Finite Group Databasebeta

← #10742728

Subgroups — #10742728

Order 768.

2462 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#924C211yesmaximal, characteristic, complemented
2C22×#896C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4956C211yesmaximal, characteristic
7#71568C211yesmaximal, characteristic, complemented
8#71565C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69424C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15951—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C2×#924—24no—
35C2×#924—24no—
36C2×#924—24no—
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C2×#896—24no—
42C2×#896—24no—
43C2×#896—24no—
44C3×#385—24no—
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47#5213—24no—
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60#4989—24no—
61#4956—24no—
62C22×C22⋊Q8—31no—
63C22×C22⋊Q8—31no—
64C2×#386—31no—
65C2×#386—31no—
66C2×#385—31no—
67C2×#385D311yescharacteristic, complemented
68#1446—31no—
69#1444—31no—
70#1441—31no—
71#1441—31no—
72#1439—31no—
73#1439—31no—
74#1439—31no—
75#1439—31no—
76#1438—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—41no—
85C23×C3×C4—41no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67Q814yescomplemented
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—41no—
118C22×Dic6—41no—
119C22×Dic6D414yescomplemented
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—41no—
125C2×C3×C4⋊C4D414yescomplemented
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—41no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—41no—
140C2×#217D414yes—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4D414yes—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159#924—232no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4D414yescomplemented
172#896—232no—
173C3×#95—22no—
174C3×#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95—41no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C23×Q8—31no—
188C23×D4—31no—
189C24×C4—31no—
190C24×C4C2×D311yescharacteristic
191C2×C22⋊Q8—64no—
192C2×C22⋊Q8—64no—
193C2×C22⋊Q8—64no—
194C2×C22⋊Q8—64no—
195C2×C22⋊Q8—64no—
196C2×C22⋊Q8—64no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4C2×D311yescharacteristic
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214#386—64no—
215#386—64no—
216#385—24no—
217#385—64no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95C2×D311yescharacteristic
231C2×#95C2×D311yescharacteristic
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3C2×D412yes—
245C24×C3C2×Q812yes—
246C24×C3#4112yes—
247C24×C3C2411yescharacteristic
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3C2×D412yes—
261C23×D3C2×Q812yes—
262C23×D3#4112yes—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—28no—
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×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—44no—
300C22×C3×C4—44no—
301C22×C3×C4—44no—
302C22×C3×C4—44no—
303C22×C3×C4—44no—
304C22×C3×C4—44no—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4#4112yes—
312C2×#67—28no—
313C2×#67—28no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—44no—
318C2×#67—44no—
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—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×D412yes—
365C22×Dic3C2×D412yes—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×Q812yes—
368C2×C4×D3—28no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C2×Dic6—28no—
376C2×Dic6—28no—
377C2×Dic6—44no—
378C2×Dic6—44no—
379C2×Dic6—44no—
380C2×Dic6—44no—
381C2×Dic6—44no—
382C3×C4⋊C4—28no—
383C3×C4⋊C4—44no—
384C3×C22⋊C4—28no—
385C3×C22⋊C4—44no—
386#217—28no—
387#217—28no—
388#217—44no—
389(C2×D3)⋊C4—28no—
390(C2×D3)⋊C4—28no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394C4⋊Dic3—28no—
395Dic3⋊C4—28no—
396Dic3⋊C4—28no—
397Dic3⋊C4—28no—
398Dic3⋊C4—28no—
399C25—31no—
400C25C22×D311yescharacteristic
401C22×Q8—34no—
402C22×Q8—62no—
403C22×Q8—62no—
404C22×Q8—62no—
405C22×Q8—62no—
406C22×Q8—121no—
407C22×Q8—121no—
408C22×D4—34no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—121no—
414C22×D4—121no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—62no—
433C23×C4—62no—
434C23×C4—121no—
435C23×C4—121no—
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C22⋊Q8—632no—
443C22⋊Q8—632no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—34no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—62no—
463C2×C4⋊C4—62no—
464C2×C4⋊C4#6714yescomplemented
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—34no—
471C2×C22⋊C4—34no—
472C2×C22⋊C4—41no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495#95—22no—
496#95—22no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—62no—
503#95—62no—
504#95—121no—
505#95—121no—
506#95—121no—
507#95—121no—
508#95—121no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3C22⋊Q814yescomplemented
544C23×C3C22×D411yescharacteristic
545C23×C3C22×D411yescharacteristic
546C23×C3C22×D411yescharacteristic
547C23×C3C22×D411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3C22×Q811yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3C2×#4111yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C3H(5,𝔽2)11yescharacteristic
556C23×C32−1+411yescharacteristic
557C23×C32−1+411yescharacteristic
558C23×C32−1+411yescharacteristic
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3C22⋊Q814yescomplemented
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—416no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4#12014yes—
637#67—416no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3#12014yes—
687C4×D3—416no—
688Dic6—416no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—32no—
702C24—32no—
703C24—32no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24#23512yes—
717C24D3×D412yes—
718C24D3×Q812yes—
719C24C23×D311yescharacteristic
720C2×Q8—68no—
721C2×Q8—68no—
722C2×Q8—124no—
723C2×Q8—124no—
724C2×Q8—124no—
725C2×Q8—124no—
726C2×Q8—124no—
727C2×D4—68no—
728C2×D4—68no—
729C2×D4—124no—
730C2×D4—124no—
731C2×D4—124no—
732C2×D4—124no—
733C2×D4—124no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—28no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—32no—
771C22×C4—32no—
772C22×C4—32no—
773C22×C4—32no—
774C22×C4—32no—
775C22×C4—32no—
776C22×C4—32no—
777C22×C4—32no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—68no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4—61no—
818C22×C4—61no—
819C22×C4—61no—
820C22×C4—61no—
821C22×C4—61no—
822C22×C4—61no—
823C22×C4—61no—
824C22×C4—61no—
825C22×C4—61no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4—124no—
829C22×C4—124no—
830C22×C4—124no—
831C22×C4—124no—
832C22×C4#23512yes—
833C22×C4D3×D412yes—
834C22×C4D3×D412yes—
835C22×C4D3×D412yes—
836C22×C4C2×#6712yes—
837C22×C4C2×#6712yes—
838C22×C4C2×#6712yes—
839C4⋊C4—28no—
840C4⋊C4—44no—
841C4⋊C4—68no—
842C4⋊C4—68no—
843C4⋊C4—68no—
844C4⋊C4—68no—
845C4⋊C4—68no—
846C22⋊C4—28no—
847C22⋊C4—44no—
848C22⋊C4—68no—
849C22⋊C4—68no—
850C22⋊C4—68no—
851C22⋊C4—68no—
852C22⋊C4—68no—
853C22⋊C4—124no—
854C22⋊C4—124no—
855C22⋊C4—124no—
856C22×C3—24no—
857C22×C3—24no—
858C22×C3—24no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3C2×#12011yescharacteristic
872C22×C3C2×#12011yescharacteristic
873C22×C3C2×C22⋊Q811yescharacteristic
874C22×C3C2×C22⋊Q811yescharacteristic
875C22×C3#52511yescharacteristic
876C22×C3#52511yescharacteristic
877C22×C3#53411yescharacteristic
878C22×C3#53611yescharacteristic
879C22×C3#53611yescharacteristic
880C22×C3#53711yescharacteristic
881C22×C3#53711yescharacteristic
882C22×C3#53911yescharacteristic
883C22×C3#53911yescharacteristic
884C22×C3#53911yescharacteristic
885C22×C3#54311yescharacteristic
886C22×C3D4211yescharacteristic
887C22×C3D4211yescharacteristic
888C22×C3D4211yescharacteristic
889C22×C3D4211yescharacteristic
890C22×C3#54611yescharacteristic
891C22×C3#54611yescharacteristic
892C22×C3#54711yescharacteristic
893C22×C3#54711yescharacteristic
894C22×C3#54811yescharacteristic
895C22×C3#54811yescharacteristic
896C22×C3#54811yescharacteristic
897C22×C3#54811yescharacteristic
898C22×C3D4×Q811yescharacteristic
899C22×C3D4×Q811yescharacteristic
900C22×C3D4×Q811yescharacteristic
901C22×C3#55011yescharacteristic
902C22×C3#55111yescharacteristic
903C22×C3#55411yescharacteristic
904C22×C3#56211yescharacteristic
905C22×C3#56311yescharacteristic
906C2×D3—24no—
907C2×D3—24no—
908C2×D3—24no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C2×D3—42no—
915C2×D3—42no—
916C2×D3—42no—
917C2×D3—42no—
918C2×D3—42no—
919C2×D3—42no—
920C2×D3—42no—
921C3×C4—24no—
922C3×C4—42no—
923C3×C4—42no—
924C3×C4—42no—
925C3×C4—42no—
926C3×C4—81no—
927Dic3—24no—
928Dic3—42no—
929Dic3—42no—
930Dic3—42no—
931Dic3—42no—
932Dic3—42no—
933Dic3—81no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—34no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—121no—
988C23—121no—
989C23—121no—
990C23—121no—
991C23—121no—
992C23—121no—
993C23—121no—
994C23—121no—
995C23—121no—
996C23—121no—
997C23—121no—
998C23—121no—
999C23—121no—
1000C23—121no—
1001C23—121no—
1002C23—121no—
1003C23#89614yescomplemented
1004C23C2×#23511yescharacteristic
1005C23C2×#23511yescharacteristic
1006C23C2×D3×D411yescharacteristic
1007C23C2×D3×D411yescharacteristic
1008C23C2×D3×D411yescharacteristic
1009C23C2×D3×D411yescharacteristic
1010C23#100411yescharacteristic
1011C23#100411yescharacteristic
1012C23C2×D3×Q811yescharacteristic
1013C23#100711yescharacteristic
1014C23D3×#4111yescharacteristic
1015C23#100911yescharacteristic
1016C23#101011yescharacteristic
1017C23#101011yescharacteristic
1018C23C22×#6711yescharacteristic
1019Q8—1216no—
1020D4—1216no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—34no—
1040C2×C4—416no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—62no—
1080C2×C4—62no—
1081C2×C4—62no—
1082C2×C4—62no—
1083C2×C4—62no—
1084C2×C4—62no—
1085C2×C4—1216no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C4—121no—
1107C2×C4—121no—
1108C2×C4—121no—
1109C2×C4—121no—
1110C2×C4—121no—
1111C2×C4—121no—
1112C2×C4—121no—
1113C2×C4#93714yes—
1114C2×C3—44no—
1115C2×C3#240311yescharacteristic
1116C2×C3#240711yescharacteristic
1117C2×C3#240711yescharacteristic
1118C2×C3#240911yescharacteristic
1119C2×C3#240911yescharacteristic
1120C2×C3#243711yescharacteristic
1121C2×C3#244911yescharacteristic
1122C2×C3#244911yescharacteristic
1123C2×C3#246311yescharacteristic
1124C2×C3#268011yescharacteristic
1125C2×C3#268111yescharacteristic
1126C2×C3#268111yescharacteristic
1127C2×C3#268311yescharacteristic
1128C2×C3#272811yescharacteristic
1129C2×C3#273211yescharacteristic
1130D3—44no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—64no—
1147C22—64no—
1148C22—64no—
1149C22—122no—
1150C22—122no—
1151C22—122no—
1152C22—122no—
1153C22—122no—
1154C22—122no—
1155C22—122no—
1156C22—122no—
1157C22—122no—
1158C22—122no—
1159C22—122no—
1160C22—122no—
1161C22#550711yescharacteristic
1162C22C2×#89611yescharacteristic
1163C22#551111yescharacteristic
1164C22#551511yescharacteristic
1165C22#554711yescharacteristic
1166C22#555011yescharacteristic
1167C22#555111yescharacteristic
1168C22#555211yescharacteristic
1169C22#555211yescharacteristic
1170C22#555311yescharacteristic
1171C22#555611yescharacteristic
1172C22#556411yescharacteristic
1173C22D3×#12011yescharacteristic
1174C22#558911yescharacteristic
1175C22#559011yescharacteristic
1176C22#559011yescharacteristic
1177C22D3×C22⋊Q811yescharacteristic
1178C22#562811yescharacteristic
1179C22#562911yescharacteristic
1180C22#563211yescharacteristic
1181C22#563211yescharacteristic
1182C22#563311yescharacteristic
1183C22#563411yescharacteristic
1184C22#564611yescharacteristic
1185C22#564811yescharacteristic
1186C22#565411yescharacteristic
1187C22#566011yescharacteristic
1188C22#566711yescharacteristic
1189C22#579111yescharacteristic
1190C22C2×#93711yescharacteristic
1191C22D4×#6711yescharacteristic
1192C22D4×#6711yescharacteristic
1193C22Q8×#6711yescharacteristic
1194C22#583111yescharacteristic
1195C22#583311yescharacteristic
1196C4—24no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—64no—
1202C4—81no—
1203C4—122no—
1204C4—122no—
1205C4—122no—
1206C4—122no—
1207C4—122no—
1208C4—241no—
1209C3#1595111yescharacteristic, complemented, Sylow
1210C2—44no—
1211C2—124no—
1212C2#7440411yescharacteristic
1213C2#7440511yescharacteristic
1214C2#7454111yescharacteristic
1215C2#7460711yescharacteristic
1216C2#7460911yescharacteristic
1217C2#7463111yescharacteristic
1218C2#7463211yescharacteristic
1219C2#7464111yescharacteristic
1220C2#8217311yescharacteristic
1221C2#8236811yescharacteristic
1222C2#8240211yescharacteristic
1223C2#8260411yescharacteristic
1224C2#8275111yescharacteristic
1225C2#8279311yescharacteristic
1226C2#8287211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#385C2
prime radicalC23×#67C22
hypercenterC2×#385D3
hypocenterC3#15951
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#924C2semidirect
2. C22×#896C2semidirect
3. C2×C3×#385C2semidirect
5. C2×#4989C2semidirect
7. #71568C2semidirect
8. #71565C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. #69427C2semidirect
14. #69424C2semidirect
15. #69409C2semidirect
67. C2×#385D3semidirect
98. C22×#67Q8semidirect
119. C22×Dic6D4semidirect
125. C2×C3×C4⋊C4D4semidirect
171. C2×Dic3⋊C4D4semidirect
464. C2×C4⋊C4#67semidirect
543. C23×C3C22⋊Q8semidirect
593. C22×D3C22⋊Q8semidirect
1003. C23#896semidirect
1209. C3#15951semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C22×#8962
C2×C3×#3852
C2×#52132
C2×#49892
C2×#49562
#715682
#715652
#715502
#715472
#694282
#694272
#694242
#694092
#159513