Finite Group Databasebeta

← #370500

Subgroups — #370500

Order 512.

1596 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic
2C2×#1997C211yesmaximal, characteristic, complemented
3#20837C211yesmaximal, characteristic
4C22⋊C4×M16C211yesmaximal, characteristic
5C22×#343C211yesmaximal, characteristic
6#11382C211yesmaximal, characteristic, complemented
7#11354C211yesmaximal, characteristic, complemented
8#11204C211yesmaximal, characteristic, complemented
9#11204C211yesmaximal, characteristic, complemented
10#10913C211yesmaximal, characteristic, complemented
11#10913C211yesmaximal, characteristic, complemented
12#10857C211yesmaximal, characteristic, complemented
13#10739C211yesmaximal, characteristic
14#10739C211yesmaximal, characteristic
15#10727C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C412yes—
20C23×C4⋊C4C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C2×#407C2211yescharacteristic
24C2×#407C2211yescharacteristic
25C2×C4×M16C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27#2440—21no—
28#2440—21no—
29#2440—21no—
30#2440—21no—
31#2440—21no—
32#2440—21no—
33#2440—21no—
34#2440—21no—
35C2×#398C412yes—
36C2×#395C412yes—
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#385C412yes—
40C2×#384C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#1997—24no—
44#1851—21no—
45#1851—21no—
46#1850—21no—
47#1850—21no—
48#1753—21no—
49#1753—21no—
50#1752—21no—
51C8×C22⋊C4—21no—
52C2×#343—24no—
53C2×#343C2211yescharacteristic
54C2×#343C2211yescharacteristic
55C2×#343C2211yescharacteristic
56C2×#343C2211yescharacteristic
57C2×#343C2211yescharacteristic
58C2×#343C2211yescharacteristic
59C2×#343C2211yescharacteristic
60C2×#343C2211yescharacteristic
61C2×#343C2211yescharacteristic
62C2×#343C2211yescharacteristic
63C2×#343C2211yescharacteristic
64C2×#343C2211yescharacteristic
65C2×#343C2211yescharacteristic
66C2×#343C2211yescharacteristic
67C2×#343C2211yescharacteristic
68C2×#343C2211yescharacteristic
69#1728C2211yescharacteristic
70#1728C2211yescharacteristic
71#1728C2211yescharacteristic
72#1728C2211yescharacteristic
73C23×Q8C2×C412yes—
74C24×C4C2×C412yes—
75C24×C4C2311yescharacteristic
76C22×M16—21no—
77C22×M16—22no—
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—41no—
86C22×M16—41no—
87C22×M16—41no—
88C22×M16—41no—
89C22×M16Q814yescomplemented
90C22×M16C2311yescharacteristic
91C22×M16C2311yescharacteristic
92C22×M16C2311yescharacteristic
93C22×M16C2311yescharacteristic
94C22×M16C2311yescharacteristic
95C22×M16C2311yescharacteristic
96C22×M16C2311yescharacteristic
97C22×M16C2311yescharacteristic
98C23×C8—21no—
99C23×C8—21no—
100C2×C4⋊Q8—22no—
101C2×C4⋊Q8—22no—
102C2×C4⋊Q8—21no—
103C2×C4⋊Q8—21no—
104C2×C4⋊Q8—21no—
105C2×C4⋊Q8—21no—
106C2×C4⋊Q8—41no—
107C2×C4⋊Q8—41no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—48no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—22no—
119C22×C4⋊C4—41no—
120C22×C4⋊C4—41no—
121C22×C4⋊C4C2×C412yes—
122C22×C4⋊C4C2×C412yes—
123C22×C4⋊C4C2×C412yes—
124C22×C4⋊C4C2×C412yes—
125C22×C4⋊C4C2×C412yes—
126C22×C4⋊C4C2×C412yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4C2×C411yescharacteristic
132C22×C22⋊C4C2×C411yescharacteristic
133C22×C22⋊C4C2×C412yes—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#423—22no—
137#423—22no—
138#423—41no—
139#423—41no—
140C2×C4⋊C8—21no—
141C2×C4⋊C8—21no—
142C2×C4⋊C8—21no—
143C2×C4⋊C8—21no—
144#407—22no—
145#407—22no—
146#407—22no—
147#407Q814yescomplemented
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C4×M16—22no—
153C4×M16—22no—
154C4×M16—41no—
155C4×M16—41no—
156C2×#97—21no—
157C2×#97—21no—
158C2×C4×C8—21no—
159C2×C4×C8—21no—
160#398—22no—
161#398—22no—
162#398—22no—
163#398—22no—
164#395—22no—
165#395—22no—
166#395—22no—
167#395—22no—
168#389—21no—
169#389—21no—
170#389—21no—
171#389—21no—
172#389—21no—
173#389—21no—
174#389—21no—
175#389—21no—
176#385—22no—
177#385—22no—
178#385—22no—
179#385—22no—
180#384—21no—
181#384—21no—
182#384—21no—
183#384—21no—
184#380—21no—
185#380—21no—
186#380—21no—
187#380—21no—
188C4×C22⋊C4D411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C2×#95C2×C412yes—
197C2×#95C2×C412yes—
198C2×#95C2×C412yes—
199C2×#95C2×C411yescharacteristic
200C2×#95C2×C411yescharacteristic
201#343—22no—
202#343—22no—
203#343—22no—
204#343—22no—
205#343—22no—
206#343—22no—
207#343—22no—
208#343—22no—
209#343—22no—
210#343—41no—
211#343—41no—
212#343—41no—
213#343—41no—
214#343—41no—
215#343—41no—
216#343D414yes—
217#336—21no—
218#336—21no—
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225C25C22×C411yescharacteristic
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—24no—
229C22×Q8—42no—
230C22×Q8—44no—
231C22×Q8—82no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—42no—
244C23×C4—44no—
245C23×C4—82no—
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C22×C412yes—
252C23×C4C22×C412yes—
253C23×C4C22×C412yes—
254C23×C4C22×C412yes—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×Q812yes—
260C23×C4C2×Q812yes—
261C23×C4#4112yes—
262C23×C4#4112yes—
263C23×C4C2411yescharacteristic
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—24no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—28no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—28no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—21no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—21no—
307C2×M16—42no—
308C2×M16—42no—
309C2×M16—42no—
310C2×M16—42no—
311C2×M16—44no—
312C2×M16—44no—
313C2×M16—44no—
314C2×M16—44no—
315C2×M16—44no—
316C2×M16—44no—
317C2×M16—42no—
318C2×M16C2×D412yes—
319C2×M16C2×D412yes—
320C2×M16C2×Q812yes—
321C2×M16C2×Q812yes—
322C2×M16C2×Q812yes—
323C2×M16C2×Q812yes—
324C2×M16#4112yes—
325C2×M16#4112yes—
326C22×C8—21no—
327C22×C8—24no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—42no—
336C22×C8—42no—
337C22×C8—42no—
338C22×C8—42no—
339C22×C8—42no—
340C4⋊Q8—42no—
341C4⋊Q8—42no—
342C4⋊Q8—42no—
343C4⋊Q8—42no—
344C4⋊Q8—42no—
345C4⋊Q8—42no—
346C4⋊Q8—42no—
347C4⋊Q8—42no—
348C22⋊Q8—48no—
349C22⋊Q8—48no—
350C22⋊Q8—48no—
351C22⋊Q8—48no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—82no—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4#4112yes—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4C22⋊C411yescharacteristic
410C2×C22⋊C4C22⋊C411yescharacteristic
411C2×C22⋊C4C22⋊C411yescharacteristic
412C2×C22⋊C4C22⋊C411yescharacteristic
413C2×C22⋊C4C22⋊C411yescharacteristic
414C2×C22⋊C4C22⋊C411yescharacteristic
415C2×C22⋊C4C22⋊C411yescharacteristic
416C2×C22⋊C4C22⋊C411yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C4⋊C8—42no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436C4⋊C8—42no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—42no—
440C22⋊C8—42no—
441#97—42no—
442#97—42no—
443C4×C8—42no—
444C4×C8—42no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95C22⋊C411yescharacteristic
452#95C22⋊C411yescharacteristic
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—41no—
466C24—41no—
467C24C2×C22⋊C411yescharacteristic
468C24C2×C22⋊C411yescharacteristic
469C24C4×Q812yes—
470C24C4×Q812yes—
471C24C23×C411yescharacteristic
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—82no—
477C2×Q8—82no—
478C2×Q8—88no—
479C2×Q8—88no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C411yescharacteristic
561C22×C4C2×C22⋊C411yescharacteristic
562C22×C4C2×C22⋊C411yescharacteristic
563C22×C4C2×C22⋊C411yescharacteristic
564C22×C4C2×C22⋊C411yescharacteristic
565C22×C4C2×C22⋊C411yescharacteristic
566C22×C4C2×C22⋊C411yescharacteristic
567C22×C4C2×C22⋊C411yescharacteristic
568C22×C4C2×C22⋊C411yescharacteristic
569C22×C4C4×D414yes—
570C22×C4C4×Q812yes—
571C22×C4C4×Q812yes—
572C22×C4C22⋊Q812yes—
573C22×C4C22⋊Q812yes—
574C22×C4C22⋊Q812yes—
575C22×C4C22⋊Q812yes—
576C22×C4#12412yes—
577C22×C4#12412yes—
578C22×C4C4⋊Q812yes—
579C22×C4C4⋊Q812yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×Q811yescharacteristic
584C22×C4C22×Q811yescharacteristic
585C22×C4C2×#4111yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C4H(5,𝔽2)11yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C42−1+411yescharacteristic
594M16—22no—
595M16—22no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—22no—
607M16—48no—
608M16—48no—
609M16—41no—
610M16—41no—
611M16—41no—
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—41no—
617M16—41no—
618M16—41no—
619M16—41no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—41no—
625M16—41no—
626M16—41no—
627M16C22⋊Q814yescomplemented
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—48no—
637C2×C8—48no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4#10014yes—
691C22⋊C4#10114yes—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—24no—
726C23—24no—
727C23—22no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23#39112yes—
739C23#39112yes—
740C23C2×#10012yes—
741C23C2×#10112yes—
742C23C22×C22⋊C411yescharacteristic
743C23C2×C4×D411yescharacteristic
744C23C2×C4×Q811yescharacteristic
745C23C2×C4×Q811yescharacteristic
746C23C4×#4111yescharacteristic
747C23#51811yescharacteristic
748C23#52011yescharacteristic
749Q8—88no—
750Q8—88no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—24no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—88no—
818C2×C4—88no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—82no—
824C2×C4—82no—
825C2×C4#39112yes—
826C2×C4#39112yes—
827C2×C4C2×#10012yes—
828C2×C4C2×#10012yes—
829C2×C4C2×#10112yes—
830C2×C4C2×#10112yes—
831C2×C4C2×C22⋊Q811yescharacteristic
832C2×C4C2×C22⋊Q811yescharacteristic
833C2×C4C2×C22⋊Q811yescharacteristic
834C2×C4#52511yescharacteristic
835C2×C4C2×#12411yescharacteristic
836C2×C4#52911yescharacteristic
837C2×C4C2×C4⋊Q811yescharacteristic
838C2×C4#53311yescharacteristic
839C2×C4#53811yescharacteristic
840C2×C4#53911yescharacteristic
841C2×C4#54311yescharacteristic
842C2×C4#54411yescharacteristic
843C2×C4D4211yescharacteristic
844C2×C4D4211yescharacteristic
845C2×C4#54611yescharacteristic
846C2×C4#54611yescharacteristic
847C2×C4#54611yescharacteristic
848C2×C4#54611yescharacteristic
849C2×C4#54611yescharacteristic
850C2×C4#54711yescharacteristic
851C2×C4#54711yescharacteristic
852C2×C4D4×Q811yescharacteristic
853C2×C4#55111yescharacteristic
854C2×C4#55111yescharacteristic
855C2×C4#55211yescharacteristic
856C2×C4#55411yescharacteristic
857C2×C4#55411yescharacteristic
858C2×C4#55411yescharacteristic
859C8—24no—
860C8—42no—
861C8—42no—
862C8—42no—
863C8—42no—
864C8—42no—
865C8—81no—
866C8—81no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—21no—
873C22—21no—
874C22—22no—
875C22—21no—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—21no—
880C22—22no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22#199714yescomplemented
897C22C2×#39111yescharacteristic
898C22C4×C22⋊Q811yescharacteristic
899C22#232911yescharacteristic
900C22D4×C22⋊C411yescharacteristic
901C22#233911yescharacteristic
902C22#236011yescharacteristic
903C22#236811yescharacteristic
904C22C22×#10011yescharacteristic
905C22C22×#10111yescharacteristic
906C22#288811yescharacteristic
907C22#288911yescharacteristic
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—22no—
913C4—22no—
914C4—41no—
915C4—44no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4#243711yescharacteristic
923C4#243811yescharacteristic
924C4#244011yescharacteristic
925C4#244911yescharacteristic
926C4#245011yescharacteristic
927C4#247211yescharacteristic
928C4#248811yescharacteristic
929C4#254911yescharacteristic
930C2—21no—
931C2—21no—
932C2—21no—
933C2—24no—
934C2—21no—
935C2—42no—
936C2#1405211yescharacteristic
937C2C2×#199711yescharacteristic
938C2#2133811yescharacteristic
939C2D4×#10011yescharacteristic
940C2D4×#10111yescharacteristic
941C2#2247911yescharacteristic
942C2#2248111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ 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×#1997C2semidirect
6. #11382C2semidirect
7. #11354C2semidirect
8. #11204C2semidirect
9. #11204C2semidirect
10. #10913C2semidirect
11. #10913C2semidirect
12. #10857C2semidirect
89. C22×M16Q8semidirect
147. #407Q8semidirect
627. M16C22⋊Q8semidirect
896. C22#1997semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#19972
#208372
C22⋊C4×M162
C22×#3432
#113822
#113542
#112042
#109132
#108572
#107392
#107272