Finite Group Databasebeta

← #10740315

Subgroups — #10740315

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×#4984C211yesmaximal, characteristic, complemented
2C2×#4961C211yesmaximal, characteristic
3C2×#4961C211yesmaximal, characteristic
4C2×#4670C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic
8#71546C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69417C211yesmaximal, characteristic, complemented
13#69415C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#15777—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×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
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#4984—24no—
53#4961—24no—
54#4961—24no—
55#4670—24no—
56C2×#394—31no—
57C2×#394—31no—
58C2×#389—31no—
59C2×#388—31no—
60#1443—31no—
61#1442—31no—
62#1440—31no—
63#1439—31no—
64#1439—31no—
65#1439D311yescharacteristic, complemented
66#1438—31no—
67#1437—31no—
68#1437—31no—
69#1437—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—22no—
95C2×C3×C4⋊C4—22no—
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—22no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217—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)⋊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—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—41no—
137C2×C4⋊Dic3—41no—
138C2×C4⋊Dic3—41no—
139C2×C4⋊Dic3—41no—
140C2×C4⋊Dic3D414yes—
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—41no—
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#389—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×C3#4112yes—
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×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4#4112yes—
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×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3C2×D412yes—
327C22×Dic3C2×D412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3#4112yes—
330C22×Dic3#4112yes—
331C3×C4⋊C4—28no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335#217—44no—
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—
345C4⋊Dic3—44no—
346C4⋊Dic3—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—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—121no—
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—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—62no—
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—121no—
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—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
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#12414yes—
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—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
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—
647C24#23912yes—
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—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
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#23512yes—
742C22×C4D3×D412yes—
743C22×C4D3×D412yes—
744C22×C4#23712yes—
745C22×C4#23712yes—
746C22×C4#23712yes—
747C4⋊C4—28no—
748C4⋊C4—124no—
749C4⋊C4—124no—
750C4⋊C4—124no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—68no—
755C22⋊C4—124no—
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×C3C2×#12411yescharacteristic
783C22×C3#52911yescharacteristic
784C22×C3#52911yescharacteristic
785C22×C3#53211yescharacteristic
786C22×C3#53411yescharacteristic
787C22×C3#53411yescharacteristic
788C22×C3#53811yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#53811yescharacteristic
791C22×C3#54011yescharacteristic
792C22×C3#54211yescharacteristic
793C22×C3#54211yescharacteristic
794C22×C3#54211yescharacteristic
795C22×C3D4211yescharacteristic
796C22×C3#54611yescharacteristic
797C22×C3#54611yescharacteristic
798C22×C3#54611yescharacteristic
799C22×C3#54711yescharacteristic
800C22×C3#54811yescharacteristic
801C22×C3#55011yescharacteristic
802C22×C3#55111yescharacteristic
803C22×C3#55211yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55311yescharacteristic
806C22×C3#55311yescharacteristic
807C22×C3#55311yescharacteristic
808C22×C3#55311yescharacteristic
809C22×C3#55311yescharacteristic
810C22×C3#55311yescharacteristic
811C22×C3#55511yescharacteristic
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—24no—
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—81no—
842Dic3—81no—
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
918C23C2×#23711yescharacteristic
919C23#100411yescharacteristic
920C23#100411yescharacteristic
921C23C2×#23911yescharacteristic
922C23D3×#4111yescharacteristic
923C23D3×#4111yescharacteristic
924C23#100911yescharacteristic
925C23#100911yescharacteristic
926C23#100911yescharacteristic
927C23#101011yescharacteristic
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—22no—
942C2×C4—22no—
943C2×C4—22no—
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—62no—
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—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
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#88514yes—
1020C2×C3—82no—
1021C2×C3#245611yescharacteristic
1022C2×C3#245811yescharacteristic
1023C2×C3#247011yescharacteristic
1024C2×C3#249011yescharacteristic
1025C2×C3#249111yescharacteristic
1026C2×C3#251811yescharacteristic
1027C2×C3#255911yescharacteristic
1028C2×C3#259111yescharacteristic
1029C2×C3#260211yescharacteristic
1030C2×C3#266811yescharacteristic
1031C2×C3#270111yescharacteristic
1032C2×C3#273011yescharacteristic
1033C2×C3#277911yescharacteristic
1034C2×C3#280111yescharacteristic
1035C2×C3#280311yescharacteristic
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—
1067C22C2×#88511yescharacteristic
1068C22#551411yescharacteristic
1069C22#553011yescharacteristic
1070C22#554811yescharacteristic
1071C22#556111yescharacteristic
1072C22#556511yescharacteristic
1073C22#556511yescharacteristic
1074C22#558611yescharacteristic
1075C22#559111yescharacteristic
1076C22#559311yescharacteristic
1077C22#559911yescharacteristic
1078C22#560111yescharacteristic
1079C22#560611yescharacteristic
1080C22#561111yescharacteristic
1081C22#561611yescharacteristic
1082C22#561811yescharacteristic
1083C22#561811yescharacteristic
1084C22#561911yescharacteristic
1085C22#562411yescharacteristic
1086C22#562411yescharacteristic
1087C22#563011yescharacteristic
1088C22#563011yescharacteristic
1089C22#564211yescharacteristic
1090C22#564411yescharacteristic
1091C22#565311yescharacteristic
1092C22#565311yescharacteristic
1093C22#565711yescharacteristic
1094C22#566611yescharacteristic
1095C22#566711yescharacteristic
1096C22#567711yescharacteristic
1097C22#568111yescharacteristic
1098C22#568211yescharacteristic
1099C22#570511yescharacteristic
1100C22#571011yescharacteristic
1101C22#571711yescharacteristic
1102C4—24no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—81no—
1108C4—122no—
1109C4—122no—
1110C4—122no—
1111C4—122no—
1112C4—122no—
1113C4—241no—
1114C4—241no—
1115C3#1577711yescharacteristic, complemented, Sylow
1116C2—82no—
1117C2—242no—
1118C2#7391411yescharacteristic
1119C2#7447611yescharacteristic
1120C2#7456311yescharacteristic
1121C2#7477111yescharacteristic
1122C2#7580411yescharacteristic
1123C2#7589811yescharacteristic
1124C2#7645111yescharacteristic
1125C2#7667711yescharacteristic
1126C2#7678411yescharacteristic
1127C2#7707911yescharacteristic
1128C2#7714811yescharacteristic
1129C2#7729911yescharacteristic
1130C2#7730811yescharacteristic
1131C2#7759711yescharacteristic
1132C2#7811211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15777
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#4984C2semidirect
4. C2×#4670C2semidirect
5. C3×#1439C2semidirect
6. #71570C2semidirect
8. #71546C2semidirect
9. #71545C2semidirect
10. #71545C2semidirect
11. #69429C2semidirect
12. #69417C2semidirect
13. #69415C2semidirect
14. #69408C2semidirect
15. #69407C2semidirect
65. #1439D3semidirect
1115. C3#15777semidirect

Maximal subgroups

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

subgroupindex
C2×#49842
C2×#49612
C2×#46702
C3×#14392
#715702
#715502
#715462
#715452
#694292
#694172
#694152
#694082
#694072
#157773