Finite Group Databasebeta

← #10733136

Subgroups — #10733136

Order 768.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic, complemented
3C2×#5230C211yesmaximal, characteristic, complemented
4C2×#4981C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic
6C2×#4668C211yesmaximal, characteristic
7#71570C211yesmaximal, characteristic
8#71536C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic
10#69428C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic
12#69420C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69412C211yesmaximal, characteristic, complemented
15#69410C211yesmaximal, characteristic, complemented
16#15279—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C2×#946—24no—
22C2×#946—24no—
23C2×#946—24no—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C3×#391—24no—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42#5230—24no—
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#4981—24no—
58#4940—24no—
59#4668—24no—
60C22×C22⋊Q8—31no—
61C2×#398—31no—
62C2×#395—31no—
63C2×#391D311yescharacteristic, complemented
64C2×#388—31no—
65C2×#385—31no—
66#1444—31no—
67#1442—31no—
68#1442—31no—
69#1441—31no—
70#1440—31no—
71#1439—31no—
72#1439—31no—
73#1436—31no—
74C22⋊#95—31no—
75C24×D3C2311yescharacteristic
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8D414yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—41no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—41no—
110#946—232no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4D414yes—
128C2×(C2×D3)⋊C4Q814yescomplemented
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—41no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4—41no—
149C2×Dic3⋊C4D414yes—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95D414yes—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—41no—
168C23×Q8C2×D311yescharacteristic
169C24×C4—31no—
170C2×C22⋊Q8—64no—
171C2×C22⋊Q8—64no—
172C2×C22⋊Q8—64no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C42C2×D311yescharacteristic
188#398—64no—
189#395—64no—
190#391—24no—
191#388—64no—
192#385—64no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3C2411yescharacteristic
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3C2×D412yes—
225C23×D3C2×Q812yes—
226C23×D3#4112yes—
227C2×C3×Q8—28no—
228C2×C3×Q8—28no—
229C2×C3×Q8—44no—
230C2×C3×Q8—44no—
231C2×C3×Q8—44no—
232C2×C3×Q8—44no—
233C2×C3×Q8—44no—
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×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×Q812yes—
282C22×C3×C4#4112yes—
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—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×Dic3C2×D412yes—
327C22×Dic3C2×D412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3C2×Q812yes—
330C22×Dic3#4112yes—
331C22×Dic3#4112yes—
332C2×C4×D3—28no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C3×C4⋊C4—44no—
340C3×C42—44no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347C4⋊Dic3—28no—
348C4⋊Dic3—44no—
349Dic3⋊C4—28no—
350Dic3⋊C4—28no—
351Dic3⋊C4—44no—
352Dic3⋊C4—44no—
353Dic3⋊C4—44no—
354C25—31no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—41no—
360C22×Q8—41no—
361C22×Q8D1214yes—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—121no—
375C23×C4—121no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C22⋊Q8—632no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—121no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—41no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—62no—
442#95—62no—
443#95—62no—
444#95—62no—
445#95—121no—
446#95#6714yes—
447C23×C3C22×D411yescharacteristic
448C23×C3C22×D411yescharacteristic
449C23×C3C22×D411yescharacteristic
450C23×C3C22×D411yescharacteristic
451C23×C3C22×Q811yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C32−1+411yescharacteristic
459C23×C32−1+411yescharacteristic
460C23×C32−1+411yescharacteristic
461C23×C32−1+411yescharacteristic
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3C22⋊Q814yes—
497C3×Q8—416no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4#12014yes—
546C2×C3×C4#12114yes—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
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—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C4×D3—416no—
597C24—32no—
598C24—32no—
599C24—32no—
600C24—61no—
601C24—61no—
602C24—61no—
603C24—61no—
604C24—61no—
605C24—61no—
606C24—61no—
607C24—61no—
608C24—61no—
609C24—61no—
610C24—61no—
611C24—61no—
612C24C23×D311yescharacteristic
613C2×Q8—28no—
614C2×Q8—28no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
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—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—68no—
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—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—124no—
710C22×C4—124no—
711C22×C4—124no—
712C22×C4—124no—
713C22×C4—124no—
714C22×C4—124no—
715C22×C4C2×D1212yes—
716C22×C4C2×D1212yes—
717C22×C4C2×D1212yes—
718C22×C4#23512yes—
719C22×C4D3×D412yes—
720C22×C4D3×D412yes—
721C22×C4D3×Q812yes—
722C22×C4C2×#6712yes—
723C22×C4C2×#6712yes—
724C22×C4C2×#6712yes—
725C4⋊C4—44no—
726C4⋊C4—68no—
727C4⋊C4—68no—
728C4⋊C4—68no—
729C4⋊C4—124no—
730C4⋊C4—124no—
731C4⋊C4—124no—
732C4⋊C4—124no—
733C22⋊C4—68no—
734C22⋊C4—68no—
735C22⋊C4—68no—
736C22⋊C4—68no—
737C22⋊C4—124no—
738C22⋊C4—124no—
739C42—44no—
740C22×C3C2×#12011yescharacteristic
741C22×C3C2×#12111yescharacteristic
742C22×C3C2×C22⋊Q811yescharacteristic
743C22×C3#52511yescharacteristic
744C22×C3#53211yescharacteristic
745C22×C3#53311yescharacteristic
746C22×C3#53411yescharacteristic
747C22×C3#53611yescharacteristic
748C22×C3#53611yescharacteristic
749C22×C3#53611yescharacteristic
750C22×C3#53911yescharacteristic
751C22×C3#53911yescharacteristic
752C22×C3#54111yescharacteristic
753C22×C3#54211yescharacteristic
754C22×C3#54411yescharacteristic
755C22×C3D4211yescharacteristic
756C22×C3D4211yescharacteristic
757C22×C3#54611yescharacteristic
758C22×C3#54611yescharacteristic
759C22×C3#54711yescharacteristic
760C22×C3#54711yescharacteristic
761C22×C3#54711yescharacteristic
762C22×C3#54811yescharacteristic
763C22×C3#54811yescharacteristic
764C22×C3#54811yescharacteristic
765C22×C3#54811yescharacteristic
766C22×C3D4×Q811yescharacteristic
767C22×C3D4×Q811yescharacteristic
768C22×C3D4×Q811yescharacteristic
769C22×C3#55111yescharacteristic
770C22×C3#55211yescharacteristic
771C22×C3#55211yescharacteristic
772C22×C3#55411yescharacteristic
773C22×C3#56311yescharacteristic
774C22×C3#56311yescharacteristic
775C2×D3—24no—
776C2×D3—24no—
777C2×D3—24no—
778C2×D3—42no—
779C2×D3—42no—
780C2×D3—42no—
781C2×D3—42no—
782C2×D3—42no—
783C2×D3—42no—
784C2×D3—42no—
785C2×D3—42no—
786C2×D3—42no—
787C2×D3—42no—
788C2×D3—42no—
789C2×D3—42no—
790C3×C4—24no—
791C3×C4—24no—
792C3×C4—42no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—81no—
797Dic3—42no—
798Dic3—42no—
799Dic3—42no—
800Dic3—42no—
801Dic3—42no—
802Dic3—42no—
803Dic3—81no—
804C23—34no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—121no—
824C23—121no—
825C23—121no—
826C23—121no—
827C23—121no—
828C23—121no—
829C23—121no—
830C23—121no—
831C23—121no—
832C23—121no—
833C23—121no—
834C23—121no—
835C23—121no—
836C23—121no—
837C23—121no—
838C23—121no—
839C23C22×D1211yescharacteristic
840C23C2×#23511yescharacteristic
841C23C2×D3×D411yescharacteristic
842C23C2×D3×D411yescharacteristic
843C23#100411yescharacteristic
844C23#100411yescharacteristic
845C23C2×D3×Q811yescharacteristic
846C23#100711yescharacteristic
847C23#100711yescharacteristic
848C23#100711yescharacteristic
849C23D3×#4111yescharacteristic
850C23D3×#4111yescharacteristic
851C23D3×#4111yescharacteristic
852C23#101011yescharacteristic
853C23C22×#6711yescharacteristic
854Q8—416no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—1216no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—121no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4—121no—
950C2×C4—121no—
951C2×C4—121no—
952C2×C4#88214yes—
953C2×C4#93014yes—
954C2×C3#240911yescharacteristic
955C2×C3#241011yescharacteristic
956C2×C3#242911yescharacteristic
957C2×C3#243211yescharacteristic
958C2×C3#243811yescharacteristic
959C2×C3#244911yescharacteristic
960C2×C3#246111yescharacteristic
961C2×C3#253611yescharacteristic
962C2×C3#255611yescharacteristic
963C2×C3#267711yescharacteristic
964C2×C3#268011yescharacteristic
965C2×C3#269011yescharacteristic
966C2×C3#269811yescharacteristic
967C2×C3#272811yescharacteristic
968C2×C3#272911yescharacteristic
969D3—44no—
970C22—64no—
971C22—64no—
972C22—64no—
973C22—122no—
974C22—122no—
975C22—122no—
976C22—122no—
977C22—122no—
978C22—122no—
979C22—122no—
980C22—122no—
981C22—122no—
982C22—122no—
983C22—122no—
984C22—122no—
985C22C2×#88211yescharacteristic
986C22#549011yescharacteristic
987C22#549011yescharacteristic
988C22#549311yescharacteristic
989C22Q8×D1211yescharacteristic
990C22#557611yescharacteristic
991C22#557611yescharacteristic
992C22#557611yescharacteristic
993C22#557811yescharacteristic
994C22#558111yescharacteristic
995C22#558111yescharacteristic
996C22#558311yescharacteristic
997C22D3×C22⋊Q811yescharacteristic
998C22#562811yescharacteristic
999C22#563111yescharacteristic
1000C22#563111yescharacteristic
1001C22#563611yescharacteristic
1002C22#563811yescharacteristic
1003C22#563811yescharacteristic
1004C22#564611yescharacteristic
1005C22#566811yescharacteristic
1006C22#566911yescharacteristic
1007C22#567711yescharacteristic
1008C22#567911yescharacteristic
1009C22#572411yescharacteristic
1010C22#572711yescharacteristic
1011C22#572911yescharacteristic
1012C22#573511yescharacteristic
1013C22C2×#93011yescharacteristic
1014C22D4×#6711yescharacteristic
1015C22D4×#6711yescharacteristic
1016C22Q8×#6711yescharacteristic
1017C22#581611yescharacteristic
1018C22#582411yescharacteristic
1019C22#582811yescharacteristic
1020C4—24no—
1021C4—24no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—81no—
1027C4—122no—
1028C4—122no—
1029C4—122no—
1030C4—122no—
1031C4—122no—
1032C4—122no—
1033C4—241no—
1034C3#1527911yescharacteristic, complemented, Sylow
1035C2—124no—
1036C2#7649811yescharacteristic
1037C2#7653811yescharacteristic
1038C2#7656311yescharacteristic
1039C2#7661911yescharacteristic
1040C2#7662711yescharacteristic
1041C2#7664811yescharacteristic
1042C2#7665411yescharacteristic
1043C2#7665511yescharacteristic
1044C2#8212711yescharacteristic
1045C2#8249611yescharacteristic
1046C2#8249911yescharacteristic
1047C2#8281711yescharacteristic
1048C2#8282811yescharacteristic
1049C2#8296411yescharacteristic
1050C2#8326611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#391C2
prime radicalC24×D3C23
hypercenterC2×#391D3
hypocenterC3#15279
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×C3×#391C2semidirect
3. C2×#5230C2semidirect
4. C2×#4981C2semidirect
8. #71536C2semidirect
12. #69420C2semidirect
13. #69413C2semidirect
14. #69412C2semidirect
15. #69410C2semidirect
63. C2×#391D3semidirect
128. C2×(C2×D3)⋊C4Q8semidirect
1034. C3#15279semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×C3×#3912
C2×#52302
C2×#49812
C2×#49402
C2×#46682
#715702
#715362
#694292
#694282
(C2×D3)⋊#952
#694202
#694132
#694122
#694102
#152793