Finite Group Databasebeta

← #364148

Subgroups — #364148

Order 512.

1842 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×#1871C212yesmaximal
3C2×#1728C211yesmaximal, characteristic, complemented
4C4×#380C211yesmaximal, characteristic, complemented
5#11226C212yesmaximal, complemented
6#11075C212yesmaximal, complemented
7#10808C212yesmaximal, complemented
8#10790C212yesmaximal, complemented
9#10732C212yesmaximal, complemented
10C23×M16C2212yes—
11C2×#525C2211yescharacteristic
12C2×C4×#41C2211yescharacteristic
13C23×C42C2211yescharacteristic
14C22×#104C2214yes—
15C4×C22⋊Q8C411yescharacteristic, complemented
16C4×C22⋊Q8C411yescharacteristic, complemented
17C4×C22⋊Q8C411yescharacteristic, complemented
18C4×C22⋊Q8C411yescharacteristic, complemented
19C4×#123—21no—
20C4×#123—21no—
21C4×#121C411yescharacteristic, complemented
22C4×#121C411yescharacteristic, complemented
23C4×#121C411yescharacteristic, complemented
24C4×#121C411yescharacteristic, complemented
25C4×#120—21no—
26C4×#120—21no—
27#2297C2211yescharacteristic
28#2296C2211yescharacteristic
29#2290—21no—
30#2290—21no—
31#2280C2211yescharacteristic
32C2×#380—21no—
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C2211yescharacteristic
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C22⋊C4C2212yes—
38#1871—28no—
39C2×#339C2214yes—
40C2×#339C2214yes—
41C2×#339C2214yes—
42#1728—21no—
43#1728—21no—
44#1728C2212yes—
45#1728C2212yes—
46C2×#336—21no—
47C2×#336—21no—
48C4⋊#95—21no—
49#1434—21no—
50C22⋊#95—21no—
51C4×#95C2212yes—
52C22×#41C2311yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4D411yescharacteristic
55C24×C4C2311yescharacteristic
56C22×M16—22no—
57C22×M16—28no—
58C22×M16—24no—
59C22×M16—24no—
60C22×M16—44no—
61C22×M16C2314yes—
62C23×C8—22no—
63#525—22no—
64#525—22no—
65#525D414yes—
66#525Q814yes—
67C2×#123—21no—
68C2×C22⋊Q8C2×C411yescharacteristic
69C2×C22⋊Q8C2×C411yescharacteristic
70C2×#121C2×C411yescharacteristic
71C2×#121C2×C411yescharacteristic
72C2×#120—21no—
73C4×#41—44no—
74C2×C4×Q8C2×C411yescharacteristic
75C2×C4×Q8C2×C411yescharacteristic
76C2×C4×D4—21no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4—21no—
80C2×C4×D4—21no—
81C2×C4×D4—21no—
82C2×C4×D4—21no—
83C2×C4×D4—21no—
84C2×C4×D4C2×C411yescharacteristic
85C2×C4×D4C2×C411yescharacteristic
86C2×#117—21no—
87C2×#117C2311yescharacteristic
88C2×#117C2311yescharacteristic
89C2×#117C2311yescharacteristic
90C22×C4⋊C4—22no—
91C22×C22⋊C4—22no—
92C22×C42—21no—
93C22×C42—44no—
94C22×C42C2×C411yescharacteristic
95C22×C42C2×C411yescharacteristic
96C22×C42C2×C411yescharacteristic
97C22×C42C2×C411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42D411yescharacteristic
100C22×C42D411yescharacteristic
101C22×C42D411yescharacteristic
102C22×C42D411yescharacteristic
103C22×C42D411yescharacteristic
104C22×C42C2314yes—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C2×#104—28no—
108C2×#104—28no—
109C2×#104—44no—
110#391C2×C411yescharacteristic
111#391C2×C411yescharacteristic
112#390C2×C411yescharacteristic
113#390C2×C411yescharacteristic
114#389C2×C411yescharacteristic
115#389C2×C411yescharacteristic
116#389C2×C411yescharacteristic
117#389C2×C411yescharacteristic
118#388—21no—
119#388—21no—
120#388—21no—
121#388—21no—
122#387—21no—
123#387—21no—
124#387—21no—
125#387—21no—
126#386—21no—
127#386—21no—
128#386—21no—
129#386—21no—
130#386—21no—
131#386—21no—
132#385—21no—
133#385—21no—
134#385—21no—
135#385—21no—
136#385—21no—
137#385—21no—
138#381—21no—
139#380—28no—
140#380C2×C411yescharacteristic
141#380C2×C411yescharacteristic
142#380C2×C411yescharacteristic
143#380C2×C411yescharacteristic
144#379—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150C4×C4⋊C4—21no—
151C4×C4⋊C4—44no—
152C4×C4⋊C4C2×C411yescharacteristic
153C4×C4⋊C4C2×C411yescharacteristic
154C4×C4⋊C4C2×C411yescharacteristic
155C4×C4⋊C4C2×C411yescharacteristic
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—21no—
168C4×C22⋊C4—21no—
169C4×C22⋊C4—21no—
170C4×C22⋊C4—24no—
171C4×C22⋊C4—24no—
172#376—21no—
173C2×#95—22no—
174C2×#95—22no—
175C2×#95—22no—
176C2×#95—22no—
177C43—21no—
178#339—28no—
179#339—28no—
180#339—44no—
181#336—22no—
182#336—22no—
183#336—22no—
184#336—22no—
185C25C2×D411yescharacteristic
186C2×#41—21no—
187C2×#41—21no—
188C2×#41—24no—
189C2×#41—24no—
190C2×#41C2×D412yes—
191C2×#41C2×Q812yes—
192C22×Q8C22×C411yescharacteristic
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4C22×C411yescharacteristic
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—21no—
201C23×C4—24no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22⋊C411yescharacteristic
211C23×C4C22⋊C411yescharacteristic
212C23×C4C22⋊C411yescharacteristic
213C23×C4C22⋊C411yescharacteristic
214C23×C4C22⋊C411yescharacteristic
215C23×C4C22⋊C411yescharacteristic
216C23×C4C22⋊C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D412yes—
226C23×C4C2×D411yescharacteristic
227C23×C4C2×Q812yes—
228C23×C4#4112yes—
229C23×C4#4112yes—
230C23×C4C2411yescharacteristic
231C2×M16—28no—
232C2×M16—24no—
233C2×M16—24no—
234C2×M16—24no—
235C2×M16—24no—
236C2×M16—24no—
237C2×M16—416no—
238C2×M16—416no—
239C2×M16—44no—
240C2×M16—44no—
241C2×M16#4118yes—
242C22×C8—28no—
243C22×C8—24no—
244C22×C8—44no—
245C22×C8—44no—
246#123—24no—
247#123—24no—
248C22⋊Q8—22no—
249C22⋊Q8—22no—
250C22⋊Q8C4⋊C414yescomplemented
251C22⋊Q8C4⋊C414yescomplemented
252#121—22no—
253#121—22no—
254#121C4⋊C414yescomplemented
255#121C4⋊C414yescomplemented
256#120—24no—
257#120—24no—
258C4×Q8—42no—
259C4×Q8—42no—
260C4×D4—24no—
261C4×D4—24no—
262C4×D4—24no—
263C4×D4—24no—
264C4×D4—42no—
265C4×D4—42no—
266C4×D4—44no—
267C4×D4—44no—
268C4×D4—44no—
269C4×D4—44no—
270C4×D4—44no—
271C4×D4—44no—
272#117—21no—
273#117—21no—
274#117—24no—
275#117—24no—
276#117—44no—
277#117C2×D412yes—
278#117C2×Q812yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—28no—
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—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
294C2×C4⋊C4C22×C411yescharacteristic
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C42—21no—
317C2×C42—24no—
318C2×C42—24no—
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—24no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—44no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42C22⋊C411yescharacteristic
345C2×C42C22⋊C411yescharacteristic
346C2×C42C22⋊C411yescharacteristic
347C2×C42C22⋊C411yescharacteristic
348C2×C42C22⋊C411yescharacteristic
349C2×C42C22⋊C411yescharacteristic
350C2×C42C22⋊C411yescharacteristic
351C2×C42C22⋊C411yescharacteristic
352C2×C42C22×C411yescharacteristic
353C2×C42C22×C411yescharacteristic
354C2×C42C22×C411yescharacteristic
355C2×C42C22×C411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360#104—416no—
361#95—28no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—44no—
379#95—44no—
380#95—44no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—41no—
387C24—41no—
388C24C2×C22⋊C411yescharacteristic
389C24C2×C22⋊C411yescharacteristic
390C24#12112yes—
391C24C22⋊Q812yes—
392C24C22×D411yescharacteristic
393#41—28no—
394#41—28no—
395#41—44no—
396#41—44no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8C2×C4⋊C412yes—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4C2×C4⋊C412yes—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
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—416no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—416no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4#10414yescomplemented
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C2×C22⋊C411yescharacteristic
501C22×C4C2×C4⋊C412yes—
502C22×C4C2×C4⋊C412yes—
503C22×C4#11712yes—
504C22×C4#11712yes—
505C22×C4#12112yes—
506C22×C4#12112yes—
507C22×C4#12112yes—
508C22×C4C22⋊Q812yes—
509C22×C4C22⋊Q812yes—
510C22×C4C22⋊Q812yes—
511C22×C4C23×C411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×Q811yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4114yes—
518C22×C4H(5,𝔽2)14yes—
519M16—28no—
520M16—28no—
521M16—416no—
522M16—44no—
523M16—44no—
524C2×C8—28no—
525C2×C8—416no—
526C2×C8—44no—
527C2×C8—44no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—416no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4C2×C4⋊C412yes—
544C4⋊C4C2×C4⋊C412yes—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—416no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42—42no—
586C42—42no—
587C42—42no—
588C42—42no—
589C42—42no—
590C42—44no—
591C42—44no—
592C42—44no—
593C42—44no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—24no—
611C23—21no—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23#38012yes—
626C23#38012yes—
627C23C2×#10412yes—
628C23#42112yes—
629C23C22×C22⋊C411yescharacteristic
630C23C2×#12111yescharacteristic
631C23C2×C22⋊Q811yescharacteristic
632C23#53212yes—
633C23#53412yes—
634Q8—24no—
635Q8—42no—
636D4—24no—
637D4—48no—
638D4—44no—
639D4—48no—
640D4—44no—
641D4—42no—
642C2×C4—28no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—24no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4#38012yes—
721C2×C4#38012yes—
722C2×C4C2×#10412yes—
723C2×C4C2×#10412yes—
724C2×C4#42112yes—
725C2×C4#42112yes—
726C2×C4C22×C4⋊C411yescharacteristic
727C2×C4C2×#11711yescharacteristic
728C2×C4C4×#4112yes—
729C2×C4#51812yes—
730C2×C4C2×#12111yescharacteristic
731C2×C4C2×C22⋊Q811yescharacteristic
732C2×C4#52512yes—
733C2×C4#53412yes—
734C2×C4#54614yes—
735C2×C4#55114yes—
736C2×C4#55314yes—
737C2×C4#55414yes—
738C8—48no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—48no—
757C22—48no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22#180614yes—
770C22C2×#38011yescharacteristic
771C22#229711yescharacteristic
772C22#230811yescharacteristic
773C22#254312yes—
774C22#256412yes—
775C22C22×#10411yescharacteristic
776C22C2×#42111yescharacteristic
777C22C2×#42111yescharacteristic
778C22C2×#42111yescharacteristic
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—88no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4#234912yes—
798C4#235312yes—
799C4#253412yes—
800C4#257912yes—
801C2—22no—
802C2—22no—
803C2—24no—
804C2—42no—
805C2—82no—
806C2#1396011yescharacteristic
807C2C2×#180611yescharacteristic
808C2#2065411yescharacteristic
809C2#2138211yescharacteristic
810C2#2138311yescharacteristic
811C2#2177311yescharacteristic
812C2#2177411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1728C2semidirect
4. C4×#380C2semidirect
5. #11226C2semidirect
6. #11075C2semidirect
7. #10808C2semidirect
8. #10790C2semidirect
9. #10732C2semidirect
15. C4×C22⋊Q8C4semidirect
16. C4×C22⋊Q8C4semidirect
17. C4×C22⋊Q8C4semidirect
18. C4×C22⋊Q8C4semidirect
21. C4×#121C4semidirect
22. C4×#121C4semidirect
23. C4×#121C4semidirect
24. C4×#121C4semidirect
250. C22⋊Q8C4⋊C4semidirect
251. C22⋊Q8C4⋊C4semidirect
254. #121C4⋊C4semidirect
255. #121C4⋊C4semidirect
490. C22×C4#104semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
C2×#18712
C2×#17282
C4×#3802
#112262
#110752
#108082
#107902
#107322