Finite Group Databasebeta

← #10718561

Subgroups — #10718561

Order 768.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67⋊C4C211yesmaximal, characteristic
2C2×#4989C211yesmaximal, characteristic, complemented
3C2×#4956C211yesmaximal, characteristic
4C2×#4956C211yesmaximal, characteristic
5C2×D3×#95C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71564C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14016—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×#67⋊C4—24no—
35C2×#67⋊C4—24no—
36C2×#67⋊C4—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4989—24no—
56#4956—24no—
57#4956C418yescomplemented
58D3×#95—24no—
59C22×C4×D4—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#385—31no—
63C22×#95—31no—
64#1442—31no—
65#1442—31no—
66#1439—31no—
67#1439D311yescharacteristic, complemented
68#1436—31no—
69#1436—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C22⋊#95—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67C2×C414yes—
87C22×#67D414yes—
88C22×#67Q814yes—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—41no—
95C23×Dic3—41no—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3—41no—
117C22×C4×D3—41no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3C2×C414yescomplemented
123C22×C4×D3D414yes—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—41no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4—41no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4C2×C414yescomplemented
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217C2×C414yescomplemented
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4C2×C414yescomplemented
150C2×(C2×D3)⋊C4D414yes—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—41no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160#67⋊C4—232no—
161C3×#95—22no—
162C3×#95—41no—
163C3×#95—41no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95C2×C414yescomplemented
178C3⋊#95C2×C414yescomplemented
179C23×D4—31no—
180C24×C4—31no—
181C24×C4—31no—
182C24×C4—31no—
183C24×C4—31no—
184C2×C4×D4—64no—
185C2×C4×D4—64no—
186C2×C4×D4—64no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4C2×D311yescharacteristic
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C42—31no—
199#386—38no—
200#386—64no—
201#385—64no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—64no—
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3C22×C412yes—
234C24×C3C2×D412yes—
235C24×C3C2×Q812yes—
236C24×C3C2411yescharacteristic
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3C22×C412yes—
246C23×D3C2×D412yes—
247C23×D3C2×D412yes—
248C23×D3C2×D412yes—
249C23×D3C2×Q812yes—
250C23×D3#4112yes—
251C23×D3#4112yes—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C22×C412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4#4112yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67C4⋊C4116yescomplemented
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—28no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—44no—
342C22×Dic3—44no—
343C22×Dic3—44no—
344C22×Dic3—44no—
345C22×Dic3—44no—
346C22×Dic3—44no—
347C22×Dic3C22×C412yes—
348C22×Dic3C22×C412yes—
349C22×Dic3C22×C412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3C2×Q812yes—
354C22×Dic3#4112yes—
355C22×Dic3#4112yes—
356C22×Dic3#4112yes—
357C2×C4×D3—28no—
358C2×C4×D3—28no—
359C2×C4×D3—28no—
360C2×C4×D3—28no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C2×C4×D3—44no—
376C2×C4×D3—44no—
377C2×C4×D3—44no—
378C3×C4⋊C4—44no—
379C3×C22⋊C4—28no—
380C3×C22⋊C4—44no—
381C3×C22⋊C4—44no—
382#217—44no—
383#217—44no—
384(C2×D3)⋊C4—28no—
385(C2×D3)⋊C4—28no—
386(C2×D3)⋊C4—44no—
387Dic3⋊C4—28no—
388Dic3⋊C4—44no—
389C4×Dic3—28no—
390C25—31no—
391C25C22×D311yescharacteristic
392C22×D4—34no—
393C22×D4—34no—
394C22×D4—34no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—62no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—34no—
406C23×C4—34no—
407C23×C4—31no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—62no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—121no—
425C23×C4—121no—
426C23×C4—121no—
427C23×C4—121no—
428C23×C4—121no—
429C23×C4—121no—
430C23×C4—121no—
431C23×C4—121no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C4×D4—632no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—121no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—41no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4C4×D314yescomplemented
474C2×C42—62no—
475C2×C42—62no—
476C2×C42—62no—
477#95—22no—
478#95—34no—
479#95—34no—
480#95—41no—
481#95—41no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—121no—
492#95—121no—
493#95—121no—
494#95—121no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3C2×C4⋊C414yes—
530C23×C3C23×C411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C22×Q811yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C23×C3H(5,𝔽2)11yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3C2×C4⋊C414yes—
574C22×D3C4×D414yes—
575C22×D3C4×D414yes—
576C22×D3#12014yes—
577C22×D3C22⋊Q814yes—
578C22×D3C22⋊Q814yes—
579C22×D3#12314yes—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622#67—232no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—416no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3C2×C4⋊C414yes—
672C2×Dic3#12314yes—
673C4×D3—416no—
674C4×D3—416no—
675C4×D3—416no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—32no—
689C24—32no—
690C24—32no—
691C24—32no—
692C24—32no—
693C24—32no—
694C24—32no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24C2×C4×D312yes—
704C24D3×D412yes—
705C24D3×Q812yes—
706C24C23×D311yescharacteristic
707C2×D4—316no—
708C2×D4—68no—
709C2×D4—68no—
710C2×D4—68no—
711C2×D4—68no—
712C2×D4—68no—
713C2×D4—68no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—68no—
762C22×C4—68no—
763C22×C4—68no—
764C22×C4—68no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—68no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—124no—
806C22×C4—124no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4—124no—
818C22×C4—124no—
819C22×C4—124no—
820C22×C4—124no—
821C22×C4—124no—
822C22×C4—124no—
823C22×C4—124no—
824C22×C4—124no—
825C22×C4—124no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4C2×C4×D312yes—
829C22×C4C2×C4×D312yes—
830C22×C4D3×D412yes—
831C22×C4D3×D412yes—
832C22×C4#23712yes—
833C4⋊C4—44no—
834C4⋊C4—68no—
835C4⋊C4—124no—
836C22⋊C4—28no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—68no—
840C22⋊C4—68no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—68no—
845C22×C3—24no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3C22×C4⋊C411yescharacteristic
861C22×C3C2×C4×D411yescharacteristic
862C22×C3C2×C4×D411yescharacteristic
863C22×C3C4×#4111yescharacteristic
864C22×C3C4×#4111yescharacteristic
865C22×C3#51811yescharacteristic
866C22×C3#51811yescharacteristic
867C22×C3C2×#12011yescharacteristic
868C22×C3C2×C22⋊Q811yescharacteristic
869C22×C3C2×C22⋊Q811yescharacteristic
870C22×C3C2×#12311yescharacteristic
871C22×C3C2×#12311yescharacteristic
872C22×C3#52511yescharacteristic
873C22×C3#52911yescharacteristic
874C22×C3#52911yescharacteristic
875C22×C3#53411yescharacteristic
876C22×C3#53511yescharacteristic
877C22×C3#53811yescharacteristic
878C22×C3#53811yescharacteristic
879C22×C3#54611yescharacteristic
880C22×C3#54611yescharacteristic
881C22×C3#54611yescharacteristic
882C22×C3#54611yescharacteristic
883C22×C3#54611yescharacteristic
884C22×C3#54611yescharacteristic
885C22×C3#54611yescharacteristic
886C22×C3#54611yescharacteristic
887C22×C3#55311yescharacteristic
888C22×C3#55311yescharacteristic
889C22×C3#55311yescharacteristic
890C22×C3#55311yescharacteristic
891C22×C3#55411yescharacteristic
892C22×C3#55411yescharacteristic
893C22×C3#55411yescharacteristic
894C22×C3#55411yescharacteristic
895C2×D3—24no—
896C2×D3—24no—
897C2×D3—24no—
898C2×D3—24no—
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—24no—
903C2×D3—24no—
904C2×D3—24no—
905C2×D3—24no—
906C2×D3—24no—
907C2×D3—24no—
908C2×D3—24no—
909C2×D3#38518yes—
910C3×C4—42no—
911C3×C4—42no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—81no—
916Dic3—24no—
917Dic3—24no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—81no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—34no—
942C23—34no—
943C23—34no—
944C23—34no—
945C23—34no—
946C23—34no—
947C23—34no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23D3×C4⋊C414yes—
993C23C22×C4×D311yescharacteristic
994C23C2×D3×D411yescharacteristic
995C23C2×D3×D411yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×#23711yescharacteristic
998C23#100411yescharacteristic
999C23#100411yescharacteristic
1000C23#100411yescharacteristic
1001C23C2×D3×Q811yescharacteristic
1002C23D3×#4111yescharacteristic
1003C23D3×#4111yescharacteristic
1004C23D3×#4111yescharacteristic
1005C23D3×#4111yescharacteristic
1006C23D3×#4111yescharacteristic
1007C23#100911yescharacteristic
1008D4—632no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—34no—
1025C2×C4—34no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—1216no—
1078C2×C4—1216no—
1079C2×C4—1216no—
1080C2×C4—1216no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C3—44no—
1105C2×C3C2×#38511yescharacteristic
1106C2×C3C4×#12311yescharacteristic
1107C2×C3#232111yescharacteristic
1108C2×C3#234911yescharacteristic
1109C2×C3#234911yescharacteristic
1110C2×C3#236411yescharacteristic
1111C2×C3#236411yescharacteristic
1112C2×C3#240411yescharacteristic
1113C2×C3#240511yescharacteristic
1114C2×C3#244411yescharacteristic
1115C2×C3#244411yescharacteristic
1116C2×C3#245011yescharacteristic
1117C2×C3#245011yescharacteristic
1118C2×C3#248711yescharacteristic
1119C2×C3#257911yescharacteristic
1120D3—28no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—38no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—64no—
1138C22—64no—
1139C22—64no—
1140C22—64no—
1141C22—64no—
1142C22—64no—
1143C22—64no—
1144C22—64no—
1145C22—64no—
1146C22—64no—
1147C22—64no—
1148C22—64no—
1149C22—64no—
1150C22—64no—
1151C22#548611yescharacteristic
1152C22C2×D3×C4⋊C411yescharacteristic
1153C22#552211yescharacteristic
1154C22C4×#23711yescharacteristic
1155C22C4×D3×D411yescharacteristic
1156C22C4×D3×D411yescharacteristic
1157C22#554511yescharacteristic
1158C22D3×#12011yescharacteristic
1159C22#559111yescharacteristic
1160C22#559111yescharacteristic
1161C22#560511yescharacteristic
1162C22#560611yescharacteristic
1163C22#561011yescharacteristic
1164C22#561011yescharacteristic
1165C22#561011yescharacteristic
1166C22#561211yescharacteristic
1167C22#561311yescharacteristic
1168C22#561411yescharacteristic
1169C22D3×C22⋊Q811yescharacteristic
1170C22D3×C22⋊Q811yescharacteristic
1171C22#563511yescharacteristic
1172C22#563611yescharacteristic
1173C22#563611yescharacteristic
1174C22#563611yescharacteristic
1175C22D3×#12311yescharacteristic
1176C22D3×#12311yescharacteristic
1177C22#565411yescharacteristic
1178C22#566111yescharacteristic
1179C22#566111yescharacteristic
1180C22#567611yescharacteristic
1181C22#567811yescharacteristic
1182C22#568011yescharacteristic
1183C22#570611yescharacteristic
1184C22#570911yescharacteristic
1185C22#571511yescharacteristic
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—64no—
1192C4—64no—
1193C4—81no—
1194C4—122no—
1195C4—122no—
1196C4—122no—
1197C4—122no—
1198C4—241no—
1199C3#1401611yescharacteristic, complemented, Sylow
1200C2—44no—
1201C2—68no—
1202C2#7401111yescharacteristic
1203C2#7439411yescharacteristic
1204C2D3×#38511yescharacteristic
1205C2#7488111yescharacteristic
1206C2#7545311yescharacteristic
1207C2#7583911yescharacteristic
1208C2#7642911yescharacteristic
1209C2#7675411yescharacteristic
1210C2#7686611yescharacteristic
1211C2#7710611yescharacteristic
1212C2#7711811yescharacteristic
1213C2#7742011yescharacteristic
1214C2#7742211yescharacteristic
1215C2#7767411yescharacteristic
1216C2#7802911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14016
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4989C2semidirect
5. C2×D3×#95C2semidirect
6. C3×#1439C2semidirect
7. #71564C2semidirect
8. #71547C2semidirect
9. #71544C2semidirect
10. #71544C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69414C2semidirect
14. #69413C2semidirect
15. #69405C2semidirect
57. #4956C4semidirect
67. #1439D3semidirect
122. C22×C4×D3C2×C4semidirect
135. C2×C3×C22⋊C4C2×C4semidirect
141. C2×#217C2×C4semidirect
149. C2×(C2×D3)⋊C4C2×C4semidirect
177. C3⋊#95C2×C4semidirect
178. C3⋊#95C2×C4semidirect
300. C2×#67C4⋊C4semidirect
473. C2×C22⋊C4C4×D3semidirect
1199. C3#14016semidirect

Maximal subgroups

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

subgroupindex
C22×#67⋊C42
C2×#49892
C2×#49562
C2×D3×#952
C3×#14392
#715642
#715472
#715442
(C2×D3)⋊#952
#694142
#694132
#694052
#140163