412yes—
229D3×D4—28no—
230D3×D4—28no—
231D3×D4—28no—
232D3×D4—28no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—22no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—28no—
241C2×C4×D3—24no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—42no—
251C2×C4×D3—44no—
252C2×C4×D3—42no—
253C2×C4×D3—44no—
254C2×C4×D3—42no—
255C2×C4×D3—44no—
256C2×C4×D3—44no—
257C2×C4×D3—44no—
258C2×C4×D3—44no—
259C2×C4×D3—44no—
260C2×C4×D3—42no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3C22⋊C411yescharacteristic
265C2×C4×D3C22⋊C411yescharacteristic
266C2×C4×D3C22⋊C411yescharacteristic
267C2×C4×D3C22⋊C412yes—
268C2×C4×D3C22⋊C412yes—
269C2×C4×D3C22⋊C412yes—
270C2×C4×D3C22⋊C412yes—
271C2×C4×D3C22⋊C412yes—
272C2×C4×D3C22⋊C412yes—
273C2×C4×D3C22⋊C411yescharacteristic
274C3×C4⋊C4—22no—
275C3×C4⋊C4—44no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C42—21no—
281C3×C42—21no—
282#217—22no—
283#217—22no—
284#217—24no—
285#217—24no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—48no—
291(C2×D3)⋊C4—48no—
292C4⋊Dic3—22no—
293C4⋊Dic3—44no—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—21no—
299C4×Dic3—21no—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C4×Dic3—48no—
303C25—31no—
304C25—31no—
305C22×D4—31no—
306C22×D4—31no—
307C22×D4—31no—
308C22×D4—64no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—62no—
312C22×D4—62no—
313C22×D4C22×D311yescharacteristic
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—32no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—32no—
321C23×C4—32no—
322C23×C4—32no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—61no—
330C23×C4—61no—
331C23×C4—61no—
332C23×C4—61no—
333C23×C4—124no—
334C23×C4—124no—
335C23×C4C4×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—62no—
342C4×D4—62no—
343C4×D4—62no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347C4×D4—62no—
348C4×D4—62no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—62no—
352C4×D4—62no—
353#117—128no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4C4×D311yescharacteristic
362C2×C22⋊C4—31no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—64no—
375C2×C22⋊C4C4×D311yescharacteristic
376C2×C22⋊C4C22×D314yes—
377C2×C22⋊C4C22×D311yescharacteristic
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—61no—
382C2×C42—61no—
383C2×C42—61no—
384C2×C42—61no—
385C2×C42—64no—
386C2×C42C4×D311yescharacteristic
387#99—24no—
388#99—68no—
389#99—64no—
390#95—22no—
391#95—64no—
392#95—62no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3#11712yescomplemented
400C23×C3C23×C411yescharacteristic
401C23×C3C22×D412yes—
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4112yes—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—24no—
420C22×D3—24no—
421C22×D3—41no—
422C22×D3—42no—
423C22×D3—41no—
424C22×D3—42no—
425C22×D3—42no—
426C22×D3—44no—
427C22×D3—44no—
428C22×D3—48no—
429C22×D3—48no—
430C22×D3—48no—
431C22×D3—42no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3C2×C22⋊C412yes—
437C22×D3C2×C22⋊C411yescharacteristic
438C22×D3C2×C22⋊C411yescharacteristic
439C22×D3#11712yescomplemented
440C3×D4—24no—
441C3×D4—24no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—24no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—41no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—44no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4C2×C22⋊C411yescharacteristic
458C2×C3×C4C2×C22⋊C412yes—
459C2×C3×C4C2×C22⋊C411yescharacteristic
460C2×C3×C4#11712yescomplemented
461#67—28no—
462#67—24no—
463#67—24no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—24no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—41no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—44no—
477C2×Dic3—44no—
478C2×Dic3—44no—
479C2×Dic3C2×C22⋊C411yescharacteristic
480C2×Dic3C2×C22⋊C412yes—
481C2×Dic3C2×C22⋊C411yescharacteristic
482C2×Dic3#11712yescomplemented
483D12—28no—
484C4×D3—24no—
485C4×D3—24no—
486C4×D3—22no—
487C4×D3—24no—
488C4×D3—22no—
489C4×D3—24no—
490C4×D3—22no—
491C4×D3—24no—
492C4×D3—42no—
493C4×D3—42no—
494C4×D3—42no—
495C4×D3—42no—
496C4×D3—42no—
497C4×D3—42no—
498C4×D3—42no—
499C4×D3—42no—
500C4×D3—42no—
501C4×D3—42no—
502C4×D3—42no—
503C4×D3#9914yescomplemented
504C24—31no—
505C24—32no—
506C24—32no—
507C24—31no—
508C24—31no—
509C24—61no—
510C24—61no—
511C24—62no—
512C24—62no—
513C24—61no—
514C24—61no—
515C24—62no—
516C24—122no—
517C24—122no—
518C24—122no—
519C24—122no—
520C24C2×C4×D311yescharacteristic
521C24C23×D311yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—34no—
525C2×D4—62no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—68no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—68no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—62no—
538C2×D4#23712yes—
539C2×D4#23912yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—24no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—32no—
547C22×C4—31no—
548C22×C4—32no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—68no—
563C22×C4—64no—
564C22×C4—62no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—62no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—64no—
579C22×C4—124no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—124no—
583C22×C4—122no—
584C22×C4—124no—
585C22×C4—122no—
586C22×C4—124no—
587C22×C4—124no—
588C22×C4—124no—
589C22×C4—124no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4C2×C4×D311yescharacteristic
596C22×C4C2×C4×D311yescharacteristic
597C22×C4C2×C4×D311yescharacteristic
598C22×C4C2×C4×D311yescharacteristic
599C22×C4C2×C4×D311yescharacteristic
600C22×C4D3×D412yes—
601C22×C4D3×D412yes—
602C4⋊C4—22no—
603C4⋊C4—44no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—62no—
607C4⋊C4—124no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—62no—
613C22⋊C4—62no—
614C22⋊C4—62no—
615C22⋊C4—62no—
616C22⋊C4—62no—
617C22⋊C4—62no—
618C22⋊C4—64no—
619C22⋊C4—64no—
620C22⋊C4—128no—
621C22⋊C4—128no—
622C42—21no—
623C42—21no—
624C42—61no—
625C42—61no—
626C42—61no—
627C42—61no—
628C42—61no—
629C42—61no—
630C42—128no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3C22×C22⋊C411yescharacteristic
644C22×C3C2×#11711yescharacteristic
645C22×C3C2×#11711yescharacteristic
646C22×C3#52512yes—
647C22×C3#52512yes—
648C2×D3—24no—
649C2×D3—24no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—44no—
659C2×D3—44no—
660C2×D3—44no—
661C2×D3—44no—
662C2×D3—48no—
663C2×D3—48no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—42no—
670C2×D3C2×#9912yes—
671C2×D3#41012yes—
672C3×C4—21no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—84no—
678C3×C4C2×#9912yes—
679Dic3—21no—
680Dic3—22no—
681Dic3—22no—
682Dic3—41no—
683Dic3—41no—
684Dic3—84no—
685Dic3C2×#9912yes—
686C23—21no—
687C23—21no—
688C23—31no—
689C23—31no—
690C23—32no—
691C23—32no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—62no—
697C23—62no—
698C23—64no—
699C23—64no—
700C23—64no—
701C23—64no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—122no—
713C23—121no—
714C23—122no—
715C23—121no—
716C23—121no—
717C23—121no—
718C23—122no—
719C23—122no—
720C23—122no—
721C23—124no—
722C23—124no—
723C23—128no—
724C23—128no—
725C23—128no—
726C23—122no—
727C23#89212yescomplemented
728C23C22×C4×D311yescharacteristic
729C23C2×D3×D412yes—
730C23C2×#23711yescharacteristic
731C23C2×#23911yescharacteristic
732C23D3×#4112yes—
733D4—24no—
734D4—24no—
735D4—68no—
736D4—68no—
737D4—64no—
738D4—64no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—34no—
747C2×C4—31no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—62no—
760C2×C4—64no—
761C2×C4—62no—
762C2×C4—64no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—62no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—64no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—122no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—121no—
786C2×C4—122no—
787C2×C4—122no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—124no—
791C2×C4—124no—
792C2×C4—124no—
793C2×C4D3×C22⋊C411yescharacteristic
794C2×C4D3×C22⋊C412yes—
795C2×C4D3×C22⋊C411yescharacteristic
796C2×C4#89212yescomplemented
797C2×C3—22no—
798C2×C3—22no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3#228011yescharacteristic
803C2×C3C22×#9911yescharacteristic
804C2×C3C2×#41011yescharacteristic
805D3—22no—
806D3—22no—
807D3—42no—
808D3—42no—
809C22—22no—
810C22—21no—
811C22—22no—
812C22—21no—
813C22—22no—
814C22—32no—
815C22—32no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—64no—
824C22—64no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—62no—
830C22—62no—
831C22—62no—
832C22—62no—
833C22—124no—
834C22—124no—
835C22—124no—
836C22—124no—
837C22—122no—
838C22—122no—
839C22—122no—
840C22—122no—
841C22—128no—
842C22—128no—
843C22—121no—
844C22—121no—
845C22C2×D3×C22⋊C411yescharacteristic
846C22C2×#89211yescharacteristic
847C22D3×#11711yescharacteristic
848C22#560612yes—
849C22#562712yes—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—32no—
854C4—41no—
855C4—41no—
856C4—61no—
857C4—62no—
858C4—62no—
859C4—84no—
860C4—121no—
861C4—121no—
862C4—244no—
863C4D3×#9912yes—
864C3#2072211yescharacteristic, complemented, Sylow
865C2—22no—
866C2—22no—
867C2—21no—
868C2—21no—
869C2—42no—
870C2—62no—
871C2—62no—
872C2—122no—
873C2—122no—
874C2#7386211yescharacteristic
875C2C2×D3×#9911yescharacteristic
876C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1799C2
socleC22×C3C22×C22⋊C4
prime radicalC22×D3×D4C22
cosocleC24×C3C24
hypercenter#1799D3
hypocenterC3#20722
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #73862C2semidirect
3. C3×#1799C2semidirect
4. #71619C2semidirect
6. Dic3×#99C2semidirect
7. #69530C2semidirect
8. #68969C2semidirect
9. #68952C2semidirect
12. C23×C4×D3C4semidirect
16. C2×C4×#67C4semidirect
22. C2×#893C4semidirect
24. C2×D3×C4⋊C4C4semidirect
25. C2×#67⋊C4C4semidirect
27. C2×D3×C22⋊C4C4semidirect
29. C2×C4×D12C4semidirect
30. C2×C42×D3C4semidirect
32. C3×#380C22semidirect
34. #5212C22semidirect
38. Dic3×C22⋊C4C22semidirect
41. C3×#342C22semidirect
42. #4527C22semidirect
43. #4526C22semidirect
49. #1799D3semidirect
169. #380C2×D3semidirect
175. #342C2×D3semidirect
399. C23×C3#117semidirect
439. C22×D3#117semidirect
460. C2×C3×C4#117semidirect
482. C2×Dic3#117semidirect
503. C4×D3#99semidirect
727. C23#892semidirect
796. C2×C4#892semidirect
864. C3#20722semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
#738622
C3×#17992
#716192
#700352
Dic3×#992
#695302
#689692
#689522
#207223