Finite Group Databasebeta

← #221724

Subgroups — #221724

Order 512.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊Q8C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic
3C2×#1508C211yesmaximal, characteristic, complemented
4C22×#328C211yesmaximal, characteristic, complemented
5#13813C211yesmaximal, characteristic
6#9711C211yesmaximal, characteristic, complemented
7#9683C211yesmaximal, characteristic, complemented
8#9146C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9115C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13#8329C211yesmaximal, characteristic, complemented
14#8329C211yesmaximal, characteristic, complemented
15#8219C211yesmaximal, characteristic, complemented
16C2×D4×Q8C411yescharacteristic, complemented
17C22×C22⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C2×#435—21no—
21C2×#407C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23#2857C2211yescharacteristic
24#2848C2211yescharacteristic
25#2848C2211yescharacteristic
26#2542C411yescharacteristic, complemented
27#2538C411yescharacteristic, complemented
28#2452—21no—
29#2449—21no—
30#2449—21no—
31#2440—21no—
32#2437—21no—
33#2437—21no—
34#2417C411yescharacteristic, complemented
35#2417C411yescharacteristic, complemented
36#2409C411yescharacteristic, complemented
37#2409C411yescharacteristic, complemented
38D4×C4⋊C4—21no—
39D4×C4⋊C4C411yescharacteristic, complemented
40D4×C22⋊C4—21no—
41C4×C22⋊Q8C2211yescharacteristic
42C2×#386—21no—
43C2×C4×C22⋊C4—21no—
44C2×C4×C22⋊C4C2211yescharacteristic
45C22×#95C2211yescharacteristic
46#1955—21no—
47#1870—21no—
48#1869—21no—
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51#1779C2211yescharacteristic
52#1749C2211yescharacteristic
53#1508—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#1437—21no—
68#1436—21no—
69#1434C2211yescharacteristic
70C22⋊#95C2211yescharacteristic
71C22⋊#95C2211yescharacteristic
72C4×#95C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C23×Q8C2×C411yescharacteristic, complemented
79C23×D4D411yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C22×M16—21no—
84C23×C8—21no—
85D4×Q8—44no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8C2×C411yescharacteristic, complemented
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8—21no—
93C2×C22⋊Q8—21no—
94C2×C22⋊Q8—22no—
95C2×C22⋊Q8—22no—
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—41no—
99C2×C22⋊Q8—41no—
100C2×C22⋊Q8—41no—
101C2×C22⋊Q8—41no—
102C2×C22⋊Q8C2×C411yescharacteristic
103C2×C22⋊Q8C2×C411yescharacteristic
104C2×C22⋊Q8C2×C411yescharacteristic
105C2×C22⋊Q8C2×C411yescharacteristic
106C2×C22⋊Q8C2×C411yescharacteristic, complemented
107C2×C22⋊Q8C2×C411yescharacteristic, complemented
108C2×C22⋊Q8C2×C411yescharacteristic, complemented
109C2×C22⋊Q8C2×C411yescharacteristic, complemented
110C2×C22⋊Q8C2311yescharacteristic
111C2×C22⋊Q8C2311yescharacteristic
112C2×C22⋊Q8C2311yescharacteristic
113C2×C4×Q8C2×C411yescharacteristic, complemented
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—44no—
117C2×C4×D4C2×C411yescharacteristic
118C2×C4×D4C2×C411yescharacteristic
119C2×C4×D4C2×C411yescharacteristic
120C2×C4×D4C2×C411yescharacteristic
121C2×C4×D4D411yescharacteristic
122C2×C4×D4D411yescharacteristic
123C2×C4×D4D411yescharacteristic
124C2×C4×D4D411yescharacteristic
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C4⋊C4C2×C411yescharacteristic, complemented
129C22×C4⋊C4D411yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4D411yescharacteristic
136C22×C22⋊C4D411yescharacteristic
137C22×C42—21no—
138C22×C42—21no—
139C22×C42C2311yescharacteristic
140#435—44no—
141C2×C4⋊C8—21no—
142#407—22no—
143#407—41no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—41no—
152C2×C22⋊C8C2311yescharacteristic
153C2×C22⋊C8C2311yescharacteristic
154C2×C22⋊C8C2311yescharacteristic
155C2×C22⋊C8C2311yescharacteristic
156C2×#97—21no—
157#399—21no—
158#399—21no—
159#398—21no—
160#398—21no—
161#396—21no—
162#396—21no—
163#396—21no—
164#396—21no—
165#395—21no—
166#395—21no—
167#393—21no—
168#393—21no—
169#391C2×C411yescharacteristic, complemented
170#391C2×C411yescharacteristic, complemented
171#391C2×C411yescharacteristic, complemented
172#390—21no—
173#390—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389C2×C411yescharacteristic, complemented
179#387—21no—
180#386—28no—
181#386—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#385—21no—
186#385—21no—
187#385—21no—
188#385—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#385—21no—
195#385—21no—
196#384—21no—
197#384C2×C411yescharacteristic, complemented
198#380—21no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380C2×C411yescharacteristic
203#380C2×C411yescharacteristic
204#380C2×C411yescharacteristic, complemented
205#380C2×C411yescharacteristic, complemented
206#380C2311yescharacteristic
207#379—21no—
208#379—21no—
209C4×C4⋊C4—21no—
210C4×C4⋊C4C2×C411yescharacteristic, complemented
211C4×C22⋊C4—21no—
212C4×C22⋊C4—22no—
213C4×C22⋊C4—41no—
214C4×C22⋊C4—44no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—22no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—41no—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227#336—21no—
228#336—21no—
229#328—22no—
230#328—22no—
231#328—22no—
232#328—22no—
233#328—22no—
234#328—22no—
235#328—22no—
236#328—41no—
237#328—41no—
238#328—41no—
239#328—41no—
240#328D414yescomplemented
241C25C2×D411yescharacteristic
242C25C2×D411yescharacteristic
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—41no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—81no—
252C22×Q8—81no—
253C22×Q8C22×C411yescharacteristic
254C22×Q8C22×C411yescharacteristic
255C22×Q8C22×C411yescharacteristic
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—42no—
260C22×D4C22⋊C411yescharacteristic
261C22×D4C22⋊C411yescharacteristic
262C22×D4C22⋊C411yescharacteristic
263C22×D4C22⋊C411yescharacteristic
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—81no—
288C23×C4—81no—
289C23×C4—81no—
290C23×C4—81no—
291C23×C4C22×C411yescharacteristic
292C23×C4C22×C411yescharacteristic
293C23×C4C22×C411yescharacteristic
294C23×C4C22×C411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×M16—42no—
305C2×M16—42no—
306C2×M16—81no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—42no—
312C22×C8—42no—
313C22×C8—81no—
314C4⋊Q8—42no—
315C4⋊Q8—44no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—42no—
331C22⋊Q8—42no—
332C22⋊Q8—42no—
333C22⋊Q8—42no—
334C22⋊Q8—44no—
335C22⋊Q8—41no—
336C22⋊Q8—41no—
337C22⋊Q8—41no—
338C22⋊Q8—41no—
339C22⋊Q8—42no—
340C22⋊Q8—42no—
341C22⋊Q8—42no—
342C22⋊Q8—42no—
343C22⋊Q8—42no—
344C22⋊Q8—44no—
345C22⋊Q8—42no—
346C22⋊Q8—81no—
347C22⋊Q8—81no—
348C22⋊Q8C2×D412yes—
349C22⋊Q8#4112yes—
350C4×Q8—42no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4—42no—
359C4×D4—44no—
360C4×D4—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
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—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4C22⋊C411yescharacteristic
390C2×C4⋊C4C22⋊C411yescharacteristic
391C2×C4⋊C4C22⋊C411yescharacteristic
392C2×C4⋊C4C22⋊C411yescharacteristic
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C411yescharacteristic
395C2×C4⋊C4C22×C411yescharacteristic
396C2×C4⋊C4C22×C411yescharacteristic
397C2×C4⋊C4C22×C411yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—81no—
428C2×C22⋊C4—81no—
429C2×C22⋊C4C22⋊C411yescharacteristic
430C2×C22⋊C4C22⋊C411yescharacteristic
431C2×C22⋊C4C22⋊C411yescharacteristic
432C2×C22⋊C4C22⋊C411yescharacteristic
433C2×C22⋊C4C22⋊C411yescharacteristic
434C2×C22⋊C4C22⋊C411yescharacteristic
435C2×C22⋊C4C22⋊C411yescharacteristic
436C2×C22⋊C4C22⋊C411yescharacteristic
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—81no—
445C2×C42—81no—
446C2×C42C22×C411yescharacteristic
447C2×C42C22×C411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C4⋊C8—42no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461C22⋊C8—42no—
462C22⋊C8—81no—
463C22⋊C8—81no—
464C22⋊C8C2×D412yes—
465#97—42no—
466#95—24no—
467#95—24no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—81no—
492#95C2×D412yes—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—41no—
507C24—41no—
508C24—41no—
509C24—41no—
510C24—41no—
511C24C2×C22⋊C411yescharacteristic
512C24C2×C22⋊C411yescharacteristic
513C24C2×C22⋊C411yescharacteristic
514C24C2×C22⋊C411yescharacteristic
515C24#13712yes—
516C24#13712yes—
517C24C22×D411yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—42no—
533C2×Q8—81no—
534C2×Q8—81no—
535C2×Q8—84no—
536C2×Q8—84no—
537C2×Q8—84no—
538C2×Q8—84no—
539C2×Q8C4×D412yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4#10414yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—48no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—42no—
636C22×C4—48no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—82no—
651C22×C4—82no—
652C22×C4—82no—
653C22×C4—82no—
654C22×C4—82no—
655C22×C4—82no—
656C22×C4—82no—
657C22×C4—82no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—84no—
663C22×C4—84no—
664C22×C4—84no—
665C22×C4—84no—
666C22×C4—84no—
667C22×C4C2×C22⋊C411yescharacteristic
668C22×C4C2×C22⋊C411yescharacteristic
669C22×C4C2×C22⋊C411yescharacteristic
670C22×C4C2×C22⋊C411yescharacteristic
671C22×C4C2×C22⋊C411yescharacteristic
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C23×C411yescharacteristic
676C22×C4C22×D411yescharacteristic
677C22×C4C22×D411yescharacteristic
678C22×C4C2×#4111yescharacteristic
679C22×C4H(5,𝔽2)11yescharacteristic
680C22×C4H(5,𝔽2)11yescharacteristic
681M16—84no—
682C2×C8—22no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—84no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—41no—
705C4⋊C4—41no—
706C4⋊C4—42no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—41no—
717C4⋊C4—41no—
718C4⋊C4—41no—
719C4⋊C4—41no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—81no—
725C4⋊C4—81no—
726C4⋊C4—81no—
727C4⋊C4—81no—
728C4⋊C4C4×D412yes—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—41no—
737C22⋊C4—41no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—42no—
745C22⋊C4—41no—
746C22⋊C4—41no—
747C22⋊C4—41no—
748C22⋊C4—41no—
749C22⋊C4—41no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—81no—
758C22⋊C4—84no—
759C22⋊C4#9914yes—
760C42—22no—
761C42—22no—
762C42—41no—
763C42—41no—
764C42—42no—
765C42—42no—
766C42—84no—
767C42—84no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—24no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23—81no—
826C23—81no—
827C23C2×#9912yes—
828C23#41912yes—
829C23#41912yes—
830C23C2×#10412yes—
831C23C2×#10412yes—
832C23C22×C22⋊C411yescharacteristic
833C23D4211yescharacteristic
834C23#54611yescharacteristic
835C23C2×#13711yescharacteristic
836C23C2×#13711yescharacteristic
837C23#57711yescharacteristic
838C23#57811yescharacteristic
839Q8—42no—
840Q8—42no—
841Q8—84no—
842Q8—81no—
843Q8—81no—
844Q8—81no—
845Q8—81no—
846Q8—84no—
847D4—28no—
848D4—44no—
849D4—44no—
850D4—44no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—84no—
945C2×C4—84no—
946C2×C4—84no—
947C2×C4—816no—
948C2×C4—84no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—81no—
952C2×C4—81no—
953C2×C4—81no—
954C2×C4—81no—
955C2×C4—81no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4C2×#9912yes—
962C2×C4C2×#9912yes—
963C2×C4C2×#10412yes—
964C2×C4C2×C4×D411yescharacteristic
965C2×C4#51811yescharacteristic
966C2×C4D4211yescharacteristic
967C2×C4#54611yescharacteristic
968C8—42no—
969C8—81no—
970C8—81no—
971C8—81no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—22no—
977C22—21no—
978C22—21no—
979C22—22no—
980C22—22no—
981C22—21no—
982C22—21no—
983C22—22no—
984C22—21no—
985C22—21no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—82no—
1016C22—82no—
1017C22—82no—
1018C22—82no—
1019C22#150814yescomplemented
1020C22D4×C22⋊C411yescharacteristic
1021C22C22×#9911yescharacteristic
1022C22#288311yescharacteristic
1023C22C2×#41911yescharacteristic
1024C22#289811yescharacteristic
1025C22C22×#10411yescharacteristic
1026C22#290111yescharacteristic
1027C22#326611yescharacteristic
1028C22#327011yescharacteristic
1029C22#331211yescharacteristic
1030C22#332011yescharacteristic
1031C4—22no—
1032C4—21no—
1033C4—21no—
1034C4—21no—
1035C4—21no—
1036C4—22no—
1037C4—22no—
1038C4—44no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—82no—
1047C4—82no—
1048C4—82no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C2—21no—
1056C2—21no—
1057C2—21no—
1058C2—21no—
1059C2—24no—
1060C2—42no—
1061C2—42no—
1062C2—81no—
1063C2C2×#150811yescharacteristic
1064C2#1754811yescharacteristic
1065C2#1760811yescharacteristic
1066C2#1762111yescharacteristic
1067C2D4×#9911yescharacteristic
1068C2#2242511yescharacteristic
1069C2D4×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1508C2semidirect
4. C22×#328C2semidirect
6. #9711C2semidirect
7. #9683C2semidirect
8. #9146C2semidirect
9. #9143C2semidirect
10. #9115C2semidirect
11. #9111C2semidirect
12. #8574C2semidirect
13. #8329C2semidirect
14. #8329C2semidirect
15. #8219C2semidirect
16. C2×D4×Q8C4semidirect
26. #2542C4semidirect
27. #2538C4semidirect
34. #2417C4semidirect
35. #2417C4semidirect
36. #2409C4semidirect
37. #2409C4semidirect
39. D4×C4⋊C4C4semidirect
78. C23×Q8C2×C4semidirect
87. C2×C4⋊Q8C2×C4semidirect
106. C2×C22⋊Q8C2×C4semidirect
107. C2×C22⋊Q8C2×C4semidirect
108. C2×C22⋊Q8C2×C4semidirect
109. C2×C22⋊Q8C2×C4semidirect
113. C2×C4×Q8C2×C4semidirect
128. C22×C4⋊C4C2×C4semidirect
169. #391C2×C4semidirect
170. #391C2×C4semidirect
171. #391C2×C4semidirect
178. #389C2×C4semidirect
197. #384C2×C4semidirect
204. #380C2×C4semidirect
205. #380C2×C4semidirect
210. C4×C4⋊C4C2×C4semidirect
240. #328D4semidirect
1019. C22#1508semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊Q82
#223992
C2×#15082
C22×#3282
#138132
#97112
#96832
#91462
#91432
#91152
#91112
#85742
#83292
#82192