Finite Group Databasebeta

← #6441639

Subgroups — #6441639

Order 512.

2480 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C211yesmaximal, characteristic, complemented
2C2×#3055C211yesmaximal, characteristic
3C2×#2504C211yesmaximal, characteristic, complemented
4#34136C211yesmaximal, characteristic, complemented
5#25231C214yesmaximal, complemented
6#25227C214yesmaximal, complemented
7#25214C214yesmaximal, complemented
8#25210C214yesmaximal, complemented
9#23659C211yesmaximal, characteristic, complemented
10#23631C211yesmaximal, characteristic, complemented
11#23618C211yesmaximal, characteristic, complemented
12#23546C211yesmaximal, characteristic, complemented
13#21172C211yesmaximal, characteristic, complemented
14#21060C211yesmaximal, characteristic, complemented
15#20928C211yesmaximal, characteristic, complemented
16#20912C211yesmaximal, characteristic, complemented
17#20837C211yesmaximal, characteristic, complemented
18#20649C211yesmaximal, characteristic, complemented
19C2×#1736C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#3092—28no—
28C2×#484C2212yescomplemented
29C2×#481C2212yescomplemented
30C2×#483C2212yescomplemented
31C2×#480C2212yescomplemented
32#3055—28no—
33C2×#469C2212yes—
34C2×#468C2212yes—
35C2×#466C2212yes—
36C2×#465C2212yes—
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#423C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C2×#407C2211yescharacteristic
49#2504—21no—
50#2504—21no—
51#2504—21no—
52#2504—21no—
53#2504C2214yes—
54#2504C2214yes—
55C2×#397—22no—
56#2363C2212yescomplemented
57#2362C2212yescomplemented
58#2361C2212yescomplemented
59#2360C2212yescomplemented
60#2359—22no—
61#2358—22no—
62#2297C2211yescharacteristic
63#2296C2211yescharacteristic
64#2293—21no—
65C2×#390C2211yescharacteristic
66C2×#390C2211yescharacteristic
67#2290—21no—
68#2290—21no—
69C2×#386—22no—
70C2×#382C2211yescharacteristic
71C2×#382C2211yescharacteristic
72C42×D4—21no—
73C4×#117C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#2085C2214yescomplemented
76#2085C2214yescomplemented
77#2074C2214yescomplemented
78#2073C2214yescomplemented
79#2067C2214yescomplemented
80#2065C2214yescomplemented
81#2055C2214yescomplemented
82#2054C2214yescomplemented
83#1949C2214yescomplemented
84#1949C2214yescomplemented
85#1926C2214yescomplemented
86#1925C2214yescomplemented
87#1880C2214yescomplemented
88#1879C2214yescomplemented
89#1875C2214yes—
90#1874C2214yes—
91#1851C2214yescomplemented
92#1850C2214yescomplemented
93#1805C2214yescomplemented
94#1804C2214yescomplemented
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1736C2214yescomplemented
102C2×#340C2214yescomplemented
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C23×D4—21no—
107C23×D4C2311yescharacteristic
108C24×C4—21no—
109C24×C4C2311yescharacteristic
110C2×AGL(1,ℤ/8)—24no—
111C2×AGL(1,ℤ/8)—24no—
112C2×AGL(1,ℤ/8)—42no—
113C22×SD16C2312yes—
114C22×D8C2312yes—
115C22×M16—24no—
116C22×M16—24no—
117C22×M16—42no—
118C22×M16C2311yescharacteristic
119C22×M16C2311yescharacteristic
120C22×M16C2311yescharacteristic
121C22×M16C2312yes—
122C22×M16C2311yescharacteristic
123C23×C8C2312yes—
124#525—24no—
125#525D418yes—
126C2×#123—21no—
127C2×C22⋊Q8C2311yescharacteristic
128C2×C22⋊Q8C2311yescharacteristic
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121C2312yes—
134C2×#121C2312yes—
135C2×#121C2311yescharacteristic
136C2×#121C2311yescharacteristic
137C2×#120—21no—
138C4×#41—24no—
139C4×#41—42no—
140C2×C4×Q8C2312yes—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—22no—
144C2×C4×D4—22no—
145C2×C4×D4C2312yes—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117—24no—
150C2×#117—42no—
151C2×#117C2311yescharacteristic
152C2×#117C2312yes—
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C22×C4⋊C4—24no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—22no—
169C22×C22⋊C4—22no—
170C22×C22⋊C4D412yes—
171C22×C42—21no—
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#484—28no—
176#483—28no—
177#481—28no—
178#480—28no—
179#469—28no—
180#468—28no—
181#466—28no—
182#465—28no—
183#428—24no—
184#428—24no—
185#428—24no—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192#423—24no—
193#423—42no—
194C2×C4⋊C8C2314yes—
195C2×C4⋊C8C2314yes—
196#418—24no—
197#418—24no—
198#418—42no—
199#417—24no—
200#417—24no—
201#417—24no—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2314yes—
211C2×#102C2314yes—
212#407—24no—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215#397—24no—
216#397—24no—
217#397—24no—
218#397—24no—
219#391C2312yes—
220#390—22no—
221#390—21no—
222#390—21no—
223#390—21no—
224#390—21no—
225#390C2312yes—
226#390C2314yes—
227#390C2314yes—
228#389—22no—
229#389C2312yes—
230#389C2312yes—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#387—22no—
236#387—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—24no—
244#385—22no—
245#385—22no—
246#385—22no—
247#382—21no—
248#382—21no—
249#382—21no—
250#382—21no—
251#382C2314yes—
252#382C2314yes—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4C2312yes—
268C4×C22⋊C4C2312yes—
269#376—21no—
270C2×#95—22no—
271C2×#95—22no—
272C2×#95D412yes—
273C43—21no—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2314yes—
282C25—21no—
283C25C2×D411yescharacteristic
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41C2×D414yes—
290C22×Q8C2411yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—48no—
304C22×D4—44no—
305C22×D4C2412yes—
306C22×D4C2411yescharacteristic
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—44no—
320C23×C4—84no—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D414yes—
325C23×C4C2×D412yes—
326C23×C4C2×D412yes—
327C23×C4#4114yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331AGL(1,ℤ/8)—416no—
332C2×SD16—24no—
333C2×SD16—24no—
334C2×SD16—42no—
335C2×D8—24no—
336C2×D8—24no—
337C2×D8—42no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—24no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—24no—
351C2×M16—42no—
352C2×M16—416no—
353C2×M16#4114yes—
354C22×C8—24no—
355C22×C8—24no—
356C22×C8—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361#123—28no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8C2×D414yes—
365C22⋊Q8C2×D414yes—
366#121—22no—
367#121—22no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—44no—
373#121—44no—
374#121C2×D414yes—
375#121C2×D414yes—
376#120—28no—
377C4×Q8—24no—
378C4×Q8—42no—
379C4×D4—28no—
380C4×D4—28no—
381C4×D4—24no—
382C4×D4—42no—
383C4×D4—48no—
384C4×D4—48no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—24no—
390#117—44no—
391#117—44no—
392#117—44no—
393#117—42no—
394#117C2×D414yes—
395#117#4114yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2412yes—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—84no—
450C2×C22⋊C4—84no—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—44no—
467C2×C42—44no—
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2412yes—
473C2×C42C2412yes—
474#107—24no—
475#107—24no—
476#107—24no—
477#106—24no—
478#106—24no—
479#106—24no—
480C4⋊C8—28no—
481C4⋊C8—44no—
482#103—24no—
483#103—24no—
484#103—24no—
485#102—24no—
486#102—24no—
487#102—24no—
488#102—24no—
489#102—24no—
490#102—28no—
491#102—44no—
492C22⋊C8—24no—
493C22⋊C8—24no—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507#95C2×D412yes—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—21no—
512C24—22no—
513C24—42no—
514C24—44no—
515C24—44no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24#12114yes—
520C24C22×D411yescharacteristic
521C24C22×D411yescharacteristic
522C24C22×D411yescharacteristic
523#41—28no—
524#41—28no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C22×D412yes—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—48no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—48no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—42no—
559C2×D4—44no—
560C2×D4—42no—
561C2×D4—82no—
562C2×D4—816no—
563C2×D4C22×D412yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—816no—
616C22×C4#12114yes—
617C22×C4#12114yes—
618C22×C4#12114yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D412yes—
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+412yes—
636C22×C4C2511yescharacteristic
637SD16—48no—
638D8—48no—
639M16—28no—
640M16—48no—
641M16—44no—
642M16—44no—
643M16—44no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—48no—
656C2×C8C2×#4114yes—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—82no—
679C4⋊C4C22×D412yes—
680C4⋊C4C22×D412yes—
681C4⋊C4C2×#4114yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—82no—
699C22⋊C4—84no—
700C22⋊C4—84no—
701C22⋊C4—84no—
702C22⋊C4—84no—
703C42—24no—
704C42—22no—
705C42—22no—
706C42—24no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—44no—
714C42—44no—
715C42—44no—
716C42—42no—
717C42—82no—
718C23—22no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—28no—
725C23—21no—
726C23—21no—
727C23—28no—
728C23—22no—
729C23—22no—
730C23—44no—
731C23—48no—
732C23—48no—
733C23—42no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—44no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—84no—
743C23—84no—
744C23—88no—
745C23—88no—
746C23—84no—
747C23C2×#12112yes—
748C23C2×#12112yes—
749C23C2×#12112yes—
750C23#54612yes—
751C23#54712yes—
752C23#57514yes—
753C23C23×D411yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—41no—
757Q8—41no—
758D4—22no—
759D4—22no—
760D4—48no—
761D4—48no—
762D4—41no—
763D4—42no—
764D4—41no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—84no—
769D4—88no—
770D4—88no—
771D4—84no—
772C2×C4—28no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—48no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—84no—
820C2×C4—84no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4—84no—
826C2×C4—88no—
827C2×C4—88no—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4#52914yes—
832C2×C4#53914yes—
833C2×C4#54612yes—
834C2×C4#54614yes—
835C2×C4#54712yes—
836C2×C4#54714yes—
837C2×C4C23×D411yescharacteristic
838C2×C4C22×#4111yescharacteristic
839C2×C4C22×#4111yescharacteristic
840C2×C4C22×#4111yescharacteristic
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×2−1+411yescharacteristic
843C8—24no—
844C8—42no—
845C8—42no—
846C8—42no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—24no—
851C22—22no—
852C22—24no—
853C22—24no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—416no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—84no—
868C22—82no—
869C22—84no—
870C22—82no—
871C22—168no—
872C22#242514yes—
873C22#304014yes—
874C22C22×#12111yescharacteristic
875C22C2×#54611yescharacteristic
876C22C2×#54711yescharacteristic
877C22C2×#57512yes—
878C22#358512yes—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4#242514yes—
894C4C2×#52911yescharacteristic
895C4C2×#53911yescharacteristic
896C4C2×#54611yescharacteristic
897C4C2×#54711yescharacteristic
898C2—24no—
899C2—24no—
900C2—42no—
901C2—82no—
902C2—162no—
903C2C2×#242511yescharacteristic
904C2C2×#304011yescharacteristic
905C2#6042611yescharacteristic
906C2#6116412yes—
907C2#6125512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3055C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3092C2semidirect
3. C2×#2504C2semidirect
4. #34136C2semidirect
5. #25231C2semidirect
6. #25227C2semidirect
7. #25214C2semidirect
8. #25210C2semidirect
9. #23659C2semidirect
10. #23631C2semidirect
11. #23618C2semidirect
12. #23546C2semidirect
13. #21172C2semidirect
14. #21060C2semidirect
15. #20928C2semidirect
16. #20912C2semidirect
17. #20837C2semidirect
18. #20649C2semidirect
19. C2×#1736C2semidirect
28. C2×#484C22semidirect
29. C2×#481C22semidirect
30. C2×#483C22semidirect
31. C2×#480C22semidirect
56. #2363C22semidirect
57. #2362C22semidirect
58. #2361C22semidirect
59. #2360C22semidirect
75. #2085C22semidirect
76. #2085C22semidirect
77. #2074C22semidirect
78. #2073C22semidirect
79. #2067C22semidirect
80. #2065C22semidirect
81. #2055C22semidirect
82. #2054C22semidirect
83. #1949C22semidirect
84. #1949C22semidirect
85. #1926C22semidirect
86. #1925C22semidirect
87. #1880C22semidirect
88. #1879C22semidirect
91. #1851C22semidirect
92. #1850C22semidirect
93. #1805C22semidirect
94. #1804C22semidirect
101. #1736C22semidirect
102. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
C2×#30552
C2×#25042
#341362
#252312
#252272
#252142
#252102
#236592
#236312
#236182
#235462
#211722
#210602
#209282
#209122
#208372
#206492
C2×#17362