Finite Group Databasebeta

← #7510393

Subgroups — #7510393

Order 512.

1695 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
1#35566C211yesmaximal, characteristic, complemented
2#35172C211yesmaximal, characteristic
3#32593C212yesmaximal, complemented
4#32592C212yesmaximal, complemented
5#32585C212yesmaximal, complemented
6#32584C212yesmaximal, complemented
7#32577C212yesmaximal, complemented
8#32576C212yesmaximal, complemented
9#32569C212yesmaximal, complemented
10#32568C212yesmaximal, complemented
11#23744C211yesmaximal, characteristic, complemented
12#23668C211yesmaximal, characteristic, complemented
13#23657C211yesmaximal, characteristic, complemented
14#23614C211yesmaximal, characteristic
15#23556C211yesmaximal, characteristic, complemented
16#23456C211yesmaximal, characteristic
17#21304C211yesmaximal, characteristic, complemented
18#21160C211yesmaximal, characteristic, complemented
19#21091C211yesmaximal, characteristic
20#21063C211yesmaximal, characteristic
21#21035C211yesmaximal, characteristic, complemented
22#20873C211yesmaximal, characteristic
23C2×#1864C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C2×#405C2211yescharacteristic
37#2848—22no—
38#2626—22no—
39#2584C2212yescomplemented
40#2584C2212yescomplemented
41#2580C2212yes—
42#2580C2212yes—
43#2567C2212yescomplemented
44#2566—21no—
45#2566—21no—
46#2563—21no—
47#2552—21no—
48#2551—21no—
49#2550—21no—
50#2550—21no—
51#2549—22no—
52#2546C2212yescomplemented
53#2542—21no—
54#2538C2212yes—
55#2538C2212yes—
56#2440—22no—
57#2317C2211yescharacteristic
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2316C2211yescharacteristic
61#2309C2211yescharacteristic
62#2309C2211yescharacteristic
63#2296C2211yescharacteristic
64C2×#389C2211yescharacteristic
65#2285C2211yescharacteristic
66#2274C2211yescharacteristic
67#2101C2211yescharacteristic, complemented
68#2101C2211yescharacteristic, complemented
69#2101C2211yescharacteristic, complemented
70#2101C2211yescharacteristic, complemented
71#2100C2211yescharacteristic, complemented
72#2100C2211yescharacteristic, complemented
73#2099C2211yescharacteristic, complemented
74#2099C2211yescharacteristic, complemented
75#2088C2212yescomplemented
76#2088C2212yescomplemented
77#2088C2212yescomplemented
78#2088C2212yescomplemented
79#2085C2212yescomplemented
80#2085C2212yescomplemented
81#2084C2212yescomplemented
82#2083C2212yescomplemented
83#2067C2212yes—
84#2067C2212yes—
85#2065C2212yes—
86#2065C2212yes—
87#2059C2212yescomplemented
88#2059C2212yescomplemented
89#2058C2212yescomplemented
90#2058C2212yescomplemented
91#2025C2212yes—
92#2025C2212yes—
93#2023C2212yes—
94#2023C2212yes—
95#1985C2212yescomplemented
96#1985C2212yescomplemented
97#1984C2212yescomplemented
98#1984C2212yescomplemented
99#1944C2212yescomplemented
100#1943C2212yescomplemented
101#1942C2212yescomplemented
102#1941C2212yescomplemented
103#1936C2212yes—
104#1936C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1926C2212yes—
108#1926C2212yes—
109#1925C2212yes—
110#1925C2212yes—
111#1921C2212yescomplemented
112#1920C2212yescomplemented
113#1919C2212yescomplemented
114#1918C2212yescomplemented
115#1864C2212yes—
116#1864C2212yes—
117#1864C2212yes—
118#1864C2212yes—
119#1864C2212yes—
120#1864C2212yes—
121#1862C2212yes—
122#1862C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1735C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130C2×#340C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#544—42no—
142#544—42no—
143#533—42no—
144#533—42no—
145C2×C4⋊Q8—22no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8D411yescharacteristic
148C2×C4⋊Q8D411yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×#125—21no—
151C2×#125D411yescharacteristic
152C2×#125D411yescharacteristic
153C2×#125C2312yes—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C22⋊Q8D412yes—
158C2×C22⋊Q8D412yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C22⋊C4—21no—
178C22×C42C2311yescharacteristic
179#428—24no—
180#428—24no—
181#428—42no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106—42no—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191#424—42no—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194#418—42no—
195#418Q818yescomplemented
196C2×#102—24no—
197C2×#102—42no—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206#405—42no—
207C2×#97C2312yes—
208C2×C4×C8C2312yes—
209#399—22no—
210#399—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#398—22no—
215#396—22no—
216#396—22no—
217#396—22no—
218#396—22no—
219#395—22no—
220#395—22no—
221#395—22no—
222#395—22no—
223#393—22no—
224#393—22no—
225#391—22no—
226#391—22no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390C2312yes—
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#389—21no—
236#389—21no—
237#389—22no—
238#389—22no—
239#389—22no—
240#389—22no—
241#389—21no—
242#389—21no—
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2311yescharacteristic
257#385—21no—
258#385—21no—
259#385—22no—
260#385—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#385—22no—
265#385—22no—
266#384—21no—
267#384—21no—
268#384—22no—
269#384—21no—
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#382—21no—
273#382—21no—
274#382—21no—
275#382C2311yescharacteristic
276#382C2311yescharacteristic
277#380—21no—
278#380—21no—
279#380—22no—
280#380—22no—
281#380—22no—
282#379—22no—
283#379—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4—22no—
293C2×#95—21no—
294#340C2311yescharacteristic
295#340C2311yescharacteristic
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×Q8—22no—
330C22×Q8C2×D412yes—
331C22×Q8C2×D412yes—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4C2×Q814yes—
339C22×D4C2412yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—44no—
346C23×C4—82no—
347C23×C4—82no—
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2411yescharacteristic
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16C2×Q814yes—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2412yes—
368C22×C8C2412yes—
369C4⋊Q8—42no—
370C4⋊Q8—42no—
371C4⋊Q8—42no—
372C4⋊Q8—42no—
373C4⋊Q8—44no—
374C4⋊Q8—84no—
375#125—42no—
376#125—42no—
377#125—42no—
378#125—42no—
379#125—44no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—48no—
383C22⋊Q8—84no—
384C22⋊Q8—84no—
385C4×Q8—42no—
386C4×Q8—42no—
387C4×Q8—42no—
388C4×Q8—42no—
389C4×D4—42no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—44no—
394C4×D4—44no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117C2×Q814yes—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—82no—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D412yes—
445C2×C4⋊C4C2×D412yes—
446C2×C4⋊C4C2×D412yes—
447C2×C4⋊C4#4114yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2412yes—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4C2×D412yes—
475C2×C22⋊C4C2×D412yes—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2412yes—
487C2×C42C2412yes—
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490#107—24no—
491#107—24no—
492#107—42no—
493#106—24no—
494#106—24no—
495#106—42no—
496#106—42no—
497#106—42no—
498C4⋊C8—42no—
499C4⋊C8—42no—
500#102—24no—
501#102—24no—
502#102—42no—
503#102—42no—
504#102—42no—
505#102—42no—
506#102C2×Q818yes—
507#102C2×Q818yes—
508#97—42no—
509C4×C8—42no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—24no—
532C24—42no—
533C24—42no—
534C24—81no—
535C24—81no—
536C24—81no—
537C24—81no—
538C24C22×D411yescharacteristic
539C2×Q8—24no—
540C2×Q8—42no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—44no—
546C2×Q8—82no—
547C2×Q8—82no—
548C2×D4—28no—
549C2×D4—24no—
550C2×D4—28no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—42no—
557C2×D4—44no—
558C2×D4—42no—
559C2×D4—44no—
560C2×D4C22×Q814yes—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—816no—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×Q812yes—
604C22×C4C2×#4112yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C42−1+412yes—
608C22×C42−1+412yes—
609C22×C4C2511yescharacteristic
610M16—28no—
611M16—44no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—44no—
630C2×C8—44no—
631C2×C8C22×Q814yes—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—82no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—81no—
677C4⋊C4—81no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4C22×Q812yes—
686C4⋊C4C22×Q812yes—
687C4⋊C4C2×#4114yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C42—22no—
705C42—22no—
706C42—24no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—22no—
714C42—22no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—82no—
719C42—82no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—24no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—48no—
731C23—42no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23#53412yes—
739C23#54812yes—
740C23D4×Q812yes—
741C23C23×D411yescharacteristic
742Q8—84no—
743Q8—84no—
744Q8—164no—
745D4—24no—
746D4—24no—
747D4—42no—
748D4—48no—
749D4—42no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—88no—
808C2×C4—82no—
809C2×C4—84no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4—162no—
813C2×C4#53412yes—
814C2×C4#54214yes—
815C2×C4#54414yes—
816C2×C4#54812yes—
817C2×C4D4×Q812yes—
818C2×C4#55414yes—
819C2×C4#56314yes—
820C2×C4#57712yes—
821C2×C4C23×Q811yescharacteristic
822C2×C4C22×#4111yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×2−1+411yescharacteristic
826C2×C4C2×2−1+411yescharacteristic
827C8—24no—
828C8—41no—
829C8—41no—
830C8—42no—
831C8—41no—
832C8—41no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—816no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22#272914yes—
848C22C2×#53411yescharacteristic
849C22C2×#54811yescharacteristic
850C22C2×D4×Q811yescharacteristic
851C22C2×#57711yescharacteristic
852C22#358411yescharacteristic
853C22#358511yescharacteristic
854C22#358511yescharacteristic
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—41no—
860C4—41no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4#272914yes—
875C4C2×#54211yescharacteristic
876C4C2×#54411yescharacteristic
877C4C2×#55411yescharacteristic
878C4C2×#56311yescharacteristic
879C2—24no—
880C2—84no—
881C2C2×#272911yescharacteristic
882C2#6075711yescharacteristic
883C2#6076011yescharacteristic
884C2#6132711yescharacteristic
885C2#6133211yescharacteristic
886C2#6138211yescharacteristic
887C2#6138511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35566C2semidirect
3. #32593C2semidirect
4. #32592C2semidirect
5. #32585C2semidirect
6. #32584C2semidirect
7. #32577C2semidirect
8. #32576C2semidirect
9. #32569C2semidirect
10. #32568C2semidirect
11. #23744C2semidirect
12. #23668C2semidirect
13. #23657C2semidirect
15. #23556C2semidirect
17. #21304C2semidirect
18. #21160C2semidirect
21. #21035C2semidirect
39. #2584C22semidirect
40. #2584C22semidirect
43. #2567C22semidirect
52. #2546C22semidirect
67. #2101C22semidirect
68. #2101C22semidirect
69. #2101C22semidirect
70. #2101C22semidirect
71. #2100C22semidirect
72. #2100C22semidirect
73. #2099C22semidirect
74. #2099C22semidirect
75. #2088C22semidirect
76. #2088C22semidirect
77. #2088C22semidirect
78. #2088C22semidirect
79. #2085C22semidirect
80. #2085C22semidirect
81. #2084C22semidirect
82. #2083C22semidirect
87. #2059C22semidirect
88. #2059C22semidirect
89. #2058C22semidirect
90. #2058C22semidirect
95. #1985C22semidirect
96. #1985C22semidirect
97. #1984C22semidirect
98. #1984C22semidirect
99. #1944C22semidirect
100. #1943C22semidirect
101. #1942C22semidirect
102. #1941C22semidirect
111. #1921C22semidirect
112. #1920C22semidirect
113. #1919C22semidirect
114. #1918C22semidirect
195. #418Q8semidirect

Maximal subgroups

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

subgroupindex
#355662
#351722
#325932
#325922
#325852
#325842
#325772
#325762
#325692
#325682
#237442
#236682
#236572
#236142
#235562
#234562
#213042
#211602
#210912
#210632
#210352
#208732
C2×#18642