Finite Group Databasebeta

← #10740277

Subgroups — #10740277

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×#5221C211yesmaximal, characteristic
2C2×#4952C211yesmaximal, characteristic, complemented
3C2×#4951C211yesmaximal, characteristic, complemented
4C2×#4661C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic
6#72131C211yesmaximal, characteristic
7#71549C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69407C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#15775—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5221—24no—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4952—24no—
54#4951—24no—
55#4661—24no—
56C2×#398—31no—
57C2×#397—31no—
58C2×#390—31no—
59C2×#388—31no—
60#1440—31no—
61#1439—31no—
62#1439—31no—
63#1439—31no—
64#1439—31no—
65#1438—31no—
66#1438D311yescharacteristic
67#1437—31no—
68#1436—31no—
69#1434—31no—
70#1434—31no—
71C25×C3C2311yescharacteristic
72C25×C3C2311yescharacteristic
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—41no—
79C22×C3×D4—41no—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊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—41no—
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—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—41no—
118C2×#217—41no—
119C2×#217—41no—
120C2×#217—41no—
121C2×#217—41no—
122C2×#217—41no—
123C2×#217—41no—
124C2×#217—41no—
125C2×#217—41no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3—41no—
133C2×C4⋊Dic3—41no—
134C2×C4⋊Dic3—41no—
135C2×C4⋊Dic3—41no—
136C2×C4⋊Dic3—41no—
137C2×C4⋊Dic3D414yes—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—41no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C3×#95—22no—
148C3×#95—22no—
149C3⋊#95—22no—
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⋊#95D414yescomplemented
163C23×D4C2×D311yescharacteristic
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42—31no—
182#398—64no—
183#397—64no—
184#390—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×#95—31no—
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—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3#4112yes—
231C24×C3#4112yes—
232C24×C3C2411yescharacteristic
233C2×C3×D4—28no—
234C2×C3×D4—44no—
235C2×C3×D4—44no—
236C2×C3×D4—44no—
237C2×C3×D4—44no—
238C2×C3×D4—44no—
239C2×C3×D4—44no—
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—
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×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×Dic3C2×D412yes—
330C22×Dic3#4112yes—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335#217—44no—
336#217—44no—
337#217—44no—
338#217—44no—
339#217—44no—
340#217—44no—
341#217—44no—
342#217—44no—
343C4⋊Dic3—44no—
344C4⋊Dic3—44no—
345C4⋊Dic3—44no—
346Dic3⋊C4—44no—
347C4×Dic3—44no—
348C4×Dic3—44no—
349C25C22×D311yescharacteristic
350C25C22×D311yescharacteristic
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—41no—
357C22×D4—41no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C2×C4⋊C4—34no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—121no—
378C2×C4⋊C4—121no—
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—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
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—121no—
408C2×C22⋊C4—121no—
409C2×C22⋊C4—121no—
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—62no—
422C2×C42—62no—
423C2×C42—121no—
424C2×C42—121no—
425#95—22no—
426#95—22no—
427#95—34no—
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—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
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×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
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×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3C22×D411yescharacteristic
512C23×C3C22×D411yescharacteristic
513C23×C3C2×#4111yescharacteristic
514C23×C3C2×#4111yescharacteristic
515C23×C3C2×#4111yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3H(5,𝔽2)11yescharacteristic
521C23×C3H(5,𝔽2)11yescharacteristic
522C23×C3H(5,𝔽2)11yescharacteristic
523C23×C3H(5,𝔽2)11yescharacteristic
524C23×C3H(5,𝔽2)11yescharacteristic
525C23×C32−1+411yescharacteristic
526C3×D4—416no—
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—22no—
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#12414yes—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
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—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
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—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24#23712yes—
647C24#23712yes—
648C24C23×D311yescharacteristic
649C2×D4—28no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—44no—
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—32no—
686C22×C4—32no—
687C22×C4—32no—
688C22×C4—32no—
689C22×C4—32no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
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—124no—
748C4⋊C4—124no—
749C4⋊C4—124no—
750C4⋊C4—124no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
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—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—81no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—81no—
795C22×C3#52511yescharacteristic
796C22×C3#52511yescharacteristic
797C22×C3C2×#12411yescharacteristic
798C22×C3#52911yescharacteristic
799C22×C3#52911yescharacteristic
800C22×C3#53211yescharacteristic
801C22×C3#53411yescharacteristic
802C22×C3#53511yescharacteristic
803C22×C3#53811yescharacteristic
804C22×C3#53811yescharacteristic
805C22×C3#53911yescharacteristic
806C22×C3#54011yescharacteristic
807C22×C3#54011yescharacteristic
808C22×C3#54211yescharacteristic
809C22×C3#54211yescharacteristic
810C22×C3D4211yescharacteristic
811C22×C3#54611yescharacteristic
812C22×C3#54611yescharacteristic
813C22×C3#54711yescharacteristic
814C22×C3#54811yescharacteristic
815C22×C3#55011yescharacteristic
816C22×C3#55011yescharacteristic
817C22×C3#55111yescharacteristic
818C22×C3#55111yescharacteristic
819C22×C3#55111yescharacteristic
820C22×C3#55111yescharacteristic
821C22×C3#55111yescharacteristic
822C22×C3#55211yescharacteristic
823C22×C3#55311yescharacteristic
824C22×C3#55311yescharacteristic
825C22×C3#55311yescharacteristic
826C22×C3#55311yescharacteristic
827C22×C3#55511yescharacteristic
828C22×C3#56011yescharacteristic
829C22×C3#56211yescharacteristic
830C3×C4—24no—
831C3×C4—42no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—81no—
835Dic3—42no—
836Dic3—42no—
837Dic3—42no—
838Dic3—42no—
839Dic3—42no—
840Dic3—81no—
841Dic3—81no—
842Dic3—81no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
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—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
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—41no—
911C23—41no—
912C23—41no—
913C23C2×#23511yescharacteristic
914C23C2×D3×D411yescharacteristic
915C23C2×D3×D411yescharacteristic
916C23C2×#23711yescharacteristic
917C23C2×#23711yescharacteristic
918C23C2×#23711yescharacteristic
919C23C2×#23711yescharacteristic
920C23C2×#23711yescharacteristic
921C23#100411yescharacteristic
922C23#100411yescharacteristic
923C23#100411yescharacteristic
924C23D3×#4111yescharacteristic
925C23#100911yescharacteristic
926C23#100911yescharacteristic
927C23#101011yescharacteristic
928D4—416no—
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—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
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—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
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—82no—
1022C2×C3#245611yescharacteristic
1023C2×C3#246011yescharacteristic
1024C2×C3#247911yescharacteristic
1025C2×C3#249011yescharacteristic
1026C2×C3#249111yescharacteristic
1027C2×C3#253111yescharacteristic
1028C2×C3#255411yescharacteristic
1029C2×C3#256111yescharacteristic
1030C2×C3#260311yescharacteristic
1031C2×C3#267311yescharacteristic
1032C2×C3#270611yescharacteristic
1033C2×C3#273011yescharacteristic
1034C2×C3#275611yescharacteristic
1035C2×C3#275711yescharacteristic
1036C2×C3#276111yescharacteristic
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22C2×#88511yescharacteristic
1068C22#549511yescharacteristic
1069C22#549511yescharacteristic
1070C22#555111yescharacteristic
1071C22#555711yescharacteristic
1072C22#556211yescharacteristic
1073C22#556311yescharacteristic
1074C22#558611yescharacteristic
1075C22#558611yescharacteristic
1076C22#558711yescharacteristic
1077C22#558711yescharacteristic
1078C22#558711yescharacteristic
1079C22#558911yescharacteristic
1080C22#559111yescharacteristic
1081C22#559311yescharacteristic
1082C22#559811yescharacteristic
1083C22#559911yescharacteristic
1084C22#560011yescharacteristic
1085C22#560311yescharacteristic
1086C22#560711yescharacteristic
1087C22#560911yescharacteristic
1088C22#561411yescharacteristic
1089C22#561711yescharacteristic
1090C22#561811yescharacteristic
1091C22#561811yescharacteristic
1092C22#561811yescharacteristic
1093C22#562111yescharacteristic
1094C22#565011yescharacteristic
1095C22#566311yescharacteristic
1096C22#566511yescharacteristic
1097C22#566611yescharacteristic
1098C22#567611yescharacteristic
1099C22#568211yescharacteristic
1100C22#571611yescharacteristic
1101C22#571811yescharacteristic
1102C4—24no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—122no—
1108C4—122no—
1109C4—122no—
1110C4—122no—
1111C4—122no—
1112C4—241no—
1113C4—241no—
1114C4—241no—
1115C3#1577511yescharacteristic, complemented, Sylow
1116C2—82no—
1117C2—82no—
1118C2#7383511yescharacteristic
1119C2#7473411yescharacteristic
1120C2#7475011yescharacteristic
1121C2#7481711yescharacteristic
1122C2#7484811yescharacteristic
1123C2#7644911yescharacteristic
1124C2#7645211yescharacteristic
1125C2#7667511yescharacteristic
1126C2#7668911yescharacteristic
1127C2#7669511yescharacteristic
1128C2#7673111yescharacteristic
1129C2#7691411yescharacteristic
1130C2#7706211yescharacteristic
1131C2#7706311yescharacteristic
1132C2#7713411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC23×C3×D4C22
hypercenter#1438D3
hypocenterC3#15775
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#4952C2semidirect
3. C2×#4951C2semidirect
4. C2×#4661C2semidirect
7. #71549C2semidirect
8. #71547C2semidirect
9. #71546C2semidirect
10. #71546C2semidirect
11. #71546C2semidirect
12. #71545C2semidirect
13. #69407C2semidirect
14. #69402C2semidirect
15. #69402C2semidirect
162. C3⋊#95D4semidirect
1115. C3#15775semidirect

Maximal subgroups

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

subgroupindex
C2×#52212
C2×#49522
C2×#49512
C2×#46612
C3×#14382
#721312
#715492
#715472
#715462
#715452
#694072
#694022
#157753