Finite Group Databasebeta

← #356226

Subgroups — #356226

Order 512.

1742 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C2×#1809C211yesmaximal, characteristic
3C2×#1776C211yesmaximal, characteristic, complemented
4C2×C4×#107C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic
6#13801C211yesmaximal, characteristic
7C22⋊C4×C4⋊C4C211yesmaximal, characteristic
8#10908C211yesmaximal, characteristic, complemented
9#10908C211yesmaximal, characteristic, complemented
10#10907C211yesmaximal, characteristic, complemented
11#10907C211yesmaximal, characteristic, complemented
12#10863C211yesmaximal, characteristic, complemented
13#10861C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic
15#10730C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C2×#428—24no—
20C2×#428—24no—
21C2×#428C418yescomplemented
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4—21no—
38C2×C4×C22⋊C4C2211yescharacteristic
39#1809C418yescomplemented
40#1776—24no—
41C4×#107—24no—
42#1753C418yescomplemented
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#1437—21no—
56#1437—21no—
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
64C22⋊#95—21no—
65C4×#95—21no—
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16C2×C414yes—
73C22×M16C2×C414yes—
74C22×M16C2×C414yes—
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—41no—
83C2×#117—41no—
84C2×#117C2×C414yes—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—41no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4C2×C414yes—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4D411yescharacteristic
104C22×C22⋊C4D411yescharacteristic
105C22×C42—21no—
106C22×C42—21no—
107C22×C42—21no—
108C22×C42—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112#428—232no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107C2×C414yes—
118C2×#107C2×C414yes—
119C2×#107C2×C414yescomplemented
120C2×#107D414yes—
121C2×#107D414yes—
122C2×#106—22no—
123C2×#106—22no—
124C2×#106—22no—
125C2×#106—22no—
126C2×#106—22no—
127C2×#106—22no—
128C2×#106C2×C414yes—
129C2×#106C2×C414yes—
130C2×#106C2×C414yescomplemented
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8C2×C414yes—
134C2×#97—22no—
135C2×#97—22no—
136C2×#97C2×C414yescomplemented
137C2×C4×C8—22no—
138C2×C4×C8—22no—
139C2×C4×C8C2×C414yescomplemented
140#380—22no—
141#380—22no—
142#380C2×C414yes—
143#380C2×C414yes—
144C4×C4⋊C4—22no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—41no—
149C4×C4⋊C4—41no—
150C4×C4⋊C4—41no—
151C4×C4⋊C4—41no—
152C4×C22⋊C4—44no—
153C4×C22⋊C4C2×C414yes—
154C4×C22⋊C4Q814yes—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95D411yescharacteristic
170C2×#95D411yescharacteristic
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340C2×C414yescomplemented
180#340C2×C414yescomplemented
181#336C2×C414yescomplemented
182#336C2×C414yescomplemented
183C25C2×D411yescharacteristic
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—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—24no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—81no—
206C23×C4—81no—
207C23×C4C22×C412yes—
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×Q812yes—
216C23×C4#4112yes—
217C23×C4#4112yes—
218C23×C4C2411yescharacteristic
219C2×M16—28no—
220C2×M16—28no—
221C2×M16—28no—
222C2×M16—28no—
223C2×M16—28no—
224C2×M16—28no—
225C2×M16C42116yescomplemented
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
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×C8C22×C412yes—
243C22×C8C22×C412yes—
244C22×C8C22×C412yes—
245C22×C8C22×C412yes—
246C22×C8C22×C412yes—
247C22×C8C22×C412yes—
248C22×C8C22×C412yes—
249C22×C8C22×C412yes—
250C22×C8C2×D412yes—
251C22×C8C2×D412yes—
252C22×C8#4112yes—
253C22×C8#4112yes—
254#117—28no—
255#117—44no—
256#117—44no—
257#117—44no—
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—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—24no—
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—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4C22×C412yes—
302C2×C4⋊C4C22×C412yes—
303C2×C4⋊C4C22×C412yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—81no—
325C2×C22⋊C4—81no—
326C2×C22⋊C4C4⋊C414yes—
327C2×C22⋊C4C4⋊C414yes—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—24no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—81no—
348C2×C42—81no—
349C2×C42—81no—
350C2×C42—81no—
351C2×C42C22×C412yes—
352C2×C42C22×C412yes—
353C2×C42C2×Q812yes—
354C2×C42C2×Q812yes—
355#107—28no—
356#107—28no—
357#107C22⋊C4116yescomplemented
358#106—28no—
359#106—28no—
360#106—28no—
361C22⋊C8—28no—
362#97—28no—
363C4×C8—28no—
364#95—24no—
365#95—24no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—81no—
375#95—81no—
376#95—81no—
377#95—81no—
378#95C4⋊C414yes—
379#95C4⋊C414yes—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24C2×C4⋊C412yes—
393C24C4×D412yes—
394C24C4×D412yes—
395C24C22×D411yescharacteristic
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—22no—
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—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
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—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—48no—
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—48no—
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—84no—
505C22×C4—84no—
506C22×C4—84no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4C2×C4214yes—
510C22×C4C2×C4⋊C412yes—
511C22×C4C2×C4⋊C412yes—
512C22×C4C2×C4⋊C412yes—
513C22×C4C2×C4⋊C412yes—
514C22×C4C2×C4⋊C412yes—
515C22×C4#11714yes—
516C22×C4C4×D412yes—
517C22×C4C4×D412yes—
518C22×C4C4×Q814yes—
519C22×C4C4×Q814yes—
520C22×C4AGL(1,ℤ/8)12yes—
521C22×C4#13712yes—
522C22×C4C23×C411yescharacteristic
523C22×C4C23×C411yescharacteristic
524C22×C4C23×C411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×Q811yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4H(5,𝔽2)11yescharacteristic
533C22×C4H(5,𝔽2)11yescharacteristic
534C22×C42−1+411yescharacteristic
535C22×C42−1+411yescharacteristic
536M16—232no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8C2×C4214yes—
558C2×C8C2×C4214yes—
559C2×C8C2×C22⋊C414yes—
560C2×C8#11714yes—
561C2×C8C4×D414yes—
562C2×C8C4×D414yes—
563C2×C8C4×D414yes—
564C2×C8C4×D414yes—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
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—41no—
585C4⋊C4—41no—
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⋊C4C2×C22⋊C414yes—
597C4⋊C4C2×C22⋊C414yes—
598C22⋊C4—28no—
599C22⋊C4—44no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—84no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—48no—
612C42—84no—
613C42—84no—
614C42—84no—
615C42—84no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
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—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C4×C4⋊C414yes—
651C23C22×C4⋊C411yescharacteristic
652C23C2×C4×D411yescharacteristic
653C23C2×C4×D411yescharacteristic
654C23D4211yescharacteristic
655C23D4211yescharacteristic
656C23#54711yescharacteristic
657C23#54711yescharacteristic
658C23C2×AGL(1,ℤ/8)11yescharacteristic
659C23C2×#13711yescharacteristic
660C23#57511yescharacteristic
661C23#57511yescharacteristic
662C23#57611yescharacteristic
663C23#57711yescharacteristic
664C23#57711yescharacteristic
665C23#57811yescharacteristic
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—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
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—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
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—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—816no—
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×C4C4×C4⋊C414yes—
765C2×C4#42814yescomplemented
766C2×C4C22×C4211yescharacteristic
767C2×C4C22×C22⋊C411yescharacteristic
768C2×C4C2×#11711yescharacteristic
769C2×C4C2×#11711yescharacteristic
770C2×C4C2×C4×D411yescharacteristic
771C2×C4C2×C4×D411yescharacteristic
772C2×C4C2×C4×D411yescharacteristic
773C2×C4C2×C4×D411yescharacteristic
774C2×C4C2×C4×Q811yescharacteristic
775C2×C4C2×C4×Q811yescharacteristic
776C2×C4#51811yescharacteristic
777C2×C4#51911yescharacteristic
778C2×C4#52011yescharacteristic
779C2×C4#52011yescharacteristic
780C2×C4#52011yescharacteristic
781C2×C4#52011yescharacteristic
782C2×C4#54611yescharacteristic
783C2×C4#54611yescharacteristic
784C2×C4#54811yescharacteristic
785C2×C4#54811yescharacteristic
786C2×C4D4×Q811yescharacteristic
787C2×C4D4×Q811yescharacteristic
788C2×C4#55211yescharacteristic
789C2×C4#55211yescharacteristic
790C2×C4#55311yescharacteristic
791C2×C4#55311yescharacteristic
792C2×C4#55411yescharacteristic
793C2×C4#55411yescharacteristic
794C8—24no—
795C8—42no—
796C8—42no—
797C8C4×C22⋊C418yescomplemented
798C22—24no—
799C22—24no—
800C22—24no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22C2×C4×C4⋊C411yescharacteristic
814C22D4×C22⋊C411yescharacteristic
815C22#234411yescharacteristic
816C22D4×C4⋊C411yescharacteristic
817C22D4×C4⋊C411yescharacteristic
818C22#236111yescharacteristic
819C22#236111yescharacteristic
820C22C2×#42811yescharacteristic
821C22#291111yescharacteristic
822C22#291211yescharacteristic
823C22#291311yescharacteristic
824C22C4×AGL(1,ℤ/8)11yescharacteristic
825C22C4×AGL(1,ℤ/8)11yescharacteristic
826C22C4×#13711yescharacteristic
827C22C4×#13711yescharacteristic
828C22#294611yescharacteristic
829C22#294611yescharacteristic
830C22#294711yescharacteristic
831C22#294711yescharacteristic
832C22#326411yescharacteristic
833C22#326711yescharacteristic
834C22#327011yescharacteristic
835C22#327111yescharacteristic
836C22#327211yescharacteristic
837C22#327311yescharacteristic
838C22#327711yescharacteristic
839C22#327811yescharacteristic
840C22#334311yescharacteristic
841C22#334611yescharacteristic
842C22#334811yescharacteristic
843C22#335011yescharacteristic
844C22#335211yescharacteristic
845C22#335411yescharacteristic
846C22#335511yescharacteristic
847C22#335611yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—44no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4C2×C4×C22⋊C411yescharacteristic
862C4#227411yescharacteristic
863C4Q8×C22⋊C411yescharacteristic
864C4#234511yescharacteristic
865C4#235211yescharacteristic
866C4#235211yescharacteristic
867C4#236011yescharacteristic
868C4#236011yescharacteristic
869C2—44no—
870C2C22⋊C4×C4⋊C411yescharacteristic
871C2C4×#42811yescharacteristic
872C2#2045311yescharacteristic
873C2#2244211yescharacteristic
874C2#2244511yescharacteristic
875C2#2262311yescharacteristic
876C2#2262411yescharacteristic
877C2#2266111yescharacteristic
878C2#2266211yescharacteristic
879C2#2266311yescharacteristic
880C2#2266411yescharacteristic
881C2#2303611yescharacteristic
882C2#2303711yescharacteristic
883C2#2304011yescharacteristic
884C2#2304111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C2×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
3. C2×#1776C2semidirect
4. C2×C4×#107C2semidirect
8. #10908C2semidirect
9. #10908C2semidirect
10. #10907C2semidirect
11. #10907C2semidirect
12. #10863C2semidirect
13. #10861C2semidirect
21. C2×#428C4semidirect
39. #1809C4semidirect
42. #1753C4semidirect
119. C2×#107C2×C4semidirect
130. C2×#106C2×C4semidirect
136. C2×#97C2×C4semidirect
139. C2×C4×C8C2×C4semidirect
179. #340C2×C4semidirect
180. #340C2×C4semidirect
181. #336C2×C4semidirect
182. #336C2×C4semidirect
225. C2×M16C42semidirect
357. #107C22⋊C4semidirect
765. C2×C4#428semidirect
797. C8C4×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#18092
C2×#17762
C2×C4×#1072
C2×#17532
#138012
C22⋊C4×C4⋊C42
#109082
#109072
#108632
#108612
#107312
#107302