Finite Group Databasebeta

← #10727090

Subgroups — #10727090

Order 768.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5220C211yesmaximal, characteristic
2C2×#4948C211yesmaximal, characteristic, complemented
3C2×#4944C211yesmaximal, characteristic, complemented
4C2×#4946C211yesmaximal, characteristic, complemented
5C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#4655C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic
8#72131C211yesmaximal, characteristic
9#71548C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69418C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14756—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5220—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#4948—24no—
54#4946—24no—
55#4944—24no—
56Dic3×C22⋊C4—24no—
57#4655—24no—
58C2×#396—31no—
59C2×#388—31no—
60C2×#387—31no—
61C2×#386—31no—
62C2×#385—31no—
63C2×C4×C22⋊C4—31no—
64#1443—31no—
65#1442—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438D311yescharacteristic
71#1437—31no—
72#1436—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—41no—
93C23×Dic3—41no—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217—41no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—41no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4D414yescomplemented
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—41no—
152C2×C4×Dic3—41no—
153C3×#95—22no—
154C3×#95—41no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95D414yes—
168C3⋊#95D414yescomplemented
169C23×D4C2×D311yescharacteristic
170C24×C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C22⋊C4C2×D311yescharacteristic
186C22×C42—31no—
187C22×C42—31no—
188#396—64no—
189#388—64no—
190#387—64no—
191#386—64no—
192#385—64no—
193C4×C22⋊C4—64no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
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—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3#4112yes—
239C24×C3#4112yes—
240C24×C3C2411yescharacteristic
241C2×C3×D4—28no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4#4112yes—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—28no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—44no—
332C22×Dic3—44no—
333C22×Dic3—44no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—44no—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3#4112yes—
344C22×Dic3#4112yes—
345C22×Dic3#4112yes—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—44no—
348C3×C22⋊C4—44no—
349C3×C22⋊C4—44no—
350#217—28no—
351#217—28no—
352#217—28no—
353#217—44no—
354#217—44no—
355#217—44no—
356#217—44no—
357C4⋊Dic3—44no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361C4×Dic3—44no—
362C4×Dic3—44no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—41no—
371C22×D4—41no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—62no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—121no—
386C23×C4—121no—
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C2×C4⋊C4—34no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—121no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—62no—
441C2×C42—121no—
442C2×C42—121no—
443#95—22no—
444#95—34no—
445#95—34no—
446#95—41no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—121no—
458#95—121no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
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×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3#12614yes—
529C23×C3C22×D411yescharacteristic
530C23×C3C22×D411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C32−1+411yescharacteristic
544C3×D4—416no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—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—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×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—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—416no—
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—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3#12114yes—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24#23512yes—
664C24#23712yes—
665C24#23712yes—
666C24#23712yes—
667C24C23×D311yescharacteristic
668C2×D4—28no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
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—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—68no—
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—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—124no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4D3×D412yes—
770C22×C4D3×D412yes—
771C22×C4D3×D412yes—
772C22×C4#23712yes—
773C4⋊C4—68no—
774C4⋊C4—124no—
775C4⋊C4—124no—
776C4⋊C4—124no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—68no—
782C22⋊C4—68no—
783C22⋊C4—68no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C42—124no—
789C42—124no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3C2×#12111yescharacteristic
821C22×C3#52511yescharacteristic
822C22×C3#52511yescharacteristic
823C22×C3#52511yescharacteristic
824C22×C3#52511yescharacteristic
825C22×C3#52511yescharacteristic
826C22×C3#52511yescharacteristic
827C22×C3C2×#12611yescharacteristic
828C22×C3#52911yescharacteristic
829C22×C3#52911yescharacteristic
830C22×C3#52911yescharacteristic
831C22×C3#52911yescharacteristic
832C22×C3#53211yescharacteristic
833C22×C3#53811yescharacteristic
834C22×C3#53811yescharacteristic
835C22×C3#53911yescharacteristic
836C22×C3#53911yescharacteristic
837C22×C3#54011yescharacteristic
838C22×C3#54211yescharacteristic
839C22×C3D4211yescharacteristic
840C22×C3D4211yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54811yescharacteristic
846C22×C3#54811yescharacteristic
847C22×C3#54811yescharacteristic
848C22×C3#55011yescharacteristic
849C22×C3#55111yescharacteristic
850C22×C3#55111yescharacteristic
851C22×C3#55111yescharacteristic
852C22×C3#55211yescharacteristic
853C22×C3#55311yescharacteristic
854C22×C3#55311yescharacteristic
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—81no—
860Dic3—24no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865Dic3—42no—
866Dic3—42no—
867Dic3—81no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—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—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23#87914yes—
938C23C2×#23511yescharacteristic
939C23C2×D3×D411yescharacteristic
940C23C2×D3×D411yescharacteristic
941C23C2×D3×D411yescharacteristic
942C23C2×#23711yescharacteristic
943C23C2×#23711yescharacteristic
944C23C2×#23711yescharacteristic
945C23C2×#23711yescharacteristic
946C23#100411yescharacteristic
947C23#100411yescharacteristic
948C23#100411yescharacteristic
949C23D3×#4111yescharacteristic
950C23D3×#4111yescharacteristic
951C23D3×#4111yescharacteristic
952C23#101011yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—34no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—1216no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C3—44no—
1047C2×C3—82no—
1048C2×C3#239211yescharacteristic
1049C2×C3#242411yescharacteristic
1050C2×C3#242611yescharacteristic
1051C2×C3#245611yescharacteristic
1052C2×C3#246311yescharacteristic
1053C2×C3#246311yescharacteristic
1054C2×C3#246411yescharacteristic
1055C2×C3#247111yescharacteristic
1056C2×C3#247711yescharacteristic
1057C2×C3#248011yescharacteristic
1058C2×C3#248111yescharacteristic
1059C2×C3#255811yescharacteristic
1060C2×C3#257611yescharacteristic
1061C2×C3#264911yescharacteristic
1062C2×C3#285211yescharacteristic
1063C22—24no—
1064C22—24no—
1065C22—24no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22C2×#87911yescharacteristic
1094C22#549011yescharacteristic
1095C22#549511yescharacteristic
1096C22#553811yescharacteristic
1097C22#554011yescharacteristic
1098C22#554711yescharacteristic
1099C22#555211yescharacteristic
1100C22#558611yescharacteristic
1101C22#558611yescharacteristic
1102C22#558711yescharacteristic
1103C22#558711yescharacteristic
1104C22#559011yescharacteristic
1105C22#559111yescharacteristic
1106C22#559111yescharacteristic
1107C22#559311yescharacteristic
1108C22#559811yescharacteristic
1109C22#559811yescharacteristic
1110C22#560011yescharacteristic
1111C22#560211yescharacteristic
1112C22D3×#12111yescharacteristic
1113C22#560611yescharacteristic
1114C22#560611yescharacteristic
1115C22#560611yescharacteristic
1116C22#561011yescharacteristic
1117C22#561311yescharacteristic
1118C22#561411yescharacteristic
1119C22#561511yescharacteristic
1120C22#564911yescharacteristic
1121C22#564911yescharacteristic
1122C22#565011yescharacteristic
1123C22#566011yescharacteristic
1124C22#566811yescharacteristic
1125C22#566911yescharacteristic
1126C22#571711yescharacteristic
1127C22#571811yescharacteristic
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—64no—
1133C4—81no—
1134C4—122no—
1135C4—122no—
1136C4—122no—
1137C4—122no—
1138C4—122no—
1139C4—122no—
1140C4—241no—
1141C3#1475611yescharacteristic, complemented, Sylow
1142C2—44no—
1143C2—82no—
1144C2#7383011yescharacteristic
1145C2#7473611yescharacteristic
1146C2#7476511yescharacteristic
1147C2#7487011yescharacteristic
1148C2#7490011yescharacteristic
1149C2#7631211yescharacteristic
1150C2#7644711yescharacteristic
1151C2#7667611yescharacteristic
1152C2#7668111yescharacteristic
1153C2#7668511yescharacteristic
1154C2#7675611yescharacteristic
1155C2#7689111yescharacteristic
1156C2#7693111yescharacteristic
1157C2#7695011yescharacteristic
1158C2#7698811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC23×C3×D4C22
hypercenter#1438D3
hypocenterC3#14756
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#4948C2semidirect
3. C2×#4944C2semidirect
4. C2×#4946C2semidirect
5. C2×Dic3×C22⋊C4C2semidirect
6. C2×#4655C2semidirect
9. #71548C2semidirect
10. #71547C2semidirect
11. #71546C2semidirect
12. #71545C2semidirect
13. #69418C2semidirect
14. #69413C2semidirect
15. #69405C2semidirect
146. C2×Dic3⋊C4D4semidirect
168. C3⋊#95D4semidirect
1141. C3#14756semidirect

Maximal subgroups

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

subgroupindex
C2×#52202
C2×#49482
C2×#49442
C2×#49462
C2×Dic3×C22⋊C42
C2×#46552
C3×#14382
#721312
#715482
#715472
#715462
#715452
#694182
#694132
#694052
#147563