Finite Group Databasebeta

← #10727101

Subgroups — #10727101

Order 768.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic
2C2×C3×#380C211yesmaximal, characteristic
3C22×C3⋊#95C211yesmaximal, characteristic
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4946C211yesmaximal, characteristic
6C2×#4942C211yesmaximal, characteristic
7#72127C211yesmaximal, characteristic
8#71568C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#71565C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic
12#69424C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14758—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#878—24no—
35C2×#878—24no—
36C2×#878—24no—
37C3×#380—24no—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3⋊#95—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4979—24no—
58#4946—24no—
59#4942—24no—
60C22×C22⋊Q8—31no—
61C2×#395—31no—
62C2×#385—31no—
63C2×#380—31no—
64C2×#380D311yescharacteristic
65C22×#95—31no—
66#1446—31no—
67#1444—31no—
68#1444—31no—
69#1444—31no—
70#1441—31no—
71#1441—31no—
72#1441—31no—
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4Q814yescomplemented
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3—41no—
100C23×Dic3—41no—
101C23×Dic3D414yes—
102C23×Dic3Q814yescomplemented
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×Dic6—22no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—41no—
117C22×Dic6—41no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—41no—
123C2×C3×C4⋊C4—41no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4D414yes—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217D414yes—
135C2×#217Q814yescomplemented
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—41no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×Dic3⋊C4—41no—
157#878—232no—
158C3×#95—22no—
159C3×#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95D414yes—
176C23×Q8—31no—
177C24×C4—31no—
178C24×C4—31no—
179C24×C4C2×D311yescharacteristic
180C2×C22⋊Q8—64no—
181C2×C22⋊Q8—64no—
182C2×C22⋊Q8—64no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4C2×D311yescharacteristic
195C22×C22⋊C4C2×D311yescharacteristic
196#395—64no—
197#385—64no—
198#380—24no—
199#380—64no—
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×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—64no—
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
228C24×C3C2×D412yes—
229C24×C3C2×D412yes—
230C24×C3C2×Q812yes—
231C24×C3C2×Q812yes—
232C24×C3C2×Q812yes—
233C24×C3#4112yes—
234C24×C3C2411yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—28no—
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—28no—
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—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×Q812yes—
282C22×C3×C4C2×Q812yes—
283C22×C3×C4#4112yes—
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—28no—
293C22×Dic3—28no—
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—28no—
331C22×Dic3—28no—
332C22×Dic3—44no—
333C22×Dic3—44no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—44no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3—44no—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×Q812yes—
349C22×Dic3C2×Q812yes—
350C22×Dic3C2×Q812yes—
351C22×Dic3C2×Q812yes—
352C22×Dic3#4112yes—
353C22×Dic3#4112yes—
354C2×Dic6—28no—
355C2×Dic6—44no—
356C2×Dic6—44no—
357C2×Dic6—44no—
358C2×Dic6—44no—
359C2×Dic6—44no—
360C2×Dic6—44no—
361C3×C4⋊C4—44no—
362C3×C4⋊C4—44no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—44no—
365#217—28no—
366#217—28no—
367C4⋊Dic3—28no—
368Dic3⋊C4—28no—
369Dic3⋊C4—28no—
370Dic3⋊C4—44no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373Dic3⋊C4—44no—
374C25C22×D311yescharacteristic
375C22×Q8—62no—
376C22×Q8—62no—
377C22×Q8—62no—
378C22×Q8—62no—
379C22×Q8—62no—
380C22×Q8—121no—
381C22×Q8—121no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—34no—
395C23×C4—34no—
396C23×C4—41no—
397C23×C4—41no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—121no—
407C23×C4—121no—
408C23×C4—121no—
409C23×C4—121no—
410C23×C4Dic614yescomplemented
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C22⋊Q8—632no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—121no—
442C2×C4⋊C4—121no—
443C2×C4⋊C4—121no—
444C2×C4⋊C4—121no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4#6714yes—
457#95—22no—
458#95—22no—
459#95—34no—
460#95—62no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—121no—
472#95—121no—
473#95—121no—
474#95—121no—
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—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3#12014yes—
504C23×C3C22⋊Q814yes—
505C23×C3C22⋊Q814yes—
506C23×C3C22⋊Q814yes—
507C23×C3C4⋊Q814yes—
508C23×C3C4⋊Q814yes—
509C23×C3C4⋊Q814yes—
510C23×C3C22×D411yescharacteristic
511C23×C3C22×D411yescharacteristic
512C23×C3C22×D411yescharacteristic
513C23×C3C22×D411yescharacteristic
514C23×C3C22×Q811yescharacteristic
515C23×C3C22×Q811yescharacteristic
516C23×C3C22×Q811yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3H(5,𝔽2)11yescharacteristic
522C23×C3H(5,𝔽2)11yescharacteristic
523C23×C3H(5,𝔽2)11yescharacteristic
524C23×C32−1+411yescharacteristic
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—416no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4C22⋊Q814yescomplemented
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—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
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—416no—
599C2×Dic3—416no—
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—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3#12114yes—
625C2×Dic3C22⋊Q814yescomplemented
626Dic6—416no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24C2×Dic612yes—
636C24#23512yes—
637C24D3×D412yes—
638C24D3×D412yes—
639C24D3×Q812yes—
640C24D3×Q812yes—
641C24C2×#6712yes—
642C24C23×D311yescharacteristic
643C2×Q8—68no—
644C2×Q8—124no—
645C2×Q8—124no—
646C2×Q8—124no—
647C2×Q8—124no—
648C2×Q8—124no—
649C2×Q8—124no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—28no—
655C22×C4—21no—
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—28no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—32no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—32no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—32no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—68no—
706C22×C4—68no—
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—68no—
716C22×C4—68no—
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—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—124no—
754C22×C4—124no—
755C22×C4—124no—
756C22×C4—124no—
757C22×C4—124no—
758C22×C4—124no—
759C22×C4—124no—
760C22×C4—124no—
761C22×C4—124no—
762C22×C4—124no—
763C22×C4C2×Dic612yes—
764C22×C4C2×Dic612yes—
765C22×C4D3×D412yes—
766C22×C4#23712yes—
767C22×C4C2×#6712yes—
768C22×C4C2×#6712yes—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—68no—
772C4⋊C4—68no—
773C4⋊C4—68no—
774C4⋊C4—124no—
775C4⋊C4—124no—
776C4⋊C4—124no—
777C4⋊C4—124no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—68no—
781C22⋊C4—68no—
782C22×C3—24no—
783C22×C3—24no—
784C22×C3—24no—
785C22×C3—24no—
786C22×C3—24no—
787C22×C3—24no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—24no—
796C22×C3#39518yescomplemented
797C22×C3C2×#12011yescharacteristic
798C22×C3C2×#12111yescharacteristic
799C22×C3C2×C22⋊Q811yescharacteristic
800C22×C3C2×C22⋊Q811yescharacteristic
801C22×C3C2×C22⋊Q811yescharacteristic
802C22×C3C2×C22⋊Q811yescharacteristic
803C22×C3C2×C22⋊Q811yescharacteristic
804C22×C3C2×C4⋊Q811yescharacteristic
805C22×C3C2×C4⋊Q811yescharacteristic
806C22×C3C2×C4⋊Q811yescharacteristic
807C22×C3#53211yescharacteristic
808C22×C3#53311yescharacteristic
809C22×C3#53311yescharacteristic
810C22×C3#53411yescharacteristic
811C22×C3#53711yescharacteristic
812C22×C3#54311yescharacteristic
813C22×C3#54311yescharacteristic
814C22×C3#54411yescharacteristic
815C22×C3#54411yescharacteristic
816C22×C3D4211yescharacteristic
817C22×C3D4211yescharacteristic
818C22×C3#54611yescharacteristic
819C22×C3#54611yescharacteristic
820C22×C3#54611yescharacteristic
821C22×C3#54611yescharacteristic
822C22×C3#54611yescharacteristic
823C22×C3#54711yescharacteristic
824C22×C3#54711yescharacteristic
825C22×C3D4×Q811yescharacteristic
826C22×C3#55111yescharacteristic
827C22×C3#55111yescharacteristic
828C22×C3#55211yescharacteristic
829C22×C3#55411yescharacteristic
830C22×C3#55411yescharacteristic
831C22×C3#55411yescharacteristic
832C3×C4—24no—
833C3×C4—42no—
834C3×C4—42no—
835C3×C4—42no—
836C3×C4—81no—
837C3×C4—81no—
838Dic3—24no—
839Dic3—24no—
840Dic3—42no—
841Dic3—42no—
842Dic3—42no—
843Dic3—42no—
844Dic3—42no—
845Dic3—42no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23#88814yes—
875C23#88814yes—
876C23#89614yes—
877C23#89614yes—
878C23#92414yes—
879C23#93714yes—
880C23#94414yes—
881C23C22×Dic611yescharacteristic
882C23C2×#23511yescharacteristic
883C23C2×D3×D411yescharacteristic
884C23C2×D3×D411yescharacteristic
885C23C2×D3×D411yescharacteristic
886C23C2×#23711yescharacteristic
887C23#100411yescharacteristic
888C23#100411yescharacteristic
889C23C2×D3×Q811yescharacteristic
890C23C2×D3×Q811yescharacteristic
891C23D3×#4111yescharacteristic
892C23D3×#4111yescharacteristic
893C23#100911yescharacteristic
894C23#101011yescharacteristic
895C23C22×#6711yescharacteristic
896Q8—1216no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—34no—
913C2×C4—34no—
914C2×C4—416no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
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—1216no—
972C2×C4—1216no—
973C2×C4—121no—
974C2×C4—121no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
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#87814yescomplemented
998C2×C3—28no—
999C2×C3C2×#39511yescharacteristic
1000C2×C3#241011yescharacteristic
1001C2×C3#241711yescharacteristic
1002C2×C3#243011yescharacteristic
1003C2×C3#243711yescharacteristic
1004C2×C3#243711yescharacteristic
1005C2×C3#243811yescharacteristic
1006C2×C3#243811yescharacteristic
1007C2×C3#244011yescharacteristic
1008C2×C3#244011yescharacteristic
1009C2×C3#254911yescharacteristic
1010C2×C3#254911yescharacteristic
1011C2×C3#256411yescharacteristic
1012C2×C3#265911yescharacteristic
1013C2×C3#285711yescharacteristic
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22#497918yescomplemented
1029C22C2×#87811yescharacteristic
1030C22#548311yescharacteristic
1031C22#549011yescharacteristic
1032C22#549511yescharacteristic
1033C22C2×#88811yescharacteristic
1034C22C2×#88811yescharacteristic
1035C22C2×#89611yescharacteristic
1036C22C2×#89611yescharacteristic
1037C22#551711yescharacteristic
1038C22#551911yescharacteristic
1039C22#552711yescharacteristic
1040C22#553111yescharacteristic
1041C22#559611yescharacteristic
1042C22#559711yescharacteristic
1043C22D3×#12111yescharacteristic
1044C22#560511yescharacteristic
1045C22#560911yescharacteristic
1046C22#561011yescharacteristic
1047C22#561011yescharacteristic
1048C22#561111yescharacteristic
1049C22#562211yescharacteristic
1050C22#562311yescharacteristic
1051C22D3×C22⋊Q811yescharacteristic
1052C22#563211yescharacteristic
1053C22#563411yescharacteristic
1054C22#563511yescharacteristic
1055C22#563611yescharacteristic
1056C22#563611yescharacteristic
1057C22C2×#92411yescharacteristic
1058C22C2×#93711yescharacteristic
1059C22D4×#6711yescharacteristic
1060C22#580611yescharacteristic
1061C22C2×#94411yescharacteristic
1062C22#582411yescharacteristic
1063C22#582911yescharacteristic
1064C4—24no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—64no—
1069C4—64no—
1070C4—81no—
1071C4—81no—
1072C4—122no—
1073C4—122no—
1074C4—122no—
1075C4—122no—
1076C4—122no—
1077C4—122no—
1078C3#1475811yescharacteristic, complemented, Sylow
1079C2—28no—
1080C2#7388911yescharacteristic
1081C2#7389611yescharacteristic
1082C2#7389711yescharacteristic
1083C2#7389911yescharacteristic
1084C2#7393811yescharacteristic
1085C2#7394311yescharacteristic
1086C2#7395711yescharacteristic
1087C2#7400111yescharacteristic
1088C2#8211011yescharacteristic
1089C2C2×#497911yescharacteristic
1090C2#8224711yescharacteristic
1091C2#8265111yescharacteristic
1092C2#8270211yescharacteristic
1093C2#8276311yescharacteristic
1094C2#8278111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC25×C3C23
hypercenterC2×#380D3
hypocenterC3#14758
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#4979C2semidirect
8. #71568C2semidirect
9. #71568C2semidirect
10. #71565C2semidirect
12. #69424C2semidirect
13. #69420C2semidirect
14. #69409C2semidirect
15. #69409C2semidirect
82. C23×C3×C4Q8semidirect
102. C23×Dic3Q8semidirect
135. C2×#217Q8semidirect
410. C23×C4Dic6semidirect
567. C2×C3×C4C22⋊Q8semidirect
625. C2×Dic3C22⋊Q8semidirect
796. C22×C3#395semidirect
997. C2×C4#878semidirect
1028. C22#4979semidirect
1078. C3#14758semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×C3×#3802
C22×C3⋊#952
C2×#49792
C2×#49462
C2×#49422
#721272
#715682
#715652
#715442
#694242
#694202
#694092
#147583