Finite Group Databasebeta

← #385369

Subgroups — #385369

Order 512.

1386 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1948C211yesmaximal, characteristic, complemented
2C2×#1923C211yesmaximal, characteristic
3C2×#1853C211yesmaximal, characteristic
4C2×#1853C211yesmaximal, characteristic
5C2×#1844C211yesmaximal, characteristic, complemented
6#13880C211yesmaximal, characteristic
7#13876C211yesmaximal, characteristic
8#11323C211yesmaximal, characteristic, complemented
9#11323C211yesmaximal, characteristic, complemented
10#11267C211yesmaximal, characteristic, complemented
11#11231C211yesmaximal, characteristic, complemented
12#11095C211yesmaximal, characteristic
13#11095C211yesmaximal, characteristic
14#10908C211yesmaximal, characteristic, complemented
15#10820C211yesmaximal, characteristic, complemented
16C23×C4⋊C4C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27C2×#388—21no—
28C2×#385—21no—
29C2×#385—21no—
30C2×#384C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#384C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#1948—24no—
39#1923C418yescomplemented
40#1853—24no—
41#1853—24no—
42#1844—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1444—21no—
56#1444—21no—
57#1442—21no—
58#1439—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—41no—
80C22×C4⋊C4—41no—
81C22×C4⋊C4—41no—
82C22×C4⋊C4—41no—
83C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
95C22×C22⋊C4D411yescharacteristic
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×#106—22no—
100C2×#106—22no—
101C2×#106—22no—
102C2×#106—22no—
103C2×#106—22no—
104C2×#106—22no—
105C2×#106—22no—
106C2×#106—22no—
107C2×#106—41no—
108C2×#106—41no—
109C2×#106—41no—
110C2×#106—41no—
111C2×#106—41no—
112C2×#106—41no—
113C2×#106—41no—
114C2×#106—41no—
115C2×#106—41no—
116C2×#106D414yes—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8C2×C414yescomplemented
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8C2×C414yes—
125C2×C22⋊C8C2×C414yes—
126C2×C4×C8—22no—
127C2×C4×C8—22no—
128C2×C4×C8C2×C414yescomplemented
129#388—44no—
130#385—44no—
131#385—44no—
132#384—22no—
133#384—22no—
134#384—22no—
135#384—41no—
136#384—41no—
137#384—41no—
138#380—22no—
139#380—22no—
140#380—41no—
141#380—41no—
142#380—41no—
143#380—41no—
144C4×C4⋊C4—22no—
145C4×C4⋊C4—41no—
146C4×C22⋊C4C2×C414yes—
147C4×C22⋊C4Q814yes—
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×#95—21no—
160C2×#95D411yescharacteristic
161C2×#95D411yescharacteristic
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#340D414yes—
172#336C2×C414yescomplemented
173#336C2×C414yescomplemented
174C25C2×D411yescharacteristic
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
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×C4C22×C412yes—
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×Q812yes—
209C23×C4C2411yescharacteristic
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×C8C22×C412yes—
231C22×C8C22×C412yes—
232C22×C8C22×C412yes—
233C22×C8C22×C412yes—
234C22×C8C2×D412yes—
235C22×C8C2×D412yes—
236C22×C8#4112yes—
237C22×C8#4112yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
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—21no—
256C2×C4⋊C4—21no—
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—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
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—81no—
321C2×C22⋊C4—81no—
322C2×C22⋊C4C4⋊C414yes—
323C2×C22⋊C4C4⋊C414yes—
324C2×C22⋊C4SD1614yes—
325C2×C22⋊C4SD1614yes—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—81no—
337C2×C42C22×C412yes—
338C2×C42C22×C412yes—
339C2×C42C2×Q812yes—
340C2×C42C2×Q812yes—
341#106—44no—
342#106—44no—
343#106—44no—
344#106—44no—
345#106—44no—
346#106—44no—
347C4⋊C8—28no—
348C22⋊C8—28no—
349C22⋊C8—28no—
350C4×C8—28no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—81no—
363#95C4⋊C414yes—
364#95C4⋊C414yes—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24C2×C4⋊C412yes—
378C24C2×SD1612yes—
379C24C2×SD1612yes—
380C24C22×D411yescharacteristic
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—48no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
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—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—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—84no—
491C22×C4—84no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4C2×C4⋊C412yes—
497C22×C4C2×C4⋊C412yes—
498C22×C4C2×C4⋊C412yes—
499C22×C4C2×C4⋊C412yes—
500C22×C4C2×C4⋊C412yes—
501C22×C4C2×SD1612yes—
502C22×C4C2×SD1612yes—
503C22×C4C2×SD1612yes—
504C22×C4C2×SD1612yes—
505C22×C4AGL(1,ℤ/8)12yes—
506C22×C4#13712yes—
507C22×C4C23×C411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×Q811yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C4H(5,𝔽2)11yescharacteristic
517C22×C42−1+411yescharacteristic
518C22×C42−1+411yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521C2×C8—22no—
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—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
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×C8C4×D414yes—
548C2×C8C4×D414yes—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—48no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
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—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—84no—
583C4⋊C4—84no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—84no—
588C22⋊C4—28no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C22⋊C4#106116yescomplemented
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—84no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23C2×#10614yes—
637C23C22×C4⋊C411yescharacteristic
638C23#53511yescharacteristic
639C23#53611yescharacteristic
640C23D4211yescharacteristic
641C23D4211yescharacteristic
642C23#54711yescharacteristic
643C23#54711yescharacteristic
644C23C22×SD1611yescharacteristic
645C23C22×SD1611yescharacteristic
646C23C2×AGL(1,ℤ/8)11yescharacteristic
647C23C2×#13711yescharacteristic
648C23#57711yescharacteristic
649C23#57711yescharacteristic
650C23#57711yescharacteristic
651C23#57711yescharacteristic
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—816no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
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×C4C2×#10614yes—
750C2×C4C2×#10614yes—
751C2×C4#42814yes—
752C2×C4C2×C4×D411yescharacteristic
753C2×C4C2×C4×D411yescharacteristic
754C2×C4#52011yescharacteristic
755C2×C4#52011yescharacteristic
756C2×C4#52011yescharacteristic
757C2×C4#52011yescharacteristic
758C2×C4#53411yescharacteristic
759C2×C4#53511yescharacteristic
760C2×C4#53611yescharacteristic
761C2×C4#53611yescharacteristic
762C2×C4#53911yescharacteristic
763C2×C4#53911yescharacteristic
764C2×C4#54211yescharacteristic
765C2×C4#54211yescharacteristic
766C2×C4#54411yescharacteristic
767C2×C4#54411yescharacteristic
768C2×C4D4211yescharacteristic
769C2×C4#54711yescharacteristic
770C2×C4#54811yescharacteristic
771C2×C4D4×Q811yescharacteristic
772C2×C4D4×Q811yescharacteristic
773C2×C4#55311yescharacteristic
774C2×C4#55411yescharacteristic
775C2×C4#55411yescharacteristic
776C2×C4#56011yescharacteristic
777C2×C4#56311yescharacteristic
778C2×C4#56311yescharacteristic
779C2×C4#56311yescharacteristic
780C8—24no—
781C8—24no—
782C8—42no—
783C8—42no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22#231711yescharacteristic
800C22D4×C4⋊C411yescharacteristic
801C22D4×C4⋊C411yescharacteristic
802C22#266911yescharacteristic
803C22#267411yescharacteristic
804C22#268011yescharacteristic
805C22#271811yescharacteristic
806C22C22×#10611yescharacteristic
807C22C2×#42811yescharacteristic
808C22#291211yescharacteristic
809C22#291211yescharacteristic
810C22#320611yescharacteristic
811C22#320811yescharacteristic
812C22#322111yescharacteristic
813C22#322211yescharacteristic
814C22#322711yescharacteristic
815C22#322911yescharacteristic
816C22#324411yescharacteristic
817C22#324411yescharacteristic
818C22#326511yescharacteristic
819C22#326611yescharacteristic
820C22#327211yescharacteristic
821C22#327811yescharacteristic
822C22D4×SD1611yescharacteristic
823C22D4×SD1611yescharacteristic
824C22D4×SD1611yescharacteristic
825C22D4×SD1611yescharacteristic
826C22#333511yescharacteristic
827C22#333511yescharacteristic
828C22#333511yescharacteristic
829C22#333511yescharacteristic
830C22#334411yescharacteristic
831C22#334511yescharacteristic
832C22#335411yescharacteristic
833C22#335611yescharacteristic
834C4—24no—
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—161no—
844C4—161no—
845C4—161no—
846C4—161no—
847C4#232211yescharacteristic
848C4#232611yescharacteristic
849C4#236111yescharacteristic
850C4#238311yescharacteristic
851C4#267711yescharacteristic
852C4#272011yescharacteristic
853C4#272911yescharacteristic
854C4#279011yescharacteristic
855C2—44no—
856C2#1440511yescharacteristic
857C2#2198111yescharacteristic
858C2#2199011yescharacteristic
859C2D4×#10611yescharacteristic
860C2D4×#10611yescharacteristic
861C2#2265911yescharacteristic
862C2#2266311yescharacteristic
863C2#3045311yescharacteristic
864C2#3045611yescharacteristic
865C2#3077511yescharacteristic
866C2#3077711yescharacteristic
867C2#3108611yescharacteristic
868C2#3108911yescharacteristic
869C2#3228011yescharacteristic
870C2#3228211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
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×#1948C2semidirect
5. C2×#1844C2semidirect
8. #11323C2semidirect
9. #11323C2semidirect
10. #11267C2semidirect
11. #11231C2semidirect
14. #10908C2semidirect
15. #10820C2semidirect
39. #1923C4semidirect
119. C2×C4⋊C8C2×C4semidirect
128. C2×C4×C8C2×C4semidirect
172. #336C2×C4semidirect
173. #336C2×C4semidirect
592. C22⋊C4#106semidirect

Maximal subgroups

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

subgroupindex
C2×#19482
C2×#19232
C2×#18532
C2×#18442
#138802
#138762
#113232
#112672
#112312
#110952
#109082
#108202