Finite Group Databasebeta

← #10732618

Subgroups — #10732618

Order 768.

1550 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#889C211yesmaximal, characteristic
2C2×#4975C211yesmaximal, characteristic
3C2×#4647C211yesmaximal, characteristic
4C2×#4650C211yesmaximal, characteristic
5C3×#1441C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic
7#71566C211yesmaximal, characteristic
8#69420C211yesmaximal, characteristic
9#69420C211yesmaximal, characteristic
10#69419C211yesmaximal, characteristic
11#69411C211yesmaximal, characteristic
12#69409C211yesmaximal, characteristic
13Dic3⋊#95C211yesmaximal, characteristic
14Dic3⋊#95C211yesmaximal, characteristic
15Dic3×#95C211yesmaximal, characteristic
16#15228—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×#889—24no—
35C2×#889—24no—
36C2×#889—24no—
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#4975—24no—
56#4650—24no—
57#4647—24no—
58C22×#125—31no—
59C2×#389—31no—
60C2×#384—31no—
61C2×#382—31no—
62#1444—31no—
63#1444—31no—
64#1444—31no—
65#1444—31no—
66#1441—31no—
67#1441—31no—
68#1441—31no—
69#1441D311yescharacteristic
70C4⋊#95—31no—
71C4⋊#95—31no—
72C4×#95—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
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—41no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—41no—
101C2×C4⋊Dic3—41no—
102C2×C4⋊Dic3—41no—
103C2×Dic3⋊C4—22no—
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⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—41no—
124C2×Dic3⋊C4—41no—
125C2×Dic3⋊C4—41no—
126C2×Dic3⋊C4—41no—
127C2×Dic3⋊C4D414yes—
128C2×Dic3⋊C4D414yes—
129C2×Dic3⋊C4Q814yes—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3D414yes—
137C2×C4×Dic3Q814yes—
138C2×C4×Dic3Q814yes—
139#889—232no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—41no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C2×#125—64no—
159C2×#125—64no—
160C2×#125—64no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C4⋊C4C2×D311yescharacteristic
175C22×C42—31no—
176C22×C42—31no—
177C22×C42—31no—
178#389—64no—
179#384—64no—
180#382—64no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95C2×D311yescharacteristic
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C24×C3C2411yescharacteristic
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×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×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×Q812yes—
245C22×C3×C4C2×Q812yes—
246C22×C3×C4C2×Q812yes—
247C22×C3×C4#4112yes—
248C22×C3×C4#4112yes—
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×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3C2×D412yes—
291C22×Dic3C2×D412yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×D412yes—
295C22×Dic3C2×D412yes—
296C22×Dic3C2×Q812yes—
297C22×Dic3C2×Q812yes—
298C22×Dic3C2×Q812yes—
299C22×Dic3C2×Q812yes—
300C22×Dic3C2×Q812yes—
301C22×Dic3C2×Q812yes—
302C22×Dic3#4112yes—
303C22×Dic3#4112yes—
304C22×Dic3#4112yes—
305C3×C4⋊C4—28no—
306C3×C4⋊C4—44no—
307C4⋊Dic3—28no—
308C4⋊Dic3—44no—
309C4⋊Dic3—44no—
310Dic3⋊C4—28no—
311Dic3⋊C4—28no—
312Dic3⋊C4—28no—
313Dic3⋊C4—28no—
314Dic3⋊C4—28no—
315Dic3⋊C4—44no—
316Dic3⋊C4—44no—
317Dic3⋊C4—44no—
318Dic3⋊C4—44no—
319C4×Dic3—28no—
320C4×Dic3—28no—
321C4×Dic3—28no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337#125—632no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—34no—
344C2×C4⋊C4—34no—
345C2×C4⋊C4—34no—
346C2×C4⋊C4—41no—
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×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—121no—
374C2×C4⋊C4—121no—
375C2×C4⋊C4—121no—
376C2×C4⋊C4—121no—
377C2×C4⋊C4—121no—
378C2×C4⋊C4—121no—
379C2×C4⋊C4—121no—
380C2×C42—34no—
381C2×C42—34no—
382C2×C42—34no—
383C2×C42—62no—
384C2×C42—62no—
385C2×C42—62no—
386C2×C42—62no—
387C2×C42—62no—
388C2×C42—62no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—41no—
394#95—62no—
395#95—62no—
396#95—62no—
397#95—62no—
398#95—62no—
399#95—62no—
400#95—62no—
401#95—62no—
402#95—62no—
403#95—62no—
404#95—121no—
405#95—121no—
406#95—121no—
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C22×Q811yescharacteristic
411C23×C3C22×Q811yescharacteristic
412C23×C3C22×Q811yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4111yescharacteristic
415C23×C3C2×#4111yescharacteristic
416C23×C3C2×#4111yescharacteristic
417C23×C3C2×#4111yescharacteristic
418C23×C3H(5,𝔽2)11yescharacteristic
419C23×C3H(5,𝔽2)11yescharacteristic
420C23×C32−1+411yescharacteristic
421C23×C32−1+411yescharacteristic
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
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×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4#12514yescomplemented
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—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
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—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3#12014yes—
520C2×Dic3C22⋊Q814yes—
521C2×Dic3C22⋊Q814yes—
522C2×Dic3C22⋊Q814yes—
523C2×Dic3#12514yescomplemented
524C2×Dic3C4⋊Q814yes—
525C2×Dic3C4⋊Q814yes—
526C2×Dic3C4⋊Q814yes—
527C24C23×D311yescharacteristic
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—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
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—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4#23512yes—
626C22×C4D3×D412yes—
627C22×C4D3×D412yes—
628C22×C4D3×D412yes—
629C22×C4#23712yes—
630C22×C4D3×Q812yes—
631C22×C4D3×Q812yes—
632C22×C4D3×Q812yes—
633C4⋊C4—28no—
634C4⋊C4—44no—
635C4⋊C4—68no—
636C4⋊C4—68no—
637C4⋊C4—68no—
638C4⋊C4—68no—
639C4⋊C4—68no—
640C4⋊C4—68no—
641C4⋊C4—124no—
642C4⋊C4—124no—
643C4⋊C4—124no—
644C4⋊C4—124no—
645C4⋊C4—124no—
646C4⋊C4—124no—
647C42—68no—
648C42—68no—
649C42—68no—
650C22×C3C2×#12011yescharacteristic
651C22×C3C2×C22⋊Q811yescharacteristic
652C22×C3C2×C22⋊Q811yescharacteristic
653C22×C3C2×C22⋊Q811yescharacteristic
654C22×C3C2×#12511yescharacteristic
655C22×C3C2×#12511yescharacteristic
656C22×C3C2×C4⋊Q811yescharacteristic
657C22×C3C2×C4⋊Q811yescharacteristic
658C22×C3C2×C4⋊Q811yescharacteristic
659C22×C3#53211yescharacteristic
660C22×C3#53211yescharacteristic
661C22×C3#53311yescharacteristic
662C22×C3#53311yescharacteristic
663C22×C3#53511yescharacteristic
664C22×C3#53611yescharacteristic
665C22×C3#54411yescharacteristic
666C22×C3#54411yescharacteristic
667C22×C3#54411yescharacteristic
668C22×C3#54411yescharacteristic
669C22×C3#54611yescharacteristic
670C22×C3#54611yescharacteristic
671C22×C3#54711yescharacteristic
672C22×C3#54711yescharacteristic
673C22×C3#54811yescharacteristic
674C22×C3#54811yescharacteristic
675C22×C3#55011yescharacteristic
676C22×C3#55011yescharacteristic
677C22×C3#55211yescharacteristic
678C22×C3#55211yescharacteristic
679C22×C3#55311yescharacteristic
680C22×C3#55311yescharacteristic
681C22×C3#55411yescharacteristic
682C22×C3#55411yescharacteristic
683C22×C3#55711yescharacteristic
684C22×C3#55711yescharacteristic
685C3×C4—24no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—81no—
692Dic3—24no—
693Dic3—42no—
694Dic3—42no—
695Dic3—42no—
696Dic3—42no—
697Dic3—42no—
698Dic3—81no—
699Dic3#39518yes—
700C23C2×#23511yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703C23C2×D3×D411yescharacteristic
704C23C2×#23711yescharacteristic
705C23#100411yescharacteristic
706C23C2×D3×Q811yescharacteristic
707C23C2×D3×Q811yescharacteristic
708C23C2×D3×Q811yescharacteristic
709C23D3×#4111yescharacteristic
710C23D3×#4111yescharacteristic
711C23D3×#4111yescharacteristic
712C23#100911yescharacteristic
713C23#101011yescharacteristic
714C23#101011yescharacteristic
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—34no—
737C2×C4—34no—
738C2×C4—34no—
739C2×C4—34no—
740C2×C4—34no—
741C2×C4—34no—
742C2×C4—34no—
743C2×C4—34no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
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—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4#88914yescomplemented
820C2×C3C2×#39511yescharacteristic
821C2×C3#243111yescharacteristic
822C2×C3#243211yescharacteristic
823C2×C3#244111yescharacteristic
824C2×C3#244111yescharacteristic
825C2×C3#244211yescharacteristic
826C2×C3#244211yescharacteristic
827C2×C3#255011yescharacteristic
828C2×C3#255011yescharacteristic
829C2×C3#255211yescharacteristic
830C2×C3#255211yescharacteristic
831C2×C3#256511yescharacteristic
832C2×C3#256611yescharacteristic
833C2×C3#266011yescharacteristic
834C2×C3#285911yescharacteristic
835C22#549011yescharacteristic
836C22C2×#88911yescharacteristic
837C22#553111yescharacteristic
838C22#554811yescharacteristic
839C22#555311yescharacteristic
840C22#556711yescharacteristic
841C22#557811yescharacteristic
842C22D3×#12011yescharacteristic
843C22#559611yescharacteristic
844C22#559811yescharacteristic
845C22#559911yescharacteristic
846C22#560111yescharacteristic
847C22#560711yescharacteristic
848C22#561111yescharacteristic
849C22#562211yescharacteristic
850C22#562311yescharacteristic
851C22#562311yescharacteristic
852C22D3×C22⋊Q811yescharacteristic
853C22D3×C22⋊Q811yescharacteristic
854C22D3×C22⋊Q811yescharacteristic
855C22#563511yescharacteristic
856C22#563611yescharacteristic
857C22#564811yescharacteristic
858C22#565411yescharacteristic
859C22#565511yescharacteristic
860C22#567711yescharacteristic
861C22#568511yescharacteristic
862C22D3×#12511yescharacteristic
863C22#568911yescharacteristic
864C22#568911yescharacteristic
865C22#570811yescharacteristic
866C22#570911yescharacteristic
867C22D3×C4⋊Q811yescharacteristic
868C22D3×C4⋊Q811yescharacteristic
869C22D3×C4⋊Q811yescharacteristic
870C4—24no—
871C4—38no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—64no—
878C4—81no—
879C4—122no—
880C4—122no—
881C4—122no—
882C4—122no—
883C4—122no—
884C4—241no—
885C3#1522811yescharacteristic, complemented, Sylow
886C2#7390211yescharacteristic
887C2#7470011yescharacteristic
888C2#7498411yescharacteristic
889C2#7507611yescharacteristic
890C2#7606611yescharacteristic
891C2#7619011yescharacteristic
892C2#7653711yescharacteristic
893C2#7690411yescharacteristic
894C2D3×#39511yescharacteristic
895C2#7728911yescharacteristic
896C2#7732011yescharacteristic
897C2#7778611yescharacteristic
898C2#7778711yescharacteristic
899C2#7783711yescharacteristic
900C2#7813511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1441C2
hypercenter#1441D3
hypocenterC3#15228
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
470. C2×C3×C4#125semidirect
523. C2×Dic3#125semidirect
819. C2×C4#889semidirect
885. C3#15228semidirect

Maximal subgroups

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

subgroupindex
C22×#8892
C2×#49752
C2×#46472
C2×#46502
C3×#14412
#715682
#715662
#694202
#694192
#694112
#694092
Dic3⋊#952
Dic3×#952
#152283