Finite Group Databasebeta

← #10721663

Subgroups — #10721663

Order 768.

1414 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#4945C211yesmaximal, characteristic
3C2×#4951C211yesmaximal, characteristic
4C3×#1439C211yesmaximal, characteristic
5#71568C211yesmaximal, characteristic, complemented
6#71549C211yesmaximal, characteristic
7#71547C211yesmaximal, characteristic
8#71546C211yesmaximal, characteristic
9#71545C211yesmaximal, characteristic
10#69423C211yesmaximal, characteristic, complemented
11#69415C211yesmaximal, characteristic, complemented
12#69411C211yesmaximal, characteristic, complemented
13#69405C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14268—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
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
52Dic3×C4⋊C4—24no—
53#4951C418yescomplemented
54#4945—24no—
55C2×#388—31no—
56C2×#388—31no—
57C2×C4×C4⋊C4—31no—
58#1445—31no—
59#1444—31no—
60#1442—31no—
61#1441—31no—
62#1440—31no—
63#1439—31no—
64#1439—31no—
65#1439D311yescharacteristic
66#1437—31no—
67#1436—31no—
68#1434—31no—
69#1434—31no—
70C25×C3C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—41no—
93C2×C3×C22⋊C4—41no—
94C2×C3×C22⋊C4—41no—
95C2×C3×C22⋊C4—41no—
96C2×C3×C22⋊C4C2×C414yes—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217—41no—
102C2×#217—41no—
103C2×#217—41no—
104C2×#217—41no—
105C2×#217—41no—
106C2×#217—41no—
107C2×#217C2×C414yes—
108C2×#217C2×C414yes—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—41no—
113C2×C4⋊Dic3—41no—
114C2×C4⋊Dic3C2×C414yes—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—41no—
118C2×Dic3⋊C4—41no—
119C2×Dic3⋊C4—41no—
120C2×Dic3⋊C4—41no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—22no—
124C2×C4×Dic3—41no—
125C2×C4×Dic3—41no—
126C2×C4×Dic3—41no—
127C2×C4×Dic3—41no—
128C2×C4×Dic3C2×C414yes—
129C2×C4×Dic3D414yes—
130C3×#95—22no—
131C3×#95—41no—
132C3×#95—41no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95C2×C414yes—
149C3⋊#95C2×C414yes—
150C22×C4⋊C4—31no—
151C22×C4⋊C4—31no—
152C22×C4⋊C4—31no—
153C22×C4⋊C4—31no—
154C22×C4⋊C4C2×D311yescharacteristic
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4C2×D311yescharacteristic
160C22×C22⋊C4C2×D311yescharacteristic
161C22×C22⋊C4C2×D311yescharacteristic
162C22×C42—31no—
163C22×C42—31no—
164C22×C42—31no—
165#388—38no—
166#388—64no—
167C4×C4⋊C4—64no—
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×#95C2×D311yescharacteristic
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3C22×C412yes—
203C24×C3C2411yescharacteristic
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×C4C22×C412yes—
241C22×C3×C4C22×C412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
245C22×C3×C4#4112yes—
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×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3C22×C412yes—
295C22×Dic3C22×C412yes—
296C22×Dic3C22×C412yes—
297C22×Dic3C22×C412yes—
298C22×Dic3C2×D412yes—
299C22×Dic3C2×D412yes—
300C22×Dic3#4112yes—
301C22×Dic3#4112yes—
302C3×C4⋊C4—28no—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306#217—28no—
307#217—44no—
308#217—44no—
309#217—44no—
310C4⋊Dic3—28no—
311C4⋊Dic3—44no—
312Dic3⋊C4—44no—
313Dic3⋊C4—44no—
314C4×Dic3—28no—
315C4×Dic3—44no—
316C4×Dic3—44no—
317C25C22×D311yescharacteristic
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—34no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—121no—
342C2×C4⋊C4—121no—
343C2×C4⋊C4—121no—
344C2×C4⋊C4—121no—
345C2×C4⋊C4—121no—
346C2×C4⋊C4—121no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—62no—
361C2×C22⋊C4—121no—
362C2×C22⋊C4—121no—
363C2×C22⋊C4—121no—
364C2×C22⋊C4—121no—
365C2×C22⋊C4—121no—
366C2×C22⋊C4—121no—
367C2×C22⋊C4C4×D314yes—
368C2×C42—34no—
369C2×C42—34no—
370C2×C42—62no—
371C2×C42—62no—
372C2×C42—62no—
373C2×C42—121no—
374C2×C42—121no—
375C2×C42—121no—
376C2×C42—121no—
377#95—22no—
378#95—34no—
379#95—34no—
380#95—41no—
381#95—41no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95—121no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95—121no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3C23×C411yescharacteristic
433C23×C3C22×D411yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C3H(5,𝔽2)11yescharacteristic
441C23×C3H(5,𝔽2)11yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C32−1+411yescharacteristic
445C23×C32−1+411yescharacteristic
446C23×C32−1+411yescharacteristic
447C2×C3×C4—22no—
448C2×C3×C4—22no—
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—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—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#11714yes—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
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—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—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×Dic3C4×D414yes—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24C2×C4×D312yes—
560C24C23×D311yescharacteristic
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—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—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
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—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×C4C2×C4×D312yes—
654C22×C4C2×C4×D312yes—
655C22×C4D3×D412yes—
656C22×C4#23712yes—
657C22×C4#23712yes—
658C22×C4#23712yes—
659C4⋊C4—28no—
660C4⋊C4—68no—
661C4⋊C4—124no—
662C4⋊C4—124no—
663C4⋊C4—124no—
664C22⋊C4—28no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—68no—
668C22⋊C4—124no—
669C22⋊C4—124no—
670C22⋊C4—124no—
671C42—68no—
672C42—124no—
673C42—124no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3C2×#11711yescharacteristic
690C22×C3C2×C4×D411yescharacteristic
691C22×C3C4×#4111yescharacteristic
692C22×C3#51811yescharacteristic
693C22×C3#52011yescharacteristic
694C22×C3#52011yescharacteristic
695C22×C3#52011yescharacteristic
696C22×C3#52511yescharacteristic
697C22×C3#52511yescharacteristic
698C22×C3#52911yescharacteristic
699C22×C3#52911yescharacteristic
700C22×C3#53411yescharacteristic
701C22×C3#53511yescharacteristic
702C22×C3#53611yescharacteristic
703C22×C3#53711yescharacteristic
704C22×C3#53811yescharacteristic
705C22×C3#53811yescharacteristic
706C22×C3#53811yescharacteristic
707C22×C3#53911yescharacteristic
708C22×C3#53911yescharacteristic
709C22×C3#53911yescharacteristic
710C22×C3#54011yescharacteristic
711C22×C3#54011yescharacteristic
712C22×C3#54011yescharacteristic
713C22×C3#54011yescharacteristic
714C22×C3#54111yescharacteristic
715C22×C3#54111yescharacteristic
716C22×C3#54211yescharacteristic
717C22×C3#54211yescharacteristic
718C22×C3#54211yescharacteristic
719C22×C3#54211yescharacteristic
720C22×C3#54211yescharacteristic
721C22×C3#54211yescharacteristic
722C22×C3#54211yescharacteristic
723C22×C3#54211yescharacteristic
724C3×C4—24no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—81no—
729C3×C4—81no—
730Dic3—24no—
731Dic3—42no—
732Dic3—42no—
733Dic3—42no—
734Dic3—42no—
735Dic3—42no—
736Dic3—81no—
737Dic3—81no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23C22×C4×D311yescharacteristic
774C23C2×D3×D411yescharacteristic
775C23C2×#23711yescharacteristic
776C23C2×#23711yescharacteristic
777C23C2×#23711yescharacteristic
778C23#100411yescharacteristic
779C23#100411yescharacteristic
780C23#100411yescharacteristic
781C23#100711yescharacteristic
782C23D3×#4111yescharacteristic
783C23D3×#4111yescharacteristic
784C23#100911yescharacteristic
785C23#100911yescharacteristic
786C23#101011yescharacteristic
787C23#101011yescharacteristic
788C2×C4—22no—
789C2×C4—22no—
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—34no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
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—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
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—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
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#87714yes—
886C2×C3—82no—
887C2×C3#229011yescharacteristic
888C2×C3#231411yescharacteristic
889C2×C3#231911yescharacteristic
890C2×C3#232211yescharacteristic
891C2×C3#232411yescharacteristic
892C2×C3#233411yescharacteristic
893C2×C3#233711yescharacteristic
894C2×C3#263011yescharacteristic
895C2×C3#263211yescharacteristic
896C2×C3#263511yescharacteristic
897C2×C3#263711yescharacteristic
898C2×C3#265011yescharacteristic
899C2×C3#265111yescharacteristic
900C2×C3#265111yescharacteristic
901C2×C3#265411yescharacteristic
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#87711yescharacteristic
918C22#550411yescharacteristic
919C22#552311yescharacteristic
920C22C4×#23711yescharacteristic
921C22C4×D3×D411yescharacteristic
922C22#554511yescharacteristic
923C22#554611yescharacteristic
924C22#558611yescharacteristic
925C22#559211yescharacteristic
926C22#559311yescharacteristic
927C22#560011yescharacteristic
928C22#560311yescharacteristic
929C22#560311yescharacteristic
930C22#560511yescharacteristic
931C22#560611yescharacteristic
932C22#561711yescharacteristic
933C22#561911yescharacteristic
934C22#561911yescharacteristic
935C22#562511yescharacteristic
936C22#562511yescharacteristic
937C22#562911yescharacteristic
938C22#563811yescharacteristic
939C22#564011yescharacteristic
940C22#564311yescharacteristic
941C22#564911yescharacteristic
942C22#566011yescharacteristic
943C22#566211yescharacteristic
944C22#566211yescharacteristic
945C22#566311yescharacteristic
946C22#567511yescharacteristic
947C22#568211yescharacteristic
948C22#568211yescharacteristic
949C22#570411yescharacteristic
950C22#570711yescharacteristic
951C22#571911yescharacteristic
952C4—24no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—64no—
957C4—81no—
958C4—81no—
959C4—122no—
960C4—122no—
961C4—122no—
962C4—122no—
963C4—122no—
964C4—241no—
965C4—241no—
966C3#1426811yescharacteristic, complemented, Sylow
967C2—82no—
968C2#7386811yescharacteristic
969C2#7438511yescharacteristic
970C2#7438811yescharacteristic
971C2#7465711yescharacteristic
972C2#7547211yescharacteristic
973C2#7582811yescharacteristic
974C2#7629511yescharacteristic
975C2#7670211yescharacteristic
976C2#7681311yescharacteristic
977C2#7697711yescharacteristic
978C2#7699011yescharacteristic
979C2#7733311yescharacteristic
980C2#7734011yescharacteristic
981C2#7755611yescharacteristic
982C2#7805611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC25×C3C23
hypercenter#1439D3
hypocenterC3#14268
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×C4⋊C4C2semidirect
5. #71568C2semidirect
10. #69423C2semidirect
11. #69415C2semidirect
12. #69411C2semidirect
13. #69405C2semidirect
14. #69402C2semidirect
15. #69401C2semidirect
53. #4951C4semidirect
966. C3#14268semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×C4⋊C42
C2×#49452
C2×#49512
C3×#14392
#715682
#715492
#715472
#715462
#715452
#694232
#694152
#694112
#694052
#694022
#694012
#142683