Finite Group Databasebeta

← #6596109

Subgroups — #6596109

Order 512.

3295 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#3356C212yesmaximal, complemented
3#36161C211yesmaximal, characteristic
4#32982C212yesmaximal, complemented
5#32954C211yesmaximal, characteristic, complemented
6#25811C211yesmaximal, characteristic, complemented
7#25702C212yesmaximal, complemented
8#25561C214yesmaximal, complemented
9#24386C212yesmaximal, complemented
10#24302C211yesmaximal, characteristic, complemented
11#24122C212yesmaximal, complemented
12#24109C214yesmaximal, complemented
13#24010C212yesmaximal, complemented
14#22502C212yesmaximal, complemented
15#22401C211yesmaximal, characteristic
16C4×#451C211yesmaximal, characteristic, complemented
17#20844C212yesmaximal, complemented
18C2×#556C2211yescharacteristic
19C2×#554—216no—
20C2×#554—21no—
21C2×#554—21no—
22C2×#554—22no—
23C2×#554C2214yes—
24C2×#554C2212yes—
25C2×#554C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125—21no—
28C22×C22⋊Q8—22no—
29C22×C22⋊Q8C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4—21no—
32C22×C4×D4C2211yescharacteristic
33C23×C4⋊C4C2212yes—
34#3356—216no—
35C2×#498C2212yescomplemented
36C2×#485C2214yescomplemented
37C2×#483C2214yescomplemented
38C2×#477C2212yescomplemented
39C2×#475C2212yescomplemented
40C2×#470C2214yescomplemented
41C2×#451C2211yescharacteristic
42C2×C4×Q16C2212yescomplemented
43C2×#436C2212yes—
44C2×#428C2214yescomplemented
45C2×#407C2212yes—
46#2857C2211yescharacteristic
47#2848C2212yes—
48#2547C2211yescharacteristic
49#2538C2211yescharacteristic
50#2485C2212yes—
51#2480—22no—
52#2466—22no—
53#2447—21no—
54#2435—21no—
55#2415C2212yes—
56#2367—21no—
57#2360—21no—
58#2354C2211yescharacteristic
59C4×C22⋊Q8C2211yescharacteristic
60#2280C2212yes—
61#2058C2214yescomplemented
62#2057C2212yescomplemented
63#2036C2214yescomplemented
64#2035C2214yescomplemented
65#2035C2214yescomplemented
66#2024C2212yescomplemented
67#2001C2214yescomplemented
68#1990C2212yescomplemented
69#1987C2212yescomplemented
70#1954C2212yes—
71#1894C2214yescomplemented
72#1878C2212yescomplemented
73#1873C2214yescomplemented
74#1872C2212yes—
75#1872C2211yescharacteristic
76#1872C2214yescomplemented
77#1870C2214yes—
78#1865C2214yescomplemented
79#1863C2212yescomplemented
80#1853C2212yes—
81#1853C2212yes—
82#1853C2212yes—
83#1853C2214yescomplemented
84#1853C2214yescomplemented
85#1852C2211yescharacteristic
86#1852C2212yes—
87#1852C2214yescomplemented
88#1823C2214yescomplemented
89#1803C2212yescomplemented
90#1797C2211yescharacteristic
91#1787C2212yes—
92#1787C2211yescharacteristic
93#1779C2212yes—
94C4×#103C2212yescomplemented
95C4×C22⋊C8C2211yescharacteristic
96#1736C2214yescomplemented
97C23×Q8—21no—
98C23×Q8C2311yescharacteristic
99C23×D4D411yescharacteristic
100C24×C4—22no—
101C24×C4C2312yes—
102C22×Q16C2312yes—
103C22×M16C2314yes—
104#556—28no—
105#554—216no—
106#554—232no—
107#554—216no—
108#554—28no—
109#554—216no—
110#554—28no—
111#554—28no—
112#554—216no—
113#554D4116yes—
114C2×C4⋊Q8—28no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2312yes—
120C2×#126—22no—
121C2×#125—216no—
122C2×#125—24no—
123C2×#125—22no—
124C2×#125—22no—
125C2×#124—21no—
126C2×#124—21no—
127C2×C22⋊Q8—232no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8—216no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8C2312yes—
137C2×C22⋊Q8C2311yescharacteristic
138C2×C22⋊Q8C2314yes—
139C2×C22⋊Q8C2314yes—
140C2×C22⋊Q8C2312yes—
141C2×C4×Q8—28no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×D4—216no—
149C2×C4×D4—24no—
150C2×C4×D4—22no—
151C2×C4×D4—22no—
152C2×C4×D4—28no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D412yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×#117C2312yes—
160C2×#117C2312yes—
161C22×C4⋊C4—22no—
162C22×C4⋊C4—22no—
163C22×C4⋊C4—22no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—22no—
167C22×C4⋊C4—216no—
168C22×C4⋊C4D411yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2314yes—
172C22×C4⋊C4C2314yes—
173C22×C22⋊C4—22no—
174C22×C22⋊C4D412yes—
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177#498—28no—
178#485—216no—
179#483—216no—
180#477—28no—
181#475—28no—
182#470—216no—
183#451—24no—
184C4×Q16—28no—
185#436—28no—
186#428—216no—
187C2×#107C2314yes—
188C2×#107C2312yes—
189C2×#106C2314yes—
190C2×#106C2314yes—
191C2×#106C2314yes—
192C2×C4⋊C8C2312yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2314yes—
199C2×#103C2312yes—
200#407—28no—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2314yes—
203C2×C22⋊C8C2314yes—
204C2×C22⋊C8C2311yescharacteristic
205C2×C22⋊C8C2314yes—
206C2×C22⋊C8C2311yescharacteristic
207C2×C4×C8C2312yes—
208#397—22no—
209#397—22no—
210#397—22no—
211#396—22no—
212#394—22no—
213#394—22no—
214#391—21no—
215#391—21no—
216#391C2311yescharacteristic
217#390—21no—
218#390—21no—
219#389—22no—
220#389—21no—
221#389—21no—
222#389C2311yescharacteristic
223#389C2312yes—
224#388—22no—
225#388—22no—
226#388—22no—
227#387—22no—
228#387—21no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—21no—
233#384C2311yescharacteristic
234#381—22no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2311yescharacteristic
240#380C2312yes—
241#380C2312yes—
242#379—22no—
243#379—22no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4C2311yescharacteristic
247C4×C22⋊C4—21no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2312yes—
255#340C2312yes—
256#340C2314yes—
257#336C2312yes—
258#336C2312yes—
259C25C2×D412yes—
260C22×Q8—28no—
261C22×Q8—24no—
262C22×Q8—21no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—21no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—42no—
269C22×Q8—82no—
270C22×Q8—82no—
271C22×Q8C2411yescharacteristic
272C22×Q8C2412yes—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—24no—
276C22×D4C2×D412yes—
277C22×D4C2×D411yescharacteristic
278C22×D4C2×D411yescharacteristic
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—21no—
282C23×C4—216no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—28no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—44no—
289C23×C4—84no—
290C23×C4—84no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C2×Q16—24no—
300C2×Q16—24no—
301C2×Q16—42no—
302C2×M16—28no—
303C2×M16—28no—
304C2×M16—44no—
305C22×C8C2414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C4⋊Q8—28no—
309C4⋊Q8—28no—
310C4⋊Q8—28no—
311C4⋊Q8—24no—
312C4⋊Q8—24no—
313C4⋊Q8C2×D418yes—
314#126—48no—
315#125—232no—
316#125—216no—
317#125—216no—
318#124—44no—
319#124—44no—
320C22⋊Q8—216no—
321C22⋊Q8—232no—
322C22⋊Q8—232no—
323C22⋊Q8—216no—
324C22⋊Q8—232no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—232no—
329C22⋊Q8—28no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8C2×D4116yes—
335C4×Q8—28no—
336C4×Q8—28no—
337C4×Q8—24no—
338C4×Q8—24no—
339C4×Q8—24no—
340C4×Q8—24no—
341C4×Q8—44no—
342C4×Q8C2×D418yes—
343C4×D4—232no—
344C4×D4—216no—
345C4×D4—216no—
346C4×D4—24no—
347C4×D4—28no—
348C4×D4—24no—
349C4×D4—28no—
350C4×D4—24no—
351C4×D4C2×D418yes—
352#117—28no—
353#117—44no—
354C2×C4⋊C4—216no—
355C2×C4⋊C4—216no—
356C2×C4⋊C4—216no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—216no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D4116yes—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2414yes—
396C2×C22⋊C4—216no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4C2×D412yes—
412C2×C22⋊C4C2×D412yes—
413C2×C22⋊C4C2×D412yes—
414C2×C22⋊C4C2×D412yes—
415C2×C42—28no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—22no—
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#107—24no—
428#107—28no—
429#106—28no—
430#106—28no—
431#106—28no—
432C4⋊C8—24no—
433#103—24no—
434#103—28no—
435#103—24no—
436#103—24no—
437#103—28no—
438#103—42no—
439#103—44no—
440C22⋊C8—28no—
441C22⋊C8—24no—
442C22⋊C8—22no—
443C22⋊C8—28no—
444C22⋊C8—44no—
445C22⋊C8#4114yes—
446C4×C8—24no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—21no—
452#95—21no—
453#95—22no—
454#95—21no—
455#95—21no—
456#95—22no—
457#95—22no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—42no—
464C24—42no—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C22×D411yescharacteristic
468C2×Q8—24no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—82no—
488C2×Q8—82no—
489C2×Q8—82no—
490C2×Q8—82no—
491C2×Q8—816no—
492C2×Q8C22×D414yes—
493C2×D4—232no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4#12014yes—
502C2×D4#13714yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—28no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—41no—
540C22×C4—416no—
541C22×C4—416no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—832no—
553C22×C4#13714yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D418yes—
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C2×#4112yes—
563C22×C42−1+412yes—
564C22×C4C2511yescharacteristic
565Q16—48no—
566M16—416no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—24no—
575C2×C8C2×#4114yes—
576C4⋊C4—24no—
577C4⋊C4—216no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—216no—
582C4⋊C4—216no—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—216no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—81no—
603C4⋊C4—81no—
604C4⋊C4—82no—
605C4⋊C4#12014yes—
606C4⋊C4C22×D414yes—
607C4⋊C4C22×D418yes—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—42no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—42no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4#12018yes—
625C42—28no—
626C42—28no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—44no—
631C42—42no—
632C42—42no—
633C42—82no—
634C42C22×D414yes—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—216no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—48no—
654C23—48no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23C2×#12014yes—
659C23#54712yes—
660C23C2×#13714yes—
661C23C2×#13712yes—
662C23#57712yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—24no—
666Q8—48no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—88no—
672Q8—88no—
673Q8—84no—
674D4—216no—
675D4—28no—
676D4—28no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—21no—
691C2×C4—24no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—416no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—816no—
733C2×C4—816no—
734C2×C4C2×#12012yes—
735C2×C4C2×#12014yes—
736C2×C4C2×#12012yes—
737C2×C4#54712yes—
738C2×C4C2×#13712yes—
739C2×C4C2×#13712yes—
740C2×C4C2×#13712yes—
741C2×C4C23×D412yes—
742C2×C4C22×#4111yescharacteristic
743C2×C4C2×2−1+411yescharacteristic
744C2×C4#58512yes—
745C8—24no—
746C8—44no—
747C8—42no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—432no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22#335614yescomplemented
770C22C22×#12011yescharacteristic
771C22C2×#54711yescharacteristic
772C22#348511yescharacteristic
773C22C22×#13711yescharacteristic
774C22C22×#13711yescharacteristic
775C22C2×#57711yescharacteristic
776C22#358511yescharacteristic
777C4—22no—
778C4—24no—
779C4—22no—
780C4—22no—
781C4—42no—
782C4—44no—
783C4—41no—
784C4—44no—
785C4—48no—
786C4—82no—
787C4—81no—
788C4—81no—
789C4—81no—
790C4—82no—
791C4—81no—
792C4#300414yes—
793C4D4×#4112yes—
794C4#348912yes—
795C2—24no—
796C2—44no—
797C2—44no—
798C2#3621311yescharacteristic
799C2C2×#300411yescharacteristic
800C2#6037311yescharacteristic
801C2C2×#335611yescharacteristic
802C2#6125411yescharacteristic
803C2#6171911yescharacteristic
804C2#6173511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
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
2. C2×#3356C2semidirect
4. #32982C2semidirect
5. #32954C2semidirect
6. #25811C2semidirect
7. #25702C2semidirect
8. #25561C2semidirect
9. #24386C2semidirect
10. #24302C2semidirect
11. #24122C2semidirect
12. #24109C2semidirect
13. #24010C2semidirect
14. #22502C2semidirect
16. C4×#451C2semidirect
17. #20844C2semidirect
35. C2×#498C22semidirect
36. C2×#485C22semidirect
37. C2×#483C22semidirect
38. C2×#477C22semidirect
39. C2×#475C22semidirect
40. C2×#470C22semidirect
42. C2×C4×Q16C22semidirect
44. C2×#428C22semidirect
61. #2058C22semidirect
62. #2057C22semidirect
63. #2036C22semidirect
64. #2035C22semidirect
65. #2035C22semidirect
66. #2024C22semidirect
67. #2001C22semidirect
68. #1990C22semidirect
69. #1987C22semidirect
71. #1894C22semidirect
72. #1878C22semidirect
73. #1873C22semidirect
76. #1872C22semidirect
78. #1865C22semidirect
79. #1863C22semidirect
83. #1853C22semidirect
84. #1853C22semidirect
87. #1852C22semidirect
88. #1823C22semidirect
89. #1803C22semidirect
94. C4×#103C22semidirect
96. #1736C22semidirect
769. C22#3356semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#33562
#361612
#329822
#329542
#258112
#257022
#255612
#243862
#243022
#241222
#241092
#240102
#225022
#224012
C4×#4512
#208442