Finite Group Databasebeta

← #370495

Subgroups — #370495

Order 512.

1580 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2439C211yesmaximal, characteristic
2C2×#1993C211yesmaximal, characteristic, complemented
3C2×#1753C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5#13881C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic, complemented
7#11358C211yesmaximal, characteristic, complemented
8#11208C211yesmaximal, characteristic, complemented
9#11208C211yesmaximal, characteristic, complemented
10#10881C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10842C211yesmaximal, characteristic, complemented
13#10731C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10722C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×#97C2211yescharacteristic
22C22×C4×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×#382C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1993—24no—
38#1753—24no—
39#1736—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×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1442—21no—
59#1442—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—21no—
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—41no—
72C22×M16—41no—
73C22×M16Q814yescomplemented
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—22no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—41no—
99C22×C4⋊C4—41no—
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×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8Q814yescomplemented
119C2×#97—22no—
120C2×#97—22no—
121C2×#97—41no—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8—41no—
125#396—28no—
126#393—28no—
127#391—28no—
128#389—22no—
129#389—22no—
130#389C2×C414yescomplemented
131#389C2×C414yescomplemented
132#387—28no—
133#382—22no—
134#382—22no—
135#382—22no—
136#382—41no—
137#382—41no—
138#382C2×C414yescomplemented
139#380—22no—
140#380—22no—
141#380—22no—
142#380C2×C414yes—
143C4×C22⋊C4C2×C414yes—
144C4×C22⋊C4D414yes—
145C2×#95—21no—
146C2×#95—21no—
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×#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—22no—
169#340—22no—
170#340—41no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340D414yes—
177#336—22no—
178#336—22no—
179C25C2×D411yescharacteristic
180C22×Q8—24no—
181C22×Q8—42no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—42no—
185C22×Q8—81no—
186C22×Q8—81no—
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—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4—81no—
209C23×C4—81no—
210C23×C4C22×C412yes—
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D412yes—
217C23×C4C2×Q812yes—
218C23×C4C2×Q812yes—
219C23×C4#4112yes—
220C23×C4#4112yes—
221C23×C4C2411yescharacteristic
222C2×M16—28no—
223C2×M16—28no—
224C2×M16—44no—
225C2×M16—44no—
226C2×M16—44no—
227C2×M16—44no—
228C2×M16—44no—
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—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8C2×D412yes—
252C22×C8C2×Q812yes—
253C22×C8C2×Q812yes—
254C22×C8C2×Q812yes—
255C22×C8C2×Q812yes—
256C22×C8#4112yes—
257C4⋊Q8—28no—
258C4⋊Q8—44no—
259C4⋊Q8—44no—
260C4⋊Q8—44no—
261#117—28no—
262#117—44no—
263#117—44no—
264#117—44no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—28no—
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—24no—
290C2×C4⋊C4—24no—
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—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—81no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C22×C412yes—
323C2×C4⋊C4C22×C412yes—
324C2×C4⋊C4C22×C412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4C2×D412yes—
327C2×C4⋊C4#4112yes—
328C2×C4⋊C4#4112yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—81no—
341C2×C22⋊C4—81no—
342C2×C22⋊C4C22⋊C414yes—
343C2×C22⋊C4C22⋊C414yes—
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—24no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42C22×C412yes—
356C2×C42C22×C412yes—
357C2×C42C2×D412yes—
358C2×C42C2×D412yes—
359C22⋊C8—28no—
360#97—44no—
361C4×C8—44no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—81no—
373#95—81no—
374#95—81no—
375#95—81no—
376#95C22⋊C414yes—
377#95C22⋊C414yes—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24C2×C22⋊C412yes—
391C24#12412yes—
392C24C4⋊Q812yes—
393C24C22×D411yescharacteristic
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—84no—
397C2×Q8—84no—
398C2×Q8—84no—
399C2×Q8—84no—
400C2×Q8—84no—
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—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—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
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—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—48no—
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—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—84no—
511C22×C4—84no—
512C22×C4—84no—
513C22×C4—84no—
514C22×C4—84no—
515C22×C4—84no—
516C22×C4C2×C22⋊C412yes—
517C22×C4C2×C22⋊C412yes—
518C22×C4C2×C22⋊C412yes—
519C22×C4C2×C22⋊C412yes—
520C22×C4C2×C22⋊C412yes—
521C22×C4C4×Q814yes—
522C22×C4C4×Q814yes—
523C22×C4C22⋊Q814yes—
524C22×C4C22⋊Q814yes—
525C22×C4#12412yes—
526C22×C4C4⋊Q812yes—
527C22×C4C23×C411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×Q811yescharacteristic
531C22×C4C22×Q811yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C4H(5,𝔽2)11yescharacteristic
539C22×C4H(5,𝔽2)11yescharacteristic
540C22×C42−1+411yescharacteristic
541M16—416no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
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×C8C22⋊Q814yes—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
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—48no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
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—84no—
605C4⋊C4C4×D414yes—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—48no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23#39114yes—
655C23C22×C22⋊C411yescharacteristic
656C23C2×#12411yescharacteristic
657C23C2×C4⋊Q811yescharacteristic
658C23D4211yescharacteristic
659C23#54611yescharacteristic
660C23#54611yescharacteristic
661C23#54711yescharacteristic
662C23#57511yescharacteristic
663C23#57511yescharacteristic
664C23#57511yescharacteristic
665C23#57511yescharacteristic
666C23#57611yescharacteristic
667C23#57711yescharacteristic
668C23#57711yescharacteristic
669C23#57811yescharacteristic
670Q8—816no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—816no—
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×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#39114yes—
771C2×C4C2×C4×D411yescharacteristic
772C2×C4C2×C4×Q811yescharacteristic
773C2×C4C2×C4×Q811yescharacteristic
774C2×C4C4×#4111yescharacteristic
775C2×C4#51811yescharacteristic
776C2×C4#52011yescharacteristic
777C2×C4C2×C22⋊Q811yescharacteristic
778C2×C4C2×C22⋊Q811yescharacteristic
779C2×C4C2×C22⋊Q811yescharacteristic
780C2×C4#52511yescharacteristic
781C2×C4#52911yescharacteristic
782C2×C4#53311yescharacteristic
783C2×C4#53811yescharacteristic
784C2×C4#53911yescharacteristic
785C2×C4#54311yescharacteristic
786C2×C4#54411yescharacteristic
787C2×C4D4211yescharacteristic
788C2×C4#54611yescharacteristic
789C2×C4#54611yescharacteristic
790C2×C4#54611yescharacteristic
791C2×C4#54711yescharacteristic
792C2×C4D4×Q811yescharacteristic
793C2×C4#55111yescharacteristic
794C2×C4#55111yescharacteristic
795C2×C4#55211yescharacteristic
796C2×C4#55411yescharacteristic
797C2×C4#55411yescharacteristic
798C2×C4#55411yescharacteristic
799C8—24no—
800C8—42no—
801C8—42no—
802C8—42no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22C2×#39111yescharacteristic
819C22D4×C22⋊C411yescharacteristic
820C22#233911yescharacteristic
821C22#244011yescharacteristic
822C22#247211yescharacteristic
823C22#248811yescharacteristic
824C22#254911yescharacteristic
825C22#289611yescharacteristic
826C22#289611yescharacteristic
827C22#289711yescharacteristic
828C22#289811yescharacteristic
829C22#313611yescharacteristic
830C22#313711yescharacteristic
831C22#314011yescharacteristic
832C22#314011yescharacteristic
833C22#316311yescharacteristic
834C22#316411yescharacteristic
835C22#316611yescharacteristic
836C22#316611yescharacteristic
837C22#327311yescharacteristic
838C22#327511yescharacteristic
839C22#327511yescharacteristic
840C22#327711yescharacteristic
841C22#331111yescharacteristic
842C22#331311yescharacteristic
843C22#331911yescharacteristic
844C22#332111yescharacteristic
845C22#332211yescharacteristic
846C22#332311yescharacteristic
847C22#332611yescharacteristic
848C22#332711yescharacteristic
849C22#334711yescharacteristic
850C22#334811yescharacteristic
851C22#334911yescharacteristic
852C22#335011yescharacteristic
853C4—24no—
854C4—42no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—161no—
865C4—161no—
866C4C4×C22⋊Q811yescharacteristic
867C4#232911yescharacteristic
868C4#236011yescharacteristic
869C4#236811yescharacteristic
870C4#243711yescharacteristic
871C4#243811yescharacteristic
872C4#244911yescharacteristic
873C4#245011yescharacteristic
874C2—44no—
875C2#1405211yescharacteristic
876C2#2132311yescharacteristic
877C2#2132611yescharacteristic
878C2#2242711yescharacteristic
879C2#2242911yescharacteristic
880C2#2249211yescharacteristic
881C2#2249411yescharacteristic
882C2#2607611yescharacteristic
883C2#2607911yescharacteristic
884C2#2728111yescharacteristic
885C2#2728511yescharacteristic
886C2#2770311yescharacteristic
887C2#2770511yescharacteristic
888C2#2878511yescharacteristic
889C2#2878711yescharacteristic
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×#1993C2semidirect
6. #11384C2semidirect
7. #11358C2semidirect
8. #11208C2semidirect
9. #11208C2semidirect
10. #10881C2semidirect
11. #10880C2semidirect
12. #10842C2semidirect
24. #2439C4semidirect
73. C22×M16Q8semidirect
83. C2×C4⋊Q8C2×C4semidirect
118. C2×C22⋊C8Q8semidirect
130. #389C2×C4semidirect
131. #389C2×C4semidirect
138. #382C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24392
C2×#19932
C2×#17532
C2×#17362
#138812
#113842
#113582
#112082
#108812
#108802
#108422
#107312
#107302
#107222