Finite Group Databasebeta

← #10733851

Subgroups — #10733851

Order 768.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#5210C211yesmaximal, characteristic, complemented
4C2×#4948C211yesmaximal, characteristic, complemented
5#72131C211yesmaximal, characteristic
6#72127C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69423C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15328—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C3×#386—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37#5220—24no—
38#5210—24no—
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#4948—24no—
56C2×#396—31no—
57C2×#386—31no—
58C2×#386D311yescharacteristic
59C2×#385—31no—
60#1445—31no—
61#1443—31no—
62#1442—31no—
63#1441—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1438—31no—
68C22⋊#95—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C25×C3C2311yescharacteristic
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—41no—
78C22×C3×D4—41no—
79C22×C3×D4Q814yes—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—41no—
84C23×C3×C4—41no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—41no—
96C23×Dic3—41no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4D414yes—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217D414yes—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—22no—
139C2×C4⋊Dic3—41no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4—41no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4—41no—
149C3×#95—22no—
150C3×#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C23×D4C2×D311yescharacteristic
168C24×C4—31no—
169C24×C4C2×D311yescharacteristic
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C22⋊C4C2×D311yescharacteristic
184#396—64no—
185#386—24no—
186#386—64no—
187#385—64no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
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×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3C2×D412yes—
231C24×C3C2×D412yes—
232C24×C3C2×Q812yes—
233C24×C3C2×Q812yes—
234C24×C3#4112yes—
235C24×C3#4112yes—
236C24×C3C2411yescharacteristic
237C2×C3×D4—28no—
238C2×C3×D4—28no—
239C2×C3×D4—44no—
240C2×C3×D4—44no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
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×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4—44no—
281C22×C3×C4—44no—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×Q812yes—
285C22×C3×C4#4112yes—
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×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3—44no—
342C22×Dic3—44no—
343C22×Dic3—44no—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C22×Dic3#4112yes—
349C3×C22⋊C4—44no—
350C3×C22⋊C4—44no—
351C3×C22⋊C4—44no—
352#217—28no—
353#217—44no—
354#217—44no—
355#217—44no—
356#217—44no—
357#217—44no—
358#217—44no—
359C4⋊Dic3—44no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
362Dic3⋊C4—44no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—41no—
370C22×D4—41no—
371C22×D4Dic614yes—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—41no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—121no—
391C23×C4—121no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
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—62no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C4⋊C4—121no—
409C2×C4⋊C4—121no—
410C2×C4⋊C4—121no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4—121no—
440C2×C22⋊C4#6714yes—
441#95—22no—
442#95—22no—
443#95—62no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—121no—
451#95—121no—
452#95—121no—
453#95—121no—
454#95—121no—
455#95—121no—
456#95—121no—
457#95—121no—
458#95—121no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3C22⋊Q814yes—
528C23×C3C22⋊Q814yes—
529C23×C3C22×D411yescharacteristic
530C23×C3C22×D411yescharacteristic
531C23×C3C22×Q811yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C3×D4—416no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—416no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—416no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24C2×Dic612yes—
663C24C2×Dic612yes—
664C24#23512yes—
665C24D3×D412yes—
666C24#23712yes—
667C24C2×#6712yes—
668C24C23×D311yescharacteristic
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4C2×Dic612yes—
778C22×C4#23712yes—
779C22×C4C2×#6712yes—
780C22×C4C2×#6712yes—
781C4⋊C4—124no—
782C4⋊C4—124no—
783C4⋊C4—124no—
784C4⋊C4—124no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—68no—
789C22⋊C4—124no—
790C22⋊C4—124no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C22⋊C4—124no—
795C22×C3—24no—
796C22×C3—24no—
797C22×C3—24no—
798C22×C3—24no—
799C22×C3—24no—
800C22×C3—24no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3C2×C22⋊Q811yescharacteristic
826C22×C3C2×C22⋊Q811yescharacteristic
827C22×C3#52511yescharacteristic
828C22×C3#52911yescharacteristic
829C22×C3#52911yescharacteristic
830C22×C3#53211yescharacteristic
831C22×C3#53411yescharacteristic
832C22×C3#53411yescharacteristic
833C22×C3#53811yescharacteristic
834C22×C3#53811yescharacteristic
835C22×C3#53811yescharacteristic
836C22×C3#53811yescharacteristic
837C22×C3#54011yescharacteristic
838C22×C3#54011yescharacteristic
839C22×C3#54311yescharacteristic
840C22×C3D4211yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#55111yescharacteristic
848C22×C3#55111yescharacteristic
849C22×C3#55111yescharacteristic
850C22×C3#55311yescharacteristic
851C22×C3#55311yescharacteristic
852C22×C3#55311yescharacteristic
853C22×C3#55311yescharacteristic
854C22×C3#55411yescharacteristic
855C22×C3#55411yescharacteristic
856C22×C3#55411yescharacteristic
857C22×C3#55411yescharacteristic
858C22×C3#56011yescharacteristic
859C22×C3#56011yescharacteristic
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—81no—
865Dic3—42no—
866Dic3—42no—
867Dic3—42no—
868Dic3—42no—
869Dic3—42no—
870Dic3—81no—
871Dic3—81no—
872Dic3—81no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23#87814yes—
942C23#92414yes—
943C23C22×Dic611yescharacteristic
944C23C2×#23511yescharacteristic
945C23C2×D3×D411yescharacteristic
946C23C2×#23711yescharacteristic
947C23C2×#23711yescharacteristic
948C23#100411yescharacteristic
949C23#100411yescharacteristic
950C23#100411yescharacteristic
951C23#100411yescharacteristic
952C23#100411yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23#100911yescharacteristic
957C23C22×#6711yescharacteristic
958D4—416no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—416no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—1216no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C3—44no—
1053C2×C3—44no—
1054C2×C3#243711yescharacteristic
1055C2×C3#245011yescharacteristic
1056C2×C3#245011yescharacteristic
1057C2×C3#245711yescharacteristic
1058C2×C3#246411yescharacteristic
1059C2×C3#255911yescharacteristic
1060C2×C3#256411yescharacteristic
1061C2×C3#257611yescharacteristic
1062C2×C3#257911yescharacteristic
1063C2×C3#266811yescharacteristic
1064C2×C3#268811yescharacteristic
1065C2×C3#269711yescharacteristic
1066C2×C3#274911yescharacteristic
1067C2×C3#278011yescharacteristic
1068C2×C3#278011yescharacteristic
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22C2×#87811yescharacteristic
1100C22#548311yescharacteristic
1101C22#549011yescharacteristic
1102C22#549511yescharacteristic
1103C22#553811yescharacteristic
1104C22#553911yescharacteristic
1105C22#553911yescharacteristic
1106C22#553911yescharacteristic
1107C22#554311yescharacteristic
1108C22#555611yescharacteristic
1109C22#555611yescharacteristic
1110C22#556011yescharacteristic
1111C22#558911yescharacteristic
1112C22#559111yescharacteristic
1113C22#559311yescharacteristic
1114C22#559511yescharacteristic
1115C22#560011yescharacteristic
1116C22#560111yescharacteristic
1117C22#560111yescharacteristic
1118C22#561311yescharacteristic
1119C22#561411yescharacteristic
1120C22#561511yescharacteristic
1121C22#561711yescharacteristic
1122C22#562011yescharacteristic
1123C22#565411yescharacteristic
1124C22#565611yescharacteristic
1125C22#566111yescharacteristic
1126C22#566311yescharacteristic
1127C22C2×#92411yescharacteristic
1128C22D4×#6711yescharacteristic
1129C22#580411yescharacteristic
1130C22#580611yescharacteristic
1131C22#580611yescharacteristic
1132C22#582911yescharacteristic
1133C22#583211yescharacteristic
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—122no—
1140C4—122no—
1141C4—122no—
1142C4—122no—
1143C4—122no—
1144C4—241no—
1145C4—241no—
1146C4—241no—
1147C3#1532811yescharacteristic, complemented, Sylow
1148C2—44no—
1149C2—44no—
1150C2#7471111yescharacteristic
1151C2#7471411yescharacteristic
1152C2#7476611yescharacteristic
1153C2#7477011yescharacteristic
1154C2#7484111yescharacteristic
1155C2#7485711yescharacteristic
1156C2#7485811yescharacteristic
1157C2#7492411yescharacteristic
1158C2#8211011yescharacteristic
1159C2#8236111yescharacteristic
1160C2#8238511yescharacteristic
1161C2#8260811yescharacteristic
1162C2#8267311yescharacteristic
1163C2#8268911yescharacteristic
1164C2#8285311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#15328
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#5210C2semidirect
4. C2×#4948C2semidirect
6. #72127C2semidirect
7. #71547C2semidirect
8. #71547C2semidirect
9. #71546C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
12. #69423C2semidirect
13. #69417C2semidirect
14. #69414C2semidirect
15. #69409C2semidirect
1147. C3#15328semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52202
C2×#52102
C2×#49482
#721312
#721272
#715472
#715462
#715442
#694232
#694172
#694142
#694092
#153283