Finite Group Databasebeta

← #10740372

Subgroups — #10740372

Order 768.

1586 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#869C211yesmaximal, characteristic
2C2×#4982C211yesmaximal, characteristic
3C2×#4660C211yesmaximal, characteristic
4C2×#4646C211yesmaximal, characteristic
5C3×#1436C211yesmaximal, characteristic
6#71565C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8#69424C211yesmaximal, characteristic
9#69424C211yesmaximal, characteristic
10#69424C211yesmaximal, characteristic
11#69415C211yesmaximal, characteristic
12#69412C211yesmaximal, characteristic
13#69410C211yesmaximal, characteristic
14#69407C211yesmaximal, characteristic
15#69407C211yesmaximal, characteristic
16#15783—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C2×#869—24no—
29C2×#869—24no—
30C2×#869—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#4982—24no—
56#4660—24no—
57#4646—24no—
58C22×C4⋊Q8—31no—
59C2×#400—31no—
60C2×#398—31no—
61C2×#391—31no—
62#1446—31no—
63#1446—31no—
64#1446—31no—
65#1442—31no—
66#1442—31no—
67#1441—31no—
68#1441—31no—
69#1436—31no—
70#1436—31no—
71#1436—31no—
72#1436D311yescharacteristic
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×Dic6—22no—
95C22×Dic6—22no—
96C22×Dic6—22no—
97C22×Dic6—41no—
98C22×Dic6—41no—
99C22×Dic6—41no—
100C22×Dic6—41no—
101C22×Dic6D414yes—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3D414yes—
119C2×C4⋊Dic3D414yes—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×C4×Dic3—22no—
127C2×C4×Dic3—41no—
128C2×C4×Dic3—41no—
129#869—232no—
130C3×#95—22no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95Q814yescomplemented
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—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95Q814yescomplemented
154C23×Q8—31no—
155C23×Q8—31no—
156C2×C4⋊Q8—64no—
157C2×C4⋊Q8—64no—
158C2×C4⋊Q8—64no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C42—31no—
167C22×C42C2×D311yescharacteristic
168#400—64no—
169#398—64no—
170#391—64no—
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×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C2×#95C2×D311yescharacteristic
193C2×#95C2×D311yescharacteristic
194C2×#95C2×D311yescharacteristic
195C24×C3C2411yescharacteristic
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×C4—21no—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2×Q812yes—
238C22×C3×C4C2×Q812yes—
239C22×C3×C4C2×Q812yes—
240C22×C3×C4C2×Q812yes—
241C22×C3×C4#4112yes—
242C22×C3×C4#4112yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
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×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×D412yes—
295C22×Dic3C2×D412yes—
296C22×Dic3C2×D412yes—
297C22×Dic3C2×D412yes—
298C22×Dic3C2×D412yes—
299C22×Dic3C2×Q812yes—
300C22×Dic3C2×Q812yes—
301C2×Dic6—28no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—44no—
305C2×Dic6—44no—
306C2×Dic6—44no—
307C2×Dic6—44no—
308C2×Dic6—44no—
309C2×Dic6—44no—
310C2×Dic6—44no—
311C2×Dic6—44no—
312C2×Dic6—44no—
313C2×Dic6—44no—
314C2×Dic6—44no—
315C3×C4⋊C4—44no—
316C3×C42—28no—
317C4⋊Dic3—28no—
318C4⋊Dic3—28no—
319C4⋊Dic3—28no—
320C4⋊Dic3—28no—
321Dic3⋊C4—44no—
322Dic3⋊C4—44no—
323C4×Dic3—44no—
324C22×Q8—34no—
325C22×Q8—62no—
326C22×Q8—62no—
327C22×Q8—62no—
328C22×Q8—62no—
329C22×Q8—62no—
330C22×Q8—62no—
331C22×Q8—62no—
332C22×Q8—62no—
333C22×Q8—62no—
334C22×Q8—121no—
335C22×Q8—121no—
336C22×Q8—121no—
337C22×Q8—121no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C4⋊Q8—632no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
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—62no—
374C2×C4⋊C4—62no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—62no—
379C2×C42—121no—
380C2×C42—121no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—34no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—62no—
393#95—62no—
394#95—62no—
395#95—62no—
396#95—62no—
397#95—62no—
398#95—121no—
399#95—121no—
400#95—121no—
401#95—121no—
402#95—121no—
403#95—121no—
404#95Dic614yescomplemented
405C23×C3C22×D411yescharacteristic
406C23×C3C22×D411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×Q811yescharacteristic
409C23×C3C22×Q811yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3H(5,𝔽2)11yescharacteristic
415C23×C3H(5,𝔽2)11yescharacteristic
416C23×C32−1+411yescharacteristic
417C23×C32−1+411yescharacteristic
418C23×C32−1+411yescharacteristic
419C23×C32−1+411yescharacteristic
420C2×C3×C4—22no—
421C2×C3×C4—22no—
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—22no—
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#12314yes—
467C2×C3×C4#12414yes—
468C2×C3×C4C4⋊Q814yes—
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—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—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—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—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3#12014yes—
525Dic6—416no—
526Dic6—416no—
527C24C23×D311yescharacteristic
528C2×Q8—68no—
529C2×Q8—68no—
530C2×Q8—68no—
531C2×Q8—124no—
532C2×Q8—124no—
533C2×Q8—124no—
534C2×Q8—124no—
535C2×Q8—124no—
536C2×Q8—124no—
537C2×Q8—124no—
538C2×Q8—124no—
539C2×Q8—124no—
540C2×Q8—124no—
541C2×Q8—124no—
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—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—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—32no—
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—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×C4C2×Dic612yes—
637C22×C4C2×Dic612yes—
638C22×C4C2×Dic612yes—
639C22×C4#23512yes—
640C22×C4#23512yes—
641C22×C4D3×D412yes—
642C22×C4D3×D412yes—
643C22×C4D3×D412yes—
644C22×C4#23712yes—
645C22×C4D3×Q812yes—
646C22×C4#23912yes—
647C4⋊C4—44no—
648C4⋊C4—68no—
649C4⋊C4—68no—
650C4⋊C4—68no—
651C4⋊C4—68no—
652C4⋊C4—124no—
653C4⋊C4—124no—
654C42—28no—
655C42—124no—
656C22×C3C2×#12011yescharacteristic
657C22×C3C2×#12311yescharacteristic
658C22×C3C2×#12411yescharacteristic
659C22×C3C2×C4⋊Q811yescharacteristic
660C22×C3#53311yescharacteristic
661C22×C3#53311yescharacteristic
662C22×C3#53411yescharacteristic
663C22×C3#53611yescharacteristic
664C22×C3#53611yescharacteristic
665C22×C3#54111yescharacteristic
666C22×C3#54111yescharacteristic
667C22×C3#54211yescharacteristic
668C22×C3#54211yescharacteristic
669C22×C3#54411yescharacteristic
670C22×C3#54411yescharacteristic
671C22×C3#54611yescharacteristic
672C22×C3#54611yescharacteristic
673C22×C3#54611yescharacteristic
674C22×C3#54611yescharacteristic
675C22×C3#54811yescharacteristic
676C22×C3#54811yescharacteristic
677C22×C3#54811yescharacteristic
678C22×C3#54811yescharacteristic
679C22×C3D4×Q811yescharacteristic
680C22×C3D4×Q811yescharacteristic
681C22×C3D4×Q811yescharacteristic
682C22×C3D4×Q811yescharacteristic
683C22×C3#55411yescharacteristic
684C22×C3#55411yescharacteristic
685C22×C3#55611yescharacteristic
686C22×C3#55611yescharacteristic
687C22×C3#55711yescharacteristic
688C22×C3#55711yescharacteristic
689C22×C3#56311yescharacteristic
690C22×C3#56311yescharacteristic
691C3×C4—24no—
692C3×C4—24no—
693C3×C4—24no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—81no—
697C3×C4—81no—
698Dic3—24no—
699Dic3—42no—
700Dic3—42no—
701Dic3—42no—
702Dic3—42no—
703Dic3—42no—
704Dic3—81no—
705Dic3—81no—
706C23C22×Dic611yescharacteristic
707C23C2×#23511yescharacteristic
708C23C2×#23511yescharacteristic
709C23C2×D3×D411yescharacteristic
710C23C2×D3×D411yescharacteristic
711C23C2×D3×D411yescharacteristic
712C23C2×#23711yescharacteristic
713C23C2×D3×Q811yescharacteristic
714C23C2×#23911yescharacteristic
715C23#100911yescharacteristic
716C23#100911yescharacteristic
717C23#101011yescharacteristic
718C23#101011yescharacteristic
719C23#101011yescharacteristic
720C23#101011yescharacteristic
721Q8—1216no—
722Q8—1216no—
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—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—34no—
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—62no—
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—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—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—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4#88514yes—
826C2×C4#88814yes—
827C2×C4#89414yes—
828C2×C3#240511yescharacteristic
829C2×C3#243411yescharacteristic
830C2×C3#243611yescharacteristic
831C2×C3#244611yescharacteristic
832C2×C3#244611yescharacteristic
833C2×C3#249211yescharacteristic
834C2×C3#249211yescharacteristic
835C2×C3#255011yescharacteristic
836C2×C3#255011yescharacteristic
837C2×C3#271311yescharacteristic
838C2×C3#271311yescharacteristic
839C2×C3#271611yescharacteristic
840C2×C3#271611yescharacteristic
841C2×C3#272911yescharacteristic
842C2×C3#272911yescharacteristic
843C22#547011yescharacteristic
844C22C2×#88511yescharacteristic
845C22C2×#88811yescharacteristic
846C22C2×#89411yescharacteristic
847C22#551811yescharacteristic
848C22#551911yescharacteristic
849C22#553411yescharacteristic
850C22D4×Dic611yescharacteristic
851C22D4×Dic611yescharacteristic
852C22#554211yescharacteristic
853C22#554311yescharacteristic
854C22#555011yescharacteristic
855C22#555011yescharacteristic
856C22#555211yescharacteristic
857C22#555211yescharacteristic
858C22#556711yescharacteristic
859C22#557011yescharacteristic
860C22#557911yescharacteristic
861C22#558411yescharacteristic
862C22D3×#12011yescharacteristic
863C22#559811yescharacteristic
864C22#559811yescharacteristic
865C22#563011yescharacteristic
866C22#563011yescharacteristic
867C22#563211yescharacteristic
868C22#563211yescharacteristic
869C22#564811yescharacteristic
870C22#564811yescharacteristic
871C22#565311yescharacteristic
872C22#568211yescharacteristic
873C22#568911yescharacteristic
874C22#569811yescharacteristic
875C22#571211yescharacteristic
876C22#571211yescharacteristic
877C22#572811yescharacteristic
878C4—24no—
879C4—24no—
880C4—24no—
881C4—42no—
882C4—42no—
883C4—64no—
884C4—81no—
885C4—81no—
886C4—122no—
887C4—122no—
888C4—122no—
889C4—122no—
890C4—122no—
891C4—241no—
892C4—241no—
893C3#1578311yescharacteristic, complemented, Sylow
894C2#7350811yescharacteristic
895C2#7367211yescharacteristic
896C2#7371311yescharacteristic
897C2#7441211yescharacteristic
898C2#7459911yescharacteristic
899C2#7470111yescharacteristic
900C2#7515811yescharacteristic
901C2#7515911yescharacteristic
902C2#7516411yescharacteristic
903C2#7517711yescharacteristic
904C2#7569511yescharacteristic
905C2#7570611yescharacteristic
906C2#7600511yescharacteristic
907C2#7606111yescharacteristic
908C2#7663311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1436C2
hypercenter#1436D3
hypocenterC3#15783
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
134. C3×#95Q8semidirect
153. C3⋊#95Q8semidirect
404. #95Dic6semidirect
893. C3#15783semidirect

Maximal subgroups

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

subgroupindex
C22×#8692
C2×#49822
C2×#46602
C2×#46462
C3×#14362
#715652
#715362
#694242
#694152
#694122
#694102
#694072
#157833