Finite Group Databasebeta

← #6451830

Subgroups — #6451830

Order 512.

4270 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#3007C211yesmaximal, characteristic, complemented
3C22×#417C211yesmaximal, characteristic, complemented
4#34736C211yesmaximal, characteristic
5#23981C218yesmaximal, complemented
6#23970C214yesmaximal, complemented
7#23969C214yesmaximal, complemented
8#23452C212yesmaximal, complemented
9#23392C212yesmaximal, complemented
10#20972C211yesmaximal, characteristic, complemented
11#20926C212yesmaximal, complemented
12#20909C212yesmaximal, complemented
13#20898C211yesmaximal, characteristic, complemented
14#20700C211yesmaximal, characteristic, complemented
15C23×#41C2211yescharacteristic
16C22×#137C2212yes—
17C23×M16C2211yescharacteristic
18C2×#554—28no—
19C2×#554—22no—
20C2×#554—22no—
21C2×#554—28no—
22C2×#554C2214yes—
23C2×#554C2214yescomplemented
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#125—21no—
26C2×#525C2212yes—
27C22×C22⋊Q8—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic, complemented
31C22×C4×Q8C2211yescharacteristic, complemented
32C22×C4×D4—21no—
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic, complemented
36#3007—28no—
37C2×#452C2214yescomplemented
38C2×#451C2212yescomplemented
39C2×#450C2212yescomplemented
40C2×#417—28no—
41C2×#417C2212yes—
42C2×#417C2212yes—
43C2×#417C2212yes—
44C2×#417C2214yescomplemented
45C2×#419C2212yescomplemented
46C22×#103C2212yescomplemented
47C22×#102C2212yescomplemented
48C2×#407C2211yescharacteristic
49C2×#407C2212yescomplemented
50#2409C2212yes—
51#2408C2212yes—
52#2407C2214yes—
53#2406—21no—
54#2405—21no—
55#2404—21no—
56#2403—21no—
57#2388—22no—
58C4×#120—22no—
59#2297C2212yes—
60#2280C2211yescharacteristic
61#2024C2218yescomplemented
62#2023C2218yescomplemented
63#2001C2218yescomplemented
64#2000C2218yescomplemented
65#1894C2214yescomplemented
66#1892C2214yescomplemented
67#1880C2218yescomplemented
68#1878C2218yescomplemented
69#1874C2218yescomplemented
70#1872C2218yescomplemented
71#1870C2214yescomplemented
72#1869C2214yes—
73#1824C2214yescomplemented
74#1823C2214yescomplemented
75#1736C2212yescomplemented
76#1736C2212yescomplemented
77#1736C2212yescomplemented
78#1728C2212yescomplemented
79C22×#41—21no—
80C22×#41—21no—
81C22×#41—28no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—44no—
85C22×#41C2312yes—
86C22×#41C2312yes—
87C23×Q8—21no—
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4—21no—
91C23×D4D411yescharacteristic
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4—21no—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C2×#137—28no—
99C2×#137—28no—
100C2×#137—44no—
101C22×Q16C2314yes—
102C22×SD16C2314yes—
103C22×M16—24no—
104C22×M16—44no—
105C22×M16C2312yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108C23×C8C2312yes—
109#554—232no—
110#554—232no—
111#554—216no—
112#554—216no—
113#554—216no—
114#554—216no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8C2314yes—
119C2×#125—216no—
120C2×#125—24no—
121C2×#125—24no—
122#525—28no—
123#525—44no—
124C2×#123—22no—
125C2×C22⋊Q8—216no—
126C2×C22⋊Q8—216no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8D418yescomplemented
138C2×C22⋊Q8C2314yes—
139C2×C22⋊Q8C2314yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121C2314yes—
143C2×#120—22no—
144C2×#120—22no—
145C2×C4×Q8—24no—
146C2×C4×Q8—24no—
147C2×C4×Q8—22no—
148C2×C4×Q8C2314yes—
149C2×C4×D4—216no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4D412yes—
156C2×C4×D4D412yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117C2312yes—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—24no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4D411yescharacteristic
173C22×C4⋊C4D418yescomplemented
174C22×C4⋊C4C2314yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4D411yescharacteristic
183C22×C22⋊C4D411yescharacteristic
184C22×C42—21no—
185C22×C42C2311yescharacteristic
186#452—216no—
187#451—28no—
188#450—28no—
189#419—44no—
190#417—28no—
191#417—28no—
192#417—216no—
193#417—28no—
194C2×#103—28no—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2318yes—
199C2×#102—28no—
200C2×#102C2314yes—
201C2×#102C2314yes—
202C2×#102C2314yes—
203#407—24no—
204#407—44no—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2318yes—
208#395—22no—
209#394—22no—
210#394—24no—
211#393—22no—
212#392—24no—
213#392—22no—
214#391C2314yes—
215#390C2314yes—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—24no—
220#385—24no—
221#385—22no—
222#381—21no—
223#380C2312yes—
224#380C2312yes—
225#379—21no—
226#379—22no—
227C4×C22⋊C4—21no—
228C4×C22⋊C4—21no—
229C4×C22⋊C4—24no—
230#340C2318yes—
231#340C2318yes—
232#340C2318yes—
233#336C2318yes—
234C25—21no—
235C25C2×D411yescharacteristic
236C25C2×D411yescharacteristic
237C2×#41—24no—
238C2×#41—232no—
239C2×#41—24no—
240C2×#41—24no—
241C2×#41—24no—
242C2×#41—24no—
243C2×#41—24no—
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—24no—
247C2×#41—48no—
248C2×#41—42no—
249C2×#41—42no—
250C2×#41—48no—
251C2×#41—432no—
252C2×#41—416no—
253C2×#41—44no—
254C2×#41—44no—
255C2×#41#4118yes—
256C22×Q8—28no—
257C22×Q8—22no—
258C22×Q8—21no—
259C22×Q8—24no—
260C22×Q8—21no—
261C22×Q8—24no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—24no—
265C22×Q8—24no—
266C22×Q8—42no—
267C22×Q8—84no—
268C22×Q8C2×D414yes—
269C22×Q8C2412yes—
270C22×Q8C2412yes—
271C22×D4—24no—
272C22×D4—28no—
273C22×D4—24no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—24no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—21no—
280C22×D4—42no—
281C22×D4—48no—
282C22×D4—44no—
283C22×D4C2×D412yes—
284C22×D4C2×D412yes—
285C22×D4C2412yes—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—28no—
293C23×C4—28no—
294C23×C4—24no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—21no—
303C23×C4—22no—
304C23×C4—48no—
305C23×C4—44no—
306C23×C4—84no—
307C23×C4—84no—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D412yes—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321#137—432no—
322C2×Q16—28no—
323C2×Q16—28no—
324C2×Q16—44no—
325C2×SD16—28no—
326C2×SD16—28no—
327C2×SD16—44no—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—44no—
336C2×M16—416no—
337C22×C8—24no—
338C22×C8—44no—
339C22×C8C2414yes—
340C22×C8C2414yes—
341C4⋊Q8—216no—
342C4⋊Q8—28no—
343C4⋊Q8—28no—
344#125—232no—
345#125—232no—
346#123—48no—
347C22⋊Q8—216no—
348C22⋊Q8—232no—
349C22⋊Q8—232no—
350C22⋊Q8—232no—
351C22⋊Q8—232no—
352C22⋊Q8—28no—
353C22⋊Q8—28no—
354C22⋊Q8—28no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—28no—
358C22⋊Q8—28no—
359C22⋊Q8—44no—
360C22⋊Q8C2×D418yes—
361C22⋊Q8C2×D418yes—
362#121—28no—
363#121—44no—
364#120—48no—
365#120—48no—
366C4×Q8—216no—
367C4×Q8—28no—
368C4×Q8—28no—
369C4×D4—232no—
370C4×D4—232no—
371C4×D4—28no—
372C4×D4—28no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—416no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—216no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4C2×D412yes—
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D414yes—
412C2×C4⋊C4C2×D414yes—
413C2×C4⋊C4C2×D414yes—
414C2×C4⋊C4C2×D418yes—
415C2×C4⋊C4C2×D418yes—
416C2×C4⋊C4C2414yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4C2×D412yes—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C22⋊C4C2×D412yes—
438C2×C42—28no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—24no—
442C2×C42—22no—
443C2×C42C2×D412yes—
444C2×C42C2412yes—
445#103—28no—
446#103—28no—
447#103—28no—
448#103—48no—
449#102—28no—
450#102—28no—
451#102—28no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—48no—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—24no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—22no—
465C24—42no—
466C24—42no—
467C24—44no—
468C24—42no—
469C24—44no—
470C24—82no—
471C24#12014yes—
472C24C22×D411yescharacteristic
473C24C22×D412yes—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476#41—216no—
477#41—216no—
478#41—216no—
479#41—48no—
480#41—48no—
481#41—432no—
482#41—432no—
483#41—48no—
484#41—48no—
485#41—48no—
486C2×Q8—216no—
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—28no—
491C2×Q8—216no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—22no—
496C2×Q8—24no—
497C2×Q8—22no—
498C2×Q8—44no—
499C2×Q8—48no—
500C2×Q8—44no—
501C2×Q8—42no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—88no—
506C2×Q8—816no—
507C2×Q8C22×D414yes—
508C2×Q8C2×#4114yes—
509C2×D4—232no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—432no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—42no—
534C2×D4—84no—
535C2×D4#13718yescomplemented
536C2×D4C2×#4114yes—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—24no—
542C22×C4—216no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—432no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—88no—
591C22×C4—816no—
592C22×C4—816no—
593C22×C4#12014yes—
594C22×C4#12014yes—
595C22×C4#12014yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C2×#4114yes—
609C22×C4H(5,𝔽2)14yes—
610C22×C4C2511yescharacteristic
611Q16—416no—
612SD16—416no—
613M16—48no—
614M16—48no—
615M16—48no—
616C2×C8—24no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—48no—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—24no—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—48no—
642C4⋊C4C22×D414yes—
643C4⋊C4C22×D414yes—
644C4⋊C4C22×D414yes—
645C22⋊C4—216no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—48no—
657C22⋊C4—84no—
658C22⋊C4—82no—
659C42—216no—
660C42—24no—
661C42—22no—
662C42—22no—
663C42—44no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—28no—
669C23—22no—
670C23—24no—
671C23—28no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—28no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—44no—
680C23—416no—
681C23—416no—
682C23—44no—
683C23—48no—
684C23—44no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—816no—
690C23—84no—
691C23—84no—
692C23C2×#12012yes—
693C23C2×#12012yes—
694C23C2×#12012yes—
695C23#54614yes—
696C23C2×#13714yes—
697C23C2×#13714yes—
698C23C23×D411yescharacteristic
699Q8—24no—
700Q8—28no—
701Q8—24no—
702Q8—48no—
703Q8—48no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—42no—
708Q8—816no—
709D4—216no—
710D4—216no—
711D4—24no—
712D4—24no—
713D4—48no—
714D4—416no—
715D4—416no—
716D4—42no—
717D4—42no—
718D4—816no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—416no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—88no—
765C2×C4—88no—
766C2×C4—816no—
767C2×C4C2×#12012yes—
768C2×C4C2×#12012yes—
769C2×C4C2×#12012yes—
770C2×C4#52514yes—
771C2×C4#53514yes—
772C2×C4#54614yes—
773C2×C4#54618yes—
774C2×C4C2×#13714yes—
775C2×C4C23×D411yescharacteristic
776C2×C4C23×D411yescharacteristic
777C2×C4C22×#4112yes—
778C2×C4C2×H(5,𝔽2)12yes—
779C8—44no—
780C8—44no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—28no—
786C22—28no—
787C22—22no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—28no—
792C22—416no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—48no—
800C22—816no—
801C22—82no—
802C22—82no—
803C22—84no—
804C22#240414yes—
805C22#300414yes—
806C22C22×#12011yescharacteristic
807C22C2×#54612yes—
808C22C22×#13712yes—
809C22#358512yes—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—42no—
814C4—44no—
815C4—44no—
816C4—42no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—84no—
821C4#240414yes—
822C4C2×#52511yescharacteristic
823C4C2×#53511yescharacteristic
824C4C2×#54612yes—
825C2—24no—
826C2—24no—
827C2—42no—
828C2—44no—
829C2—84no—
830C2C2×#240411yescharacteristic
831C2C2×#300411yescharacteristic
832C2#6036711yescharacteristic
833C2#6116214yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34736C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#554C2semidirect
2. C2×#3007C2semidirect
3. C22×#417C2semidirect
5. #23981C2semidirect
6. #23970C2semidirect
7. #23969C2semidirect
8. #23452C2semidirect
9. #23392C2semidirect
10. #20972C2semidirect
11. #20926C2semidirect
12. #20909C2semidirect
13. #20898C2semidirect
14. #20700C2semidirect
23. C2×#554C22semidirect
24. C22×C4⋊Q8C22semidirect
30. C22×C22⋊Q8C22semidirect
31. C22×C4×Q8C22semidirect
35. C23×C4⋊C4C22semidirect
37. C2×#452C22semidirect
38. C2×#451C22semidirect
39. C2×#450C22semidirect
44. C2×#417C22semidirect
45. C2×#419C22semidirect
46. C22×#103C22semidirect
47. C22×#102C22semidirect
49. C2×#407C22semidirect
61. #2024C22semidirect
62. #2023C22semidirect
63. #2001C22semidirect
64. #2000C22semidirect
65. #1894C22semidirect
66. #1892C22semidirect
67. #1880C22semidirect
68. #1878C22semidirect
69. #1874C22semidirect
70. #1872C22semidirect
71. #1870C22semidirect
73. #1824C22semidirect
74. #1823C22semidirect
75. #1736C22semidirect
76. #1736C22semidirect
77. #1736C22semidirect
78. #1728C22semidirect
137. C2×C22⋊Q8D4semidirect
173. C22×C4⋊C4D4semidirect
535. C2×D4#137semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#30072
C22×#4172
#347362
#239812
#239702
#239692
#234522
#233922
#209722
#209262
#209092
#208982
#207002