Finite Group Databasebeta

← #370510

Subgroups — #370510

Order 512.

1848 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic
2C2×#1988C211yesmaximal, characteristic, complemented
3C2×#1850C211yesmaximal, characteristic
4C22×#340C211yesmaximal, characteristic
5C22⋊C4×C4⋊C4C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic, complemented
7#11373C211yesmaximal, characteristic, complemented
8#11227C211yesmaximal, characteristic, complemented
9#11227C211yesmaximal, characteristic, complemented
10#10884C211yesmaximal, characteristic, complemented
11#10884C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10730C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10721C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8—21no—
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24#2440—24no—
25#2440C418yescomplemented
26C2×#398—21no—
27C2×#395—21no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#385—21no—
31C2×#384C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4—21no—
37C2×C4×C22⋊C4C2211yescharacteristic
38#1988—24no—
39#1850—24no—
40C2×#340—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1436—21no—
60#1436—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C22⋊#95—21no—
64C23×Q8—21no—
65C24×C4—21no—
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—41no—
83C2×C4⋊Q8—41no—
84C2×C4⋊Q8C2×C414yescomplemented
85C2×C22⋊Q8—28no—
86C2×C22⋊Q8—44no—
87C2×C22⋊Q8—44no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—41no—
102C22×C4⋊C4—41no—
103C22×C4⋊C4—41no—
104C22×C4⋊C4—41no—
105C22×C4⋊C4C2×C414yes—
106C22×C4⋊C4Q814yescomplemented
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4D411yescharacteristic
118C22×C22⋊C4D411yescharacteristic
119C22×C42—21no—
120C22×C42—21no—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8—41no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132#398—28no—
133#395—28no—
134#389—22no—
135#389—22no—
136#389C2×C414yescomplemented
137#389C2×C414yescomplemented
138#385—28no—
139#384—22no—
140#384C2×C414yescomplemented
141#380—22no—
142#380—22no—
143#380C2×C414yes—
144#380Q814yescomplemented
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—41no—
148C4×C4⋊C4—41no—
149C4×C22⋊C4—44no—
150C4×C22⋊C4C2×C414yes—
151C4×C22⋊C4D414yes—
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×#95—21no—
161C2×#95—21no—
162C2×#95D411yescharacteristic
163C2×#95D411yescharacteristic
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340D414yes—
180#336—22no—
181#336—22no—
182C25C2×D411yescharacteristic
183C22×Q8—24no—
184C22×Q8—42no—
185C22×Q8—42no—
186C22×Q8—42no—
187C22×Q8—42no—
188C22×Q8—81no—
189C22×Q8—81no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
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—24no—
207C23×C4—24no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—81no—
217C23×C4—81no—
218C23×C4—81no—
219C23×C4—81no—
220C23×C4C22×C412yes—
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D412yes—
227C23×C4C2×Q812yes—
228C23×C4C2×Q812yes—
229C23×C4#4112yes—
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C22×C8—28no—
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—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—44no—
260C22×C8—44no—
261C22×C8—44no—
262C22×C8—44no—
263C22×C8—44no—
264C22×C8—44no—
265C22×C8C2×D412yes—
266C22×C8#4112yes—
267C4⋊Q8—28no—
268C4⋊Q8—44no—
269C4⋊Q8—44no—
270C4⋊Q8—44no—
271C22⋊Q8—432no—
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—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
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—24no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4—81no—
337C2×C4⋊C4C22×C412yes—
338C2×C4⋊C4C22×C412yes—
339C2×C4⋊C4C22×C412yes—
340C2×C4⋊C4C22×C412yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4C2×Q812yes—
344C2×C4⋊C4C2×Q812yes—
345C2×C4⋊C4C2×Q812yes—
346C2×C4⋊C4C2×Q812yes—
347C2×C4⋊C4#4112yes—
348C2×C4⋊C4#4112yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4C22⋊C414yes—
358C2×C22⋊C4C22⋊C414yes—
359C2×C22⋊C4D814yes—
360C2×C22⋊C4SD1614yes—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—81no—
374C2×C42—81no—
375C2×C42C22×C412yes—
376C2×C42C22×C412yes—
377C2×C42C2×D412yes—
378C2×C42C2×D412yes—
379C4⋊C8—44no—
380C4⋊C8—44no—
381C22⋊C8—44no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—81no—
391#95—81no—
392#95C22⋊C414yes—
393#95C22⋊C414yes—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24C2×C22⋊C412yes—
403C24C22⋊Q812yes—
404C24C22⋊Q812yes—
405C24C2×D812yes—
406C24C2×SD1612yes—
407C24#13712yes—
408C24#13712yes—
409C24C22×D411yescharacteristic
410C2×Q8—48no—
411C2×Q8—48no—
412C2×Q8—84no—
413C2×Q8—84no—
414C2×Q8—84no—
415C2×Q8—84no—
416C2×Q8—84no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
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—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—48no—
478C22×C4—48no—
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—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—48no—
524C22×C4—48no—
525C22×C4—84no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4C2×C22⋊C412yes—
536C22×C4C2×C22⋊C412yes—
537C22×C4C2×C22⋊C412yes—
538C22×C4C2×C22⋊C412yes—
539C22×C4C2×C22⋊C412yes—
540C22×C4C4×Q814yes—
541C22×C4C4×Q814yes—
542C22×C4C22⋊Q812yes—
543C22×C4C22⋊Q812yes—
544C22×C4#12414yes—
545C22×C4C4⋊Q814yes—
546C22×C4C2×D812yes—
547C22×C4C2×D812yes—
548C22×C4C2×SD1612yes—
549C22×C4C2×SD1612yes—
550C22×C4C23×C411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×Q811yescharacteristic
554C22×C4C22×Q811yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C4H(5,𝔽2)11yescharacteristic
562C22×C4H(5,𝔽2)11yescharacteristic
563C22×C42−1+411yescharacteristic
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—416no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
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—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
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—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—84no—
630C4⋊C4C4×D414yes—
631C4⋊C4C22⋊Q814yescomplemented
632C22⋊C4—28no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4#102116yes—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—84no—
645C42—84no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
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—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23#39114yes—
675C23C2×#10214yes—
676C23#41914yes—
677C23#47414yes—
678C23#47414yes—
679C23#47514yes—
680C23#47514yes—
681C23C22×C22⋊C411yescharacteristic
682C23C2×C22⋊Q811yescharacteristic
683C23C2×C22⋊Q811yescharacteristic
684C23D4211yescharacteristic
685C23#54611yescharacteristic
686C23#54611yescharacteristic
687C23#54711yescharacteristic
688C23C22×D811yescharacteristic
689C23C22×SD1611yescharacteristic
690C23C2×#13711yescharacteristic
691C23C2×#13711yescharacteristic
692C23#57611yescharacteristic
693C23#57711yescharacteristic
694C23#57711yescharacteristic
695C23#57811yescharacteristic
696Q8—816no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—816no—
770C2×C4—816no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4#39114yes—
796C2×C4C2×#10214yes—
797C2×C4C2×#10214yes—
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C2×C4×Q811yescharacteristic
800C2×C4C2×C4×Q811yescharacteristic
801C2×C4C4×#4111yescharacteristic
802C2×C4#51811yescharacteristic
803C2×C4#52011yescharacteristic
804C2×C4C2×C22⋊Q811yescharacteristic
805C2×C4#52511yescharacteristic
806C2×C4C2×#12411yescharacteristic
807C2×C4#52911yescharacteristic
808C2×C4C2×C4⋊Q811yescharacteristic
809C2×C4#53311yescharacteristic
810C2×C4#53811yescharacteristic
811C2×C4#53911yescharacteristic
812C2×C4#54311yescharacteristic
813C2×C4#54411yescharacteristic
814C2×C4D4211yescharacteristic
815C2×C4#54611yescharacteristic
816C2×C4#54611yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54711yescharacteristic
819C2×C4D4×Q811yescharacteristic
820C2×C4#55111yescharacteristic
821C2×C4#55111yescharacteristic
822C2×C4#55211yescharacteristic
823C2×C4#55411yescharacteristic
824C2×C4#55411yescharacteristic
825C2×C4#55411yescharacteristic
826C8—42no—
827C8—42no—
828C8—81no—
829C8—81no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22#198818yescomplemented
845C22C2×#39111yescharacteristic
846C22D4×C22⋊C411yescharacteristic
847C22#233911yescharacteristic
848C22#243711yescharacteristic
849C22#243811yescharacteristic
850C22#244911yescharacteristic
851C22#245011yescharacteristic
852C22C22×#10211yescharacteristic
853C22C2×#41911yescharacteristic
854C22#289711yescharacteristic
855C22#289811yescharacteristic
856C22C2×#47411yescharacteristic
857C22C2×#47411yescharacteristic
858C22C2×#47511yescharacteristic
859C22C2×#47511yescharacteristic
860C22#308111yescharacteristic
861C22#308211yescharacteristic
862C22#308311yescharacteristic
863C22#308411yescharacteristic
864C22#326611yescharacteristic
865C22#327011yescharacteristic
866C22D4×D811yescharacteristic
867C22D4×SD1611yescharacteristic
868C22#329411yescharacteristic
869C22#329411yescharacteristic
870C22#329511yescharacteristic
871C22#329811yescharacteristic
872C22#331211yescharacteristic
873C22#331411yescharacteristic
874C22#331611yescharacteristic
875C22#332011yescharacteristic
876C22#333411yescharacteristic
877C22#333511yescharacteristic
878C22#334411yescharacteristic
879C22#334611yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—44no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4C4×C22⋊Q811yescharacteristic
894C4#232911yescharacteristic
895C4#236011yescharacteristic
896C4#236811yescharacteristic
897C4#244011yescharacteristic
898C4#247211yescharacteristic
899C4#248811yescharacteristic
900C4#254911yescharacteristic
901C2—28no—
902C2#1405211yescharacteristic
903C2C2×#198811yescharacteristic
904C2#2131511yescharacteristic
905C2D4×#10211yescharacteristic
906C2#2242511yescharacteristic
907C2#2248511yescharacteristic
908C2#2249711yescharacteristic
909C2#2595011yescharacteristic
910C2#2595511yescharacteristic
911C2#2598811yescharacteristic
912C2#2599211yescharacteristic
913C2#2633611yescharacteristic
914C2#2634011yescharacteristic
915C2#2640811yescharacteristic
916C2#2641211yescharacteristic
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
2. C2×#1988C2semidirect
6. #11384C2semidirect
7. #11373C2semidirect
8. #11227C2semidirect
9. #11227C2semidirect
10. #10884C2semidirect
11. #10884C2semidirect
12. #10849C2semidirect
25. #2440C4semidirect
84. C2×C4⋊Q8C2×C4semidirect
106. C22×C4⋊C4Q8semidirect
136. #389C2×C4semidirect
137. #389C2×C4semidirect
140. #384C2×C4semidirect
144. #380Q8semidirect
631. C4⋊C4C22⋊Q8semidirect
844. C22#1988semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#19882
C2×#18502
C22×#3402
C22⋊C4×C4⋊C42
#113842
#113732
#112272
#108842
#108492
#107302
#107212