Finite Group Databasebeta

← #188466

Subgroups — #188466

Order 512.

1332 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34233C211yesmaximal, characteristic
2#21932C211yesmaximal, characteristic, complemented
3C2×#1504C211yesmaximal, characteristic
4C2×#1501C211yesmaximal, characteristic
5#13782C211yesmaximal, characteristic, complemented
6#8578C211yesmaximal, characteristic, complemented
7#8577C211yesmaximal, characteristic, complemented
8#8576C211yesmaximal, characteristic, complemented
9#8575C211yesmaximal, characteristic, complemented
10#8574C211yesmaximal, characteristic, complemented
11#8573C211yesmaximal, characteristic, complemented
12#8572C211yesmaximal, characteristic, complemented
13#8571C211yesmaximal, characteristic, complemented
14#8019C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C2×#407C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19#2361C411yescharacteristic, complemented
20#2361C411yescharacteristic, complemented
21#2360C411yescharacteristic, complemented
22#2360C411yescharacteristic, complemented
23#2358—21no—
24#2358—21no—
25#2353—21no—
26#2349—21no—
27#2347C411yescharacteristic, complemented
28#2346C411yescharacteristic, complemented
29#2341C411yescharacteristic, complemented
30#2339C411yescharacteristic, complemented
31#2335—21no—
32#2335—21no—
33#2318—21no—
34C4×C22⋊Q8C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C2×#385—21no—
39C2×#380C2211yescharacteristic
40#2275—21no—
41C2×C4×C22⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1851—21no—
45#1851—21no—
46#1850—21no—
47#1850—21no—
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52#1504—24no—
53#1501—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62#1436—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66#1434C2211yescharacteristic
67#1434C2211yescharacteristic
68C22⋊#95—21no—
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C24×C4—21no—
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81C23×C8—21no—
82#525—22no—
83#525—22no—
84#525D414yes—
85#525Q814yes—
86C2×#123—21no—
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×C22⋊Q8C2311yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#121C2311yescharacteristic
91C2×#120—21no—
92C2×C4×Q8C2×C411yescharacteristic, complemented
93C2×C4×Q8C2×C411yescharacteristic, complemented
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4C2×C411yescharacteristic, complemented
101C2×C4×D4C2×C411yescharacteristic, complemented
102C2×#117C2×C411yescharacteristic
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4D411yescharacteristic
110C22×C22⋊C4D411yescharacteristic
111C22×C42—21no—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118#407—22no—
119#407—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8C2311yescharacteristic
125C2×C22⋊C8C2311yescharacteristic
126C2×C22⋊C8C2311yescharacteristic
127C2×C22⋊C8C2311yescharacteristic
128#391C2×C411yescharacteristic, complemented
129#391C2×C411yescharacteristic, complemented
130#390—21no—
131#390—21no—
132#390C2×C411yescharacteristic, complemented
133#390C2×C411yescharacteristic, complemented
134#389—21no—
135#389—21no—
136#389C2×C411yescharacteristic, complemented
137#389C2×C411yescharacteristic, complemented
138#389C2×C411yescharacteristic, complemented
139#389C2×C411yescharacteristic, complemented
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#386—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#385—28no—
159#385—21no—
160#385—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—21no—
165#383—21no—
166#382—21no—
167#381—21no—
168#380—21no—
169#380—21no—
170#380—21no—
171#380C2×C411yescharacteristic
172#380C2×C411yescharacteristic
173#380C2311yescharacteristic
174#380C2311yescharacteristic
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×C411yescharacteristic, complemented
179C4×C4⋊C4C2×C411yescharacteristic, complemented
180C4×C4⋊C4C2×C411yescharacteristic, complemented
181C4×C4⋊C4C2×C411yescharacteristic, complemented
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—22no—
189C4×C22⋊C4—22no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4C2×C411yescharacteristic
192C4×C22⋊C4C2×C411yescharacteristic
193C4×C22⋊C4C2×C411yescharacteristic
194C4×C22⋊C4C2×C411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199#376—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—22no—
205C2×#95—22no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95D411yescharacteristic
212C2×#95D411yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217#336—21no—
218#336—21no—
219#336—21no—
220#336—21no—
221#328—22no—
222#328—22no—
223#328—22no—
224#328—22no—
225#327—22no—
226#327—22no—
227#327—22no—
228#327—22no—
229C25C2×D411yescharacteristic
230C2×#41—22no—
231C2×#41—81no—
232C2×#41—81no—
233C2×#41C4⋊C414yescomplemented
234C22×Q8C22×C411yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C22×C411yescharacteristic
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—24no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—81no—
252C23×C4—81no—
253C23×C4—81no—
254C23×C4—81no—
255C23×C4—81no—
256C23×C4—81no—
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D412yes—
267C23×C4C2×Q812yes—
268C23×C4#4112yes—
269C23×C4#4112yes—
270C23×C4C2411yescharacteristic
271C2×M16—42no—
272C2×M16—81no—
273C2×M16—81no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—42no—
279C22×C8—81no—
280C22×C8—81no—
281#123—24no—
282#123—24no—
283C22⋊Q8—22no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8C4⋊C414yescomplemented
287C22⋊Q8C2×D412yes—
288C22⋊Q8C2×Q812yes—
289#121—22no—
290#121—21no—
291#121—21no—
292#121C4⋊C414yescomplemented
293#121C2×D412yes—
294#121C2×Q812yes—
295#120—24no—
296#120—24no—
297C4×Q8—81no—
298C4×Q8—81no—
299C4×D4—24no—
300C4×D4—24no—
301C4×D4—24no—
302C4×D4—24no—
303C4×D4—44no—
304C4×D4—44no—
305C4×D4—81no—
306C4×D4—81no—
307C4×D4—81no—
308C4×D4—81no—
309C4×D4—81no—
310C4×D4—81no—
311#117—22no—
312#117C4⋊C414yescomplemented
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—81no—
326C2×C4⋊C4—81no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4—81no—
329C2×C4⋊C4—81no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4C22×C411yescharacteristic
332C2×C4⋊C4C22×C411yescharacteristic
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4—81no—
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22⋊C411yescharacteristic
361C2×C22⋊C4C22⋊C411yescharacteristic
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—42no—
375C2×C42—81no—
376C2×C42—81no—
377C2×C42—81no—
378C2×C42—81no—
379C2×C42C22×C411yescharacteristic
380C2×C42C22×C411yescharacteristic
381C2×C42C22×C411yescharacteristic
382C2×C42C22×C411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C4⋊C8—81no—
388C4⋊C8—81no—
389C4⋊C8—81no—
390C4⋊C8—81no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—42no—
400C22⋊C8—42no—
401#95—24no—
402#95—24no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
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—42no—
428#95—81no—
429#95—81no—
430#95—81no—
431#95—81no—
432#95C22⋊C411yescharacteristic
433#95C22⋊C411yescharacteristic
434#95C22⋊C411yescharacteristic
435#95C22⋊C411yescharacteristic
436#95C22⋊C411yescharacteristic
437#95C22⋊C411yescharacteristic
438#95C22⋊C411yescharacteristic
439#95C22⋊C411yescharacteristic
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—41no—
448C24—41no—
449C24C2×C22⋊C411yescharacteristic
450C24C2×C22⋊C411yescharacteristic
451C24#12112yes—
452C24C22⋊Q812yes—
453C24C22×D411yescharacteristic
454#41—84no—
455#41—84no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8C2×C4⋊C412yes—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4C2×C4⋊C412yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
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—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—48no—
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—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4C2×C22⋊C411yescharacteristic
566C22×C4C2×C22⋊C411yescharacteristic
567C22×C4C2×C22⋊C411yescharacteristic
568C22×C4C2×C22⋊C411yescharacteristic
569C22×C4C2×C22⋊C411yescharacteristic
570C22×C4C2×C22⋊C411yescharacteristic
571C22×C4C2×C22⋊C411yescharacteristic
572C22×C4C2×C22⋊C411yescharacteristic
573C22×C4C2×C22⋊C411yescharacteristic
574C22×C4C2×C22⋊C411yescharacteristic
575C22×C4C2×C4⋊C412yes—
576C22×C4C2×C4⋊C412yes—
577C22×C4#11712yes—
578C22×C4#11712yes—
579C22×C4#12112yes—
580C22×C4#12112yes—
581C22×C4#12112yes—
582C22×C4C22⋊Q812yes—
583C22×C4C22⋊Q812yes—
584C22×C4C22⋊Q812yes—
585C22×C4C23×C411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×Q811yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591M16—84no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—84no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—81no—
617C4⋊C4—81no—
618C4⋊C4—81no—
619C4⋊C4—81no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4C2×C4⋊C412yes—
625C4⋊C4C2×C4⋊C412yes—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—24no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—42no—
641C22⋊C4—48no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—41no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—81no—
650C22⋊C4—81no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4#10414yes—
654C42—24no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—42no—
664C42—42no—
665C42—81no—
666C42—81no—
667C42—81no—
668C42—81no—
669C42—84no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#38012yes—
708C23#38012yes—
709C23C2×#10412yes—
710C23#42112yes—
711C23C22×C22⋊C411yescharacteristic
712C23C2×#12111yescharacteristic
713C23C2×C22⋊Q811yescharacteristic
714C23#57611yescharacteristic
715C23#57711yescharacteristic
716C23#57711yescharacteristic
717C23#57811yescharacteristic
718Q8—42no—
719Q8—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—84no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
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—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—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
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—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—84no—
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—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—816no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—162no—
832C2×C4—162no—
833C2×C4—162no—
834C2×C4—162no—
835C2×C4#38012yes—
836C2×C4#38012yes—
837C2×C4C2×#10412yes—
838C2×C4C2×#10412yes—
839C2×C4C22×C4⋊C411yescharacteristic
840C2×C4C2×#11711yescharacteristic
841C2×C4C2×#12111yescharacteristic
842C2×C4C2×C22⋊Q811yescharacteristic
843C8—81no—
844C8—81no—
845C8—81no—
846C8—81no—
847C22—21no—
848C22—21no—
849C22—22no—
850C22—21no—
851C22—21no—
852C22—22no—
853C22—21no—
854C22—21no—
855C22—22no—
856C22—22no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22#180614yes—
884C22C2×#38011yescharacteristic
885C22#288311yescharacteristic
886C22#288311yescharacteristic
887C22#289711yescharacteristic
888C22#289811yescharacteristic
889C22C22×#10411yescharacteristic
890C22C2×#42111yescharacteristic
891C22#304511yescharacteristic
892C22#304611yescharacteristic
893C22#308311yescharacteristic
894C22#308411yescharacteristic
895C4—22no—
896C4—22no—
897C4—21no—
898C4—22no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—42no—
907C4—42no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C4—81no—
917C4—81no—
918C4—81no—
919C4—81no—
920C2—21no—
921C2—21no—
922C2—21no—
923C2—21no—
924C2—24no—
925C2—42no—
926C2—82no—
927C2#1754711yescharacteristic
928C2#1754811yescharacteristic
929C2#1759711yescharacteristic
930C2#1759811yescharacteristic
931C2#2063311yescharacteristic
932C2#2065211yescharacteristic
933C2C2×#180611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#525C22
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
2. #21932C2semidirect
5. #13782C2semidirect
6. #8578C2semidirect
7. #8577C2semidirect
8. #8576C2semidirect
9. #8575C2semidirect
10. #8574C2semidirect
11. #8573C2semidirect
12. #8572C2semidirect
13. #8571C2semidirect
14. #8019C2semidirect
15. C2×#1294C2semidirect
19. #2361C4semidirect
20. #2361C4semidirect
21. #2360C4semidirect
22. #2360C4semidirect
27. #2347C4semidirect
28. #2346C4semidirect
29. #2341C4semidirect
30. #2339C4semidirect
92. C2×C4×Q8C2×C4semidirect
93. C2×C4×Q8C2×C4semidirect
100. C2×C4×D4C2×C4semidirect
101. C2×C4×D4C2×C4semidirect
128. #391C2×C4semidirect
129. #391C2×C4semidirect
132. #390C2×C4semidirect
133. #390C2×C4semidirect
136. #389C2×C4semidirect
137. #389C2×C4semidirect
138. #389C2×C4semidirect
139. #389C2×C4semidirect
178. C4×C4⋊C4C2×C4semidirect
179. C4×C4⋊C4C2×C4semidirect
180. C4×C4⋊C4C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect
233. C2×#41C4⋊C4semidirect
286. C22⋊Q8C4⋊C4semidirect
292. #121C4⋊C4semidirect
312. #117C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
#342332
#219322
C2×#15042
C2×#15012
#137822
#85782
#85772
#85762
#85752
#85742
#85732
#85722
#85712
#80192
C2×#12942