Finite Group Databasebeta

← #123960

Subgroups — #123960

Order 512.

2430 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#340C212yesmaximal
3C22×#340C212yesmaximal
4C22×#336C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C24×C8C2212yes—
7C23×C4⋊C4—21no—
8C23×C4⋊C4C2211yescharacteristic
9C23×C4⋊C4C2212yes—
10C23×C4⋊C4C2211yescharacteristic
11C23×C42C2211yescharacteristic
12C2×#389—22no—
13C2×#389—24no—
14C2×#389—24no—
15C2×#389C414yescomplemented
16C22×#95—21no—
17C22×#95—21no—
18C22×#95—21no—
19C2×#340—24no—
20C2×#340—24no—
21C2×#340—24no—
22C2×#340—24no—
23C2×#340—24no—
24C2×#340C418yescomplemented
25C2×#336—22no—
26C2×#336—24no—
27C4⋊#95—24no—
28C24×C4—21no—
29C24×C4—21no—
30C24×C4—22no—
31C24×C4D411yescharacteristic
32C24×C4D411yescharacteristic
33C24×C4C2311yescharacteristic
34C23×C8—22no—
35C23×C8—22no—
36C23×C8—22no—
37C23×C8—22no—
38C23×C8—22no—
39C23×C8—22no—
40C23×C8—22no—
41C23×C8—22no—
42C23×C8—22no—
43C23×C8—22no—
44C23×C8—22no—
45C23×C8—22no—
46C23×C8C2×C414yes—
47C23×C8D414yes—
48C23×C8Q814yes—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—28no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—44no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4C2×C412yes—
77C22×C4⋊C4C2×C414yes—
78C22×C4⋊C4C2×C414yes—
79C22×C4⋊C4C2×C412yes—
80C22×C4⋊C4D414yes—
81C22×C4⋊C4D414yes—
82C22×C4⋊C4D412yes—
83C22×C4⋊C4D414yes—
84C22×C4⋊C4Q814yes—
85C22×C4⋊C4Q812yes—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42C2×C412yes—
93C22×C42D412yes—
94#389—216no—
95#389—28no—
96#389—28no—
97C2×#95—28no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—42no—
102C2×#95—42no—
103C2×#95—42no—
104C2×#95—42no—
105#340—216no—
106#340—216no—
107#336—28no—
108C25C2×D411yescharacteristic
109C23×C4—22no—
110C23×C4—24no—
111C23×C4—22no—
112C23×C4—24no—
113C23×C4—22no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—24no—
132C23×C4—24no—
133C23×C4—24no—
134C23×C4—24no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—42no—
138C23×C4—42no—
139C23×C4—41no—
140C23×C4—41no—
141C23×C4—41no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—41no—
147C23×C4—42no—
148C23×C4—41no—
149C23×C4—42no—
150C23×C4—41no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—41no—
157C23×C4—42no—
158C23×C4—42no—
159C23×C4—42no—
160C23×C4—41no—
161C23×C4—42no—
162C23×C4C22⋊C412yes—
163C23×C4C22⋊C412yes—
164C23×C4D812yes—
165C23×C4SD1612yes—
166C23×C4SD1612yes—
167C23×C4Q1612yes—
168C23×C4C22×C411yescharacteristic
169C23×C4C22×C412yes—
170C23×C4C2×D412yes—
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D412yes—
173C23×C4C2×D412yes—
174C23×C4C2×D412yes—
175C23×C4C2×D411yescharacteristic
176C23×C4C2×Q811yescharacteristic
177C23×C4C2×Q812yes—
178C23×C4C2×Q812yes—
179C23×C4#4111yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4112yes—
182C23×C4#4112yes—
183C23×C4#4112yes—
184C23×C4#4112yes—
185C23×C4#4112yes—
186C22×C8—24no—
187C22×C8—24no—
188C22×C8—24no—
189C22×C8—24no—
190C22×C8—24no—
191C22×C8—24no—
192C22×C8—24no—
193C22×C8—24no—
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—24no—
197C22×C8—24no—
198C22×C8—24no—
199C22×C8—24no—
200C22×C8—24no—
201C22×C8—24no—
202C22×C8—24no—
203C22×C8—24no—
204C22×C8—42no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—42no—
208C22×C8—42no—
209C22×C8—42no—
210C22×C8—42no—
211C22×C8—42no—
212C22×C8—42no—
213C22×C8—42no—
214C22×C8—42no—
215C22×C8—42no—
216C22×C8—42no—
217C22×C8—42no—
218C22×C8—42no—
219C22×C8—42no—
220C22×C8C4⋊C418yescomplemented
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—216no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4—416no—
260C2×C4⋊C4—416no—
261C2×C4⋊C4—48no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4C4214yes—
282C2×C4⋊C4C22⋊C414yes—
283C2×C4⋊C4C22⋊C418yes—
284C2×C4⋊C4C22⋊C414yes—
285C2×C4⋊C4C4⋊C414yes—
286C2×C4⋊C4C4⋊C418yes—
287C2×C4⋊C4C4⋊C418yescomplemented
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—24no—
291C2×C42—24no—
292C2×C42—22no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—22no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42—42no—
304#95—216no—
305#95—48no—
306#95—48no—
307C24C2×C22⋊C411yescharacteristic
308C24C4×D412yes—
309C24#12012yes—
310C24#12011yescharacteristic
311C24#12111yescharacteristic
312C24#12112yes—
313C24C22⋊Q811yescharacteristic
314C24C22⋊Q812yes—
315C24#12311yescharacteristic
316C24#12411yescharacteristic
317C24C4⋊Q811yescharacteristic
318C24C2×D811yescharacteristic
319C24C2×SD1611yescharacteristic
320C24C2×SD1611yescharacteristic
321C24C2×Q1611yescharacteristic
322C24#13512yes—
323C24#13512yes—
324C24AGL(1,ℤ/8)11yescharacteristic
325C24AGL(1,ℤ/8)11yescharacteristic
326C24AGL(1,ℤ/8)12yes—
327C24#13711yescharacteristic
328C24#13711yescharacteristic
329C24#13712yes—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—28no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—28no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—28no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4—44no—
376C22×C4—44no—
377C22×C4—44no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—44no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—81no—
430C22×C4—82no—
431C22×C4—81no—
432C22×C4—82no—
433C22×C4—82no—
434C22×C4—82no—
435C22×C4—82no—
436C22×C4—82no—
437C22×C4—82no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—82no—
441C22×C4—82no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4—82no—
445C22×C4—82no—
446C22×C4—82no—
447C22×C4—82no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—82no—
451C22×C4—82no—
452C22×C4—82no—
453C22×C4—82no—
454C22×C4—82no—
455C22×C4#10214yes—
456C22×C4#10314yes—
457C22×C4C2×C4211yescharacteristic
458C22×C4C2×C22⋊C412yes—
459C22×C4C2×C22⋊C411yescharacteristic
460C22×C4C2×C22⋊C411yescharacteristic
461C22×C4C2×C4⋊C411yescharacteristic
462C22×C4C2×C4⋊C412yes—
463C22×C4C2×C4⋊C412yes—
464C22×C4C2×C4⋊C412yes—
465C22×C4#11711yescharacteristic
466C22×C4#11712yes—
467C22×C4#11712yes—
468C22×C4#11711yescharacteristic
469C22×C4C4×D412yes—
470C22×C4C4×D412yes—
471C22×C4C4×D412yes—
472C22×C4C4×D412yes—
473C22×C4C4×D412yes—
474C22×C4C4×D412yes—
475C22×C4C4×D412yes—
476C22×C4C4×Q812yes—
477C22×C4C4×Q812yes—
478C22×C4C4×Q812yes—
479C22×C4C4×Q812yes—
480C22×C4#12012yes—
481C22×C4#12011yescharacteristic
482C22×C4#12012yes—
483C22×C4#12112yes—
484C22×C4#12112yes—
485C22×C4#12112yes—
486C22×C4#12112yes—
487C22×C4#12112yes—
488C22×C4#12111yescharacteristic
489C22×C4#12112yes—
490C22×C4#12112yes—
491C22×C4#12112yes—
492C22×C4C22⋊Q812yes—
493C22×C4C22⋊Q812yes—
494C22×C4C22⋊Q812yes—
495C22×C4C22⋊Q812yes—
496C22×C4C22⋊Q812yes—
497C22×C4C22⋊Q811yescharacteristic
498C22×C4C22⋊Q812yes—
499C22×C4C22⋊Q812yes—
500C22×C4C22⋊Q812yes—
501C22×C4C22⋊Q812yes—
502C22×C4C22⋊Q812yes—
503C22×C4C22⋊Q812yes—
504C22×C4C22⋊Q812yes—
505C22×C4#12312yes—
506C22×C4#12312yes—
507C22×C4#12312yes—
508C22×C4#12312yes—
509C22×C4#12312yes—
510C22×C4#12312yes—
511C22×C4#12311yescharacteristic
512C22×C4#12312yes—
513C22×C4#12412yes—
514C22×C4#12412yes—
515C22×C4#12412yes—
516C22×C4#12411yescharacteristic
517C22×C4#12512yes—
518C22×C4#12512yes—
519C22×C4#12512yes—
520C22×C4#12512yes—
521C22×C4#12512yes—
522C22×C4#12512yes—
523C22×C4#12612yes—
524C22×C4#12612yes—
525C22×C4#12612yes—
526C22×C4#12612yes—
527C22×C4#12712yes—
528C22×C4C4⋊Q812yes—
529C22×C4C4⋊Q812yes—
530C22×C4C4⋊Q812yes—
531C22×C4C4⋊Q812yes—
532C22×C4C4⋊Q811yescharacteristic
533C2×C8—28no—
534C2×C8—28no—
535C2×C8—28no—
536C2×C8—44no—
537C2×C8—44no—
538C2×C8—44no—
539C2×C8—44no—
540C2×C8—44no—
541C2×C8—44no—
542C2×C8—44no—
543C2×C8—44no—
544C2×C8—44no—
545C2×C8—44no—
546C2×C8—44no—
547C2×C8—44no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—432no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4#9518yescomplemented
567C42—44no—
568C42—44no—
569C42—44no—
570C42—44no—
571C23C4×C22⋊C411yescharacteristic
572C23#37911yescharacteristic
573C23#38011yescharacteristic
574C23#38512yes—
575C23#38512yes—
576C23#38611yescharacteristic
577C23#38612yes—
578C23#38611yescharacteristic
579C23#38712yes—
580C23#38812yes—
581C23#38912yes—
582C23#39111yescharacteristic
583C23#39111yescharacteristic
584C23#39212yes—
585C23#39312yes—
586C23#39412yes—
587C23#39411yescharacteristic
588C23#39511yescharacteristic
589C23#39512yes—
590C23#39612yes—
591C23#39811yescharacteristic
592C23#39812yes—
593C23#40011yescharacteristic
594C23C2×#10211yescharacteristic
595C23C2×#10311yescharacteristic
596C23#41611yescharacteristic
597C23#41611yescharacteristic
598C23#41711yescharacteristic
599C23#41711yescharacteristic
600C23#41811yescharacteristic
601C23#41911yescharacteristic
602C23C4×D812yes—
603C23C4×SD1612yes—
604C23C4×SD1612yes—
605C23C4×Q1612yes—
606C23#44012yes—
607C23#44012yes—
608C23#44112yes—
609C23#44212yes—
610C23#44711yescharacteristic
611C23#44712yes—
612C23#44811yescharacteristic
613C23#44812yes—
614C23#44912yes—
615C23#44912yes—
616C23#44912yes—
617C23#45011yescharacteristic
618C23#45012yes—
619C23#45111yescharacteristic
620C23#45112yes—
621C23#45212yes—
622C23#45212yes—
623C23#45212yes—
624C23#45911yescharacteristic
625C23#46011yescharacteristic
626C23#46111yescharacteristic
627C23#46211yescharacteristic
628C23#46312yes—
629C23#46412yes—
630C23#46512yes—
631C23#46512yes—
632C23#46612yes—
633C23#46712yes—
634C23#46812yes—
635C23#46812yes—
636C23#46912yes—
637C23#47012yes—
638C23#47411yescharacteristic
639C23#47412yes—
640C23#47511yescharacteristic
641C23#47512yes—
642C23#47611yescharacteristic
643C23#47612yes—
644C23#47711yescharacteristic
645C23#47712yes—
646C23#47812yes—
647C23#47812yes—
648C23#47812yes—
649C23#47912yes—
650C23#47912yes—
651C23#47912yes—
652C23#48011yescharacteristic
653C23#48111yescharacteristic
654C23#48212yes—
655C23#48311yescharacteristic
656C23#48411yescharacteristic
657C23#48512yes—
658C23#48611yescharacteristic
659C23#48711yescharacteristic
660C23#48812yes—
661C23#48912yes—
662C23#49011yescharacteristic
663C23#49111yescharacteristic
664C23#49811yescharacteristic
665C23#49912yes—
666C23#50011yescharacteristic
667C23#50112yes—
668C23#50111yescharacteristic
669C23#50111yescharacteristic
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—48no—
680C2×C4—48no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4C2×#9511yescharacteristic
730C2×C4C4×C22⋊C411yescharacteristic
731C2×C4C4×C4⋊C412yes—
732C2×C4C4×C4⋊C412yes—
733C2×C4#38012yes—
734C2×C4#38012yes—
735C2×C4#38011yescharacteristic
736C2×C4#38111yescharacteristic
737C2×C4#38212yes—
738C2×C4#38412yes—
739C2×C4#38512yes—
740C2×C4#38512yes—
741C2×C4#38512yes—
742C2×C4#38512yes—
743C2×C4#38612yes—
744C2×C4#38612yes—
745C2×C4#38712yes—
746C2×C4#38712yes—
747C2×C4#38712yes—
748C2×C4#38712yes—
749C2×C4#38712yes—
750C2×C4#38712yes—
751C2×C4#38712yes—
752C2×C4#38812yes—
753C2×C4#38812yes—
754C2×C4#38812yes—
755C2×C4#38912yes—
756C2×C4#38912yes—
757C2×C4#38912yes—
758C2×C4#38912yes—
759C2×C4#38912yes—
760C2×C4#38912yes—
761C2×C4#38912yes—
762C2×C4#39012yes—
763C2×C4#39012yes—
764C2×C4#39112yes—
765C2×C4#39112yes—
766C2×C4#39112yes—
767C2×C4#39212yes—
768C2×C4#39312yes—
769C2×C4#39411yescharacteristic
770C2×C4#39412yes—
771C2×C4#39412yes—
772C2×C4#39512yes—
773C2×C4#39512yes—
774C2×C4#39511yescharacteristic
775C2×C4#39612yes—
776C2×C4#39612yes—
777C2×C4#39612yes—
778C2×C4#39712yes—
779C2×C4#39712yes—
780C2×C4#39812yes—
781C2×C4#39811yescharacteristic
782C2×C4#39812yes—
783C2×C4#39812yes—
784C2×C4#39812yes—
785C2×C4#39812yes—
786C2×C4#39812yes—
787C2×C4#39912yes—
788C2×C4#39912yes—
789C2×C4#40012yes—
790C2×C4#40012yes—
791C2×C4#40011yescharacteristic
792C2×C4#40012yes—
793C8—48no—
794C22C22⋊#9511yescharacteristic
795C22#143611yescharacteristic
796C22#143611yescharacteristic
797C22#143811yescharacteristic
798C22#143912yes—
799C22#144111yescharacteristic
800C22#144112yes—
801C22#144111yescharacteristic
802C22#144212yes—
803C22#144412yes—
804C22#144611yescharacteristic
805C22C4×#10211yescharacteristic
806C22C4×#10311yescharacteristic
807C22#176211yescharacteristic
808C22#176311yescharacteristic
809C22#178611yescharacteristic
810C22#178711yescharacteristic
811C22#178811yescharacteristic
812C22#178811yescharacteristic
813C22#180211yescharacteristic
814C22#180311yescharacteristic
815C22#180411yescharacteristic
816C22#180511yescharacteristic
817C22#186212yes—
818C22#186212yes—
819C22#186312yes—
820C22#186312yes—
821C22#186412yes—
822C22#186412yes—
823C22#186512yes—
824C22#186512yes—
825C22#187211yescharacteristic
826C22#187311yescharacteristic
827C22#187411yescharacteristic
828C22#187511yescharacteristic
829C22#187712yes—
830C22#187812yes—
831C22#187912yes—
832C22#188012yes—
833C22#189211yescharacteristic
834C22#189311yescharacteristic
835C22#189411yescharacteristic
836C22#189511yescharacteristic
837C22#191812yes—
838C22#191912yes—
839C22#192012yes—
840C22#192112yes—
841C22#193312yes—
842C22#193412yes—
843C22#193512yes—
844C22#193612yes—
845C22#194112yes—
846C22#194212yes—
847C22#194312yes—
848C22#194412yes—
849C22#198711yescharacteristic
850C22#198811yescharacteristic
851C22#198911yescharacteristic
852C22#198911yescharacteristic
853C22#199011yescharacteristic
854C22#199111yescharacteristic
855C22#199211yescharacteristic
856C22#199311yescharacteristic
857C22#199912yes—
858C22#200012yes—
859C22#200012yes—
860C22#200112yes—
861C22#202312yes—
862C22#202412yes—
863C22#202512yes—
864C22#202612yes—
865C22#203312yes—
866C22#203412yes—
867C22#203512yes—
868C22#203612yes—
869C22#204111yescharacteristic
870C22#204212yes—
871C22#204311yescharacteristic
872C22#205711yescharacteristic
873C22#205712yes—
874C22#205811yescharacteristic
875C22#205812yes—
876C22#205912yes—
877C22#205912yes—
878C22#205912yes—
879C22#206512yes—
880C22#206612yes—
881C22#206712yes—
882C22#206812yes—
883C22#208311yescharacteristic
884C22#208411yescharacteristic
885C22#208512yes—
886C22#208612yes—
887C22#208712yes—
888C22#208812yes—
889C22#208812yes—
890C22#209911yescharacteristic
891C22#210011yescharacteristic
892C22#210112yes—
893C4—48no—
894C4—44no—
895C4—44no—
896C4—88no—
897C4—84no—
898C4C4⋊#9512yes—
899C4#143612yes—
900C4#143912yes—
901C4#144112yes—
902C4#144112yes—
903C4#144212yes—
904C4#144412yes—
905C4#144512yes—
906C2#755711yescharacteristic
907C2#1078811yescharacteristic
908C2#1078911yescharacteristic
909C2#1088011yescharacteristic
910C2#1088111yescharacteristic
911C2#1088411yescharacteristic
912C2#1088511yescharacteristic
913C2#1096911yescharacteristic
914C2#1097011yescharacteristic
915C2#1106612yes—
916C2#1106712yes—
917C2#1120711yescharacteristic
918C2#1120811yescharacteristic
919C2#1121912yes—
920C2#1122012yes—
921C2#1122711yescharacteristic
922C2#1122811yescharacteristic
923C2#1129212yes—
924C2#1129312yes—
925C2#1132712yes—
926C2#1132812yes—
927C2#1138411yescharacteristic
928C2#1138511yescharacteristic
subgroupG/H
center, socle, prime radicalC25C2×D4
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
15. C2×#389C4semidirect
24. C2×#340C4semidirect
220. C22×C8C4⋊C4semidirect
287. C2×C4⋊C4C4⋊C4semidirect
566. C4⋊C4#95semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3402
C22×#3362
C2×C4⋊#952