Finite Group Databasebeta

← #10720139

Subgroups — #10720139

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4989C211yesmaximal, characteristic
2C2×#4980C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×#4668C211yesmaximal, characteristic
5C2×D3×#95C211yesmaximal, characteristic
6C3×#1436C211yesmaximal, characteristic, complemented
7#71534C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11#69421C211yesmaximal, characteristic, complemented
12#69418C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14131—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
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#4989C418yescomplemented
53#4980—24no—
54C4×(C2×D3)⋊C4—24no—
55#4668—24no—
56D3×#95—24no—
57C2×#387—31no—
58C2×#385—31no—
59C2×#385—31no—
60C2×C4×C22⋊C4—31no—
61C22×#95—31no—
62#1445—31no—
63#1443—31no—
64#1442—31no—
65#1441—31no—
66#1436—31no—
67#1436D311yescharacteristic, complemented
68#1434—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3—41no—
107C22×C4×D3C2×C414yes—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4C2×C414yescomplemented
111C2×C3×C42—22no—
112C2×C3×C42—22no—
113C2×C3×C42—41no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4C2×C414yes—
123C2×(C2×D3)⋊C4C2×C414yes—
124C2×(C2×D3)⋊C4D414yes—
125C2×(C2×D3)⋊C4Q814yes—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—41no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—41no—
132C2×Dic3⋊C4—41no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4C2×C414yescomplemented
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3—41no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—41no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95C2×C414yescomplemented
158C3⋊#95C2×C414yescomplemented
159C3⋊#95D414yes—
160C24×C4—31no—
161C24×C4—31no—
162C24×C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C42—31no—
172C22×C42C2×D311yescharacteristic
173#387—64no—
174#385—38no—
175#385—64no—
176C4×C22⋊C4—64no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—64no—
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C24×C3C2411yescharacteristic
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3C22×C412yes—
210C23×D3C2×D412yes—
211C23×D3C2×Q812yes—
212C23×D3#4112yes—
213C23×D3#4112yes—
214C23×D3#4112yes—
215C23×D3#4112yes—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
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×C4C22×C412yes—
257C22×C3×C4C22×C412yes—
258C22×C3×C4C22×C412yes—
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×Q812yes—
262C22×C3×C4#4112yes—
263C22×C3×C4#4112yes—
264C22×C3×C4#4112yes—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
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×Dic3C22×C412yes—
308C22×Dic3C22×C412yes—
309C22×Dic3C22×C412yes—
310C22×Dic3C2×D412yes—
311C22×Dic3C2×D412yes—
312C22×Dic3C2×D412yes—
313C22×Dic3C2×Q812yes—
314C2×C4×D3—28no—
315C2×C4×D3—28no—
316C2×C4×D3—28no—
317C2×C4×D3—28no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3—44no—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C2×C4×D3—44no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3—44no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C3×C4⋊C4—28no—
336C3×C42—44no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—28no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—28no—
341C4⋊Dic3—44no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344C4×Dic3—44no—
345C25—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—34no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
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—121no—
369C23×C4—121no—
370C23×C4—121no—
371C23×C4—121no—
372C23×C4—121no—
373C23×C4—121no—
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C4⋊C4—121no—
392C2×C4⋊C4C4×D314yescomplemented
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—41no—
408C2×C42—62no—
409C2×C42—62no—
410C2×C42—121no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—34no—
416#95—34no—
417#95—34no—
418#95—41no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—62no—
426#95—62no—
427#95—62no—
428#95—121no—
429#95—121no—
430#95—121no—
431#95—121no—
432#95—121no—
433C23×C3C23×C411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C22×D411yescharacteristic
436C23×C3C22×Q811yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3H(5,𝔽2)11yescharacteristic
445C23×C3H(5,𝔽2)11yescharacteristic
446C23×C3H(5,𝔽2)11yescharacteristic
447C23×C32−1+411yescharacteristic
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3#11714yes—
477C22×D3C4×D414yes—
478C22×D3C4×Q814yes—
479C22×D3C22⋊Q814yes—
480C22×D3#12314yes—
481C22×D3#12514yes—
482C22×D3#12614yes—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4C4×D414yes—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C4×D3—416no—
582C4×D3—416no—
583C4×D3—416no—
584C24—32no—
585C24—32no—
586C24—32no—
587C24—32no—
588C24—32no—
589C24—32no—
590C24—32no—
591C24—61no—
592C24—61no—
593C24—61no—
594C24—61no—
595C24—61no—
596C24—61no—
597C24—61no—
598C24—61no—
599C24C23×D311yescharacteristic
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—68no—
648C22×C4—68no—
649C22×C4—68no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—68no—
693C22×C4—124no—
694C22×C4—124no—
695C22×C4—124no—
696C22×C4—124no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—124no—
700C22×C4—124no—
701C22×C4—124no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—124no—
705C22×C4—124no—
706C22×C4—124no—
707C22×C4—124no—
708C22×C4—124no—
709C22×C4—124no—
710C22×C4C2×C4×D312yes—
711C22×C4C2×C4×D312yes—
712C22×C4C2×C4×D312yes—
713C22×C4#23512yes—
714C22×C4#23512yes—
715C22×C4D3×D412yes—
716C22×C4D3×D412yes—
717C22×C4#23712yes—
718C22×C4D3×Q812yes—
719C4⋊C4—28no—
720C4⋊C4—124no—
721C4⋊C4—124no—
722C4⋊C4—124no—
723C22⋊C4—68no—
724C22⋊C4—68no—
725C22⋊C4—68no—
726C22⋊C4—68no—
727C42—44no—
728C42—124no—
729C22×C3C2×#11711yescharacteristic
730C22×C3C2×C4×D411yescharacteristic
731C22×C3C2×C4×D411yescharacteristic
732C22×C3C2×C4×Q811yescharacteristic
733C22×C3C4×#4111yescharacteristic
734C22×C3#51811yescharacteristic
735C22×C3#52011yescharacteristic
736C22×C3C2×C22⋊Q811yescharacteristic
737C22×C3C2×#12311yescharacteristic
738C22×C3#52511yescharacteristic
739C22×C3#52511yescharacteristic
740C22×C3C2×#12511yescharacteristic
741C22×C3C2×#12611yescharacteristic
742C22×C3#52911yescharacteristic
743C22×C3#52911yescharacteristic
744C22×C3#53811yescharacteristic
745C22×C3#53811yescharacteristic
746C22×C3#53911yescharacteristic
747C22×C3#53911yescharacteristic
748C22×C3D4211yescharacteristic
749C22×C3#54611yescharacteristic
750C22×C3#54611yescharacteristic
751C22×C3#54611yescharacteristic
752C22×C3#54611yescharacteristic
753C22×C3#54711yescharacteristic
754C22×C3D4×Q811yescharacteristic
755C22×C3#55111yescharacteristic
756C22×C3#55111yescharacteristic
757C22×C3#55111yescharacteristic
758C22×C3#55111yescharacteristic
759C22×C3#55211yescharacteristic
760C22×C3#55211yescharacteristic
761C22×C3#55411yescharacteristic
762C22×C3#55411yescharacteristic
763C22×C3#55411yescharacteristic
764C2×D3—24no—
765C2×D3—24no—
766C2×D3—24no—
767C2×D3—24no—
768C2×D3—24no—
769C2×D3—24no—
770C2×D3—24no—
771C2×D3—24no—
772C2×D3—24no—
773C2×D3—24no—
774C2×D3—24no—
775C2×D3—24no—
776C2×D3—24no—
777C2×D3—24no—
778C2×D3#38718yescomplemented
779C3×C4—24no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4—42no—
785C3×C4—42no—
786Dic3—42no—
787Dic3—42no—
788Dic3—42no—
789Dic3—42no—
790Dic3—42no—
791Dic3—42no—
792Dic3—42no—
793C23—34no—
794C23—34no—
795C23—34no—
796C23—34no—
797C23—34no—
798C23—34no—
799C23—34no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23C22×C4×D311yescharacteristic
829C23C2×#23511yescharacteristic
830C23C2×#23511yescharacteristic
831C23C2×D3×D411yescharacteristic
832C23C2×D3×D411yescharacteristic
833C23C2×#23711yescharacteristic
834C23#100411yescharacteristic
835C23C2×D3×Q811yescharacteristic
836C23#100711yescharacteristic
837C23D3×#4111yescharacteristic
838C23D3×#4111yescharacteristic
839C23D3×#4111yescharacteristic
840C23D3×#4111yescharacteristic
841C23#100911yescharacteristic
842C23#100911yescharacteristic
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—1216no—
913C2×C4—1216no—
914C2×C4—1216no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4#67⋊C414yes—
944C2×C3C2×#38711yescharacteristic
945C2×C3#229011yescharacteristic
946C2×C3#231811yescharacteristic
947C2×C3#235811yescharacteristic
948C2×C3#235911yescharacteristic
949C2×C3#236011yescharacteristic
950C2×C3#236811yescharacteristic
951C2×C3#241811yescharacteristic
952C2×C3#241911yescharacteristic
953C2×C3#244911yescharacteristic
954C2×C3#245011yescharacteristic
955C2×C3#247311yescharacteristic
956C2×C3#248011yescharacteristic
957C2×C3#249311yescharacteristic
958C2×C3#250511yescharacteristic
959D3—28no—
960C22—38no—
961C22—64no—
962C22—64no—
963C22—64no—
964C22—64no—
965C22—64no—
966C22—64no—
967C22—64no—
968C22—64no—
969C22—64no—
970C22—64no—
971C22—64no—
972C22—64no—
973C22—64no—
974C22—64no—
975C22C4×#23511yescharacteristic
976C22C2×#67⋊C411yescharacteristic
977C22#550711yescharacteristic
978C22#551111yescharacteristic
979C22D3×#11711yescharacteristic
980C22#552711yescharacteristic
981C22#552711yescharacteristic
982C22C4×D3×D411yescharacteristic
983C22#554511yescharacteristic
984C22#554711yescharacteristic
985C22#554711yescharacteristic
986C22#555011yescharacteristic
987C22#555611yescharacteristic
988C22#555711yescharacteristic
989C22#555711yescharacteristic
990C22C4×D3×Q811yescharacteristic
991C22#557411yescharacteristic
992C22#557911yescharacteristic
993C22#558111yescharacteristic
994C22#559111yescharacteristic
995C22#560911yescharacteristic
996C22#561011yescharacteristic
997C22D3×C22⋊Q811yescharacteristic
998C22#563511yescharacteristic
999C22#563811yescharacteristic
1000C22#563911yescharacteristic
1001C22D3×#12311yescharacteristic
1002C22#565711yescharacteristic
1003C22#565811yescharacteristic
1004C22#567611yescharacteristic
1005C22D3×#12511yescharacteristic
1006C22#569211yescharacteristic
1007C22D3×#12611yescharacteristic
1008C22#570411yescharacteristic
1009C22#572711yescharacteristic
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4—122no—
1021C4—122no—
1022C4—122no—
1023C4—122no—
1024C3#1413111yescharacteristic, complemented, Sylow
1025C2—68no—
1026C2#7356211yescharacteristic
1027C2#7377211yescharacteristic
1028C2#7377511yescharacteristic
1029C2#7460411yescharacteristic
1030C2#7461011yescharacteristic
1031C2#7487911yescharacteristic
1032C2#7494511yescharacteristic
1033C2D3×#38711yescharacteristic
1034C2#7533711yescharacteristic
1035C2#7534011yescharacteristic
1036C2#7554111yescharacteristic
1037C2#7584511yescharacteristic
1038C2#7602311yescharacteristic
1039C2#7622511yescharacteristic
1040C2#7661511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14131
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4980C2semidirect
6. C3×#1436C2semidirect
7. #71534C2semidirect
11. #69421C2semidirect
12. #69418C2semidirect
13. #69414C2semidirect
14. #69410C2semidirect
15. #69406C2semidirect
52. #4989C4semidirect
67. #1436D3semidirect
110. C2×C3×C4⋊C4C2×C4semidirect
134. C2×Dic3⋊C4C2×C4semidirect
157. C3⋊#95C2×C4semidirect
158. C3⋊#95C2×C4semidirect
392. C2×C4⋊C4C4×D3semidirect
778. C2×D3#387semidirect
1024. C3#14131semidirect

Maximal subgroups

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

subgroupindex
C2×#49892
C2×#49802
C2×C4×(C2×D3)⋊C42
C2×#46682
C2×D3×#952
C3×#14362
#715342
(C2×D3)⋊#952
#694212
#694182
#694142
#694102
#694062
#141313