Finite Group Databasebeta

← #10740362

Subgroups — #10740362

Order 768.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4959C211yesmaximal, characteristic
2C2×#4961C211yesmaximal, characteristic
3C2×#4945C211yesmaximal, characteristic, complemented
4C2×#4669C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71569C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71548C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69420C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15782—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
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
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
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#4961—24no—
53#4959—24no—
54#4945—24no—
55#4669—24no—
56C2×#394—31no—
57C2×#394—31no—
58C2×#388—31no—
59C2×#388—31no—
60#1445—31no—
61#1444—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439D311yescharacteristic, complemented
66#1438—31no—
67#1437—31no—
68#1437—31no—
69#1436—31no—
70#1436—31no—
71C25×C3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—41no—
83C22×#67—41no—
84C22×#67—41no—
85C22×#67—41no—
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C4⋊C4—41no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—41no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—41no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217D414yes—
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)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4D414yes—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—41no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—41no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42—31no—
182#394—64no—
183#394—64no—
184#388—64no—
185#388—64no—
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—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
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×C3C2×D412yes—
217C24×C3C2411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
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×D3C2×D412yes—
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×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×C4C2×D412yes—
272C22×C3×C4#4112yes—
273C22×C3×C4#4112yes—
274C22×C3×C4#4112yes—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
280C2×#67—44no—
281C2×#67—44no—
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×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×Dic3C2×D412yes—
325C22×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3#4112yes—
328C22×Dic3#4112yes—
329C22×Dic3#4112yes—
330C22×Dic3#4112yes—
331C3×C4⋊C4—44no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335#217—28no—
336#217—44no—
337#217—44no—
338(C2×D3)⋊C4—28no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344C4⋊Dic3—44no—
345Dic3⋊C4—44no—
346Dic3⋊C4—44no—
347C4×Dic3—44no—
348C4×Dic3—44no—
349C25—31no—
350C25C22×D311yescharacteristic
351C22×D4—62no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—121no—
355C22×D4—121no—
356C22×D4—121no—
357C22×D4—121no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—121no—
381C2×C4⋊C4—121no—
382C2×C4⋊C4—121no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
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×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—121no—
422C2×C42—121no—
423C2×C42—121no—
424C2×C42—121no—
425#95—22no—
426#95—22no—
427#95—41no—
428#95—62no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C32−1+411yescharacteristic
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
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—
568#67—416no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
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—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—32no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24D3×D412yes—
648C24C23×D311yescharacteristic
649C2×D4—124no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—124no—
653C2×D4—124no—
654C2×D4—124no—
655C2×D4—124no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
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—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
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#23512yes—
744C22×C4D3×D412yes—
745C22×C4#23712yes—
746C22×C4#23712yes—
747C4⋊C4—44no—
748C4⋊C4—124no—
749C4⋊C4—124no—
750C4⋊C4—124no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—68no—
755C22⋊C4—68no—
756C22⋊C4—124no—
757C22⋊C4—124no—
758C22⋊C4—124no—
759C22⋊C4—124no—
760C22⋊C4—124no—
761C22⋊C4—124no—
762C22⋊C4—124no—
763C42—124no—
764C42—124no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3—81no—
779C22×C3—81no—
780C22×C3#52511yescharacteristic
781C22×C3#52511yescharacteristic
782C22×C3#52911yescharacteristic
783C22×C3#52911yescharacteristic
784C22×C3#53211yescharacteristic
785C22×C3#53211yescharacteristic
786C22×C3#53411yescharacteristic
787C22×C3#53411yescharacteristic
788C22×C3#53811yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#53911yescharacteristic
791C22×C3#54011yescharacteristic
792C22×C3#54011yescharacteristic
793C22×C3#54211yescharacteristic
794C22×C3#54211yescharacteristic
795C22×C3D4211yescharacteristic
796C22×C3#54611yescharacteristic
797C22×C3#54611yescharacteristic
798C22×C3#54611yescharacteristic
799C22×C3#54611yescharacteristic
800C22×C3#54711yescharacteristic
801C22×C3#54711yescharacteristic
802C22×C3#55111yescharacteristic
803C22×C3#55111yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55311yescharacteristic
806C22×C3#55311yescharacteristic
807C22×C3#55311yescharacteristic
808C22×C3#55511yescharacteristic
809C22×C3#55511yescharacteristic
810C22×C3#55611yescharacteristic
811C22×C3#55911yescharacteristic
812C22×C3#55911yescharacteristic
813C22×C3#56011yescharacteristic
814C22×C3#56211yescharacteristic
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—81no—
823C2×D3—81no—
824C2×D3—81no—
825C2×D3—81no—
826C2×D3—81no—
827C2×D3—81no—
828C2×D3—81no—
829C2×D3—81no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—81no—
835C3×C4—81no—
836Dic3—42no—
837Dic3—42no—
838Dic3—42no—
839Dic3—42no—
840Dic3—42no—
841Dic3—42no—
842Dic3—42no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23C2×#23511yescharacteristic
914C23C2×D3×D411yescharacteristic
915C23C2×D3×D411yescharacteristic
916C23C2×#23711yescharacteristic
917C23C2×#23711yescharacteristic
918C23#100411yescharacteristic
919C23#100411yescharacteristic
920C23#100411yescharacteristic
921C23#100711yescharacteristic
922C23D3×#4111yescharacteristic
923C23D3×#4111yescharacteristic
924C23D3×#4111yescharacteristic
925C23D3×#4111yescharacteristic
926C23#100911yescharacteristic
927C23#100911yescharacteristic
928D4—1216no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C3—82no—
1021C2×C3#245511yescharacteristic
1022C2×C3#247611yescharacteristic
1023C2×C3#247611yescharacteristic
1024C2×C3#252111yescharacteristic
1025C2×C3#252111yescharacteristic
1026C2×C3#255511yescharacteristic
1027C2×C3#259311yescharacteristic
1028C2×C3#260211yescharacteristic
1029C2×C3#260211yescharacteristic
1030C2×C3#266811yescharacteristic
1031C2×C3#270111yescharacteristic
1032C2×C3#270111yescharacteristic
1033C2×C3#275211yescharacteristic
1034C2×C3#279511yescharacteristic
1035C2×C3#280811yescharacteristic
1036D3—82no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—241no—
1060C22—241no—
1061C22—241no—
1062C22—241no—
1063C22—241no—
1064C22—241no—
1065C22—241no—
1066C22—241no—
1067C22#549511yescharacteristic
1068C22#550711yescharacteristic
1069C22#552811yescharacteristic
1070C22#554711yescharacteristic
1071C22#555911yescharacteristic
1072C22#556211yescharacteristic
1073C22#556511yescharacteristic
1074C22#559011yescharacteristic
1075C22#559111yescharacteristic
1076C22#559311yescharacteristic
1077C22#559611yescharacteristic
1078C22#560111yescharacteristic
1079C22#560511yescharacteristic
1080C22#561011yescharacteristic
1081C22#561211yescharacteristic
1082C22#561511yescharacteristic
1083C22#561611yescharacteristic
1084C22#562011yescharacteristic
1085C22#563111yescharacteristic
1086C22#563811yescharacteristic
1087C22#564011yescharacteristic
1088C22#564111yescharacteristic
1089C22#564311yescharacteristic
1090C22#564711yescharacteristic
1091C22#564911yescharacteristic
1092C22#565311yescharacteristic
1093C22#565411yescharacteristic
1094C22#565611yescharacteristic
1095C22#565811yescharacteristic
1096C22#567011yescharacteristic
1097C22#567811yescharacteristic
1098C22#568111yescharacteristic
1099C22#570911yescharacteristic
1100C22#570911yescharacteristic
1101C22#571611yescharacteristic
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—81no—
1108C4—122no—
1109C4—122no—
1110C4—122no—
1111C4—122no—
1112C4—122no—
1113C4—122no—
1114C4—122no—
1115C3#1578211yescharacteristic, complemented, Sylow
1116C2—82no—
1117C2—242no—
1118C2#7392911yescharacteristic
1119C2#7452211yescharacteristic
1120C2#7461111yescharacteristic
1121C2#7484511yescharacteristic
1122C2#7562011yescharacteristic
1123C2#7586211yescharacteristic
1124C2#7637011yescharacteristic
1125C2#7669011yescharacteristic
1126C2#7685211yescharacteristic
1127C2#7692811yescharacteristic
1128C2#7712711yescharacteristic
1129C2#7739811yescharacteristic
1130C2#7743911yescharacteristic
1131C2#7753511yescharacteristic
1132C2#7803411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15782
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#4945C2semidirect
4. C2×#4669C2semidirect
5. C3×#1439C2semidirect
6. #71570C2semidirect
7. #71569C2semidirect
9. #71548C2semidirect
10. #71545C2semidirect
11. #69429C2semidirect
12. #69420C2semidirect
13. #69408C2semidirect
14. #69407C2semidirect
15. #69405C2semidirect
65. #1439D3semidirect
1115. C3#15782semidirect

Maximal subgroups

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

subgroupindex
C2×#49592
C2×#49612
C2×#49452
C2×#46692
C3×#14392
#715702
#715692
#715502
#715482
#715452
#694292
#694202
#694082
#694072
#694052
#157823