Finite Group Databasebeta

← #387978

Subgroups — #387978

Order 512.

1454 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic
2C2×#1923C211yesmaximal, characteristic
3#13876C211yesmaximal, characteristic
4#11371C211yesmaximal, characteristic, complemented
5#11357C211yesmaximal, characteristic, complemented
6#11077C211yesmaximal, characteristic, complemented
7#11050C211yesmaximal, characteristic, complemented
8#10970C211yesmaximal, characteristic
9#10970C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic, complemented
11#10926C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10841C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic
15#10730C211yesmaximal, characteristic
16C22×C22⋊Q8C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26#2502—24no—
27#2502C418yescomplemented
28C2×#398—21no—
29C2×#398—21no—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#388—21no—
33C2×#385—21no—
34C2×#385—21no—
35C2×#384C2211yescharacteristic
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42#1923—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1442—21no—
58#1439—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C24×C4—21no—
64C24×C4C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C22⋊Q8—22no—
70C2×C22⋊Q8—41no—
71C2×C22⋊Q8—41no—
72C2×C22⋊Q8—41no—
73C2×C22⋊Q8—41no—
74C2×C22⋊Q8C2×C414yes—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—41no—
85C22×C4⋊C4—41no—
86C22×C4⋊C4—41no—
87C22×C4⋊C4—41no—
88C22×C4⋊C4C2×C414yes—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4D411yescharacteristic
100C22×C22⋊C4D411yescharacteristic
101C22×C42—21no—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—41no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103—41no—
116C2×#103—41no—
117C2×#103—41no—
118C2×#103—41no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—41no—
124C2×C22⋊C8—41no—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—41no—
128#398—28no—
129#398—28no—
130#391—22no—
131#391—22no—
132#391C2×C414yes—
133#391C2×C414yes—
134#388—44no—
135#385—28no—
136#385—28no—
137#384—22no—
138#384—22no—
139#384—22no—
140#384—41no—
141#384C2×C414yes—
142#384C2×C414yes—
143#380—22no—
144#380—22no—
145#380—41no—
146#380—41no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—41no—
149C4×C22⋊C4C2×C414yes—
150C4×C22⋊C4D414yes—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95D411yescharacteristic
163C2×#95D411yescharacteristic
164#340—41no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#336—22no—
177#336—22no—
178C25C2×D411yescharacteristic
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8C22×C412yes—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—24no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—81no—
217C23×C4—81no—
218C23×C4—81no—
219C23×C4—81no—
220C23×C4C22×C412yes—
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D412yes—
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2411yescharacteristic
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8#4112yes—
255C22×C8#4112yes—
256C22⋊Q8—44no—
257C22⋊Q8—44no—
258C22⋊Q8—44no—
259C22⋊Q8—44no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—81no—
316C2×C4⋊C4—81no—
317C2×C4⋊C4—81no—
318C2×C4⋊C4—81no—
319C2×C4⋊C4—81no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4C22×C412yes—
326C2×C4⋊C4C22×C412yes—
327C2×C4⋊C4C22×C412yes—
328C2×C4⋊C4#4112yes—
329C2×C4⋊C4#4112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—81no—
340C2×C22⋊C4—81no—
341C2×C22⋊C4C22⋊C414yes—
342C2×C22⋊C4C22⋊C414yes—
343C2×C22⋊C4SD1614yes—
344C2×C22⋊C4Q1614yes—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—81no—
356C2×C42C22×C412yes—
357C2×C42C22×C412yes—
358C2×C42C2×D412yes—
359C2×C42C2×D412yes—
360C4⋊C8—44no—
361#103—44no—
362#103—44no—
363#103—44no—
364#103—44no—
365C22⋊C8—44no—
366C22⋊C8—44no—
367C4×C8—44no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—81no—
379#95C22⋊C414yes—
380#95C22⋊C414yes—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24C2×C22⋊C412yes—
394C24C2×SD1612yes—
395C24C2×Q1612yes—
396C24C22×D411yescharacteristic
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—48no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4C2×C22⋊C412yes—
541C22×C4C2×C22⋊C412yes—
542C22×C4C2×C22⋊C412yes—
543C22×C4C2×C22⋊C412yes—
544C22×C4C2×C22⋊C412yes—
545C22×C4C2×SD1612yes—
546C22×C4C2×SD1612yes—
547C22×C4C2×Q1612yes—
548C22×C4C2×Q1612yes—
549C22×C4#13712yes—
550C22×C4#13712yes—
551C22×C4C23×C411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4H(5,𝔽2)11yescharacteristic
558C22×C4H(5,𝔽2)11yescharacteristic
559C22×C4H(5,𝔽2)11yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C4H(5,𝔽2)11yescharacteristic
562C22×C4H(5,𝔽2)11yescharacteristic
563C22×C42−1+411yescharacteristic
564C22×C42−1+411yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C22⋊C4—28no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4#103116yescomplemented
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—84no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C2×#10314yes—
678C23C22×C22⋊C411yescharacteristic
679C23#53511yescharacteristic
680C23#53511yescharacteristic
681C23#54611yescharacteristic
682C23#54611yescharacteristic
683C23#54711yescharacteristic
684C23#54711yescharacteristic
685C23C22×SD1611yescharacteristic
686C23C22×Q1611yescharacteristic
687C23C2×#13711yescharacteristic
688C23C2×#13711yescharacteristic
689C23#57611yescharacteristic
690C23#57611yescharacteristic
691C23#57711yescharacteristic
692C23#57711yescharacteristic
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—81no—
698Q8—81no—
699Q8—81no—
700Q8—81no—
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—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
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—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—816no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4C2×#10314yes—
799C2×C4C2×#10314yes—
800C2×C4#41914yes—
801C2×C4C4×#4111yescharacteristic
802C2×C4C4×#4111yescharacteristic
803C2×C4#51811yescharacteristic
804C2×C4#51811yescharacteristic
805C2×C4#52011yescharacteristic
806C2×C4#52011yescharacteristic
807C2×C4#53511yescharacteristic
808C2×C4#53511yescharacteristic
809C2×C4#53811yescharacteristic
810C2×C4#53811yescharacteristic
811C2×C4#53911yescharacteristic
812C2×C4#53911yescharacteristic
813C2×C4#54011yescharacteristic
814C2×C4#54011yescharacteristic
815C2×C4#54211yescharacteristic
816C2×C4#54211yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54611yescharacteristic
819C2×C4#54711yescharacteristic
820C2×C4#54711yescharacteristic
821C2×C4#55111yescharacteristic
822C2×C4#55311yescharacteristic
823C2×C4#55311yescharacteristic
824C2×C4#55911yescharacteristic
825C2×C4#56011yescharacteristic
826C2×C4#56211yescharacteristic
827C2×C4#56211yescharacteristic
828C2×C4#56311yescharacteristic
829C8—42no—
830C8—42no—
831C8—81no—
832C8—81no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22#230911yescharacteristic
849C22#233911yescharacteristic
850C22#233911yescharacteristic
851C22#270311yescharacteristic
852C22#270611yescharacteristic
853C22#271011yescharacteristic
854C22#271811yescharacteristic
855C22C22×#10311yescharacteristic
856C22C2×#41911yescharacteristic
857C22#289711yescharacteristic
858C22#289711yescharacteristic
859C22#320611yescharacteristic
860C22#320611yescharacteristic
861C22#320911yescharacteristic
862C22#320911yescharacteristic
863C22#322011yescharacteristic
864C22#322211yescharacteristic
865C22#322411yescharacteristic
866C22#322411yescharacteristic
867C22#329511yescharacteristic
868C22#329511yescharacteristic
869C22#329911yescharacteristic
870C22#329911yescharacteristic
871C22#331411yescharacteristic
872C22#331611yescharacteristic
873C22#333111yescharacteristic
874C22#333311yescharacteristic
875C22#333511yescharacteristic
876C22#333511yescharacteristic
877C22#333811yescharacteristic
878C22#333811yescharacteristic
879C22#334411yescharacteristic
880C22#334611yescharacteristic
881C22#335611yescharacteristic
882C22#335711yescharacteristic
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—161no—
895C4—161no—
896C4#233511yescharacteristic
897C4#233511yescharacteristic
898C4#237411yescharacteristic
899C4#237611yescharacteristic
900C4#270311yescharacteristic
901C4#270611yescharacteristic
902C4#271011yescharacteristic
903C4#271811yescharacteristic
904C2—44no—
905C2#1450611yescharacteristic
906C2#2180411yescharacteristic
907C2#2181311yescharacteristic
908C2#2248711yescharacteristic
909C2#2248711yescharacteristic
910C2#2249711yescharacteristic
911C2#2250211yescharacteristic
912C2#3183811yescharacteristic
913C2#3184011yescharacteristic
914C2#3193411yescharacteristic
915C2#3193611yescharacteristic
916C2#3204811yescharacteristic
917C2#3205211yescharacteristic
918C2#3228011yescharacteristic
919C2#3228411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11371C2semidirect
5. #11357C2semidirect
6. #11077C2semidirect
7. #11050C2semidirect
10. #10932C2semidirect
11. #10926C2semidirect
12. #10849C2semidirect
13. #10841C2semidirect
27. #2502C4semidirect
633. C22⋊C4#103semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#19232
#138762
#113712
#113572
#110772
#110502
#109702
#109322
#109262
#108492
#108412
#107302