Finite Group Databasebeta

← #385351

Subgroups — #385351

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1942C211yesmaximal, characteristic, complemented
2C2×#1934C211yesmaximal, characteristic
3C2×#1925C211yesmaximal, characteristic
4C2×#1862C211yesmaximal, characteristic
5C2×#1862C211yesmaximal, characteristic
6#14018C211yesmaximal, characteristic
7#13910C211yesmaximal, characteristic, complemented
8#11328C211yesmaximal, characteristic, complemented
9#11324C211yesmaximal, characteristic, complemented
10#11292C211yesmaximal, characteristic, complemented
11#11219C211yesmaximal, characteristic, complemented
12#11066C211yesmaximal, characteristic
13#11049C211yesmaximal, characteristic
14#10874C211yesmaximal, characteristic, complemented
15#10806C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#385—21no—
33C2×#384—21no—
34C2×#384C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#1942—24no—
38#1934—24no—
39#1925C418yescomplemented
40#1862—24no—
41#1862—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1444—21no—
57#1444—21no—
58#1439—21no—
59#1439—21no—
60C4⋊#95—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C22⋊#95—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—41no—
73C2×C4×D4—41no—
74C2×C4×D4—41no—
75C2×C4×D4—41no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4D411yescharacteristic
84C22×C4⋊C4D411yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C42—21no—
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×#107—22no—
102C2×#107—22no—
103C2×#107—22no—
104C2×#107—22no—
105C2×#107—22no—
106C2×#107—41no—
107C2×#107—41no—
108C2×#107—41no—
109C2×#107C2×C414yescomplemented
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—22no—
115C2×#102—41no—
116C2×#102—41no—
117C2×#102—41no—
118C2×#102C2×C414yes—
119C2×#102C2×C414yes—
120C2×#102D414yes—
121C2×#102Q814yes—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8—41no—
125#390—22no—
126#390—22no—
127#390—41no—
128#390C2×C414yes—
129#389—22no—
130#389—22no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—41no—
135#389—41no—
136#389—41no—
137#389—41no—
138#389—41no—
139#385—44no—
140#384—41no—
141#384—41no—
142#384—44no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4—41no—
145C4×C4⋊C4—41no—
146C4×C4⋊C4C2×C414yescomplemented
147C2×#95—21no—
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×#95D411yescharacteristic
158C2×#95D411yescharacteristic
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—41no—
165#340—41no—
166#340C2×C414yescomplemented
167#340D414yes—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—41no—
172#336C2×C414yescomplemented
173C25—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4C22×C412yes—
186C22×D4C2×D412yes—
187C22×D4C2×Q812yes—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—81no—
201C23×C4—81no—
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2411yescharacteristic
209C22×C8—21no—
210C22×C8—21no—
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×C8C22×C412yes—
233C22×C8C22×C412yes—
234C22×C8C2×D412yes—
235C22×C8C2×D412yes—
236C22×C8C2×Q812yes—
237C4×D4—44no—
238C4×D4—44no—
239C4×D4—44no—
240C4×D4—44no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
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—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—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4—81no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4—81no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4D814yes—
302C2×C4⋊C4C22×C412yes—
303C2×C4⋊C4C22×C412yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×Q812yes—
309C2×C4⋊C4#4112yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—81no—
322C2×C22⋊C4—81no—
323C2×C22⋊C4—81no—
324C2×C22⋊C4—81no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—24no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42C22×C412yes—
345C2×C42#4112yes—
346#107—28no—
347#107—44no—
348#107—44no—
349#102—28no—
350#102—44no—
351#102—44no—
352#102C4⋊C4116yescomplemented
353C4×C8—44no—
354#95—24no—
355#95—41no—
356#95—41no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—81no—
365#95—81no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24C22×D411yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4C2×C4⋊C414yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
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—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
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—48no—
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×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4—84no—
501C22×C4C4×D412yes—
502C22×C4C4×D412yes—
503C22×C4C2×D812yes—
504C22×C4C2×D812yes—
505C22×C4C2×D812yes—
506C22×C4#13512yes—
507C22×C4#13712yes—
508C22×C4C23×C411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×Q811yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C4H(5,𝔽2)11yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C42−1+411yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521C22×C42−1+411yescharacteristic
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8C2×C4⋊C414yes—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—84no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C4⋊C4—84no—
583C4⋊C4—84no—
584C4⋊C4—84no—
585C4⋊C4C2×C4⋊C414yes—
586C4⋊C4C4×D414yes—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—48no—
605C23—24no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23C2×C4×D411yescharacteristic
641C23#53411yescharacteristic
642C23#53611yescharacteristic
643C23D4211yescharacteristic
644C23D4211yescharacteristic
645C23#54811yescharacteristic
646C23D4×Q811yescharacteristic
647C23C22×D811yescharacteristic
648C23C2×#13511yescharacteristic
649C23C2×#13711yescharacteristic
650C23#57511yescharacteristic
651C23#57611yescharacteristic
652C23#57611yescharacteristic
653C23#57711yescharacteristic
654C23#57811yescharacteristic
655D4—24no—
656D4—24no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—816no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C4×D814yes—
755C2×C4C22×C4⋊C411yescharacteristic
756C2×C4C2×C4×D411yescharacteristic
757C2×C4#52011yescharacteristic
758C2×C4#52011yescharacteristic
759C2×C4#52011yescharacteristic
760C2×C4#52011yescharacteristic
761C2×C4#53511yescharacteristic
762C2×C4#53511yescharacteristic
763C2×C4#53611yescharacteristic
764C2×C4#53611yescharacteristic
765C2×C4#53911yescharacteristic
766C2×C4#53911yescharacteristic
767C2×C4#54211yescharacteristic
768C2×C4#54211yescharacteristic
769C2×C4#54411yescharacteristic
770C2×C4#54411yescharacteristic
771C2×C4D4211yescharacteristic
772C2×C4#54711yescharacteristic
773C2×C4#54711yescharacteristic
774C2×C4#54711yescharacteristic
775C2×C4D4×Q811yescharacteristic
776C2×C4#55311yescharacteristic
777C2×C4#55411yescharacteristic
778C2×C4#55411yescharacteristic
779C2×C4#56011yescharacteristic
780C2×C4#56311yescharacteristic
781C2×C4#56311yescharacteristic
782C2×C4#56311yescharacteristic
783C8—24no—
784C8—42no—
785C8—42no—
786C8—81no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22#232211yescharacteristic
803C22D4×C4⋊C411yescharacteristic
804C22#236111yescharacteristic
805C22#266911yescharacteristic
806C22#267411yescharacteristic
807C22#267711yescharacteristic
808C22#272911yescharacteristic
809C22C2×C4×D811yescharacteristic
810C22C4×#13711yescharacteristic
811C22#294611yescharacteristic
812C22#295111yescharacteristic
813C22#318611yescharacteristic
814C22#319011yescharacteristic
815C22#319911yescharacteristic
816C22#320111yescharacteristic
817C22#322611yescharacteristic
818C22#323211yescharacteristic
819C22#324111yescharacteristic
820C22#324311yescharacteristic
821C22#326611yescharacteristic
822C22#326811yescharacteristic
823C22#326811yescharacteristic
824C22#327011yescharacteristic
825C22D4×D811yescharacteristic
826C22D4×D811yescharacteristic
827C22#328311yescharacteristic
828C22#328411yescharacteristic
829C22#335811yescharacteristic
830C22#336111yescharacteristic
831C22#337511yescharacteristic
832C22#337711yescharacteristic
833C22Q8×D811yescharacteristic
834C22#338011yescharacteristic
835C22#338511yescharacteristic
836C22#338811yescharacteristic
837C4—24no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—82no—
845C4—81no—
846C4—82no—
847C4—161no—
848C4—161no—
849C4—161no—
850C4#231711yescharacteristic
851C4#232611yescharacteristic
852C4D4×C4⋊C411yescharacteristic
853C4#238311yescharacteristic
854C4#268011yescharacteristic
855C4#271811yescharacteristic
856C4#272011yescharacteristic
857C4#279011yescharacteristic
858C2—84no—
859C2#1440511yescharacteristic
860C2#2207511yescharacteristic
861C2#2208811yescharacteristic
862C2#2267811yescharacteristic
863C2C4⋊C4×D811yescharacteristic
864C2#2299511yescharacteristic
865C2#2300911yescharacteristic
866C2#3049911yescharacteristic
867C2#3050411yescharacteristic
868C2#3080511yescharacteristic
869C2#3081111yescharacteristic
870C2#3094611yescharacteristic
871C2#3095111yescharacteristic
872C2#3256411yescharacteristic
873C2#3257311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
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
1. C2×#1942C2semidirect
7. #13910C2semidirect
8. #11328C2semidirect
9. #11324C2semidirect
10. #11292C2semidirect
11. #11219C2semidirect
14. #10874C2semidirect
15. #10806C2semidirect
39. #1925C4semidirect
109. C2×#107C2×C4semidirect
146. C4×C4⋊C4C2×C4semidirect
166. #340C2×C4semidirect
172. #336C2×C4semidirect
352. #102C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19422
C2×#19342
C2×#19252
C2×#18622
#140182
#139102
#113282
#113242
#112922
#112192
#110662
#110492
#108742
#108062