Finite Group Databasebeta

← #10735700

Subgroups — #10735700

Order 768.

1378 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic
3C2×#4933C211yesmaximal, characteristic, complemented
4C2×#4676C211yesmaximal, characteristic
5#71570C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic
9#69429C211yesmaximal, characteristic
10#69429C211yesmaximal, characteristic
11#69428C211yesmaximal, characteristic
12#69414C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69405C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#15455—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C3×#387—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4990—24no—
54#4933—24no—
55#4676—24no—
56C2×#396—31no—
57C2×#388—31no—
58C2×#387—31no—
59C2×#387D311yescharacteristic, complemented
60#1444—31no—
61#1442—31no—
62#1442—31no—
63#1441—31no—
64#1440—31no—
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1437—31no—
69#1436—31no—
70#1434—31no—
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—41no—
92C2×C3×C42—22no—
93C2×C3×C42—22no—
94C2×C3×C42—41no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4—41no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—41no—
126C2×Dic3⋊C4—41no—
127C2×Dic3⋊C4—41no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
130C2×C4×Dic3—41no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95D414yes—
135C3⋊#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95D414yes—
151C22×C4⋊C4—31no—
152C22×C4⋊C4—31no—
153C22×C4⋊C4—31no—
154C22×C4⋊C4—31no—
155C22×C4⋊C4C2×D311yescharacteristic
156C22×C4⋊C4C2×D311yescharacteristic
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C42—31no—
165C22×C42C2×D311yescharacteristic
166#396—64no—
167#388—64no—
168#387—24no—
169#387—64no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C24×C3C2411yescharacteristic
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3#4112yes—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4#4112yes—
254C22×C3×C4#4112yes—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3C2×D412yes—
299C22×Dic3C2×D412yes—
300C22×Dic3#4112yes—
301C22×Dic3#4112yes—
302C22×Dic3#4112yes—
303C22×Dic3#4112yes—
304C3×C4⋊C4—28no—
305C3×C4⋊C4—44no—
306C3×C42—44no—
307(C2×D3)⋊C4—28no—
308(C2×D3)⋊C4—44no—
309(C2×D3)⋊C4—44no—
310(C2×D3)⋊C4—44no—
311(C2×D3)⋊C4—44no—
312(C2×D3)⋊C4—44no—
313(C2×D3)⋊C4—44no—
314Dic3⋊C4—28no—
315Dic3⋊C4—44no—
316Dic3⋊C4—44no—
317Dic3⋊C4—44no—
318C4×Dic3—44no—
319C25—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—62no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—121no—
350C2×C4⋊C4—121no—
351C2×C4⋊C4—121no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—62no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—62no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—121no—
368C2×C22⋊C4—121no—
369C2×C22⋊C4—121no—
370C2×C22⋊C4—121no—
371C2×C22⋊C4—121no—
372C2×C22⋊C4—121no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—41no—
376C2×C42—62no—
377C2×C42—62no—
378C2×C42—121no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—34no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—121no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95—121no—
397#95—121no—
398#95#6714yes—
399C23×C3C22×D411yescharacteristic
400C23×C3C22×D411yescharacteristic
401C23×C3C2×#4111yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4111yescharacteristic
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4111yescharacteristic
408C23×C3H(5,𝔽2)11yescharacteristic
409C23×C3H(5,𝔽2)11yescharacteristic
410C23×C3H(5,𝔽2)11yescharacteristic
411C23×C32−1+411yescharacteristic
412C23×C32−1+411yescharacteristic
413C23×C32−1+411yescharacteristic
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C24—32no—
548C24—61no—
549C24—61no—
550C24—61no—
551C24—61no—
552C24—61no—
553C24—61no—
554C24—61no—
555C24—61no—
556C24—61no—
557C24—61no—
558C24—61no—
559C24—61no—
560C24—61no—
561C24—61no—
562C24C23×D311yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—32no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4#23512yes—
656C22×C4#23512yes—
657C22×C4D3×D412yes—
658C22×C4C2×#6712yes—
659C22×C4C2×#6712yes—
660C22×C4C2×#6712yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—68no—
664C4⋊C4—124no—
665C4⋊C4—124no—
666C4⋊C4—124no—
667C22⋊C4—68no—
668C22⋊C4—124no—
669C22⋊C4—124no—
670C22⋊C4—124no—
671C22⋊C4—124no—
672C22⋊C4—124no—
673C22⋊C4—124no—
674C42—44no—
675C42—124no—
676C22×C3#52511yescharacteristic
677C22×C3#52511yescharacteristic
678C22×C3#52511yescharacteristic
679C22×C3#52911yescharacteristic
680C22×C3#52911yescharacteristic
681C22×C3#53211yescharacteristic
682C22×C3#53611yescharacteristic
683C22×C3#53711yescharacteristic
684C22×C3#53911yescharacteristic
685C22×C3#53911yescharacteristic
686C22×C3#53911yescharacteristic
687C22×C3#54011yescharacteristic
688C22×C3#54011yescharacteristic
689C22×C3#54111yescharacteristic
690C22×C3#54211yescharacteristic
691C22×C3D4211yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#54611yescharacteristic
694C22×C3#54611yescharacteristic
695C22×C3#54711yescharacteristic
696C22×C3#54811yescharacteristic
697C22×C3#54811yescharacteristic
698C22×C3#55111yescharacteristic
699C22×C3#55111yescharacteristic
700C22×C3#55211yescharacteristic
701C22×C3#55211yescharacteristic
702C22×C3#55211yescharacteristic
703C22×C3#55311yescharacteristic
704C22×C3#55311yescharacteristic
705C22×C3#55511yescharacteristic
706C22×C3#55611yescharacteristic
707C22×C3#55611yescharacteristic
708C22×C3#55611yescharacteristic
709C22×C3#56211yescharacteristic
710C22×C3#56311yescharacteristic
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—42no—
718C2×D3—81no—
719C2×D3—81no—
720C2×D3—81no—
721C2×D3—81no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—81no—
733Dic3—42no—
734Dic3—42no—
735Dic3—42no—
736Dic3—42no—
737Dic3—42no—
738Dic3—42no—
739Dic3—81no—
740C23—62no—
741C23—62no—
742C23—62no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23—62no—
747C23—121no—
748C23—121no—
749C23—121no—
750C23—121no—
751C23—121no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23C2×#23511yescharacteristic
776C23C2×#23511yescharacteristic
777C23C2×D3×D411yescharacteristic
778C23#100411yescharacteristic
779C23#100711yescharacteristic
780C23#100711yescharacteristic
781C23D3×#4111yescharacteristic
782C23D3×#4111yescharacteristic
783C23D3×#4111yescharacteristic
784C23D3×#4111yescharacteristic
785C23D3×#4111yescharacteristic
786C23#100911yescharacteristic
787C23#100911yescharacteristic
788C23#101011yescharacteristic
789C23C22×#6711yescharacteristic
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C3#246311yescharacteristic
889C2×C3#246411yescharacteristic
890C2×C3#246611yescharacteristic
891C2×C3#246911yescharacteristic
892C2×C3#247611yescharacteristic
893C2×C3#251511yescharacteristic
894C2×C3#256011yescharacteristic
895C2×C3#260411yescharacteristic
896C2×C3#260911yescharacteristic
897C2×C3#267211yescharacteristic
898C2×C3#269011yescharacteristic
899C2×C3#270711yescharacteristic
900C2×C3#274011yescharacteristic
901C2×C3#278311yescharacteristic
902C2×C3#279311yescharacteristic
903D3—82no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22—241no—
917C22—241no—
918C22—241no—
919C22#552811yescharacteristic
920C22#553011yescharacteristic
921C22#553211yescharacteristic
922C22#553511yescharacteristic
923C22#554711yescharacteristic
924C22#555211yescharacteristic
925C22#555611yescharacteristic
926C22#556411yescharacteristic
927C22#556811yescharacteristic
928C22#556811yescharacteristic
929C22#558111yescharacteristic
930C22#558111yescharacteristic
931C22#562911yescharacteristic
932C22#563111yescharacteristic
933C22#564011yescharacteristic
934C22#564711yescharacteristic
935C22#565411yescharacteristic
936C22#565611yescharacteristic
937C22#566111yescharacteristic
938C22#566311yescharacteristic
939C22#569211yescharacteristic
940C22#569311yescharacteristic
941C22#569611yescharacteristic
942C22#569911yescharacteristic
943C22#570211yescharacteristic
944C22#570511yescharacteristic
945C22#570611yescharacteristic
946C22#570711yescharacteristic
947C22#579111yescharacteristic
948C22D4×#6711yescharacteristic
949C22#581611yescharacteristic
950C22#582911yescharacteristic
951C22#582911yescharacteristic
952C22#583111yescharacteristic
953C22#583211yescharacteristic
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—81no—
961C4—122no—
962C4—122no—
963C4—122no—
964C4—122no—
965C4—122no—
966C4—122no—
967C4—241no—
968C3#1545511yescharacteristic, complemented, Sylow
969C2—242no—
970C2#7500611yescharacteristic
971C2#7515411yescharacteristic
972C2#7524011yescharacteristic
973C2#7525811yescharacteristic
974C2#7533011yescharacteristic
975C2#7534411yescharacteristic
976C2#7537511yescharacteristic
977C2#7540811yescharacteristic
978C2#8228011yescharacteristic
979C2#8236811yescharacteristic
980C2#8248511yescharacteristic
981C2#8282611yescharacteristic
982C2#8285311yescharacteristic
983C2#8306811yescharacteristic
984C2#8311011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#387C2
prime radicalC24×D3C23
hypercenterC2×#387D3
hypocenterC3#15455
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C3×#387C2semidirect
3. C2×#4933C2semidirect
6. #71568C2semidirect
7. #71566C2semidirect
12. #69414C2semidirect
13. #69414C2semidirect
14. #69405C2semidirect
15. #69401C2semidirect
59. C2×#387D3semidirect
968. C3#15455semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×#49902
C2×#49332
C2×#46762
#715702
#715682
#715662
#715372
#694292
#694282
#694142
#694052
#694012
#154553