Finite Group Databasebeta

← #6441638

Subgroups — #6441638

Order 512.

2394 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C211yesmaximal, characteristic
2C2×#3056C211yesmaximal, characteristic
3C2×#2502C211yesmaximal, characteristic, complemented
4#34136C211yesmaximal, characteristic
5#25223C214yesmaximal, complemented
6#25219C214yesmaximal, complemented
7#25206C214yesmaximal, complemented
8#25202C214yesmaximal, complemented
9#23658C211yesmaximal, characteristic, complemented
10#23630C211yesmaximal, characteristic, complemented
11#23619C211yesmaximal, characteristic, complemented
12#23547C211yesmaximal, characteristic, complemented
13#21171C211yesmaximal, characteristic, complemented
14#21061C211yesmaximal, characteristic, complemented
15#20927C211yesmaximal, characteristic, complemented
16#20911C211yesmaximal, characteristic, complemented
17#20837C211yesmaximal, characteristic, complemented
18#20648C211yesmaximal, characteristic, complemented
19C2×#1736C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#3092—28no—
28C2×#484C2212yes—
29C2×#481C2212yes—
30C2×#483C2212yes—
31C2×#480C2212yes—
32#3056—28no—
33C2×#470C2212yes—
34C2×#468C2212yes—
35C2×#467C2212yes—
36C2×#465C2212yes—
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#423C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#419C2211yescharacteristic
48C2×#407C2211yescharacteristic
49#2502—21no—
50#2502—21no—
51#2502—21no—
52#2502—21no—
53#2502C2214yes—
54#2502C2214yes—
55C2×#398—22no—
56#2363C2212yes—
57#2362C2212yes—
58#2361C2212yes—
59#2360C2212yes—
60#2359—22no—
61#2358—22no—
62#2297C2211yescharacteristic
63#2296C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#391C2211yescharacteristic
66#2293—21no—
67#2290—21no—
68#2290—21no—
69C2×#385—22no—
70C2×#384C2211yescharacteristic
71C2×#384C2211yescharacteristic
72C42×D4—21no—
73C4×#117C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#2084C2214yescomplemented
76#2083C2214yescomplemented
77#2072C2214yescomplemented
78#2071C2214yescomplemented
79#2068C2214yescomplemented
80#2066C2214yescomplemented
81#2056C2214yescomplemented
82#2055C2214yescomplemented
83#1948C2214yescomplemented
84#1947C2214yescomplemented
85#1928C2214yescomplemented
86#1927C2214yescomplemented
87#1878C2214yescomplemented
88#1877C2214yescomplemented
89#1873C2214yes—
90#1872C2214yes—
91#1851C2214yes—
92#1850C2214yes—
93#1803C2214yescomplemented
94#1802C2214yescomplemented
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2214yes—
100#1736C2211yescharacteristic
101#1736C2211yescharacteristic
102C2×#340C2214yes—
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C24×C4—21no—
108C24×C4C2311yescharacteristic
109C2×#137—24no—
110C2×#137—24no—
111C2×#137—42no—
112C22×Q16C2312yes—
113C22×SD16C2312yes—
114C22×M16—24no—
115C22×M16—24no—
116C22×M16—42no—
117C22×M16C2311yescharacteristic
118C22×M16C2311yescharacteristic
119C22×M16C2311yescharacteristic
120C22×M16C2312yes—
121C22×M16C2311yescharacteristic
122C23×C8C2312yes—
123#525—24no—
124#525D418yes—
125C2×#123—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2311yescharacteristic
133C2×C22⋊Q8C2311yescharacteristic
134C2×#121C2311yescharacteristic
135C2×#121C2311yescharacteristic
136C2×#120—21no—
137C4×#41—24no—
138C4×#41—42no—
139C2×C4×Q8C2312yes—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—22no—
143C2×C4×D4—22no—
144C2×C4×D4C2312yes—
145C2×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—24no—
149C2×#117—42no—
150C2×#117C2311yescharacteristic
151C2×#117C2312yes—
152C2×#117C2311yescharacteristic
153C2×#117C2311yescharacteristic
154C22×C4⋊C4—24no—
155C22×C4⋊C4—24no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—22no—
161C22×C4⋊C4—22no—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
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#470—28no—
180#468—28no—
181#467—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#419—24no—
197#419—24no—
198#419—42no—
199#417—24no—
200#417—24no—
201#417—24no—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2314yes—
208C2×#103C2314yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212#407—24no—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215#398—24no—
216#398—24no—
217#398—24no—
218#398—24no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2314yes—
224#391C2312yes—
225#391C2314yes—
226#390—22no—
227#390C2312yes—
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#385—22no—
241#385—22no—
242#385—24no—
243#385—24no—
244#385—24no—
245#385—24no—
246#385—22no—
247#384—21no—
248#384—21no—
249#384—21no—
250#384—21no—
251#384C2314yes—
252#384C2314yes—
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—
282C25C2×D411yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41C2×D414yes—
289C22×Q8—21no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8C2412yes—
297C22×Q8C2411yescharacteristic
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2411yescharacteristic
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—44no—
316C23×C4—84no—
317C23×C4C2×D412yes—
318C23×C4C2×D412yes—
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D414yes—
323C23×C4#4114yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327#137—416no—
328C2×Q16—24no—
329C2×Q16—24no—
330C2×Q16—42no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—42no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—24no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—24no—
347C2×M16—42no—
348C2×M16—416no—
349C2×M16#4114yes—
350C22×C8—24no—
351C22×C8—24no—
352C22×C8—42no—
353C22×C8C2412yes—
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2412yes—
357#123—28no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366C22⋊Q8C2×D414yes—
367C22⋊Q8C2×D414yes—
368#121—22no—
369#121—22no—
370#121C2×D414yes—
371#121C2×D414yes—
372#120—28no—
373C4×Q8—24no—
374C4×Q8—42no—
375C4×D4—28no—
376C4×D4—28no—
377C4×D4—24no—
378C4×D4—42no—
379C4×D4—48no—
380C4×D4—48no—
381#117—22no—
382#117—22no—
383#117—22no—
384#117—22no—
385#117—24no—
386#117—44no—
387#117—44no—
388#117—44no—
389#117—42no—
390#117C2×D414yes—
391#117#4114yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—44no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4—84no—
426C2×C4⋊C4—84no—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—28no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—44no—
466C2×C42—44no—
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2412yes—
472C2×C42C2412yes—
473#107—24no—
474#107—24no—
475#107—24no—
476#106—24no—
477#106—24no—
478#106—24no—
479C4⋊C8—28no—
480C4⋊C8—44no—
481#103—24no—
482#103—24no—
483#103—24no—
484#103—24no—
485#103—24no—
486#103—28no—
487#103—44no—
488#102—24no—
489#102—24no—
490#102—24no—
491C22⋊C8—24no—
492C22⋊C8—24no—
493#95—24no—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95C2×D412yes—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507C24—22no—
508C24—22no—
509C24—24no—
510C24—21no—
511C24—42no—
512C24#12114yes—
513C24C22×D411yescharacteristic
514C24C22×D411yescharacteristic
515C24C22×D411yescharacteristic
516#41—28no—
517#41—28no—
518#41—44no—
519#41—44no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8C22×D412yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—82no—
551C2×D4C22×D412yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—816no—
608C22×C4#12114yes—
609C22×C4#12114yes—
610C22×C4#12114yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D412yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C42−1+412yes—
628C22×C4C2511yescharacteristic
629Q16—48no—
630SD16—48no—
631M16—28no—
632M16—48no—
633M16—44no—
634M16—44no—
635M16—44no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—48no—
648C2×C8C2×#4114yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—82no—
673C4⋊C4—84no—
674C4⋊C4—84no—
675C4⋊C4—84no—
676C4⋊C4—84no—
677C4⋊C4C22×D412yes—
678C4⋊C4C22×D412yes—
679C4⋊C4C2×#4114yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—82no—
696C22⋊C4#13718yescomplemented
697C42—24no—
698C42—22no—
699C42—22no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—44no—
708C42—44no—
709C42—42no—
710C42—44no—
711C42—82no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—28no—
719C23—21no—
720C23—21no—
721C23—28no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—48no—
726C23—48no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23C2×#12112yes—
732C23C2×#12112yes—
733C23C2×#12112yes—
734C23#54612yes—
735C23#54712yes—
736C23C2×#13714yes—
737C23C23×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—42no—
744Q8—42no—
745Q8—42no—
746Q8—84no—
747D4—22no—
748D4—22no—
749D4—48no—
750D4—48no—
751D4—41no—
752D4—41no—
753D4—84no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—48no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—88no—
805C2×C4—88no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—88no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4C2×#12112yes—
813C2×C4C2×#12112yes—
814C2×C4C2×#12112yes—
815C2×C4#52914yes—
816C2×C4#53914yes—
817C2×C4#54612yes—
818C2×C4#54614yes—
819C2×C4#54712yes—
820C2×C4#54714yes—
821C2×C4C2×#13714yes—
822C2×C4C2×#13714yes—
823C2×C4C23×D411yescharacteristic
824C2×C4C22×#4111yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4C2×2−1+411yescharacteristic
829C8—24no—
830C8—42no—
831C8—42no—
832C8—42no—
833C22—22no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—22no—
838C22—24no—
839C22—24no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—416no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—82no—
851C22—82no—
852C22#242514yes—
853C22#303914yes—
854C22C22×#12111yescharacteristic
855C22C2×#54611yescharacteristic
856C22C2×#54711yescharacteristic
857C22C22×#13712yes—
858C22#358512yes—
859C4—24no—
860C4—22no—
861C4—22no—
862C4—24no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—44no—
868C4—42no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4#242514yes—
875C4C2×#52911yescharacteristic
876C4C2×#53911yescharacteristic
877C4C2×#54611yescharacteristic
878C4C2×#54711yescharacteristic
879C2—24no—
880C2—24no—
881C2—42no—
882C2—82no—
883C2C2×#242511yescharacteristic
884C2C2×#303911yescharacteristic
885C2#6042611yescharacteristic
886C2#6116212yes—
887C2#6125412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
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
3. C2×#2502C2semidirect
5. #25223C2semidirect
6. #25219C2semidirect
7. #25206C2semidirect
8. #25202C2semidirect
9. #23658C2semidirect
10. #23630C2semidirect
11. #23619C2semidirect
12. #23547C2semidirect
13. #21171C2semidirect
14. #21061C2semidirect
15. #20927C2semidirect
16. #20911C2semidirect
17. #20837C2semidirect
18. #20648C2semidirect
19. C2×#1736C2semidirect
75. #2084C22semidirect
76. #2083C22semidirect
77. #2072C22semidirect
78. #2071C22semidirect
79. #2068C22semidirect
80. #2066C22semidirect
81. #2056C22semidirect
82. #2055C22semidirect
83. #1948C22semidirect
84. #1947C22semidirect
85. #1928C22semidirect
86. #1927C22semidirect
87. #1878C22semidirect
88. #1877C22semidirect
93. #1803C22semidirect
94. #1802C22semidirect
696. C22⋊C4#137semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
C2×#30562
C2×#25022
#341362
#252232
#252192
#252062
#252022
#236582
#236302
#236192
#235472
#211712
#210612
#209272
#209112
#208372
#206482
C2×#17362