Finite Group Databasebeta

← #370514

Subgroups — #370514

Order 512.

1636 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2439C211yesmaximal, characteristic
2C2×#1987C211yesmaximal, characteristic, complemented
3C2×#1851C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5C22⋊C4×C4⋊C4C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic, complemented
7#11372C211yesmaximal, characteristic, complemented
8#11228C211yesmaximal, characteristic, complemented
9#11227C211yesmaximal, characteristic, complemented
10#10884C211yesmaximal, characteristic, complemented
11#10884C211yesmaximal, characteristic, complemented
12#10850C211yesmaximal, characteristic, complemented
13#10731C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10722C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23#2439—24no—
24#2439C418yescomplemented
25C2×#396—21no—
26C2×#393—21no—
27C2×#391—21no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#387—21no—
31C2×#382C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4—21no—
37C2×C4×C22⋊C4C2211yescharacteristic
38#1987—24no—
39#1851—24no—
40#1736—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×C4C2311yescharacteristic
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—41no—
73C22×M16—41no—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4⋊Q8—22no—
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—41no—
82C2×C4⋊Q8—41no—
83C2×C4⋊Q8C2×C414yescomplemented
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—41no—
88C2×#117—41no—
89C2×#117C2×C414yes—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—41no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4Q814yescomplemented
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4D411yescharacteristic
112C22×C22⋊C4D411yescharacteristic
113C22×C42—21no—
114C22×C42—21no—
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—41no—
123C2×C4⋊C8—41no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127#396—28no—
128#393—28no—
129#391—28no—
130#389—22no—
131#389—22no—
132#389C2×C414yescomplemented
133#389C2×C414yescomplemented
134#387—28no—
135#382—22no—
136#382C2×C414yescomplemented
137#380—22no—
138#380—22no—
139#380C2×C414yes—
140#380Q814yescomplemented
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—41no—
144C4×C4⋊C4—41no—
145C4×C22⋊C4—44no—
146C4×C22⋊C4C2×C414yes—
147C4×C22⋊C4D414yes—
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—22no—
169#340—22no—
170#340—22no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340D414yes—
178#336—22no—
179#336—22no—
180C25C2×D411yescharacteristic
181C22×Q8—24no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—42no—
185C22×Q8—42no—
186C22×Q8—81no—
187C22×Q8—81no—
188C23×C4—21no—
189C23×C4—21no—
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—24no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4—81no—
210C23×C4—81no—
211C23×C4C22×C412yes—
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D412yes—
218C23×C4C2×Q812yes—
219C23×C4C2×Q812yes—
220C23×C4#4112yes—
221C23×C4#4112yes—
222C23×C4C2411yescharacteristic
223C2×M16—28no—
224C2×M16—44no—
225C2×M16—44no—
226C2×M16—44no—
227C2×M16—44no—
228C2×M16—44no—
229C2×M16—44no—
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—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×C8C2×D412yes—
257C22×C8#4112yes—
258C4⋊Q8—28no—
259C4⋊Q8—44no—
260C4⋊Q8—44no—
261C4⋊Q8—44no—
262#117—28no—
263#117—44no—
264#117—44no—
265#117—44no—
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—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
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—24no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—81no—
317C2×C4⋊C4—81no—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C22×C412yes—
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4C2×D412yes—
324C2×C4⋊C4C2×Q812yes—
325C2×C4⋊C4C2×Q812yes—
326C2×C4⋊C4C2×Q812yes—
327C2×C4⋊C4C2×Q812yes—
328C2×C4⋊C4#4112yes—
329C2×C4⋊C4#4112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—81no—
342C2×C22⋊C4—81no—
343C2×C22⋊C4C22⋊C414yes—
344C2×C22⋊C4C22⋊C414yes—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—81no—
361C2×C42—81no—
362C2×C42C22×C412yes—
363C2×C42C22×C412yes—
364C2×C42C2×D412yes—
365C2×C42C2×D412yes—
366C4⋊C8—44no—
367C4⋊C8—44no—
368C22⋊C8—44no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—81no—
380#95—81no—
381#95C22⋊C414yes—
382#95C22⋊C414yes—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24C2×C22⋊C412yes—
396C24C22⋊Q812yes—
397C24C22⋊Q812yes—
398C24C22×D411yescharacteristic
399C2×Q8—48no—
400C2×Q8—48no—
401C2×Q8—84no—
402C2×Q8—84no—
403C2×Q8—84no—
404C2×Q8—84no—
405C2×Q8—84no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
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—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
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—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—48no—
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—48no—
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—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—84no—
515C22×C4—84no—
516C22×C4—84no—
517C22×C4—84no—
518C22×C4—84no—
519C22×C4C2×C22⋊C412yes—
520C22×C4C2×C22⋊C412yes—
521C22×C4C2×C22⋊C412yes—
522C22×C4C2×C22⋊C412yes—
523C22×C4C2×C22⋊C412yes—
524C22×C4C4×Q814yes—
525C22×C4C4×Q814yes—
526C22×C4C22⋊Q812yes—
527C22×C4C22⋊Q812yes—
528C22×C4#12414yes—
529C22×C4C4⋊Q814yes—
530C22×C4AGL(1,ℤ/8)12yes—
531C22×C4#13712yes—
532C22×C4C23×C411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×Q811yescharacteristic
536C22×C4C22×Q811yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4H(5,𝔽2)11yescharacteristic
543C22×C4H(5,𝔽2)11yescharacteristic
544C22×C4H(5,𝔽2)11yescharacteristic
545C22×C42−1+411yescharacteristic
546M16—416no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—48no—
608C4⋊C4—84no—
609C4⋊C4C4×D414yes—
610C4⋊C4C22⋊Q814yes—
611C22⋊C4—28no—
612C22⋊C4—44no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—84no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—48no—
625C42—84no—
626C42—84no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23#39114yes—
662C23C22×C22⋊C411yescharacteristic
663C23C2×C22⋊Q811yescharacteristic
664C23C2×C22⋊Q811yescharacteristic
665C23D4211yescharacteristic
666C23#54611yescharacteristic
667C23#54611yescharacteristic
668C23#54711yescharacteristic
669C23C2×AGL(1,ℤ/8)11yescharacteristic
670C23C2×#13711yescharacteristic
671C23#57511yescharacteristic
672C23#57511yescharacteristic
673C23#57611yescharacteristic
674C23#57711yescharacteristic
675C23#57711yescharacteristic
676C23#57811yescharacteristic
677Q8—816no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
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—24no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—816no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4#39114yes—
777C2×C4#41714yes—
778C2×C4C2×C4×D411yescharacteristic
779C2×C4C2×C4×Q811yescharacteristic
780C2×C4C2×C4×Q811yescharacteristic
781C2×C4C4×#4111yescharacteristic
782C2×C4#51811yescharacteristic
783C2×C4#52011yescharacteristic
784C2×C4C2×C22⋊Q811yescharacteristic
785C2×C4#52511yescharacteristic
786C2×C4C2×#12411yescharacteristic
787C2×C4#52911yescharacteristic
788C2×C4C2×C4⋊Q811yescharacteristic
789C2×C4#53311yescharacteristic
790C2×C4#53811yescharacteristic
791C2×C4#53911yescharacteristic
792C2×C4#54311yescharacteristic
793C2×C4#54411yescharacteristic
794C2×C4D4211yescharacteristic
795C2×C4#54611yescharacteristic
796C2×C4#54611yescharacteristic
797C2×C4#54611yescharacteristic
798C2×C4#54711yescharacteristic
799C2×C4D4×Q811yescharacteristic
800C2×C4#55111yescharacteristic
801C2×C4#55111yescharacteristic
802C2×C4#55211yescharacteristic
803C2×C4#55411yescharacteristic
804C2×C4#55411yescharacteristic
805C2×C4#55411yescharacteristic
806C8—42no—
807C8—42no—
808C8—81no—
809C8—81no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22C2×#39111yescharacteristic
826C22D4×C22⋊C411yescharacteristic
827C22#233911yescharacteristic
828C22#243711yescharacteristic
829C22#243811yescharacteristic
830C22#244911yescharacteristic
831C22#245011yescharacteristic
832C22C2×#41711yescharacteristic
833C22#289611yescharacteristic
834C22#289711yescharacteristic
835C22#289811yescharacteristic
836C22#307711yescharacteristic
837C22#307711yescharacteristic
838C22#307811yescharacteristic
839C22#307811yescharacteristic
840C22#308111yescharacteristic
841C22#308211yescharacteristic
842C22#308311yescharacteristic
843C22#308411yescharacteristic
844C22#326511yescharacteristic
845C22#327011yescharacteristic
846C22#327311yescharacteristic
847C22#327511yescharacteristic
848C22#330811yescharacteristic
849C22#331111yescharacteristic
850C22#331311yescharacteristic
851C22#331611yescharacteristic
852C22#332211yescharacteristic
853C22#332311yescharacteristic
854C22#332511yescharacteristic
855C22#332911yescharacteristic
856C22#334911yescharacteristic
857C22#335011yescharacteristic
858C22#335411yescharacteristic
859C22#335711yescharacteristic
860C4—24no—
861C4—24no—
862C4—44no—
863C4—42no—
864C4—44no—
865C4—42no—
866C4—42no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4C4×C22⋊Q811yescharacteristic
874C4#232911yescharacteristic
875C4#236011yescharacteristic
876C4#236811yescharacteristic
877C4#244011yescharacteristic
878C4#247211yescharacteristic
879C4#248811yescharacteristic
880C4#254911yescharacteristic
881C2—44no—
882C2#1405211yescharacteristic
883C2#2131211yescharacteristic
884C2#2131511yescharacteristic
885C2#2242111yescharacteristic
886C2#2242711yescharacteristic
887C2#2249411yescharacteristic
888C2#2250311yescharacteristic
889C2#2597411yescharacteristic
890C2#2597911yescharacteristic
891C2#2600611yescharacteristic
892C2#2601011yescharacteristic
893C2#2635411yescharacteristic
894C2#2635811yescharacteristic
895C2#2642611yescharacteristic
896C2#2643011yescharacteristic
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×#1987C2semidirect
6. #11384C2semidirect
7. #11372C2semidirect
8. #11228C2semidirect
9. #11227C2semidirect
10. #10884C2semidirect
11. #10884C2semidirect
12. #10850C2semidirect
24. #2439C4semidirect
83. C2×C4⋊Q8C2×C4semidirect
99. C22×C4⋊C4Q8semidirect
132. #389C2×C4semidirect
133. #389C2×C4semidirect
136. #382C2×C4semidirect
140. #380Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24392
C2×#19872
C2×#18512
C2×#17362
C22⋊C4×C4⋊C42
#113842
#113722
#112282
#112272
#108842
#108502
#107312
#107302
#107222