Finite Group Databasebeta

← #364780

Subgroups — #364780

Order 512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#479C211yesmaximal, characteristic
2C2×#2370C211yesmaximal, characteristic
3C2×#1992C211yesmaximal, characteristic
4C2×#1763C211yesmaximal, characteristic
5#13926C211yesmaximal, characteristic
6#11220C211yesmaximal, characteristic
7#11219C211yesmaximal, characteristic
8#11067C211yesmaximal, characteristic
9#11067C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic
11#10932C211yesmaximal, characteristic
12#10908C211yesmaximal, characteristic
13#10907C211yesmaximal, characteristic
14#10849C211yesmaximal, characteristic
15#10835C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#479—24no—
19C2×#479—24no—
20C2×#479C418yescomplemented
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#97C2211yescharacteristic
29#2370—24no—
30#2370—24no—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#389—21no—
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#387—21no—
37C2×#387—21no—
38C2×#384C2211yescharacteristic
39C2×C4×C4⋊C4—21no—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44#1992—24no—
45#1763—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1441—21no—
61#1441—21no—
62C4⋊#95—21no—
63C4⋊#95—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125C2×C414yes—
75C2×#125D414yes—
76C2×#125D414yes—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8C2×C414yes—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4D411yescharacteristic
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C42—21no—
100C22×C42—21no—
101C22×C42—21no—
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106#479—232no—
107C2×#107—22no—
108C2×#107—22no—
109C2×#107C2×C414yes—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106C2×C414yes—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8C2×C414yes—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103C2×C414yes—
126C2×#103C2×C414yes—
127C2×#103Q814yes—
128C2×#97—22no—
129C2×#97—22no—
130C2×#97—22no—
131#391—22no—
132#391—22no—
133#391—41no—
134#391—41no—
135#389—28no—
136#389—22no—
137#389—22no—
138#389—22no—
139#389—22no—
140#387—28no—
141#387—28no—
142#384—22no—
143#384—22no—
144C4×C4⋊C4—28no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—22no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C4⋊C4D414yes—
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×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95D411yescharacteristic
167C2×#95D411yescharacteristic
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—41no—
177#340—41no—
178#336—22no—
179#336—22no—
180#336—41no—
181#336—41no—
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×Q8—21no—
193C22×Q8C22×C412yes—
194C22×Q8C2×Q812yes—
195C22×Q8#4112yes—
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×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2411yescharacteristic
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8C22×C412yes—
236C22×C8C22×C412yes—
237C22×C8C2×Q812yes—
238C22×C8#4112yes—
239#125—28no—
240#125—28no—
241#125—28no—
242#125C22⋊C4116yes—
243C4×Q8—28no—
244C4×Q8—28no—
245C4×Q8—44no—
246C4×Q8—44no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
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—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
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—24no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C4⋊C4C2×D412yes—
314C2×C4⋊C4C2×Q812yes—
315C2×C4⋊C4#4112yes—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—81no—
337C2×C42—81no—
338C2×C42—81no—
339C2×C42—81no—
340C2×C42C22×C412yes—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C2×C42C2×D412yes—
344C2×C42#4112yes—
345C2×C42#4112yes—
346#107—28no—
347#106—28no—
348C4⋊C8—28no—
349#103—28no—
350#103—28no—
351#103—28no—
352#103—28no—
353#97—44no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—22no—
360#95—22no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—81no—
366#95—81no—
367#95—81no—
368#95—81no—
369C24C22×D411yescharacteristic
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8C4×Q814yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
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—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
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—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4C4×D412yes—
489C22×C4C4×D412yes—
490C22×C4#12012yes—
491C22×C4#12012yes—
492C22×C4#12112yes—
493C22×C4#12112yes—
494C22×C4#13712yes—
495C22×C4#13712yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C22×Q811yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C42−1+411yescharacteristic
508C22×C42−1+411yescharacteristic
509C22×C42−1+411yescharacteristic
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—216no—
548C4⋊C4—216no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—48no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—84no—
572C4⋊C4C2×C22⋊C414yes—
573C4⋊C4C2×C22⋊C414yes—
574C4⋊C4C22⋊Q814yes—
575C42—48no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—48no—
585C42—84no—
586C42—84no—
587C42C2×C22⋊C414yes—
588C42C4×D414yes—
589C42#12114yes—
590C42#12314yes—
591C23C2×C4×D411yescharacteristic
592C23C2×#12011yescharacteristic
593C23C2×#12111yescharacteristic
594C23#54611yescharacteristic
595C23#54711yescharacteristic
596C23#54811yescharacteristic
597C23D4×Q811yescharacteristic
598C23C2×#13711yescharacteristic
599C23C2×#13711yescharacteristic
600C23#57511yescharacteristic
601C23#57511yescharacteristic
602C23#57611yescharacteristic
603C23#57711yescharacteristic
604C23#57711yescharacteristic
605C23#57811yescharacteristic
606Q8—24no—
607Q8—24no—
608Q8—42no—
609Q8—42no—
610Q8—42no—
611Q8—42no—
612Q8—42no—
613Q8—42no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4#38614yes—
711C2×C4#38614yes—
712C2×C4C22×C22⋊C411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×Q811yescharacteristic
715C2×C4C4×#4111yescharacteristic
716C2×C4#51911yescharacteristic
717C2×C4#52011yescharacteristic
718C2×C4C2×#12111yescharacteristic
719C2×C4C2×C22⋊Q811yescharacteristic
720C2×C4C2×#12311yescharacteristic
721C2×C4#52511yescharacteristic
722C2×C4#52911yescharacteristic
723C2×C4#53311yescharacteristic
724C2×C4#53611yescharacteristic
725C2×C4#53711yescharacteristic
726C2×C4#54111yescharacteristic
727C2×C4#54211yescharacteristic
728C2×C4#54811yescharacteristic
729C2×C4#54811yescharacteristic
730C2×C4#54811yescharacteristic
731C2×C4#54811yescharacteristic
732C2×C4D4×Q811yescharacteristic
733C2×C4D4×Q811yescharacteristic
734C2×C4#55011yescharacteristic
735C2×C4#55011yescharacteristic
736C2×C4#55211yescharacteristic
737C2×C4#55211yescharacteristic
738C2×C4#55411yescharacteristic
739C2×C4#55611yescharacteristic
740C8—42no—
741C8—42no—
742C8—42no—
743C8—42no—
744C22C2×#38611yescharacteristic
745C22#236011yescharacteristic
746C22#236211yescharacteristic
747C22#240711yescharacteristic
748C22#240911yescharacteristic
749C22#242611yescharacteristic
750C22#242911yescharacteristic
751C22C4×#13711yescharacteristic
752C22C4×#13711yescharacteristic
753C22#295111yescharacteristic
754C22#295211yescharacteristic
755C22#300711yescharacteristic
756C22#300711yescharacteristic
757C22#301211yescharacteristic
758C22#301311yescharacteristic
759C22#303911yescharacteristic
760C22#304011yescharacteristic
761C22#304511yescharacteristic
762C22#304611yescharacteristic
763C22#330911yescharacteristic
764C22#331211yescharacteristic
765C22#331711yescharacteristic
766C22#332011yescharacteristic
767C22#334411yescharacteristic
768C22#334611yescharacteristic
769C22#334911yescharacteristic
770C22#335011yescharacteristic
771C22#337011yescharacteristic
772C22#337111yescharacteristic
773C22#337211yescharacteristic
774C22#337411yescharacteristic
775C22#338511yescharacteristic
776C22#338711yescharacteristic
777C22#338811yescharacteristic
778C22#339011yescharacteristic
779C4—24no—
780C4—24no—
781C4—44no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—81no—
788C4—82no—
789C4—81no—
790C4—82no—
791C4—161no—
792C4—161no—
793C4C4×C22⋊Q811yescharacteristic
794C4#232311yescharacteristic
795C4Q8×C22⋊C411yescharacteristic
796C4#234111yescharacteristic
797C4#242111yescharacteristic
798C4#242311yescharacteristic
799C4#253611yescharacteristic
800C4#253811yescharacteristic
801C2#1396911yescharacteristic
802C2#2092711yescharacteristic
803C2#2093711yescharacteristic
804C2#2297611yescharacteristic
805C2#2298011yescharacteristic
806C2#2307411yescharacteristic
807C2#2307811yescharacteristic
808C2#2413811yescharacteristic
809C2#2413911yescharacteristic
810C2#2434811yescharacteristic
811C2#2434911yescharacteristic
812C2#2529011yescharacteristic
813C2#2529111yescharacteristic
814C2#2546711yescharacteristic
815C2#2546811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#479C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4792
C2×#23702
C2×#19922
C2×#17632
#139262
#112202
#112192
#110672
#109322
#109082
#109072
#108492
#108352