Finite Group Databasebeta

← #10719082

Subgroups — #10719082

Order 768.

1434 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#391C211yesmaximal, characteristic
2C2×#5229C211yesmaximal, characteristic
3C2×#4649C211yesmaximal, characteristic
4#72134C211yesmaximal, characteristic
5#71568C211yesmaximal, characteristic
6#71564C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8C4×C3⋊#95C211yesmaximal, characteristic
9#69414C211yesmaximal, characteristic
10#69411C211yesmaximal, characteristic
11#69407C211yesmaximal, characteristic
12#69406C211yesmaximal, characteristic
13#69405C211yesmaximal, characteristic
14#69402C211yesmaximal, characteristic
15#69402C211yesmaximal, characteristic
16#14059—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×Dic3⋊C4C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C3×#391—24no—
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33#5229C418yescomplemented
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
54#4649—24no—
55C2×#391—31no—
56C2×#391D311yescharacteristic
57C2×C4×C4⋊C4—31no—
58#1446—31no—
59#1444—31no—
60#1442—31no—
61#1441—31no—
62#1436—31no—
63#1436—31no—
64#1436—31no—
65#1436—31no—
66#1436—31no—
67#1434—31no—
68#1434—31no—
69C4×#95—31no—
70C22×C3×Q8—22no—
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—22no—
74C22×C3×Q8—41no—
75C22×C3×Q8—41no—
76C22×C3×Q8C2×C414yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C42—22no—
96C2×C3×C42—22no—
97C2×C3×C42—41no—
98C2×C4⋊Dic3—41no—
99C2×C4⋊Dic3—41no—
100C2×C4⋊Dic3C2×C414yes—
101C2×Dic3⋊C4—22no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—41no—
108C2×Dic3⋊C4—41no—
109C2×Dic3⋊C4Q814yescomplemented
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—41no—
118C2×C4×Dic3—41no—
119C2×C4×Dic3—41no—
120C2×C4×Dic3—41no—
121C2×C4×Dic3C2×C414yes—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95D414yes—
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—41no—
136C3⋊#95—41no—
137C3⋊#95—41no—
138C3⋊#95—41no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95C2×C414yes—
142C3⋊#95C2×C414yes—
143C3⋊#95C2×C414yes—
144C3⋊#95C2×C414yes—
145C3⋊#95Q814yescomplemented
146C23×Q8C2×D311yescharacteristic
147C22×C4⋊C4—31no—
148C22×C4⋊C4—31no—
149C22×C4⋊C4—31no—
150C22×C4⋊C4—31no—
151C22×C4⋊C4C2×D311yescharacteristic
152C22×C42—31no—
153C22×C42—31no—
154C22×C42—31no—
155C22×C42—31no—
156C22×C42C2×D311yescharacteristic
157#391—24no—
158#391—38no—
159C4×C4⋊C4—64no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
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×#95C2×D311yescharacteristic
181C2×#95C2×D311yescharacteristic
182C2×#95C2×D311yescharacteristic
183C2×#95C2×D311yescharacteristic
184C24×C3C2411yescharacteristic
185C2×C3×Q8—28no—
186C2×C3×Q8—28no—
187C2×C3×Q8—44no—
188C2×C3×Q8—44no—
189C2×C3×Q8—44no—
190C2×C3×Q8—44no—
191C2×C3×Q8—44no—
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×C4C22×C412yes—
230C22×C3×C4C22×C412yes—
231C22×C3×C4C22×C412yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×Q812yes—
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×Dic3C22×C412yes—
287C22×Dic3C22×C412yes—
288C22×Dic3C22×C412yes—
289C22×Dic3C22×C412yes—
290C22×Dic3C2×Q812yes—
291C22×Dic3C2×Q812yes—
292C22×Dic3C2×Q812yes—
293C22×Dic3C2×Q812yes—
294C22×Dic3#4112yes—
295C22×Dic3#4112yes—
296C22×Dic3#4112yes—
297C3×C4⋊C4—44no—
298C3×C42—44no—
299C4⋊Dic3—44no—
300Dic3⋊C4—28no—
301Dic3⋊C4—28no—
302Dic3⋊C4—44no—
303C4×Dic3—28no—
304C4×Dic3—44no—
305C4×Dic3—44no—
306C4×Dic3—44no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—41no—
312C22×Q8—41no—
313C22×Q8C4×D314yes—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—62no—
335C2×C4⋊C4—62no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—121no—
341C2×C4⋊C4—121no—
342C2×C4⋊C4—121no—
343C2×C4⋊C4—121no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—34no—
347C2×C42—41no—
348C2×C42—62no—
349C2×C42—62no—
350C2×C42—62no—
351C2×C42—62no—
352C2×C42—62no—
353C2×C42—62no—
354C2×C42—62no—
355C2×C42—121no—
356C2×C42—121no—
357C2×C42—121no—
358C2×C42—121no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—34no—
363#95—34no—
364#95—34no—
365#95—34no—
366#95—34no—
367#95—62no—
368#95—62no—
369#95—62no—
370#95—62no—
371#95—62no—
372#95—62no—
373#95—62no—
374#95—62no—
375#95—62no—
376#95—121no—
377#95—121no—
378#95—121no—
379#95—121no—
380#95—121no—
381#95—121no—
382#95#6714yes—
383C23×C3C23×C411yescharacteristic
384C23×C3C22×D411yescharacteristic
385C23×C3C22×Q811yescharacteristic
386C23×C3C22×Q811yescharacteristic
387C23×C3C2×#4111yescharacteristic
388C23×C3C2×#4111yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4111yescharacteristic
394C23×C3H(5,𝔽2)11yescharacteristic
395C23×C3H(5,𝔽2)11yescharacteristic
396C23×C3H(5,𝔽2)11yescharacteristic
397C23×C32−1+411yescharacteristic
398C3×Q8—416no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
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—22no—
425C2×C3×C4—22no—
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#11714yes—
446C2×C3×C4C4×D414yes—
447C2×C3×C4C22⋊Q814yes—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
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—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
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×Dic3C4×Q814yes—
503C2×Dic3C4×Q814yes—
504C24C23×D311yescharacteristic
505C2×Q8—28no—
506C2×Q8—28no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
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—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
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×C4C2×C4×D312yes—
606C22×C4C2×C4×D312yes—
607C22×C4C2×C4×D312yes—
608C22×C4#23512yes—
609C22×C4#23712yes—
610C22×C4#23712yes—
611C22×C4D3×Q812yes—
612C22×C4D3×Q812yes—
613C22×C4#23912yes—
614C22×C4C2×#6712yes—
615C22×C4C2×#6712yes—
616C22×C4C2×#6712yes—
617C4⋊C4—44no—
618C4⋊C4—68no—
619C4⋊C4—68no—
620C4⋊C4—124no—
621C4⋊C4—124no—
622C42—44no—
623C42—68no—
624C42—124no—
625C42—124no—
626C42—124no—
627C22×C3C2×#11711yescharacteristic
628C22×C3C2×C4×D411yescharacteristic
629C22×C3C2×C4×Q811yescharacteristic
630C22×C3C2×C4×Q811yescharacteristic
631C22×C3C4×#4111yescharacteristic
632C22×C3#51811yescharacteristic
633C22×C3#52011yescharacteristic
634C22×C3C2×C22⋊Q811yescharacteristic
635C22×C3#52511yescharacteristic
636C22×C3#52911yescharacteristic
637C22×C3#52911yescharacteristic
638C22×C3#52911yescharacteristic
639C22×C3#53311yescharacteristic
640C22×C3#53311yescharacteristic
641C22×C3#53311yescharacteristic
642C22×C3#53811yescharacteristic
643C22×C3#53811yescharacteristic
644C22×C3#54211yescharacteristic
645C22×C3#54211yescharacteristic
646C22×C3#54611yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3D4×Q811yescharacteristic
650C22×C3#55111yescharacteristic
651C22×C3#55111yescharacteristic
652C22×C3#55211yescharacteristic
653C22×C3#55411yescharacteristic
654C22×C3#55411yescharacteristic
655C22×C3#55411yescharacteristic
656C22×C3#55411yescharacteristic
657C22×C3#55511yescharacteristic
658C22×C3#55611yescharacteristic
659C22×C3#55711yescharacteristic
660C22×C3Q8211yescharacteristic
661C22×C3#55911yescharacteristic
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—24no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—81no—
669Dic3—24no—
670Dic3—24no—
671Dic3—42no—
672Dic3—42no—
673Dic3—42no—
674Dic3—42no—
675Dic3—42no—
676Dic3—81no—
677C23C22×C4×D311yescharacteristic
678C23C2×#23511yescharacteristic
679C23C2×#23711yescharacteristic
680C23C2×#23711yescharacteristic
681C23#100411yescharacteristic
682C23#100411yescharacteristic
683C23C2×D3×Q811yescharacteristic
684C23C2×D3×Q811yescharacteristic
685C23C2×#23911yescharacteristic
686C23#100711yescharacteristic
687C23D3×#4111yescharacteristic
688C23D3×#4111yescharacteristic
689C23D3×#4111yescharacteristic
690C23#100911yescharacteristic
691C23C22×#6711yescharacteristic
692Q8—416no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
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—22no—
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—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
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—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—121no—
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#87714yes—
796C2×C4C4×#6714yes—
797C2×C4#94614yes—
798C2×C3#229511yescharacteristic
799C2×C3C4×C22⋊Q811yescharacteristic
800C2×C3#233711yescharacteristic
801C2×C3#234211yescharacteristic
802C2×C3#235511yescharacteristic
803C2×C3#236011yescharacteristic
804C2×C3#236911yescharacteristic
805C2×C3#245011yescharacteristic
806C2×C3#245111yescharacteristic
807C2×C3#245911yescharacteristic
808C2×C3#246511yescharacteristic
809C2×C3#252011yescharacteristic
810C2×C3#253211yescharacteristic
811C2×C3#258611yescharacteristic
812C2×C3#258911yescharacteristic
813C22C2×#87711yescharacteristic
814C22#548611yescharacteristic
815C22#549511yescharacteristic
816C22#549511yescharacteristic
817C22C4×D3×Q811yescharacteristic
818C22C4×D3×Q811yescharacteristic
819C22C4×#23911yescharacteristic
820C22#557411yescharacteristic
821C22#557811yescharacteristic
822C22#557911yescharacteristic
823C22#558011yescharacteristic
824C22#558111yescharacteristic
825C22#562211yescharacteristic
826C22#562411yescharacteristic
827C22#563511yescharacteristic
828C22#563611yescharacteristic
829C22#563611yescharacteristic
830C22#564011yescharacteristic
831C22#564111yescharacteristic
832C22#564411yescharacteristic
833C22#567011yescharacteristic
834C22#567811yescharacteristic
835C22#568011yescharacteristic
836C22#568111yescharacteristic
837C22#572111yescharacteristic
838C22#572211yescharacteristic
839C22#572811yescharacteristic
840C22#573311yescharacteristic
841C22C2×C4×#6711yescharacteristic
842C22#580611yescharacteristic
843C22#580611yescharacteristic
844C22C2×#94611yescharacteristic
845C22Q8×#6711yescharacteristic
846C22#582811yescharacteristic
847C22#582911yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—64no—
855C4—64no—
856C4—81no—
857C4—122no—
858C4—122no—
859C4—122no—
860C4—122no—
861C4—122no—
862C4—241no—
863C3#1405911yescharacteristic, complemented, Sylow
864C2#7647711yescharacteristic
865C2#7648811yescharacteristic
866C2#7648911yescharacteristic
867C2#7649411yescharacteristic
868C2#7652811yescharacteristic
869C2#7653211yescharacteristic
870C2#7655011yescharacteristic
871C2#7655411yescharacteristic
872C2#8209811yescharacteristic
873C2C4×#94611yescharacteristic
874C2#8249011yescharacteristic
875C2#8276511yescharacteristic
876C2#8276811yescharacteristic
877C2#8299711yescharacteristic
878C2#8323511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#391C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×#391D3
hypocenterC3#14059
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
33. #5229C4semidirect
109. C2×Dic3⋊C4Q8semidirect
145. C3⋊#95Q8semidirect
863. C3#14059semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3912
C2×#52292
C2×#46492
#721342
#715682
#715642
#715362
C4×C3⋊#952
#694142
#694112
#694072
#694062
#694052
#694022
#140593