Finite Group Databasebeta

← #10729063

Subgroups — #10729063

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#889C211yesmaximal, characteristic, complemented
2C2×#4950C211yesmaximal, characteristic
3C2×#4946C211yesmaximal, characteristic
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic
5C3×#1439C211yesmaximal, characteristic
6#71566C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic
8#71547C211yesmaximal, characteristic
9#71547C211yesmaximal, characteristic
10#69420C211yesmaximal, characteristic, complemented
11#69413C211yesmaximal, characteristic, complemented
12#69411C211yesmaximal, characteristic, complemented
13#69407C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14916—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×#889—24no—
35C2×#889—24no—
36C2×#889—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4950—24no—
56#4946—24no—
57Dic3×C22⋊C4—24no—
58C22×#125—31no—
59C2×#385—31no—
60C2×#385—31no—
61C2×C4×C22⋊C4—31no—
62#1444—31no—
63#1442—31no—
64#1441—31no—
65#1441—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439D311yescharacteristic
70#1436—31no—
71#1436—31no—
72#1434—31no—
73C25×C3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—22no—
84C23×Dic3—22no—
85C23×Dic3—41no—
86C23×Dic3—41no—
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊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—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—41no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—41no—
115C2×#217Q814yes—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—41no—
121C2×C4⋊Dic3D414yes—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4D414yes—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—41no—
141C2×C4×Dic3—41no—
142C2×C4×Dic3D414yes—
143#889—232no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—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—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C24×C4—31no—
163C2×#125—64no—
164C2×#125—64no—
165C2×#125—64no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4C2×D311yescharacteristic
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#385—64no—
183#385—64no—
184C4×C22⋊C4—64no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
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×C3C2×Q812yes—
216C24×C3#4112yes—
217C24×C3#4112yes—
218C24×C3C2411yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4#4112yes—
260C22×C3×C4#4112yes—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—28no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—44no—
308C22×Dic3—44no—
309C22×Dic3—44no—
310C22×Dic3—44no—
311C22×Dic3—44no—
312C22×Dic3—44no—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×D412yes—
318C22×Dic3C2×D412yes—
319C22×Dic3C2×Q812yes—
320C22×Dic3C2×Q812yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C3×C4⋊C4—28no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—44no—
328#217—28no—
329#217—28no—
330#217—44no—
331C4⋊Dic3—28no—
332C4⋊Dic3—44no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—28no—
337Dic3⋊C4—44no—
338C4×Dic3—28no—
339C4×Dic3—44no—
340C25C22×D311yescharacteristic
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—62no—
350C23×C4—62no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—121no—
355C23×C4—121no—
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362#125—632no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—34no—
367C2×C4⋊C4—34no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
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—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—41no—
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—121no—
405C2×C42—34no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—62no—
409C2×C42—121no—
410C2×C42—121no—
411#95—22no—
412#95—22no—
413#95—41no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—62no—
426#95—121no—
427#95—121no—
428#95—121no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—41no—
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#12514yescomplemented
464C23×C3C22×D411yescharacteristic
465C23×C3C22×D411yescharacteristic
466C23×C3C22×D411yescharacteristic
467C23×C3C22×Q811yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3C2×#4111yescharacteristic
472C23×C3C2×#4111yescharacteristic
473C23×C3C2×#4111yescharacteristic
474C23×C3C2×#4111yescharacteristic
475C23×C3H(5,𝔽2)11yescharacteristic
476C23×C3H(5,𝔽2)11yescharacteristic
477C23×C32−1+411yescharacteristic
478C23×C32−1+411yescharacteristic
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—416no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3#12014yes—
577C2×Dic3C22⋊Q814yes—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24#23512yes—
591C24#23712yes—
592C24D3×Q812yes—
593C24C23×D311yescharacteristic
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—68no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4—124no—
694C22×C4D3×D412yes—
695C22×C4D3×D412yes—
696C22×C4D3×D412yes—
697C22×C4#23712yes—
698C22×C4#23712yes—
699C4⋊C4—28no—
700C4⋊C4—68no—
701C4⋊C4—68no—
702C4⋊C4—68no—
703C4⋊C4—68no—
704C4⋊C4—68no—
705C4⋊C4—124no—
706C4⋊C4—124no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—44no—
710C22⋊C4—68no—
711C22⋊C4—68no—
712C22⋊C4—124no—
713C42—68no—
714C42—124no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3C2×#12011yescharacteristic
731C22×C3C2×C22⋊Q811yescharacteristic
732C22×C3#52511yescharacteristic
733C22×C3#52511yescharacteristic
734C22×C3#52511yescharacteristic
735C22×C3#52511yescharacteristic
736C22×C3C2×#12511yescharacteristic
737C22×C3#52911yescharacteristic
738C22×C3#52911yescharacteristic
739C22×C3#53211yescharacteristic
740C22×C3#53211yescharacteristic
741C22×C3#53211yescharacteristic
742C22×C3#53311yescharacteristic
743C22×C3#53511yescharacteristic
744C22×C3#53611yescharacteristic
745C22×C3#53911yescharacteristic
746C22×C3#53911yescharacteristic
747C22×C3#53911yescharacteristic
748C22×C3#53911yescharacteristic
749C22×C3#54611yescharacteristic
750C22×C3#54611yescharacteristic
751C22×C3#54611yescharacteristic
752C22×C3#54611yescharacteristic
753C22×C3#54811yescharacteristic
754C22×C3#54811yescharacteristic
755C22×C3D4×Q811yescharacteristic
756C22×C3D4×Q811yescharacteristic
757C22×C3#55211yescharacteristic
758C22×C3#55211yescharacteristic
759C22×C3#55211yescharacteristic
760C22×C3#55211yescharacteristic
761C22×C3#55311yescharacteristic
762C22×C3#55311yescharacteristic
763C22×C3#55411yescharacteristic
764C22×C3#55411yescharacteristic
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—81no—
771Dic3—24no—
772Dic3—24no—
773Dic3—42no—
774Dic3—42no—
775Dic3—42no—
776Dic3—42no—
777Dic3—42no—
778Dic3—81no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23#88914yescomplemented
814C23C2×#23511yescharacteristic
815C23C2×D3×D411yescharacteristic
816C23C2×D3×D411yescharacteristic
817C23C2×D3×D411yescharacteristic
818C23C2×#23711yescharacteristic
819C23C2×#23711yescharacteristic
820C23C2×#23711yescharacteristic
821C23#100411yescharacteristic
822C23C2×D3×Q811yescharacteristic
823C23D3×#4111yescharacteristic
824C23D3×#4111yescharacteristic
825C23D3×#4111yescharacteristic
826C23#100911yescharacteristic
827C23#101011yescharacteristic
828C23#101011yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—34no—
845C2×C4—34no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—1216no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C3—44no—
929C2×C3#238811yescharacteristic
930C2×C3#240411yescharacteristic
931C2×C3#240911yescharacteristic
932C2×C3#246011yescharacteristic
933C2×C3#246011yescharacteristic
934C2×C3#247311yescharacteristic
935C2×C3#247311yescharacteristic
936C2×C3#255611yescharacteristic
937C2×C3#255611yescharacteristic
938C2×C3#255811yescharacteristic
939C2×C3#255811yescharacteristic
940C2×C3#256611yescharacteristic
941C2×C3#261111yescharacteristic
942C2×C3#263311yescharacteristic
943C2×C3#285111yescharacteristic
944C22—24no—
945C22—24no—
946C22—24no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22#549011yescharacteristic
960C22C2×#88911yescharacteristic
961C22#553111yescharacteristic
962C22#553811yescharacteristic
963C22#554111yescharacteristic
964C22#554711yescharacteristic
965C22#555011yescharacteristic
966C22#558611yescharacteristic
967C22#558611yescharacteristic
968C22D3×#12011yescharacteristic
969C22#559611yescharacteristic
970C22#559611yescharacteristic
971C22#560111yescharacteristic
972C22#560211yescharacteristic
973C22#560211yescharacteristic
974C22#560611yescharacteristic
975C22#560711yescharacteristic
976C22#561211yescharacteristic
977C22#562211yescharacteristic
978C22D3×C22⋊Q811yescharacteristic
979C22#563211yescharacteristic
980C22#563211yescharacteristic
981C22#563511yescharacteristic
982C22#563611yescharacteristic
983C22#564911yescharacteristic
984C22#565011yescharacteristic
985C22#565411yescharacteristic
986C22#566511yescharacteristic
987C22#566511yescharacteristic
988C22#567511yescharacteristic
989C22#567711yescharacteristic
990C22#567711yescharacteristic
991C22#570811yescharacteristic
992C22#570911yescharacteristic
993C22#571611yescharacteristic
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—64no—
1000C4—64no—
1001C4—81no—
1002C4—122no—
1003C4—122no—
1004C4—122no—
1005C4—122no—
1006C4—122no—
1007C4—241no—
1008C3#1491611yescharacteristic, complemented, Sylow
1009C2—44no—
1010C2#7390811yescharacteristic
1011C2#7444111yescharacteristic
1012C2#7458611yescharacteristic
1013C2#7488611yescharacteristic
1014C2#7560011yescharacteristic
1015C2#7565111yescharacteristic
1016C2#7635811yescharacteristic
1017C2#7666511yescharacteristic
1018C2#7678011yescharacteristic
1019C2#7691311yescharacteristic
1020C2#7697811yescharacteristic
1021C2#7731711yescharacteristic
1022C2#7732011yescharacteristic
1023C2#7747011yescharacteristic
1024C2#7803911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC25×C3C23
hypercenter#1439D3
hypocenterC3#14916
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#889C2semidirect
6. #71566C2semidirect
10. #69420C2semidirect
11. #69413C2semidirect
12. #69411C2semidirect
13. #69407C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
463. C23×C3#125semidirect
813. C23#889semidirect
1008. C3#14916semidirect

Maximal subgroups

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

subgroupindex
C22×#8892
C2×#49502
C2×#49462
C2×Dic3×C22⋊C42
C3×#14392
#715662
#715472
#694202
#694132
#694112
#694072
#694062
#694012
#149163