Finite Group Databasebeta

← #10728725

Subgroups — #10728725

Order 768.

1590 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic6C211yesmaximal, characteristic
2C2×#4976C211yesmaximal, characteristic
3C2×#4660C211yesmaximal, characteristic
4C2×#4658C211yesmaximal, characteristic
5C3×#1436C211yesmaximal, characteristic
6#71564C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8#69424C211yesmaximal, characteristic
9#69424C211yesmaximal, characteristic
10#69414C211yesmaximal, characteristic
11#69413C211yesmaximal, characteristic
12#69411C211yesmaximal, characteristic
13#69409C211yesmaximal, characteristic
14#69405C211yesmaximal, characteristic
15#69401C211yesmaximal, characteristic
16#14884—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×Dic3⋊C4C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C2×C4×Dic6—24no—
29C2×C4×Dic6—24no—
30C2×C4×Dic6—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4976—24no—
56#4660—24no—
57#4658—24no—
58C22×C4×Q8—31no—
59C2×#400—31no—
60C2×#400—31no—
61C2×#389—31no—
62#1446—31no—
63#1446—31no—
64#1442—31no—
65#1442—31no—
66#1441—31no—
67#1441—31no—
68#1436—31no—
69#1436—31no—
70#1436—31no—
71#1436D311yescharacteristic
72#1434—31no—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C22×Dic6—22no—
89C22×Dic6—22no—
90C22×Dic6—22no—
91C22×Dic6—22no—
92C22×Dic6—22no—
93C22×Dic6—22no—
94C22×Dic6Q814yes—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3D414yes—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4D414yes—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—22no—
124C2×C4×Dic3D414yes—
125C4×Dic6—232no—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—22no—
129C3×#95—22no—
130C3×#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
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—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C23×Q8—31no—
151C2×C4×Q8—64no—
152C2×C4×Q8—64no—
153C2×C4×Q8—64no—
154C22×C4⋊C4—31no—
155C22×C4⋊C4—31no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4C2×D311yescharacteristic
161C22×C42—31no—
162C22×C42—31no—
163C22×C42C2×D311yescharacteristic
164#400—64no—
165#400—64no—
166#389—64no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
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
190C2×#95C2×D311yescharacteristic
191C24×C3C2411yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
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×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×Q812yes—
237C22×C3×C4#4112yes—
238C22×C3×C4#4112yes—
239C22×C3×C4#4112yes—
240C22×C3×C4#4112yes—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
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×Dic3C2×D412yes—
287C22×Dic3C2×D412yes—
288C22×Dic3C2×D412yes—
289C22×Dic3C2×D412yes—
290C22×Dic3C2×D412yes—
291C22×Dic3C2×D412yes—
292C22×Dic3C2×Q812yes—
293C22×Dic3C2×Q812yes—
294C22×Dic3#4112yes—
295C22×Dic3#4112yes—
296C22×Dic3#4112yes—
297C2×Dic6—28no—
298C2×Dic6—28no—
299C2×Dic6—28no—
300C2×Dic6—28no—
301C2×Dic6—28no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C3×C4⋊C4—44no—
305C3×C42—28no—
306C4⋊Dic3—28no—
307Dic3⋊C4—28no—
308Dic3⋊C4—28no—
309Dic3⋊C4—28no—
310Dic3⋊C4—44no—
311Dic3⋊C4—44no—
312C4×Dic3—28no—
313C4×Dic3—28no—
314C22×Q8—34no—
315C22×Q8—62no—
316C22×Q8—62no—
317C22×Q8—62no—
318C22×Q8—62no—
319C22×Q8—62no—
320C22×Q8—62no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C4×Q8—632no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—34no—
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—62no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—62no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—62no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—34no—
362C2×C42—62no—
363C2×C42—62no—
364C2×C42—62no—
365C2×C42—62no—
366C2×C42—62no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—62no—
373#95—62no—
374#95—62no—
375#95—62no—
376#95—62no—
377#95—62no—
378#95—62no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391C23×C3C22×D411yescharacteristic
392C23×C3C22×D411yescharacteristic
393C23×C3C22×D411yescharacteristic
394C23×C3C22×Q811yescharacteristic
395C23×C3C2×#4111yescharacteristic
396C23×C3C2×#4111yescharacteristic
397C23×C3C2×#4111yescharacteristic
398C23×C3C2×#4111yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4111yescharacteristic
402C23×C32−1+411yescharacteristic
403C23×C32−1+411yescharacteristic
404C23×C32−1+411yescharacteristic
405C23×C32−1+411yescharacteristic
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4C22⋊Q814yes—
454C2×C3×C4#12414yes—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3#12014yes—
509C2×Dic3C22⋊Q814yes—
510C2×Dic3C22⋊Q814yes—
511Dic6—232no—
512C24C23×D311yescharacteristic
513C2×Q8—68no—
514C2×Q8—68no—
515C2×Q8—68no—
516C2×Q8—68no—
517C2×Q8—68no—
518C2×Q8—68no—
519C2×Q8—68no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4#23512yes—
618C22×C4#23512yes—
619C22×C4#23512yes—
620C22×C4D3×D412yes—
621C22×C4D3×D412yes—
622C22×C4D3×D412yes—
623C22×C4#23712yes—
624C22×C4D3×Q812yes—
625C4⋊C4—44no—
626C4⋊C4—68no—
627C4⋊C4—68no—
628C4⋊C4—68no—
629C4⋊C4—68no—
630C4⋊C4—124no—
631C4⋊C4—124no—
632C42—28no—
633C42—68no—
634C42—68no—
635C22×C3C2×#12011yescharacteristic
636C22×C3C2×C22⋊Q811yescharacteristic
637C22×C3C2×C22⋊Q811yescharacteristic
638C22×C3C2×C22⋊Q811yescharacteristic
639C22×C3#52511yescharacteristic
640C22×C3#52511yescharacteristic
641C22×C3#52511yescharacteristic
642C22×C3#52511yescharacteristic
643C22×C3C2×#12411yescharacteristic
644C22×C3#52911yescharacteristic
645C22×C3#52911yescharacteristic
646C22×C3#52911yescharacteristic
647C22×C3#52911yescharacteristic
648C22×C3#53611yescharacteristic
649C22×C3#53611yescharacteristic
650C22×C3#54111yescharacteristic
651C22×C3#54111yescharacteristic
652C22×C3#54111yescharacteristic
653C22×C3#54111yescharacteristic
654C22×C3#54711yescharacteristic
655C22×C3#54711yescharacteristic
656C22×C3#54711yescharacteristic
657C22×C3#54711yescharacteristic
658C22×C3#54811yescharacteristic
659C22×C3#54811yescharacteristic
660C22×C3#54811yescharacteristic
661C22×C3#54811yescharacteristic
662C22×C3#55611yescharacteristic
663C22×C3#55611yescharacteristic
664C22×C3#55611yescharacteristic
665C22×C3#55611yescharacteristic
666C22×C3#55711yescharacteristic
667C22×C3#55711yescharacteristic
668C22×C3#55711yescharacteristic
669C22×C3#55711yescharacteristic
670C3×C4—24no—
671C3×C4—24no—
672C3×C4—42no—
673C3×C4—42no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—81no—
677Dic3—24no—
678Dic3—24no—
679Dic3—24no—
680Dic3—42no—
681Dic3—42no—
682Dic3—81no—
683Dic3—81no—
684Dic3—81no—
685C23C2×#23511yescharacteristic
686C23C2×#23511yescharacteristic
687C23C2×#23511yescharacteristic
688C23C2×D3×D411yescharacteristic
689C23C2×D3×D411yescharacteristic
690C23C2×D3×D411yescharacteristic
691C23C2×#23711yescharacteristic
692C23C2×D3×Q811yescharacteristic
693C23#100711yescharacteristic
694C23D3×#4111yescharacteristic
695C23D3×#4111yescharacteristic
696C23D3×#4111yescharacteristic
697C23#101011yescharacteristic
698C23#101011yescharacteristic
699C23#101011yescharacteristic
700Q8—632no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—34no—
720C2×C4—34no—
721C2×C4—34no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4#88514yes—
805C2×C4#89614yes—
806C2×C3#239811yescharacteristic
807C2×C3#240611yescharacteristic
808C2×C3#243611yescharacteristic
809C2×C3#245311yescharacteristic
810C2×C3#245311yescharacteristic
811C2×C3#245311yescharacteristic
812C2×C3#245311yescharacteristic
813C2×C3#246911yescharacteristic
814C2×C3#246911yescharacteristic
815C2×C3#246911yescharacteristic
816C2×C3#246911yescharacteristic
817C2×C3#256811yescharacteristic
818C2×C3#258111yescharacteristic
819C2×C3#263411yescharacteristic
820C2×C3#284811yescharacteristic
821C22#547911yescharacteristic
822C22C2×#88511yescharacteristic
823C22#550711yescharacteristic
824C22C2×#89611yescharacteristic
825C22#551811yescharacteristic
826C22#552811yescharacteristic
827C22#553311yescharacteristic
828C22#553811yescharacteristic
829C22#554711yescharacteristic
830C22#554711yescharacteristic
831C22#554711yescharacteristic
832C22#555111yescharacteristic
833C22#555211yescharacteristic
834C22#555211yescharacteristic
835C22#555711yescharacteristic
836C22#556711yescharacteristic
837C22#556711yescharacteristic
838C22#556811yescharacteristic
839C22#558311yescharacteristic
840C22D3×#12011yescharacteristic
841C22#559811yescharacteristic
842C22#559811yescharacteristic
843C22D3×C22⋊Q811yescharacteristic
844C22D3×C22⋊Q811yescharacteristic
845C22#562811yescharacteristic
846C22#563111yescharacteristic
847C22#564811yescharacteristic
848C22#565511yescharacteristic
849C22#565611yescharacteristic
850C22#567111yescharacteristic
851C22#568511yescharacteristic
852C22#569611yescharacteristic
853C22#570111yescharacteristic
854C22#570211yescharacteristic
855C22#572111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—64no—
861C4—64no—
862C4—64no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—122no—
867C4—122no—
868C4—241no—
869C4—241no—
870C4—241no—
871C3#1488411yescharacteristic, complemented, Sylow
872C2#7348111yescharacteristic
873C2#7367611yescharacteristic
874C2#7367911yescharacteristic
875C2#7460011yescharacteristic
876C2#7465511yescharacteristic
877C2#7470111yescharacteristic
878C2#7498811yescharacteristic
879C2#7500611yescharacteristic
880C2#7509011yescharacteristic
881C2#7513511yescharacteristic
882C2#7552111yescharacteristic
883C2#7552411yescharacteristic
884C2#7601211yescharacteristic
885C2#7601411yescharacteristic
886C2#7654511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1436C2
hypercenter#1436D3
hypocenterC3#14884
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
871. C3#14884semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic62
C2×#49762
C2×#46602
C2×#46582
C3×#14362
#715642
#715362
#694242
#694142
#694132
#694112
#694092
#694052
#694012
#148843