Finite Group Databasebeta

← #10724489

Subgroups — #10724489

Order 768.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4956C211yesmaximal, characteristic
2C2×#4961C211yesmaximal, characteristic
3C2×#4958C211yesmaximal, characteristic
4C2×#4946C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6C3×#1437C211yesmaximal, characteristic, complemented
7#71549C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71536C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69422C211yesmaximal, characteristic, complemented
14#69418C211yesmaximal, characteristic, complemented
15#69411C211yesmaximal, characteristic, complemented
16#14517—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
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
52#4961C418yescomplemented
53#4958—24no—
54#4956—24no—
55#4946—24no—
56#4940—24no—
57C2×#394—31no—
58C2×#388—31no—
59C2×#386—31no—
60C2×#386—31no—
61C2×#385—31no—
62#1445—31no—
63#1443—31no—
64#1441—31no—
65#1440—31no—
66#1439—31no—
67#1437D311yescharacteristic, complemented
68#1436—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—41no—
85C22×#67—41no—
86C22×#67C2×C414yes—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—41no—
91C23×Dic3—41no—
92C23×Dic3—41no—
93C23×Dic3—41no—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4C2×C414yescomplemented
116C2×C3×C22⋊C4D414yes—
117C2×C3×C42—22no—
118C2×C3×C42—41no—
119C2×C3×C42—41no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—41no—
125C2×#217C2×C414yescomplemented
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4C2×C414yescomplemented
139C2×(C2×D3)⋊C4C2×C414yescomplemented
140C2×(C2×D3)⋊C4D414yes—
141C2×C4⋊Dic3—41no—
142C2×C4⋊Dic3—41no—
143C2×C4⋊Dic3C2×C414yescomplemented
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—41no—
149C2×Dic3⋊C4—41no—
150C3×#95—41no—
151C3×#95—41no—
152C3×#95—41no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95C2×C414yescomplemented
168C23×D4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C42C2×D311yescharacteristic
185#394—38no—
186#388—64no—
187#386—64no—
188#386—64no—
189#385—64no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3C22×C412yes—
221C24×C3C2×D412yes—
222C24×C3#4112yes—
223C24×C3C2411yescharacteristic
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3C22×C412yes—
237C23×D3C2×D412yes—
238C23×D3#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
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×C4C22×C412yes—
277C22×C3×C4C22×C412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
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—21no—
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—44no—
332C22×Dic3—44no—
333C22×Dic3—44no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—44no—
337C22×Dic3—44no—
338C22×Dic3C22×C412yes—
339C22×Dic3C22×C412yes—
340C22×Dic3C22×C412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353C3×C22⋊C4—44no—
354C3×C42—44no—
355#217—28no—
356#217—44no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4—44no—
362C4⋊Dic3—44no—
363Dic3⋊C4—44no—
364Dic3⋊C4—44no—
365C25—31no—
366C25C22×D311yescharacteristic
367C22×D4—34no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—121no—
373C22×D4—121no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—121no—
388C23×C4—121no—
389C23×C4—121no—
390C23×C4—121no—
391C23×C4—121no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4—121no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C2×C4⋊C4—34no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C4⋊C4—121no—
409C2×C4⋊C4—121no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4C4×D314yescomplemented
439C2×C22⋊C4D1214yes—
440C2×C42—22no—
441C2×C42—41no—
442C2×C42—41no—
443#95—34no—
444#95—41no—
445#95—41no—
446#95—41no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—121no—
457#95—121no—
458#95—121no—
459#95—121no—
460#95—121no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3C4×D414yes—
496C23×C3C23×C411yescharacteristic
497C23×C3C22×D411yescharacteristic
498C23×C3C22×D411yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C3H(5,𝔽2)11yescharacteristic
506C23×C3H(5,𝔽2)11yescharacteristic
507C23×C3H(5,𝔽2)11yescharacteristic
508C23×C3H(5,𝔽2)11yescharacteristic
509C23×C32−1+411yescharacteristic
510C23×C32−1+411yescharacteristic
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3C4×D414yes—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588#67—416no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—416no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C4×D3—416no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—32no—
653C24—32no—
654C24—32no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24C2×C4×D312yes—
668C24C2×D1212yes—
669C24#23512yes—
670C24C23×D311yescharacteristic
671C2×D4—68no—
672C2×D4—68no—
673C2×D4—124no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4C2×C4×D312yes—
779C22×C4C2×C4×D312yes—
780C22×C4C2×D1212yes—
781C22×C4C2×D1212yes—
782C22×C4D3×D412yes—
783C4⋊C4—124no—
784C4⋊C4—124no—
785C4⋊C4—124no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—68no—
790C22⋊C4—68no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C42—44no—
797C22×C3—24no—
798C22×C3—24no—
799C22×C3—24no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3C2×C4×D411yescharacteristic
813C22×C3C2×C4×D411yescharacteristic
814C22×C3C4×#4111yescharacteristic
815C22×C3#51811yescharacteristic
816C22×C3#51811yescharacteristic
817C22×C3#52011yescharacteristic
818C22×C3#52011yescharacteristic
819C22×C3#53411yescharacteristic
820C22×C3#53411yescharacteristic
821C22×C3#53611yescharacteristic
822C22×C3#53711yescharacteristic
823C22×C3#53811yescharacteristic
824C22×C3#53811yescharacteristic
825C22×C3#53811yescharacteristic
826C22×C3#53911yescharacteristic
827C22×C3#53911yescharacteristic
828C22×C3#53911yescharacteristic
829C22×C3#54211yescharacteristic
830C22×C3#54211yescharacteristic
831C22×C3D4211yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54611yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#54611yescharacteristic
836C22×C3#54611yescharacteristic
837C22×C3#54711yescharacteristic
838C22×C3#55111yescharacteristic
839C22×C3#55111yescharacteristic
840C22×C3#55211yescharacteristic
841C22×C3#55311yescharacteristic
842C22×C3#55311yescharacteristic
843C22×C3#56011yescharacteristic
844C22×C3#56011yescharacteristic
845C22×C3#56211yescharacteristic
846C22×C3#56211yescharacteristic
847C2×D3—24no—
848C2×D3—24no—
849C2×D3—24no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—81no—
868Dic3—42no—
869Dic3—42no—
870Dic3—42no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3—81no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—34no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23C4×D1214yes—
945C23C22×C4×D311yescharacteristic
946C23C22×D1211yescharacteristic
947C23C2×#23511yescharacteristic
948C23C2×D3×D411yescharacteristic
949C23#100411yescharacteristic
950C23#100411yescharacteristic
951C23#100411yescharacteristic
952C23#100411yescharacteristic
953C23#100411yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23D3×#4111yescharacteristic
957C23#100911yescharacteristic
958C23#101011yescharacteristic
959C23#101011yescharacteristic
960D4—1216no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—1216no—
1022C2×C4—1216no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C3—44no—
1055C2×C3#232211yescharacteristic
1056C2×C3#232511yescharacteristic
1057C2×C3#233711yescharacteristic
1058C2×C3#235811yescharacteristic
1059C2×C3#235911yescharacteristic
1060C2×C3#236411yescharacteristic
1061C2×C3#237711yescharacteristic
1062C2×C3#266811yescharacteristic
1063C2×C3#267211yescharacteristic
1064C2×C3#268711yescharacteristic
1065C2×C3#269111yescharacteristic
1066C2×C3#269711yescharacteristic
1067C2×C3#270811yescharacteristic
1068C2×C3#274611yescharacteristic
1069C2×C3#275011yescharacteristic
1070D3—44no—
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—64no—
1087C22—64no—
1088C22—64no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22C2×C4×D1211yescharacteristic
1102C22#548611yescharacteristic
1103C22#549011yescharacteristic
1104C22#549311yescharacteristic
1105C22#552211yescharacteristic
1106C22#552611yescharacteristic
1107C22#552711yescharacteristic
1108C22#554011yescharacteristic
1109C22#554011yescharacteristic
1110C22C4×D3×D411yescharacteristic
1111C22#554511yescharacteristic
1112C22#554611yescharacteristic
1113C22#554611yescharacteristic
1114C22D4×D1211yescharacteristic
1115C22#555411yescharacteristic
1116C22#555411yescharacteristic
1117C22#555411yescharacteristic
1118C22#556411yescharacteristic
1119C22#556411yescharacteristic
1120C22#558911yescharacteristic
1121C22#560811yescharacteristic
1122C22#561211yescharacteristic
1123C22#561311yescharacteristic
1124C22#561311yescharacteristic
1125C22#562011yescharacteristic
1126C22#562111yescharacteristic
1127C22#565511yescharacteristic
1128C22#565711yescharacteristic
1129C22#566011yescharacteristic
1130C22#566911yescharacteristic
1131C22#567911yescharacteristic
1132C22#568411yescharacteristic
1133C22#570811yescharacteristic
1134C22#571011yescharacteristic
1135C22#572011yescharacteristic
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—81no—
1142C4—122no—
1143C4—122no—
1144C4—122no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—241no—
1149C3#1451711yescharacteristic, complemented, Sylow
1150C2—44no—
1151C2—124no—
1152C2#7344611yescharacteristic
1153C2#7347111yescharacteristic
1154C2#7357711yescharacteristic
1155C2#7487711yescharacteristic
1156C2#7491011yescharacteristic
1157C2#7492611yescharacteristic
1158C2#7547111yescharacteristic
1159C2#7566511yescharacteristic
1160C2#7567011yescharacteristic
1161C2#7583711yescharacteristic
1162C2#7594111yescharacteristic
1163C2#7594311yescharacteristic
1164C2#7631011yescharacteristic
1165C2#7638111yescharacteristic
1166C2#7646911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14517
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#4946C2semidirect
5. C2×#4940C2semidirect
6. C3×#1437C2semidirect
7. #71549C2semidirect
8. #71544C2semidirect
9. #71536C2semidirect
10. #69428C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69422C2semidirect
14. #69418C2semidirect
15. #69411C2semidirect
52. #4961C4semidirect
67. #1437D3semidirect
115. C2×C3×C22⋊C4C2×C4semidirect
125. C2×#217C2×C4semidirect
138. C2×(C2×D3)⋊C4C2×C4semidirect
139. C2×(C2×D3)⋊C4C2×C4semidirect
143. C2×C4⋊Dic3C2×C4semidirect
167. C3⋊#95C2×C4semidirect
438. C2×C22⋊C4C4×D3semidirect
1149. C3#14517semidirect

Maximal subgroups

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

subgroupindex
C2×#49562
C2×#49612
C2×#49582
C2×#49462
C2×#49402
C3×#14372
#715492
#715442
#715362
#694282
(C2×D3)⋊#952
#694222
#694182
#694112
#145173