Finite Group Databasebeta

← #221807

Subgroups — #221807

Order 512.

1247 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36130C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic
3C2×#1518C211yesmaximal, characteristic, complemented
4C22×#328C211yesmaximal, characteristic
5#13896C211yesmaximal, characteristic
6#9714C211yesmaximal, characteristic, complemented
7#9679C211yesmaximal, characteristic, complemented
8#9152C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic
10#9112C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic
12#8572C211yesmaximal, characteristic, complemented
13#8333C211yesmaximal, characteristic, complemented
14#8329C211yesmaximal, characteristic
15#8221C211yesmaximal, 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×#382C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1923—21no—
45#1923—21no—
46#1850—21no—
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50C8×C22⋊C4—21no—
51C4×C22⋊C8C2211yescharacteristic
52#1518—24no—
53C2×#328—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#328C2211yescharacteristic
63C2×#328C2211yescharacteristic
64C2×#328C2211yescharacteristic
65C2×#328C2211yescharacteristic
66#1442—21no—
67#1442—21no—
68C4⋊#95C2211yescharacteristic
69#1434C2211yescharacteristic
70#1434C2211yescharacteristic
71C22⋊#95—21no—
72C22⋊#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×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119#431—22no—
120#431—41no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8C2311yescharacteristic
129C2×C22⋊C8C2311yescharacteristic
130C2×C22⋊C8C2311yescharacteristic
131C2×C22⋊C8C2311yescharacteristic
132C2×C4×C8—21no—
133C2×C4×C8—21no—
134#400—21no—
135#399—21no—
136#398—21no—
137#398—21no—
138#398—21no—
139#398—21no—
140#396—21no—
141#396—21no—
142#395—21no—
143#395—21no—
144#395—21no—
145#393—21no—
146#391—21no—
147#391—21no—
148#391—21no—
149#391C2×C411yescharacteristic, complemented
150#391C2×C411yescharacteristic, complemented
151#391C2×C411yescharacteristic, complemented
152#391C2×C411yescharacteristic, complemented
153#391C2×C411yescharacteristic, complemented
154#389—21no—
155#389—21no—
156#389—21no—
157#389—21no—
158#389—21no—
159#389C2×C411yescharacteristic, complemented
160#389C2×C411yescharacteristic, complemented
161#389C2×C411yescharacteristic, complemented
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#387—21no—
167#387—21no—
168#387—21no—
169#387—21no—
170#387—21no—
171#385—21no—
172#385—21no—
173#385—21no—
174#385—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—44no—
181#384C2×C411yescharacteristic, complemented
182#382—22no—
183#382—41no—
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⋊C4C2×C411yescharacteristic, complemented
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C2×#95—22no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—41no—
215C2×#95D411yescharacteristic
216C2×#95D411yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#328—22no—
226#328—22no—
227#328—22no—
228#328—22no—
229#328—22no—
230#328—22no—
231#328—22no—
232#328—41no—
233#328—41no—
234#328—41no—
235#328—41no—
236#328D414yes—
237C25C2×D411yescharacteristic
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—41no—
242C22×Q8—42no—
243C22×Q8—81no—
244C22×Q8C22×C411yescharacteristic
245C22×Q8C22×C411yescharacteristic
246C22×Q8C22×C411yescharacteristic
247C23×C4—21no—
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—21no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—81no—
264C23×C4—81no—
265C23×C4—81no—
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2411yescharacteristic
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—42no—
281C22×C8—42no—
282C22×C8—81no—
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285C4⋊Q8—41no—
286C4⋊Q8—41no—
287C4⋊Q8—81no—
288#125—42no—
289#125—42no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—22no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—22no—
302C22⋊Q8—42no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306C22⋊Q8—44no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C22⋊Q8—42no—
310C22⋊Q8—42no—
311C22⋊Q8—42no—
312C22⋊Q8—81no—
313C22⋊Q8C2×D412yes—
314C22⋊Q8#4112yes—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—41no—
318C4×Q8—41no—
319C4×Q8—42no—
320C4×Q8—42no—
321C4×Q8—81no—
322#117—42no—
323#117—42no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
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—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—81no—
354C2×C4⋊C4—81no—
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
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—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4C22⋊C411yescharacteristic
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⋊C4SD1614yes—
385C2×C22⋊C4Q1614yes—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—81no—
395C2×C42C22×C411yescharacteristic
396C2×C42C22×C411yescharacteristic
397C2×C42C22×C411yescharacteristic
398C2×C42C22×C411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C4⋊C8—42no—
404C4⋊C8—81no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—42no—
413C22⋊C8—42no—
414C22⋊C8—81no—
415C22⋊C8C2×D412yes—
416C4×C8—42no—
417C4×C8—81no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
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—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—81no—
448#95—81no—
449#95—81no—
450#95C22⋊C411yescharacteristic
451#95C22⋊C411yescharacteristic
452#95C22⋊C411yescharacteristic
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C2×D412yes—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—41no—
466C24—41no—
467C24C2×C22⋊C411yescharacteristic
468C24C2×C22⋊C411yescharacteristic
469C24C2×SD1612yes—
470C24C2×Q1612yes—
471C24C22×D411yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—81no—
488C2×Q8—81no—
489C2×Q8—84no—
490C2×Q8—84no—
491C2×Q8C4×D412yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—48no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4C2×C22⋊C411yescharacteristic
582C22×C4C2×C22⋊C411yescharacteristic
583C22×C4C2×C22⋊C411yescharacteristic
584C22×C4C2×C22⋊C411yescharacteristic
585C22×C4C2×C22⋊C411yescharacteristic
586C22×C4C2×C22⋊C411yescharacteristic
587C22×C4C2×C22⋊C411yescharacteristic
588C22×C4C2×C22⋊C411yescharacteristic
589C22×C4C2×C22⋊C411yescharacteristic
590C22×C4C2×C22⋊C411yescharacteristic
591C22×C4C2×SD1612yes—
592C22×C4C2×SD1612yes—
593C22×C4C2×Q1612yes—
594C22×C4C2×Q1612yes—
595C22×C4C23×C411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4H(5,𝔽2)11yescharacteristic
600C22×C4H(5,𝔽2)11yescharacteristic
601C2×C8—22no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—84no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—81no—
640C4⋊C4—81no—
641C4⋊C4—81no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4C4×D412yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—84no—
667C22⋊C4#10314yes—
668C22⋊C4#10314yes—
669C22⋊C4#10314yes—
670C22⋊C4#10314yes—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—42no—
684C42—42no—
685C42—81no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23#41012yes—
718C23C2×#10312yes—
719C23C2×#10312yes—
720C23#42112yes—
721C23C22×C22⋊C411yescharacteristic
722C23D4211yescharacteristic
723C23#54611yescharacteristic
724C23C22×SD1611yescharacteristic
725C23C22×Q1611yescharacteristic
726C23#57711yescharacteristic
727C23#57811yescharacteristic
728Q8—42no—
729Q8—42no—
730Q8—81no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734Q8—84no—
735Q8—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—816no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4C2×#10312yes—
846C2×C4C2×#10312yes—
847C2×C4C2×#10312yes—
848C2×C4C2×#10312yes—
849C2×C4C2×C4×D411yescharacteristic
850C2×C4#51811yescharacteristic
851C2×C4D4211yescharacteristic
852C2×C4#54611yescharacteristic
853C8—42no—
854C8—81no—
855C8—81no—
856C8—81no—
857C22—21no—
858C22—22no—
859C22—21no—
860C22—22no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—22no—
866C22—21no—
867C22—21no—
868C22—22no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—21no—
873C22—21no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22#151814yescomplemented
887C22D4×C22⋊C411yescharacteristic
888C22C2×#41011yescharacteristic
889C22#288311yescharacteristic
890C22C22×#10311yescharacteristic
891C22#289811yescharacteristic
892C22C2×#42111yescharacteristic
893C22#290111yescharacteristic
894C22D4×SD1611yescharacteristic
895C22D4×Q1611yescharacteristic
896C22#329811yescharacteristic
897C22#329911yescharacteristic
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—22no—
906C4—41no—
907C4—41no—
908C4—42no—
909C4—41no—
910C4—41no—
911C4—42no—
912C4—41no—
913C4—41no—
914C4—82no—
915C4—82no—
916C4—81no—
917C4—81no—
918C4—81no—
919C4—81no—
920C4—81no—
921C4—81no—
922C4—161no—
923C4—161no—
924C2—21no—
925C2—21no—
926C2—21no—
927C2—21no—
928C2—24no—
929C2—42no—
930C2C2×#151811yescharacteristic
931C2#1759811yescharacteristic
932C2#1760911yescharacteristic
933C2#1761411yescharacteristic
934C2#2240511yescharacteristic
935C2D4×#10311yescharacteristic
936C2#2243411yescharacteristic
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×#1518C2semidirect
6. #9714C2semidirect
7. #9679C2semidirect
8. #9152C2semidirect
10. #9112C2semidirect
12. #8572C2semidirect
13. #8333C2semidirect
15. #8221C2semidirect
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
149. #391C2×C4semidirect
150. #391C2×C4semidirect
151. #391C2×C4semidirect
152. #391C2×C4semidirect
153. #391C2×C4semidirect
159. #389C2×C4semidirect
160. #389C2×C4semidirect
161. #389C2×C4semidirect
181. #384C2×C4semidirect
193. C4×C4⋊C4C2×C4semidirect
886. C22#1518semidirect

Maximal subgroups

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

subgroupindex
#361302
#225522
C2×#15182
C22×#3282
#138962
#97142
#96792
#91522
#91432
#91122
#91112
#85722
#83332
#83292
#82212