Finite Group Databasebeta

← #374224

Subgroups — #374224

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1011 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#433C211yesmaximal, characteristic, complemented
2C2×#2624C211yesmaximal, characteristic
3C2×#1875C211yesmaximal, characteristic
4C2×#1874C211yesmaximal, characteristic
5#13795C211yesmaximal, characteristic, complemented
6#11228C211yesmaximal, characteristic, complemented
7#11227C211yesmaximal, characteristic, complemented
8#11076C211yesmaximal, characteristic, complemented
9#11076C211yesmaximal, characteristic, complemented
10#10927C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10881C211yesmaximal, characteristic, complemented
13#10880C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C2×#433—24no—
21C2×#433—24no—
22C2×#433—24no—
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33#2624—24no—
34#2624C418yescomplemented
35C2×#399—21no—
36C2×#397—21no—
37C2×#394—21no—
38C2×#394—21no—
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#380C2211yescharacteristic
44#1875—24no—
45#1874—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C4⋊#95—21no—
59C4⋊#95—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C22⋊#95—21no—
65C22⋊#95—21no—
66C23×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#121—22no—
75C2×#121—22no—
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121C2×C414yes—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—41no—
89C2×#117—41no—
90C2×#117C2×C414yes—
91C2×#117D414yes—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—41no—
100C22×C4⋊C4—41no—
101C22×C4⋊C4D411yescharacteristic
102C22×C4⋊C4D411yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4D411yescharacteristic
118C22×C22⋊C4D411yescharacteristic
119C22×C42—21no—
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122#433—232no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—22no—
128C2×C4⋊C8—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—41no—
138C2×#102—41no—
139C2×#102—41no—
140C2×#102—41no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8D414yes—
146C2×C22⋊C8D414yes—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—22no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153#399—28no—
154#397—28no—
155#394—28no—
156#394—28no—
157#390—22no—
158#390—22no—
159#390C2×C414yescomplemented
160#390C2×C414yescomplemented
161#389—22no—
162#389—22no—
163#389C2×C414yescomplemented
164#389C2×C414yescomplemented
165#380—22no—
166#380C2×C414yes—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—41no—
187#340—41no—
188#340—41no—
189#340—41no—
190C25—21no—
191C25C2×D411yescharacteristic
192C22×D4—24no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4—81no—
209C22×D4—81no—
210C22×D4—81no—
211C22×D4—81no—
212C22×D4C22×C412yes—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—24no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—81no—
232C23×C4—81no—
233C23×C4—81no—
234C23×C4—81no—
235C23×C4C22×C412yes—
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4#4112yes—
245C23×C4#4112yes—
246C23×C4C2411yescharacteristic
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C2×D412yes—
272C22×C8C2×D412yes—
273C22×C8C2×D412yes—
274C22×C8C2×D412yes—
275#121—28no—
276#121—28no—
277#121—44no—
278#121—44no—
279#117—28no—
280#117—28no—
281#117—28no—
282#117—28no—
283#117—44no—
284#117—44no—
285#117—44no—
286#117—44no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
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—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4—81no—
337C2×C4⋊C4—81no—
338C2×C4⋊C4—81no—
339C2×C4⋊C4C22⋊C414yes—
340C2×C4⋊C4C22⋊C414yes—
341C2×C4⋊C4C22×C412yes—
342C2×C4⋊C4C22×C412yes—
343C2×C4⋊C4C22×C412yes—
344C2×C4⋊C4#4112yes—
345C2×C4⋊C4#4112yes—
346C2×C4⋊C4#4112yes—
347C2×C4⋊C4#4112yes—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4—81no—
365C2×C22⋊C4—81no—
366C2×C22⋊C4—81no—
367C2×C22⋊C4—81no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C22⋊C4—81no—
373C2×C22⋊C4C22⋊C414yes—
374C2×C22⋊C4C22⋊C414yes—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—24no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42C22×C412yes—
387C2×C42C22×C412yes—
388C2×C42C2×D412yes—
389C2×C42C2×D412yes—
390C4⋊C8—28no—
391C4⋊C8—28no—
392#102—44no—
393#102—44no—
394#102—44no—
395#102—44no—
396C22⋊C8—28no—
397C22⋊C8—28no—
398#97—28no—
399C4×C8—28no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—81no—
404#95—81no—
405#95—81no—
406#95—81no—
407#95—81no—
408#95—81no—
409#95—81no—
410#95—81no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24C2×C22⋊C412yes—
439C24#12112yes—
440C24#12112yes—
441C24C22×D411yescharacteristic
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—48no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—84no—
472C2×D4—84no—
473C2×D4—84no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—48no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4C2×C22⋊C412yes—
586C22×C4C2×C22⋊C412yes—
587C22×C4C2×C22⋊C412yes—
588C22×C4C2×C22⋊C412yes—
589C22×C4C2×C22⋊C412yes—
590C22×C4C4×D414yes—
591C22×C4C4×D414yes—
592C22×C4#12014yes—
593C22×C4#12112yes—
594C22×C4#12112yes—
595C22×C4#12314yes—
596C22×C4C23×C411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4H(5,𝔽2)11yescharacteristic
607C22×C4H(5,𝔽2)11yescharacteristic
608C22×C42−1+411yescharacteristic
609C22×C42−1+411yescharacteristic
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—48no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—48no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—81no—
758C23#38614yes—
759C23C22×C22⋊C411yescharacteristic
760C23C2×#12111yescharacteristic
761C23C2×#12111yescharacteristic
762C23#52511yescharacteristic
763C23#52511yescharacteristic
764C23#53511yescharacteristic
765C23#53611yescharacteristic
766C23#57611yescharacteristic
767C23#57611yescharacteristic
768C23#57611yescharacteristic
769C23#57711yescharacteristic
770C23#57711yescharacteristic
771C23#57711yescharacteristic
772C23#57711yescharacteristic
773C23#57811yescharacteristic
774D4—42no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—816no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—816no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4#38614yes—
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C2×C4×D411yescharacteristic
878C2×C4C4×#4111yescharacteristic
879C2×C4C4×#4111yescharacteristic
880C2×C4#52011yescharacteristic
881C2×C4#52011yescharacteristic
882C2×C4C2×#12011yescharacteristic
883C2×C4C2×#12311yescharacteristic
884C2×C4#53211yescharacteristic
885C2×C4#53211yescharacteristic
886C2×C4#53711yescharacteristic
887C2×C4#53711yescharacteristic
888C2×C4#54611yescharacteristic
889C2×C4#54611yescharacteristic
890C2×C4#54611yescharacteristic
891C2×C4#54611yescharacteristic
892C2×C4#54711yescharacteristic
893C2×C4#54711yescharacteristic
894C2×C4#54711yescharacteristic
895C2×C4#54711yescharacteristic
896C2×C4#55111yescharacteristic
897C2×C4#55111yescharacteristic
898C2×C4#55111yescharacteristic
899C2×C4#55111yescharacteristic
900C2×C4#55211yescharacteristic
901C2×C4#55211yescharacteristic
902C2×C4#55211yescharacteristic
903C2×C4#55211yescharacteristic
904C8—42no—
905C8—42no—
906C8—42no—
907C8—42no—
908C22—24no—
909C22—24no—
910C22—24no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—161no—
931C22—161no—
932C22—161no—
933C22—161no—
934C22—161no—
935C22—161no—
936C22—161no—
937C22—161no—
938C22C2×#38611yescharacteristic
939C22#229711yescharacteristic
940C22#231111yescharacteristic
941C22#241111yescharacteristic
942C22#241111yescharacteristic
943C22#241311yescharacteristic
944C22#241311yescharacteristic
945C22#289711yescharacteristic
946C22#289711yescharacteristic
947C22#289711yescharacteristic
948C22#289811yescharacteristic
949C22#305711yescharacteristic
950C22#305811yescharacteristic
951C22#306011yescharacteristic
952C22#306111yescharacteristic
953C22#306211yescharacteristic
954C22#306211yescharacteristic
955C22#306211yescharacteristic
956C22#306311yescharacteristic
957C22#311811yescharacteristic
958C22#311911yescharacteristic
959C22#311911yescharacteristic
960C22#312111yescharacteristic
961C22#312211yescharacteristic
962C22#312411yescharacteristic
963C22#312511yescharacteristic
964C22#312611yescharacteristic
965C22#322011yescharacteristic
966C22#322111yescharacteristic
967C22#322411yescharacteristic
968C22#322511yescharacteristic
969C22#324111yescharacteristic
970C22#324111yescharacteristic
971C22#324311yescharacteristic
972C22#324411yescharacteristic
973C4—24no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—82no—
979C4—82no—
980C4—82no—
981C4—82no—
982C4—82no—
983C4—82no—
984C4—82no—
985C4#235911yescharacteristic
986C4#235911yescharacteristic
987C4#235911yescharacteristic
988C4#235911yescharacteristic
989C4#243011yescharacteristic
990C4#243011yescharacteristic
991C4#249811yescharacteristic
992C4#249811yescharacteristic
993C2—44no—
994C2—162no—
995C2#1413511yescharacteristic
996C2#2097511yescharacteristic
997C2#2097611yescharacteristic
998C2#2139711yescharacteristic
999C2#2139911yescharacteristic
1000C2#2187111yescharacteristic
1001C2#2187211yescharacteristic
1002C2#2451211yescharacteristic
1003C2#2451311yescharacteristic
1004C2#2451811yescharacteristic
1005C2#2451911yescharacteristic
1006C2#2461211yescharacteristic
1007C2#2461511yescharacteristic
1008C2#2461711yescharacteristic
1009C2#2461811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#433C2semidirect
5. #13795C2semidirect
6. #11228C2semidirect
7. #11227C2semidirect
8. #11076C2semidirect
9. #11076C2semidirect
10. #10927C2semidirect
11. #10925C2semidirect
12. #10881C2semidirect
13. #10880C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
34. #2624C4semidirect
159. #390C2×C4semidirect
160. #390C2×C4semidirect
163. #389C2×C4semidirect
164. #389C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4332
C2×#26242
C2×#18752
C2×#18742
#137952
#112282
#112272
#110762
#109272
#109252
#108812
#108802
#107312
#107302