Finite Group Databasebeta

← #219853

Subgroups — #219853

Order 512.

1331 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36130C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic
3C2×#1503C211yesmaximal, characteristic, complemented
4C22×#328C211yesmaximal, characteristic
5#13814C211yesmaximal, characteristic
6#9711C211yesmaximal, characteristic, complemented
7#9679C211yesmaximal, characteristic, complemented
8#9144C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic
10#9112C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic
12#8578C211yesmaximal, characteristic, complemented
13#8333C211yesmaximal, characteristic, complemented
14#8329C211yesmaximal, characteristic
15C4×#328C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20#2857C2211yescharacteristic
21#2855C2211yescharacteristic
22#2848C2211yescharacteristic
23#2556—21no—
24#2549—21no—
25#2492C411yescharacteristic, complemented
26#2473—21no—
27#2465—21no—
28#2440C411yescharacteristic, complemented
29#2438—21no—
30#2437—21no—
31#2434C411yescharacteristic, complemented
32#2429C411yescharacteristic, complemented
33#2429C411yescharacteristic, complemented
34#2423C411yescharacteristic, complemented
35#2360—21no—
36#2360C411yescharacteristic, complemented
37#2342—21no—
38Q8×C22⋊C4C411yescharacteristic, complemented
39C4×C22⋊Q8C2211yescharacteristic
40C2×#385—21no—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4—21no—
43C2×C4×C22⋊C4C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1923—21no—
46#1923—21no—
47#1850—21no—
48#1817C2211yescharacteristic
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51C8×C22⋊C4—21no—
52C4×C22⋊C8C2211yescharacteristic
53#1503—24no—
54C2×#328—24no—
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#328C2211yescharacteristic
63C2×#328C2211yescharacteristic
64C2×#328C2211yescharacteristic
65C2×#328C2211yescharacteristic
66C2×#328C2211yescharacteristic
67#1436—21no—
68#1436—21no—
69C4⋊#95C2211yescharacteristic
70#1434C2211yescharacteristic
71C22⋊#95C2211yescharacteristic
72C4×#95C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C24×C4—21no—
79C24×C4C2311yescharacteristic
80C23×C8—21no—
81#533—22no—
82#533—22no—
83#533—41no—
84#533—41no—
85C2×C4⋊Q8C2×C411yescharacteristic, complemented
86C2×C4⋊Q8C2×C411yescharacteristic, complemented
87C2×C4⋊Q8C2×C411yescharacteristic, complemented
88C2×#125—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8—21no—
93C2×C22⋊Q8—22no—
94C2×C22⋊Q8—22no—
95C2×C22⋊Q8—41no—
96C2×C22⋊Q8—41no—
97C2×C22⋊Q8C2×C411yescharacteristic
98C2×C22⋊Q8C2×C411yescharacteristic
99C2×C22⋊Q8C2×C411yescharacteristic
100C2×C22⋊Q8C2×C411yescharacteristic
101C2×C22⋊Q8C2311yescharacteristic
102C2×C22⋊Q8C2311yescharacteristic
103C2×C22⋊Q8C2311yescharacteristic
104C2×C4×Q8—21no—
105C2×C4×Q8C2×C411yescharacteristic, complemented
106C2×C4×Q8C2×C411yescharacteristic, complemented
107C2×C4×Q8C2×C411yescharacteristic, complemented
108C2×#117—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4C2×C411yescharacteristic
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4D411yescharacteristic
116C22×C22⋊C4D411yescharacteristic
117C22×C42—21no—
118C22×C42—21no—
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121#431—22no—
122#431—41no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8C2311yescharacteristic
131C2×C22⋊C8C2311yescharacteristic
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C4×C8—21no—
135C2×C4×C8—21no—
136#400—21no—
137#399—21no—
138#398—21no—
139#398—21no—
140#398—21no—
141#398—21no—
142#396—21no—
143#396—21no—
144#395—21no—
145#395—21no—
146#395—21no—
147#393—21no—
148#391—21no—
149#391—21no—
150#391—21no—
151#391C2×C411yescharacteristic, complemented
152#391C2×C411yescharacteristic, complemented
153#391C2×C411yescharacteristic, complemented
154#391C2×C411yescharacteristic, complemented
155#391C2×C411yescharacteristic, complemented
156#389—21no—
157#389—21no—
158#389—21no—
159#389—21no—
160#389—21no—
161#389C2×C411yescharacteristic, complemented
162#389C2×C411yescharacteristic, complemented
163#389C2×C411yescharacteristic, complemented
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#387—21no—
169#387—21no—
170#387—21no—
171#387—21no—
172#387—21no—
173#385—28no—
174#385—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#384C2×C411yescharacteristic, complemented
184#381—21no—
185#380—21no—
186#380—21no—
187#380—21no—
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#380C2311yescharacteristic
191#379—21no—
192C4×C4⋊C4—21no—
193C4×C4⋊C4—22no—
194C4×C4⋊C4—41no—
195C4×C4⋊C4C2×C411yescharacteristic, complemented
196C4×C22⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—44no—
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4C2×C411yescharacteristic
202C4×C22⋊C4C2×C411yescharacteristic
203C4×C22⋊C4C2×C411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C4×C22⋊C4D411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—22no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—41no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#328—22no—
227#328—22no—
228#328—22no—
229#328—22no—
230#328—22no—
231#328—22no—
232#328—22no—
233#328—41no—
234#328—41no—
235#328—41no—
236#328—41no—
237#328D414yes—
238C25C2×D411yescharacteristic
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—22no—
242C22×Q8—41no—
243C22×Q8—42no—
244C22×Q8—81no—
245C22×Q8C22×C411yescharacteristic
246C22×Q8C22×C411yescharacteristic
247C22×Q8C22×C411yescharacteristic
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—24no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—81no—
265C23×C4—81no—
266C23×C4—81no—
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2411yescharacteristic
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—42no—
282C22×C8—42no—
283C22×C8—81no—
284C4⋊Q8—22no—
285C4⋊Q8—22no—
286C4⋊Q8—41no—
287C4⋊Q8—41no—
288C4⋊Q8—81no—
289#125—42no—
290#125—42no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—22no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—22no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306C22⋊Q8—42no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C22⋊Q8—42no—
310C22⋊Q8—42no—
311C22⋊Q8—44no—
312C22⋊Q8—42no—
313C22⋊Q8—81no—
314C22⋊Q8C2×D412yes—
315C22⋊Q8#4112yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—41no—
319C4×Q8—41no—
320C4×Q8—42no—
321C4×Q8—42no—
322C4×Q8—81no—
323#117—42no—
324#117—42no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—81no—
355C2×C4⋊C4—81no—
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4C22⋊C411yescharacteristic
378C2×C22⋊C4C22⋊C411yescharacteristic
379C2×C22⋊C4C22⋊C411yescharacteristic
380C2×C22⋊C4C22⋊C411yescharacteristic
381C2×C22⋊C4C22⋊C411yescharacteristic
382C2×C22⋊C4C22⋊C411yescharacteristic
383C2×C22⋊C4C22⋊C411yescharacteristic
384C2×C22⋊C4C22⋊C411yescharacteristic
385C2×C22⋊C4SD1614yes—
386C2×C22⋊C4Q1614yes—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—81no—
400C2×C42—81no—
401C2×C42—81no—
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C4⋊C8—42no—
411C4⋊C8—81no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—42no—
420C22⋊C8—42no—
421C22⋊C8—81no—
422C22⋊C8C2×D412yes—
423C4×C8—42no—
424C4×C8—81no—
425#95—24no—
426#95—24no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—81no—
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C2×D412yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—41no—
471C24—41no—
472C24C2×C22⋊C411yescharacteristic
473C24C2×C22⋊C411yescharacteristic
474C24C2×SD1612yes—
475C24C2×Q1612yes—
476C24C22×D411yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—42no—
492C2×Q8—81no—
493C2×Q8—81no—
494C2×Q8—84no—
495C2×Q8—84no—
496C2×Q8C4×D412yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—48no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—48no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4C2×C22⋊C411yescharacteristic
587C22×C4C2×C22⋊C411yescharacteristic
588C22×C4C2×C22⋊C411yescharacteristic
589C22×C4C2×C22⋊C411yescharacteristic
590C22×C4C2×C22⋊C411yescharacteristic
591C22×C4C2×C22⋊C411yescharacteristic
592C22×C4C2×C22⋊C411yescharacteristic
593C22×C4C2×C22⋊C411yescharacteristic
594C22×C4C2×C22⋊C411yescharacteristic
595C22×C4C2×C22⋊C411yescharacteristic
596C22×C4C2×SD1612yes—
597C22×C4C2×SD1612yes—
598C22×C4C2×Q1612yes—
599C22×C4C2×Q1612yes—
600C22×C4C23×C411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4H(5,𝔽2)11yescharacteristic
605C22×C4H(5,𝔽2)11yescharacteristic
606C2×C8—22no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—84no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—48no—
637C4⋊C4—42no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4—81no—
648C4⋊C4—81no—
649C4⋊C4—81no—
650C4⋊C4—81no—
651C4⋊C4—84no—
652C4⋊C4C4×D412yes—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—48no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—81no—
670C22⋊C4—81no—
671C22⋊C4#10314yes—
672C22⋊C4#10314yes—
673C22⋊C4#10314yes—
674C22⋊C4#10314yes—
675C22⋊C4#10414yes—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—42no—
689C42—42no—
690C42—81no—
691C42—81no—
692C42—84no—
693C42—84no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23#41012yes—
725C23C2×#10312yes—
726C23C2×#10312yes—
727C23C2×#10412yes—
728C23C22×C22⋊C411yescharacteristic
729C23D4211yescharacteristic
730C23#54611yescharacteristic
731C23C22×SD1611yescharacteristic
732C23C22×Q1611yescharacteristic
733C23#57711yescharacteristic
734C23#57811yescharacteristic
735Q8—42no—
736Q8—42no—
737Q8—84no—
738Q8—81no—
739Q8—81no—
740Q8—81no—
741Q8—81no—
742Q8—84no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4—816no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4C2×#10312yes—
851C2×C4C2×#10312yes—
852C2×C4C2×#10312yes—
853C2×C4C2×#10312yes—
854C2×C4C2×#10412yes—
855C2×C4C2×#10412yes—
856C2×C4C2×C4×D411yescharacteristic
857C2×C4#51811yescharacteristic
858C2×C4D4211yescharacteristic
859C2×C4#54611yescharacteristic
860C8—42no—
861C8—81no—
862C8—81no—
863C8—81no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—22no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—22no—
873C22—21no—
874C22—21no—
875C22—22no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22#150314yescomplemented
894C22D4×C22⋊C411yescharacteristic
895C22C2×#41011yescharacteristic
896C22#288311yescharacteristic
897C22C22×#10311yescharacteristic
898C22#289811yescharacteristic
899C22C22×#10411yescharacteristic
900C22#290111yescharacteristic
901C22D4×SD1611yescharacteristic
902C22D4×Q1611yescharacteristic
903C22#329811yescharacteristic
904C22#329911yescharacteristic
905C4—21no—
906C4—21no—
907C4—21no—
908C4—21no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—22no—
913C4—22no—
914C4—22no—
915C4—44no—
916C4—41no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—42no—
922C4—82no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—81no—
929C4—81no—
930C4—81no—
931C2—21no—
932C2—21no—
933C2—21no—
934C2—24no—
935C2—21no—
936C2—42no—
937C2C2×#150311yescharacteristic
938C2#1754811yescharacteristic
939C2#1760911yescharacteristic
940C2#1761411yescharacteristic
941C2#2240511yescharacteristic
942C2D4×#10311yescharacteristic
943C2D4×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#1503C2semidirect
6. #9711C2semidirect
7. #9679C2semidirect
8. #9144C2semidirect
10. #9112C2semidirect
12. #8578C2semidirect
13. #8333C2semidirect
15. C4×#328C2semidirect
25. #2492C4semidirect
28. #2440C4semidirect
31. #2434C4semidirect
32. #2429C4semidirect
33. #2429C4semidirect
34. #2423C4semidirect
36. #2360C4semidirect
38. Q8×C22⋊C4C4semidirect
85. C2×C4⋊Q8C2×C4semidirect
86. C2×C4⋊Q8C2×C4semidirect
87. C2×C4⋊Q8C2×C4semidirect
105. C2×C4×Q8C2×C4semidirect
106. C2×C4×Q8C2×C4semidirect
107. C2×C4×Q8C2×C4semidirect
151. #391C2×C4semidirect
152. #391C2×C4semidirect
153. #391C2×C4semidirect
154. #391C2×C4semidirect
155. #391C2×C4semidirect
161. #389C2×C4semidirect
162. #389C2×C4semidirect
163. #389C2×C4semidirect
183. #384C2×C4semidirect
195. C4×C4⋊C4C2×C4semidirect
893. C22#1503semidirect

Maximal subgroups

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

subgroupindex
#361302
#225522
C2×#15032
C22×#3282
#138142
#97112
#96792
#91442
#91432
#91122
#91112
#85782
#83332
#83292
C4×#3282