Finite Group Databasebeta

← #10733770

Subgroups — #10733770

Order 768.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#5212C211yesmaximal, characteristic, complemented
6C2×#4947C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic
8#71547C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69424C211yesmaximal, characteristic, complemented
13#69423C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15323—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C2×#878—24no—
37C2×#878—24no—
38C2×#878—24no—
39C3×#386—24no—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42#5220—24no—
43#5212—24no—
44#5210—24no—
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
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4947—24no—
60C22×C22⋊Q8—31no—
61C2×#393—31no—
62C2×#386—31no—
63C2×#386D311yescharacteristic
64C2×#385—31no—
65C2×#380—31no—
66#1446—31no—
67#1445—31no—
68#1441—31no—
69#1441—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C22×C3×D4Q814yescomplemented
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3—22no—
101C23×Dic3—41no—
102C23×Dic3—41no—
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×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4D414yes—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—41no—
142C2×#217—41no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217—41no—
146C2×#217—41no—
147C2×#217D414yes—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—41no—
152C2×C4⋊Dic3—41no—
153C2×C4⋊Dic3D414yescomplemented
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—41no—
162C2×Dic3⋊C4D414yescomplemented
163#878—232no—
164C3×#95—22no—
165C3×#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C23×Q8—31no—
181C23×D4C2×D311yescharacteristic
182C24×C4—31no—
183C24×C4C2×D311yescharacteristic
184C2×C22⋊Q8—64no—
185C2×C22⋊Q8—64no—
186C2×C22⋊Q8—64no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4C2×D311yescharacteristic
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202#393—64no—
203#386—24no—
204#386—64no—
205#385—64no—
206#380—64no—
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—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
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—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3C2×D412yes—
248C24×C3C2×D412yes—
249C24×C3C2×Q812yes—
250C24×C3C2×Q812yes—
251C24×C3#4112yes—
252C24×C3#4112yes—
253C24×C3C2411yescharacteristic
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—44no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—28no—
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×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—44no—
292C22×C3×C4—44no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×Q812yes—
302C22×C3×C4#4112yes—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—28no—
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—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—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3—44no—
358C22×Dic3—44no—
359C22×Dic3C2×D412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×D412yes—
365C22×Dic3#4112yes—
366C2×Dic6—28no—
367C2×Dic6—44no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C2×Dic6—44no—
372C2×Dic6—44no—
373C3×C22⋊C4—28no—
374C3×C22⋊C4—44no—
375C3×C22⋊C4—44no—
376#217—28no—
377#217—28no—
378#217—44no—
379#217—44no—
380#217—44no—
381#217—44no—
382#217—44no—
383C4⋊Dic3—28no—
384C4⋊Dic3—44no—
385Dic3⋊C4—28no—
386Dic3⋊C4—28no—
387Dic3⋊C4—44no—
388C25C22×D311yescharacteristic
389C25C22×D311yescharacteristic
390C22×Q8—62no—
391C22×Q8—62no—
392C22×Q8—62no—
393C22×Q8—62no—
394C22×Q8—62no—
395C22×Q8—121no—
396C22×Q8—121no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—41no—
402C22×D4—41no—
403C22×D4Dic614yescomplemented
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—41no—
418C23×C4—41no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—121no—
425C23×C4—121no—
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C23×C4C22×D311yescharacteristic
431C22⋊Q8—632no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
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—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4—121no—
446C2×C4⋊C4—121no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—41no—
455C2×C22⋊C4—41no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4—121no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4#6714yes—
477#95—22no—
478#95—22no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—121no—
489#95—121no—
490#95—121no—
491#95—121no—
492#95—121no—
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—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
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—22no—
528C23×C3—22no—
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×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3C22⋊Q814yes—
562C23×C3C22⋊Q814yescomplemented
563C23×C3C22×D411yescharacteristic
564C23×C3C22×D411yescharacteristic
565C23×C3C22×D411yescharacteristic
566C23×C3C22×D411yescharacteristic
567C23×C3C22×Q811yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3C2×#4111yescharacteristic
572C23×C3H(5,𝔽2)11yescharacteristic
573C23×C3H(5,𝔽2)11yescharacteristic
574C23×C3H(5,𝔽2)11yescharacteristic
575C23×C3H(5,𝔽2)11yescharacteristic
576C23×C32−1+411yescharacteristic
577C23×C32−1+411yescharacteristic
578C3×D4—416no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—416no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4#12014yes—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—416no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
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#12114yes—
672Dic6—416no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic612yes—
698C24C2×Dic612yes—
699C24#23512yes—
700C24D3×D412yes—
701C24#23712yes—
702C24C2×#6712yes—
703C24C23×D311yescharacteristic
704C2×Q8—68no—
705C2×Q8—124no—
706C2×Q8—124no—
707C2×Q8—124no—
708C2×Q8—124no—
709C2×Q8—124no—
710C2×Q8—124no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—28no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
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—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—68no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
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—124no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4C2×Dic612yes—
818C22×C4D3×D412yes—
819C22×C4D3×D412yes—
820C22×C4#23712yes—
821C22×C4C2×#6712yes—
822C22×C4C2×#6712yes—
823C4⋊C4—68no—
824C4⋊C4—68no—
825C4⋊C4—68no—
826C4⋊C4—124no—
827C4⋊C4—124no—
828C22⋊C4—28no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—68no—
832C22⋊C4—68no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C22⋊C4—124no—
836C22⋊C4—124no—
837C22⋊C4—124no—
838C22×C3—24no—
839C22×C3—24no—
840C22×C3—24no—
841C22×C3—24no—
842C22×C3—24no—
843C22×C3—24no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
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×C3C2×#12011yescharacteristic
869C22×C3C2×#12111yescharacteristic
870C22×C3C2×C22⋊Q811yescharacteristic
871C22×C3C2×C22⋊Q811yescharacteristic
872C22×C3#52511yescharacteristic
873C22×C3#52911yescharacteristic
874C22×C3#53511yescharacteristic
875C22×C3#53511yescharacteristic
876C22×C3#53611yescharacteristic
877C22×C3#53711yescharacteristic
878C22×C3#53811yescharacteristic
879C22×C3#53911yescharacteristic
880C22×C3#54211yescharacteristic
881C22×C3#54211yescharacteristic
882C22×C3#54311yescharacteristic
883C22×C3D4211yescharacteristic
884C22×C3D4211yescharacteristic
885C22×C3#54611yescharacteristic
886C22×C3#54611yescharacteristic
887C22×C3#54611yescharacteristic
888C22×C3#54611yescharacteristic
889C22×C3#54611yescharacteristic
890C22×C3#54611yescharacteristic
891C22×C3#54611yescharacteristic
892C22×C3#54711yescharacteristic
893C22×C3#54811yescharacteristic
894C22×C3#54811yescharacteristic
895C22×C3D4×Q811yescharacteristic
896C22×C3D4×Q811yescharacteristic
897C22×C3#55111yescharacteristic
898C22×C3#55211yescharacteristic
899C22×C3#55411yescharacteristic
900C22×C3#55411yescharacteristic
901C22×C3#56211yescharacteristic
902C22×C3#56211yescharacteristic
903C3×C4—24no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—42no—
907C3×C4—81no—
908Dic3—24no—
909Dic3—42no—
910Dic3—42no—
911Dic3—42no—
912Dic3—42no—
913Dic3—81no—
914Dic3—81no—
915Dic3—81no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
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—41no—
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—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23#87814yescomplemented
985C23#92414yes—
986C23C22×Dic611yescharacteristic
987C23C2×#23511yescharacteristic
988C23C2×D3×D411yescharacteristic
989C23C2×D3×D411yescharacteristic
990C23C2×D3×D411yescharacteristic
991C23C2×#23711yescharacteristic
992C23C2×#23711yescharacteristic
993C23#100411yescharacteristic
994C23#100411yescharacteristic
995C23#100411yescharacteristic
996C23D3×#4111yescharacteristic
997C23#100911yescharacteristic
998C23#101011yescharacteristic
999C23#101011yescharacteristic
1000C23C22×#6711yescharacteristic
1001Q8—1216no—
1002D4—416no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—34no—
1019C2×C4—416no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—1216no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
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#93714yes—
1096C2×C3—44no—
1097C2×C3—44no—
1098C2×C3#240411yescharacteristic
1099C2×C3#240811yescharacteristic
1100C2×C3#240911yescharacteristic
1101C2×C3#241711yescharacteristic
1102C2×C3#242711yescharacteristic
1103C2×C3#243711yescharacteristic
1104C2×C3#244911yescharacteristic
1105C2×C3#245011yescharacteristic
1106C2×C3#247711yescharacteristic
1107C2×C3#267211yescharacteristic
1108C2×C3#267611yescharacteristic
1109C2×C3#268711yescharacteristic
1110C2×C3#269211yescharacteristic
1111C2×C3#269211yescharacteristic
1112C2×C3#269611yescharacteristic
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22C2×#87811yescharacteristic
1144C22#548311yescharacteristic
1145C22#549011yescharacteristic
1146C22#549511yescharacteristic
1147C22D4×Dic611yescharacteristic
1148C22D4×Dic611yescharacteristic
1149C22#553811yescharacteristic
1150C22#553911yescharacteristic
1151C22#554311yescharacteristic
1152C22#555211yescharacteristic
1153C22#555211yescharacteristic
1154C22#556011yescharacteristic
1155C22#558611yescharacteristic
1156C22#559111yescharacteristic
1157C22#559111yescharacteristic
1158C22#559211yescharacteristic
1159C22#559711yescharacteristic
1160C22#560311yescharacteristic
1161C22D3×#12111yescharacteristic
1162C22#560711yescharacteristic
1163C22#560911yescharacteristic
1164C22#561111yescharacteristic
1165C22#561211yescharacteristic
1166C22#562111yescharacteristic
1167C22#565011yescharacteristic
1168C22#566211yescharacteristic
1169C22#566511yescharacteristic
1170C22#566711yescharacteristic
1171C22C2×#92411yescharacteristic
1172C22C2×#93711yescharacteristic
1173C22D4×#6711yescharacteristic
1174C22#580611yescharacteristic
1175C22#580611yescharacteristic
1176C22#582511yescharacteristic
1177C22#582911yescharacteristic
1178C4—24no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—64no—
1183C4—81no—
1184C4—122no—
1185C4—122no—
1186C4—122no—
1187C4—122no—
1188C4—241no—
1189C4—241no—
1190C4—241no—
1191C3#1532311yescharacteristic, complemented, Sylow
1192C2—44no—
1193C2—44no—
1194C2#7469311yescharacteristic
1195C2#7469711yescharacteristic
1196C2#7471011yescharacteristic
1197C2#7473311yescharacteristic
1198C2#7479311yescharacteristic
1199C2#7480211yescharacteristic
1200C2#7480311yescharacteristic
1201C2#7480711yescharacteristic
1202C2#8211011yescharacteristic
1203C2#8234911yescharacteristic
1204C2#8236111yescharacteristic
1205C2#8258111yescharacteristic
1206C2#8264011yescharacteristic
1207C2#8268211yescharacteristic
1208C2#8287411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#15323
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
4. C2×#5210C2semidirect
5. C2×#5212C2semidirect
6. C2×#4947C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71544C2semidirect
12. #69424C2semidirect
13. #69423C2semidirect
14. #69410C2semidirect
15. #69409C2semidirect
83. C22×C3×D4Q8semidirect
153. C2×C4⋊Dic3D4semidirect
162. C2×Dic3⋊C4D4semidirect
403. C22×D4Dic6semidirect
562. C23×C3C22⋊Q8semidirect
984. C23#878semidirect
1191. C3#15323semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×C3×#3862
C2×#52202
C2×#52102
C2×#52122
C2×#49472
#721312
#715472
#715462
#715442
#694242
#694232
#694102
#694092
#153233