Finite Group Databasebeta

← #371556

Subgroups — #371556

Order 512.

1522 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1934C211yesmaximal, characteristic, complemented
2C2×#1893C211yesmaximal, characteristic
3C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
4#13998C211yesmaximal, characteristic
5#13974C211yesmaximal, characteristic, complemented
6#11292C211yesmaximal, characteristic, complemented
7#11199C211yesmaximal, characteristic, complemented
8#11189C211yesmaximal, characteristic, complemented
9#10969C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10884C211yesmaximal, characteristic, complemented
13#10880C211yesmaximal, characteristic, complemented
14#10721C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×#102C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C2×#390—21no—
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#388—21no—
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1934—24no—
38#1893C418yescomplemented
39C8×C22⋊C4—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1443—21no—
55#1440—21no—
56#1439—21no—
57#1438—21no—
58#1437—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—41no—
68C23×C8—41no—
69C23×C8—41no—
70C23×C8—41no—
71C23×C8C2×C414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121—41no—
80C2×#121—41no—
81C2×#121C2×C414yes—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4D411yescharacteristic
100C22×C22⋊C4D411yescharacteristic
101C22×C42—21no—
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×#102—22no—
106C2×#102—22no—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102C2×C414yes—
116C2×#102C2×C414yes—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8—41no—
122C2×C4×C8—41no—
123C2×C4×C8—41no—
124C2×C4×C8—41no—
125C2×C4×C8D414yescomplemented
126#390—22no—
127#390—22no—
128#390—22no—
129#390—41no—
130#390—44no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—41no—
135#388—44no—
136#380—22no—
137#380—22no—
138#380—22no—
139#380—41no—
140#380—41no—
141#380C2×C414yes—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4—41no—
145C4×C4⋊C4—41no—
146C4×C22⋊C4—22no—
147C4×C22⋊C4—22no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
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×#95D411yescharacteristic
160C2×#95D411yescharacteristic
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340C2×C414yes—
172#340C2×C414yes—
173#336—22no—
174#336—22no—
175C25—21no—
176C25C2×D411yescharacteristic
177C22×D4—24no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—42no—
192C22×D4—42no—
193C22×D4—42no—
194C22×D4—42no—
195C22×D4—81no—
196C22×D4—81no—
197C22×D4C22×C412yes—
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—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4C22×C412yes—
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4#4112yes—
224C23×C4C2411yescharacteristic
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×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—28no—
248C22×C8—44no—
249C22×C8—44no—
250C22×C8—44no—
251C22×C8—44no—
252C22×C8—44no—
253C22×C8—44no—
254C22×C8C22×C412yes—
255C22×C8C22×C412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8#4112yes—
259C22×C8#4112yes—
260#121—28no—
261#121—44no—
262#121—44no—
263#121—44no—
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—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—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—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4#4112yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C4⋊C4#4112yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4—81no—
338C2×C22⋊C4—81no—
339C2×C22⋊C4—81no—
340C2×C22⋊C4—81no—
341C2×C22⋊C4D814yes—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—81no—
357C2×C42—81no—
358C2×C42C2×D412yes—
359C2×C42#4112yes—
360#102—28no—
361#102—44no—
362#102—44no—
363#102—44no—
364C22⋊C8—28no—
365C4×C8—44no—
366C4×C8—44no—
367#95—24no—
368#95—22no—
369#95—22no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—81no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24C4×D412yes—
408C24C2×D812yes—
409C24#13512yes—
410C24C22×D411yescharacteristic
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—84no—
442C2×D4—84no—
443C2×D4—84no—
444C2×D4—84no—
445C2×D4—84no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
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—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—41no—
535C22×C4—41no—
536C22×C4—41no—
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×C4C4×D412yes—
552C22×C4#12112yes—
553C22×C4#12112yes—
554C22×C4C2×D812yes—
555C22×C4C2×D812yes—
556C22×C4#13512yes—
557C22×C4#13512yes—
558C22×C4C23×C411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—416no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8C4×D414yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
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—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C4⋊C4#11714yes—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—84no—
650C42—84no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
705C23—81no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23C4×D814yes—
721C23C2×C4×D411yescharacteristic
722C23C2×#12111yescharacteristic
723C23#53211yescharacteristic
724C23#54611yescharacteristic
725C23#54611yescharacteristic
726C23#54611yescharacteristic
727C23#54611yescharacteristic
728C23C22×D811yescharacteristic
729C23C2×#13511yescharacteristic
730C23C2×#13511yescharacteristic
731C23C2×#13511yescharacteristic
732C23#57711yescharacteristic
733C23#57711yescharacteristic
734C23#57711yescharacteristic
735C23#57711yescharacteristic
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—816no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4#46614yes—
837C2×C4C2×#11711yescharacteristic
838C2×C4C2×C4×D411yescharacteristic
839C2×C4C4×#4111yescharacteristic
840C2×C4C4×#4111yescharacteristic
841C2×C4#51811yescharacteristic
842C2×C4#51811yescharacteristic
843C2×C4#52511yescharacteristic
844C2×C4#52911yescharacteristic
845C2×C4#52911yescharacteristic
846C2×C4#52911yescharacteristic
847C2×C4#53211yescharacteristic
848C2×C4#53211yescharacteristic
849C2×C4#53411yescharacteristic
850C2×C4#53511yescharacteristic
851C2×C4#53811yescharacteristic
852C2×C4#53811yescharacteristic
853C2×C4#55111yescharacteristic
854C2×C4#55111yescharacteristic
855C2×C4#55111yescharacteristic
856C2×C4#55311yescharacteristic
857C2×C4#55311yescharacteristic
858C2×C4#55311yescharacteristic
859C2×C4#55311yescharacteristic
860C2×C4#55311yescharacteristic
861C2×C4#55311yescharacteristic
862C2×C4#55911yescharacteristic
863C2×C4#55911yescharacteristic
864C2×C4#55911yescharacteristic
865C8—24no—
866C8—42no—
867C8—42no—
868C8—42no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—161no—
892C22—161no—
893C22—161no—
894C22—161no—
895C22—161no—
896C22—161no—
897C22—161no—
898C22—161no—
899C22C4×#12111yescharacteristic
900C22#234211yescharacteristic
901C22#236411yescharacteristic
902C22#254311yescharacteristic
903C22#254411yescharacteristic
904C22#255711yescharacteristic
905C22#255911yescharacteristic
906C22C2×C4×D811yescharacteristic
907C22C4×#13511yescharacteristic
908C22#294911yescharacteristic
909C22#295211yescharacteristic
910C22C2×#46611yescharacteristic
911C22#305011yescharacteristic
912C22#305711yescharacteristic
913C22#306011yescharacteristic
914C22#316811yescharacteristic
915C22#316911yescharacteristic
916C22#317311yescharacteristic
917C22#317411yescharacteristic
918C22#329411yescharacteristic
919C22#329411yescharacteristic
920C22#329411yescharacteristic
921C22#329411yescharacteristic
922C22#329611yescharacteristic
923C22#329611yescharacteristic
924C22#329611yescharacteristic
925C22#330111yescharacteristic
926C22#330111yescharacteristic
927C22#330111yescharacteristic
928C22#330111yescharacteristic
929C22#330111yescharacteristic
930C22#330311yescharacteristic
931C22#330411yescharacteristic
932C22#330411yescharacteristic
933C22#330411yescharacteristic
934C4—24no—
935C4—44no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—82no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—161no—
945C4—161no—
946C4#229311yescharacteristic
947C4#232111yescharacteristic
948C4#235711yescharacteristic
949C4#237411yescharacteristic
950C4#259511yescharacteristic
951C4#259711yescharacteristic
952C4#260211yescharacteristic
953C4#260311yescharacteristic
954C2—44no—
955C2—162no—
956C2#1407611yescharacteristic
957C2C4×#46611yescharacteristic
958C2#2152311yescharacteristic
959C2#2257011yescharacteristic
960C2#2257711yescharacteristic
961C2#2312711yescharacteristic
962C2#2313111yescharacteristic
963C2#2855111yescharacteristic
964C2#2855611yescharacteristic
965C2#2859711yescharacteristic
966C2#2860211yescharacteristic
967C2#2897511yescharacteristic
968C2#2898211yescharacteristic
969C2#2903911yescharacteristic
970C2#2904611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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
1. C2×#1934C2semidirect
3. C2×C8×C22⋊C4C2semidirect
5. #13974C2semidirect
6. #11292C2semidirect
7. #11199C2semidirect
8. #11189C2semidirect
10. #10931C2semidirect
11. #10925C2semidirect
12. #10884C2semidirect
13. #10880C2semidirect
14. #10721C2semidirect
15. C4×#340C2semidirect
38. #1893C4semidirect
125. C2×C4×C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#19342
C2×#18932
C2×C8×C22⋊C42
#139982
#139742
#112922
#111992
#111892
#109692
#109312
#109252
#108842
#108802
#107212
C4×#3402