Finite Group Databasebeta

← #6386071

Subgroups — #6386071

Order 512.

4440 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#41C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34057C211yesmaximal, characteristic, complemented
4#22434C2116yesmaximal, complemented
5#21816C212yesmaximal, complemented
6#21774C212yesmaximal, complemented
7#21773C212yesmaximal, complemented
8#20748C212yesmaximal, complemented
9#20605C212yesmaximal, complemented
10C2×#1789C212yesmaximal, complemented
11C23×#41C2211yescharacteristic
12C23×#41C2211yescharacteristic
13D4×#41—24no—
14D4×#41—24no—
15D4×#41C418yescomplemented
16D4×#41C2218yes—
17C2×#550C411yescharacteristic, complemented
18C2×D4×Q8C411yescharacteristic, complemented
19C2×#548C411yescharacteristic, complemented
20C2×#548C411yescharacteristic, complemented
21C2×#547—21no—
22C2×#547C411yescharacteristic, complemented
23C2×#546—21no—
24C2×#546—21no—
25C2×#546C411yescharacteristic, complemented
26C2×#546C411yescharacteristic, complemented
27C2×D42—21no—
28C2×D42C411yescharacteristic, complemented
29C2×#532—21no—
30C2×#532C2211yescharacteristic
31C2×#525—21no—
32C2×#525—21no—
33C2×#525C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×D4—21no—
37C22×C4×D4C2211yescharacteristic
38#2975—21no—
39#2974—24no—
40#2973—21no—
41#2973—21no—
42#2972—21no—
43D4×M16C2218yescomplemented
44#2920C2212yescomplemented
45C2×#421C2218yescomplemented
46C22×#104C2218yescomplemented
47C2×#407C2212yescomplemented
48C2×#407C2212yescomplemented
49#2318—24no—
50#2315—21no—
51#2313—21no—
52#2312—21no—
53#2308—21no—
54#2290C2218yescomplemented
55#2283C2212yescomplemented
56#2280C2212yescomplemented
57C2×C4×C22⋊C4C2212yescomplemented
58#1980C2218yescomplemented
59#1963C2218yescomplemented
60#1897C2218yescomplemented
61#1896C2218yescomplemented
62#1871C2218yescomplemented
63#1871C2218yescomplemented
64#1826C2214yescomplemented
65#1806C2218yescomplemented
66#1789C2214yes—
67#1789C2214yescomplemented
68#1789C2214yescomplemented
69#1789C2218yescomplemented
70#1789C2218yescomplemented
71#1759C2218yescomplemented
72C22×#41—21no—
73C22×#41—21no—
74C22×#41—21no—
75C22×#41—21no—
76C22×#41—22no—
77C22×#41—22no—
78C22×#41—22no—
79C22×#41—22no—
80C22×#41—48no—
81C22×#41—48no—
82C22×#41C2×C411yescharacteristic
83C22×#41C2×C411yescharacteristic
84C22×#41C2×C414yes—
85C22×#41C2×C411yescharacteristic, complemented
86C22×#41C2×C411yescharacteristic, complemented
87C22×#41C2×C414yescomplemented
88C22×#41C2311yescharacteristic
89C22×#41C2314yes—
90C22×#41C2314yes—
91C22×#41C2311yescharacteristic
92C22×#41C2311yescharacteristic
93C23×Q8C2×C411yescharacteristic
94C23×Q8C2×C411yescharacteristic, complemented
95C23×D4—21no—
96C23×D4—21no—
97C23×D4—21no—
98C23×D4C2×C411yescharacteristic
99C23×D4C2×C411yescharacteristic, complemented
100C23×D4D411yescharacteristic
101C24×C4—21no—
102C24×C4—21no—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C22×M16C2314yescomplemented
106C22×M16C2314yescomplemented
107#550—24no—
108#550C2×C418yescomplemented
109D4×Q8—24no—
110D4×Q8C2×C418yescomplemented
111#548—24no—
112#548—24no—
113#548C2×C418yescomplemented
114#548C2×C418yescomplemented
115#547—24no—
116#547—28no—
117#547—28no—
118#547C2×C418yescomplemented
119#546—24no—
120#546—24no—
121#546—28no—
122#546—28no—
123#546—28no—
124#546—28no—
125#546C2×C418yescomplemented
126#546C2×C418yescomplemented
127D42—28no—
128D42—28no—
129D42—24no—
130D42C2×C418yescomplemented
131#532—28no—
132#532—28no—
133#532—22no—
134#532—22no—
135#532C2×C414yescomplemented
136#532C2314yes—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8C2×C411yescharacteristic, complemented
139C2×#127—21no—
140C2×#127C2×C411yescharacteristic, complemented
141C2×#124—21no—
142C2×#124—21no—
143C2×#124C2×C411yescharacteristic, complemented
144C2×#124C2×C411yescharacteristic, complemented
145#525—22no—
146#525—22no—
147#525—22no—
148#525—22no—
149#525—28no—
150#525—28no—
151#525—28no—
152#525—28no—
153#525C2×C414yes—
154#525C2×C414yescomplemented
155#525C2314yes—
156#525C2314yes—
157C2×#123—21no—
158C2×#123—21no—
159C2×#123—21no—
160C2×#123—21no—
161C2×#123—21no—
162C2×#123—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8C2×C411yescharacteristic
168C2×C22⋊Q8C2×C411yescharacteristic
169C2×C22⋊Q8C2×C411yescharacteristic, complemented
170C2×C22⋊Q8C2×C411yescharacteristic, complemented
171C2×#121—21no—
172C2×#121—21no—
173C2×#121—21no—
174C2×#121—21no—
175C2×#121—21no—
176C2×#121—21no—
177C2×#121—21no—
178C2×#121—21no—
179C2×#121—21no—
180C2×#121—21no—
181C2×#121C2×C411yescharacteristic
182C2×#121C2×C411yescharacteristic
183C2×#121C2×C411yescharacteristic, complemented
184C2×#121C2×C411yescharacteristic, complemented
185C2×#120—21no—
186C2×#120—21no—
187C2×#120—21no—
188C2×#120—21no—
189C2×#120—21no—
190C2×#120—21no—
191C4×#41—22no—
192C4×#41—22no—
193C4×#41C2×C414yescomplemented
194C4×#41C2314yes—
195C2×C4×Q8C2×C411yescharacteristic, complemented
196C2×C4×Q8C2×C411yescharacteristic, complemented
197C2×C4×D4—21no—
198C2×C4×D4—21no—
199C2×C4×D4—21no—
200C2×C4×D4—21no—
201C2×C4×D4—21no—
202C2×C4×D4—21no—
203C2×C4×D4—21no—
204C2×C4×D4—28no—
205C2×C4×D4—28no—
206C2×C4×D4—21no—
207C2×C4×D4—21no—
208C2×C4×D4—21no—
209C2×C4×D4—21no—
210C2×C4×D4—21no—
211C2×C4×D4C2×C411yescharacteristic
212C2×C4×D4C2×C411yescharacteristic
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4C2×C411yescharacteristic
215C2×C4×D4C2×C414yes—
216C2×C4×D4C2×C411yescharacteristic, complemented
217C2×C4×D4C2×C411yescharacteristic, complemented
218C2×C4×D4D411yescharacteristic
219C2×C4×D4D411yescharacteristic
220C2×C4×D4D411yescharacteristic
221C2×C4×D4D411yescharacteristic
222C2×C4×D4D414yes—
223C2×C4×D4D414yes—
224C2×C4×D4C2314yes—
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2314yescomplemented
228C22×C4⋊C4—21no—
229C22×C4⋊C4D411yescharacteristic
230C22×C22⋊C4—21no—
231C22×C22⋊C4—21no—
232C22×C22⋊C4—22no—
233C22×C22⋊C4D411yescharacteristic
234C22×C22⋊C4D411yescharacteristic
235C22×C42—21no—
236C22×C42C2311yescharacteristic
237C22×C42C2314yescomplemented
238#436—28no—
239#435—28no—
240#435—28no—
241C8×D4—28no—
242#432—22no—
243#432—22no—
244#431—22no—
245#431—22no—
246#423C2314yescomplemented
247#421—416no—
248C2×#104—416no—
249C2×#104C23116yes—
250C2×#104C23116yescomplemented
251C2×#104C23116yescomplemented
252#407—22no—
253#407—22no—
254#407—22no—
255#407—22no—
256#407C2314yes—
257#407C2314yescomplemented
258#407C2314yescomplemented
259C2×C22⋊C8—22no—
260C2×C22⋊C8—22no—
261C2×C22⋊C8—22no—
262C2×C22⋊C8—22no—
263C4×M16C2314yescomplemented
264#388—28no—
265#387—28no—
266#386—28no—
267#385—28no—
268#383—22no—
269#382—22no—
270#381—22no—
271#381—22no—
272#380—22no—
273#380—22no—
274#380—22no—
275#379—22no—
276C4×C4⋊C4C2314yescomplemented
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4C2314yes—
280C4×C22⋊C4C2314yescomplemented
281C4×C22⋊C4C2314yescomplemented
282#376C2314yescomplemented
283C2×#95—22no—
284#339C23116yescomplemented
285C25—21no—
286C25—21no—
287C25C2×D411yescharacteristic
288C25C2×D411yescharacteristic
289C2×#41—28no—
290C2×#41—24no—
291C2×#41—24no—
292C2×#41—22no—
293C2×#41—24no—
294C2×#41—22no—
295C2×#41—24no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—24no—
301C2×#41—24no—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—216no—
309C2×#41—216no—
310C2×#41—48no—
311C2×#41—48no—
312C2×#41—44no—
313C2×#41—44no—
314C2×#41—48no—
315C2×#41—48no—
316C2×#41—48no—
317C2×#41—44no—
318C2×#41—48no—
319C2×#41—44no—
320C2×#41—48no—
321C2×#41—48no—
322C2×#41—44no—
323C2×#41—48no—
324C2×#41—44no—
325C2×#41—48no—
326C2×#41—416no—
327C2×#41—416no—
328C2×#41—416no—
329C2×#41—416no—
330C2×#41C22×C412yes—
331C2×#41C22×C414yes—
332C2×#41C22×C414yes—
333C2×#41C22×C414yes—
334C2×#41C22×C414yes—
335C2×#41C22×C412yes—
336C2×#41C22×C412yes—
337C2×#41C2412yes—
338C2×#41C2412yes—
339C2×#41C2412yes—
340C22×Q8—21no—
341C22×Q8—21no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—44no—
345C22×Q8—44no—
346C22×Q8C22×C411yescharacteristic
347C22×Q8C22×C414yes—
348C22×Q8C22×C414yes—
349C22×Q8C22×C411yescharacteristic
350C22×Q8C22×C411yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—28no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—21no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—44no—
376C22×D4—48no—
377C22×D4—48no—
378C22×D4—48no—
379C22×D4C22⋊C411yescharacteristic
380C22×D4C22⋊C411yescharacteristic
381C22×D4C22⋊C411yescharacteristic
382C22×D4C22⋊C411yescharacteristic
383C22×D4C22⋊C414yes—
384C22×D4C22×C411yescharacteristic
385C22×D4C22×C414yes—
386C22×D4C22×C414yes—
387C22×D4C22×C411yescharacteristic
388C22×D4C22×C411yescharacteristic
389C22×D4C2×D414yes—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—21no—
405C23×C4—24no—
406C23×C4—44no—
407C23×C4—44no—
408C23×C4—48no—
409C23×C4—48no—
410C23×C4C22×C411yescharacteristic
411C23×C4C22×C411yescharacteristic
412C23×C4C22×C411yescharacteristic
413C23×C4C22×C411yescharacteristic
414C23×C4C22×C412yes—
415C23×C4C22×C412yes—
416C23×C4C2×D411yescharacteristic
417C23×C4C2×D411yescharacteristic
418C23×C4C2×D411yescharacteristic
419C23×C4C2×D412yes—
420C23×C4C2×D412yes—
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D411yescharacteristic
425C23×C4C2×D412yes—
426C23×C4C2×D412yes—
427C23×C4C2×D411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2412yes—
431C2×M16—24no—
432C2×M16—24no—
433C2×M16—48no—
434C2×M16—48no—
435C2×M16C2418yes—
436C22×C8—24no—
437C22×C8—24no—
438C4⋊Q8—28no—
439C4⋊Q8—22no—
440C4⋊Q8C22×C414yes—
441#127—28no—
442#127—22no—
443#127C22×C414yes—
444#124—28no—
445#124—28no—
446#124—22no—
447#124—22no—
448#124C22×C414yes—
449#124C22×C414yes—
450#123—24no—
451#123—24no—
452#123—24no—
453#123—24no—
454#123—28no—
455#123—28no—
456#123—28no—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—28no—
463C22⋊Q8—28no—
464C22⋊Q8—28no—
465C22⋊Q8—28no—
466C22⋊Q8C22×C414yes—
467C22⋊Q8C22×C414yes—
468C22⋊Q8C22×C414yes—
469C22⋊Q8C22×C414yes—
470#121—28no—
471#121—28no—
472#121—28no—
473#121—24no—
474#121—24no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—24no—
480#121—24no—
481#121—28no—
482#121—28no—
483#121—28no—
484#121—28no—
485#121—28no—
486#121C22×C414yes—
487#121C22×C414yes—
488#121C22×C414yes—
489#121C22×C414yes—
490#120—24no—
491#120—24no—
492#120—24no—
493#120—24no—
494#120—28no—
495#120—28no—
496#120—28no—
497#120—28no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8C22×C414yes—
501C4×Q8C22×C414yes—
502C4×D4—28no—
503C4×D4—24no—
504C4×D4—24no—
505C4×D4—24no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—24no—
514C4×D4—24no—
515C4×D4—28no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—24no—
519C4×D4—24no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—24no—
523C4×D4—24no—
524C4×D4C22⋊C414yes—
525C4×D4C22⋊C414yes—
526C4×D4C22⋊C414yes—
527C4×D4C22⋊C414yes—
528C4×D4C22⋊C414yes—
529C4×D4C22⋊C414yes—
530C4×D4C22⋊C414yes—
531C4×D4C22⋊C414yes—
532C4×D4C22×C414yes—
533C4×D4C22×C414yes—
534C4×D4C22×C414yes—
535C4×D4C22×C414yes—
536C4×D4C22×C414yes—
537C4×D4C22×C414yes—
538C4×D4C2×D414yes—
539C4×D4C2×D414yes—
540C4×D4C2×D414yes—
541C4×D4C2×D414yes—
542#117—21no—
543#117—21no—
544#117—24no—
545#117—24no—
546#117—48no—
547#117C22×C412yes—
548#117C2412yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—28no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4C22⋊C411yescharacteristic
561C2×C4⋊C4C22⋊C411yescharacteristic
562C2×C4⋊C4C22⋊C411yescharacteristic
563C2×C4⋊C4C22⋊C411yescharacteristic
564C2×C4⋊C4C22⋊C414yes—
565C2×C4⋊C4C22×C411yescharacteristic
566C2×C4⋊C4C22×C411yescharacteristic
567C2×C4⋊C4C2×D414yes—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—28no—
584C2×C22⋊C4—28no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4C22⋊C411yescharacteristic
591C2×C22⋊C4C22⋊C411yescharacteristic
592C2×C22⋊C4C22⋊C411yescharacteristic
593C2×C22⋊C4C22⋊C411yescharacteristic
594C2×C22⋊C4C22⋊C411yescharacteristic
595C2×C22⋊C4C22⋊C411yescharacteristic
596C2×C22⋊C4C22⋊C411yescharacteristic
597C2×C22⋊C4C22⋊C411yescharacteristic
598C2×C22⋊C4C22⋊C414yes—
599C2×C22⋊C4C22⋊C414yes—
600C2×C22⋊C4C2×D414yes—
601C2×C22⋊C4C2×D414yes—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—48no—
609C2×C42C22×C411yescharacteristic
610C2×C42C22×C411yescharacteristic
611C2×C42C22×C412yes—
612C2×C42C2×D412yes—
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D412yes—
616C2×C42C2418yes—
617C2×C42C2412yes—
618C4⋊C8—24no—
619C4⋊C8—24no—
620#104—232no—
621#104—416no—
622#104—416no—
623C22⋊C8—24no—
624C22⋊C8—24no—
625C22⋊C8—24no—
626C22⋊C8—24no—
627C22⋊C8—24no—
628C22⋊C8—24no—
629#97—24no—
630C4×C8—24no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637C24—21no—
638C24—24no—
639C24—21no—
640C24—21no—
641C24—24no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—81no—
651C24—81no—
652C24—82no—
653C24—82no—
654C24C2×C22⋊C411yescharacteristic
655C24C2×C22⋊C411yescharacteristic
656C24C2×C22⋊C411yescharacteristic
657C24C2×C22⋊C412yes—
658C24C2×C22⋊C412yes—
659C24C2×C22⋊C411yescharacteristic
660C24C22×D411yescharacteristic
661C24C22×D412yes—
662C24C22×D412yes—
663#41—28no—
664#41—28no—
665#41—24no—
666#41—24no—
667#41—24no—
668#41—28no—
669#41—28no—
670#41—28no—
671#41—28no—
672#41—28no—
673#41—28no—
674#41—416no—
675#41—416no—
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680#41—44no—
681#41—44no—
682#41—416no—
683#41—416no—
684#41—416no—
685#41—416no—
686#41—44no—
687#41—44no—
688#41—44no—
689#41—44no—
690#41—416no—
691#41—416no—
692#41—48no—
693#41—48no—
694#41—48no—
695#41—48no—
696#41H(5,𝔽2)18yes—
697C2×Q8—24no—
698C2×Q8—21no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—48no—
712C2×Q8—48no—
713C2×Q8C23×C412yes—
714C2×Q8C23×C412yes—
715C2×Q8C23×C412yes—
716C2×D4—28no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—21no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—24no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—416no—
755C2×D4—416no—
756C2×D4—432no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—416no—
760C2×D4—416no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—82no—
770C2×D4—82no—
771C2×D4—82no—
772C2×D4C2×C22⋊C414yes—
773C2×D4C2×C22⋊C414yes—
774C2×D4C2×C22⋊C414yes—
775C2×D4C2×C22⋊C414yes—
776C2×D4C23×C412yes—
777C2×D4C23×C412yes—
778C2×D4C23×C412yes—
779C22×C4—28no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—24no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—42no—
820C22×C4—416no—
821C22×C4—416no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—416no—
827C22×C4—416no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—81no—
835C22×C4—84no—
836C22×C4—82no—
837C22×C4—84no—
838C22×C4C2×C22⋊C411yescharacteristic
839C22×C4C2×C22⋊C411yescharacteristic
840C22×C4C2×C22⋊C411yescharacteristic
841C22×C4C2×C22⋊C411yescharacteristic
842C22×C4C2×C22⋊C412yes—
843C22×C4C2×C22⋊C412yes—
844C22×C4C2×C22⋊C411yescharacteristic
845C22×C4C2×C22⋊C411yescharacteristic
846C22×C4C2×C22⋊C411yescharacteristic
847C22×C4C2×C22⋊C411yescharacteristic
848C22×C4C2×C22⋊C412yes—
849C22×C4C2×C22⋊C412yes—
850C22×C4C2×C22⋊C412yes—
851C22×C4C2×C22⋊C412yes—
852C22×C4C2×C22⋊C412yes—
853C22×C4C2×C22⋊C412yes—
854C22×C4C2×C22⋊C412yes—
855C22×C4C2×C22⋊C412yes—
856C22×C4C2×C22⋊C412yes—
857C22×C4C2×C22⋊C412yes—
858C22×C4C23×C411yescharacteristic
859C22×C4C23×C411yescharacteristic
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C23×C412yes—
863C22×C4C23×C412yes—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C2511yescharacteristic
876M16—216no—
877M16—84no—
878M16—84no—
879C2×C8—28no—
880C2×C8—84no—
881C2×C8—84no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—84no—
893C4⋊C4—84no—
894C4⋊C4C2×C22⋊C414yes—
895C4⋊C4C2×C22⋊C414yes—
896C4⋊C4C2×C22⋊C414yes—
897C4⋊C4C2×C22⋊C414yes—
898C4⋊C4C23×C412yes—
899C4⋊C4C23×C412yes—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—22no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—22no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4C2×C22⋊C414yes—
921C22⋊C4C2×C22⋊C414yes—
922C22⋊C4C2×C22⋊C414yes—
923C22⋊C4C2×C22⋊C414yes—
924C22⋊C4C2×C22⋊C414yes—
925C22⋊C4C2×C22⋊C414yes—
926C22⋊C4C2×C22⋊C414yes—
927C22⋊C4C2×C22⋊C414yes—
928C42—22no—
929C42—24no—
930C42—24no—
931C42—22no—
932C42—216no—
933C42—84no—
934C42C2×C22⋊C412yes—
935C42C2×C22⋊C412yes—
936C42C2×C22⋊C412yes—
937C42C2×C22⋊C412yes—
938C42C23×C412yes—
939C42C23×C412yes—
940C42C22×D412yes—
941C42C22×D412yes—
942C23—24no—
943C23—22no—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—22no—
950C23—24no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—41no—
956C23—41no—
957C23—42no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—42no—
962C23—41no—
963C23—41no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—48no—
973C23—48no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—48no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—48no—
982C23—42no—
983C23—42no—
984C23—84no—
985C23—84no—
986C23—88no—
987C23—816no—
988C23—88no—
989C23—816no—
990C23#42114yescomplemented
991C23C22×C22⋊C412yes—
992C23C22×C22⋊C412yes—
993C23C22×C22⋊C412yes—
994C23C22×C22⋊C411yescharacteristic
995C23C22×C22⋊C412yes—
996C23C22×C22⋊C411yescharacteristic
997C23C23×D411yescharacteristic
998Q8—24no—
999Q8—22no—
1000Q8—24no—
1001Q8—24no—
1002Q8—48no—
1003Q8—48no—
1004Q8—42no—
1005Q8—42no—
1006Q8#51814yes—
1007D4—28no—
1008D4—24no—
1009D4—28no—
1010D4—28no—
1011D4—28no—
1012D4—22no—
1013D4—24no—
1014D4—24no—
1015D4—44no—
1016D4—44no—
1017D4—48no—
1018D4—48no—
1019D4—48no—
1020D4—48no—
1021D4—48no—
1022D4—42no—
1023D4—42no—
1024D4—48no—
1025D4—48no—
1026D4—48no—
1027D4—44no—
1028D4—44no—
1029D4—48no—
1030D4—44no—
1031D4—44no—
1032D4—84no—
1033D4—84no—
1034D4—84no—
1035D4#51814yes—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—28no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—41no—
1079C2×C4—42no—
1080C2×C4—41no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—48no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—48no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—84no—
1100C2×C4—816no—
1101C2×C4C22×C22⋊C411yescharacteristic
1102C2×C4C22×C22⋊C412yes—
1103C2×C4C22×C22⋊C412yes—
1104C2×C4C22×C22⋊C411yescharacteristic
1105C2×C4C22×C22⋊C412yes—
1106C2×C4C22×C22⋊C412yes—
1107C2×C4C22×C22⋊C412yes—
1108C2×C4C22×C22⋊C412yes—
1109C2×C4C22×C22⋊C412yes—
1110C2×C4C22×C22⋊C412yes—
1111C2×C4C24×C411yescharacteristic
1112C2×C4C23×D411yescharacteristic
1113C2×C4C2×H(5,𝔽2)14yes—
1114C8—48no—
1115C22—21no—
1116C22—22no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—22no—
1121C22—22no—
1122C22—21no—
1123C22—24no—
1124C22—22no—
1125C22—22no—
1126C22—21no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—21no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—44no—
1135C22—48no—
1136C22—44no—
1137C22—48no—
1138C22—44no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—84no—
1148C22—82no—
1149C22—82no—
1150C22—84no—
1151C22—816no—
1152C22—84no—
1153C22—84no—
1154C22—84no—
1155C22—816no—
1156C22C2×#42112yes—
1157C22C2×#42114yes—
1158C22C23×C22⋊C411yescharacteristic
1159C22#348412yes—
1160C4—21no—
1161C4—24no—
1162C4—22no—
1163C4—22no—
1164C4—21no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—88no—
1176C4C2×#51812yes—
1177C4#348412yes—
1178C2—22no—
1179C2—22no—
1180C2—24no—
1181C2—42no—
1182C2—41no—
1183C2—42no—
1184C2—42no—
1185C2—44no—
1186C2—82no—
1187C2—82no—
1188C2#3417111yescharacteristic
1189C2C22×#42111yescharacteristic
1190C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radicalC2×D4×#41C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. #34057C2semidirect
4. #22434C2semidirect
5. #21816C2semidirect
6. #21774C2semidirect
7. #21773C2semidirect
8. #20748C2semidirect
9. #20605C2semidirect
10. C2×#1789C2semidirect
15. D4×#41C4semidirect
17. C2×#550C4semidirect
18. C2×D4×Q8C4semidirect
19. C2×#548C4semidirect
20. C2×#548C4semidirect
22. C2×#547C4semidirect
25. C2×#546C4semidirect
26. C2×#546C4semidirect
28. C2×D42C4semidirect
43. D4×M16C22semidirect
44. #2920C22semidirect
45. C2×#421C22semidirect
46. C22×#104C22semidirect
47. C2×#407C22semidirect
48. C2×#407C22semidirect
54. #2290C22semidirect
55. #2283C22semidirect
56. #2280C22semidirect
57. C2×C4×C22⋊C4C22semidirect
58. #1980C22semidirect
59. #1963C22semidirect
60. #1897C22semidirect
61. #1896C22semidirect
62. #1871C22semidirect
63. #1871C22semidirect
64. #1826C22semidirect
65. #1806C22semidirect
67. #1789C22semidirect
68. #1789C22semidirect
69. #1789C22semidirect
70. #1789C22semidirect
71. #1759C22semidirect
85. C22×#41C2×C4semidirect
86. C22×#41C2×C4semidirect
87. C22×#41C2×C4semidirect
94. C23×Q8C2×C4semidirect
99. C23×D4C2×C4semidirect
105. C22×M16C23semidirect
106. C22×M16C23semidirect
108. #550C2×C4semidirect
110. D4×Q8C2×C4semidirect
113. #548C2×C4semidirect
114. #548C2×C4semidirect
118. #547C2×C4semidirect
125. #546C2×C4semidirect
126. #546C2×C4semidirect
130. D42C2×C4semidirect
135. #532C2×C4semidirect
138. C2×C4⋊Q8C2×C4semidirect
140. C2×#127C2×C4semidirect
143. C2×#124C2×C4semidirect
144. C2×#124C2×C4semidirect
154. #525C2×C4semidirect
169. C2×C22⋊Q8C2×C4semidirect
170. C2×C22⋊Q8C2×C4semidirect
183. C2×#121C2×C4semidirect
184. C2×#121C2×C4semidirect
193. C4×#41C2×C4semidirect
195. C2×C4×Q8C2×C4semidirect
196. C2×C4×Q8C2×C4semidirect
216. C2×C4×D4C2×C4semidirect
217. C2×C4×D4C2×C4semidirect
227. C2×#117C23semidirect
237. C22×C42C23semidirect
246. #423C23semidirect
250. C2×#104C23semidirect
251. C2×#104C23semidirect
257. #407C23semidirect
258. #407C23semidirect
263. C4×M16C23semidirect
276. C4×C4⋊C4C23semidirect
280. C4×C22⋊C4C23semidirect
281. C4×C22⋊C4C23semidirect
282. #376C23semidirect
284. #339C23semidirect
990. C23#421semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#412
#602302
#340572
#224342
#218162
#217742
#217732
#207482
#206052
C2×#17892