Finite Group Databasebeta

← #6460266

Subgroups — #6460266

Order 512.

1680 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35585C211yesmaximal, characteristic, complemented
2#35515C211yesmaximal, characteristic
3#28974C212yesmaximal, complemented
4#28973C212yesmaximal, complemented
5#28968C212yesmaximal, complemented
6#28967C212yesmaximal, complemented
7#28950C212yesmaximal, complemented
8#28949C212yesmaximal, complemented
9#28944C212yesmaximal, complemented
10#28943C212yesmaximal, complemented
11#23731C211yesmaximal, characteristic
12#23671C211yesmaximal, characteristic, complemented
13#23614C211yesmaximal, characteristic
14#23554C211yesmaximal, characteristic, complemented
15#21318C211yesmaximal, characteristic, complemented
16#21160C211yesmaximal, characteristic, complemented
17#21160C211yesmaximal, characteristic, complemented
18#21089C211yesmaximal, characteristic
19C2×#1934C211yesmaximal, characteristic
20#21036C211yesmaximal, characteristic, complemented
21#20876C211yesmaximal, characteristic
22#20435C211yesmaximal, characteristic, complemented
23#20416C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#424C2211yescharacteristic
31C2×#418C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C2×#405C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38#2580—21no—
39#2580—21no—
40#2569—22no—
41#2538—21no—
42#2538—21no—
43#2509—21no—
44#2509C2212yescomplemented
45#2508—21no—
46#2508C2212yescomplemented
47#2507—21no—
48#2507C2212yescomplemented
49#2506—21no—
50#2506C2212yescomplemented
51#2454C2212yes—
52#2454C2212yes—
53#2452C2212yes—
54#2452C2212yes—
55#2442—22no—
56#2437—22no—
57#2437—22no—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2316C2211yescharacteristic
61#2316C2211yescharacteristic
62#2316C2211yescharacteristic
63#2309C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#389C2211yescharacteristic
67#2285C2211yescharacteristic
68#2274C2211yescharacteristic
69#2094C2212yes—
70#2093C2212yes—
71#2092C2212yes—
72#2092C2212yes—
73#2088C2212yescomplemented
74#2088C2212yescomplemented
75#2087C2212yescomplemented
76#2086C2212yescomplemented
77#2067C2212yes—
78#2067C2212yes—
79#2065C2212yes—
80#2065C2212yes—
81#2059C2212yescomplemented
82#2059C2212yescomplemented
83#2058C2212yescomplemented
84#2057C2212yescomplemented
85#1991C2211yescharacteristic, complemented
86#1991C2211yescharacteristic, complemented
87#1991C2211yescharacteristic, complemented
88#1991C2211yescharacteristic, complemented
89#1990C2211yescharacteristic, complemented
90#1990C2211yescharacteristic, complemented
91#1990C2211yescharacteristic, complemented
92#1990C2211yescharacteristic, complemented
93#1944C2212yescomplemented
94#1944C2212yescomplemented
95#1943C2212yescomplemented
96#1943C2212yescomplemented
97#1942C2212yescomplemented
98#1942C2212yescomplemented
99#1941C2212yescomplemented
100#1941C2212yescomplemented
101#1936C2212yes—
102#1936C2212yes—
103#1934C2212yes—
104#1934C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1934C2212yes—
108#1934C2212yes—
109#1921C2212yescomplemented
110#1920C2212yescomplemented
111#1919C2212yescomplemented
112#1918C2212yescomplemented
113#1864C2212yes—
114#1864C2212yes—
115#1862C2212yes—
116#1862C2212yes—
117#1771C2212yescomplemented
118#1771C2212yescomplemented
119C8×C4⋊C4C2212yescomplemented
120C8×C4⋊C4C2212yescomplemented
121#1762C2212yes—
122#1762C2212yes—
123C4×#102C2212yes—
124C4×#102C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1728C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#533—24no—
141#533—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#125—22no—
145C2×#125C2311yescharacteristic
146C2×#125C2311yescharacteristic
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151#518—24no—
152#518—42no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C22×C4⋊C4—21no—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—22no—
172C22×C42C2311yescharacteristic
173#428—24no—
174#428—24no—
175#428—24no—
176#428—42no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185#424—24no—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188#418—24no—
189#418—24no—
190C2×#102—42no—
191C2×#102Q818yescomplemented
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200#405—24no—
201#405—42no—
202C2×#97C2312yes—
203C2×#97C2312yes—
204C2×C4×C8—42no—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2312yes—
211#400—22no—
212#400—22no—
213#400—22no—
214#400—22no—
215#399—22no—
216#399—22no—
217#398—22no—
218#398—22no—
219#398—22no—
220#398—22no—
221#396—22no—
222#396—22no—
223#396—22no—
224#396—22no—
225#393—22no—
226#393—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—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389—21no—
243#389—21no—
244#389—22no—
245#389D411yescharacteristic
246#389D411yescharacteristic
247#389D411yescharacteristic
248#389D411yescharacteristic
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385D412yes—
272#385D412yes—
273#384—21no—
274#384—21no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#382—21no—
278#382—21no—
279#382—22no—
280#382C2311yescharacteristic
281#382C2311yescharacteristic
282#380—21no—
283#380—21no—
284#380—22no—
285#380—22no—
286#380—22no—
287#380—22no—
288#380—22no—
289#379—22no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C22⋊C4—22no—
299C2×#95—21no—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2312yes—
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4C2×Q814yes—
338C22×D4C2412yes—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16#4114yes—
352C2×M16#4114yes—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8C2×Q814yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—41no—
368C4⋊Q8—41no—
369#125—22no—
370#125—22no—
371#125—41no—
372#125—41no—
373#125—84no—
374C22⋊Q8—44no—
375C22⋊Q8—44no—
376C22⋊Q8—84no—
377C22⋊Q8—84no—
378C4×Q8—44no—
379C4×Q8—44no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—44no—
385C4×D4—44no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117#4114yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—82no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×Q814yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—48no—
464C2×C22⋊C4—82no—
465C2×C22⋊C4—82no—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C42—21no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—24no—
483#107—24no—
484#107—24no—
485#107—42no—
486#106—24no—
487#106—24no—
488#106—24no—
489#106—42no—
490C4⋊C8—24no—
491C4⋊C8—24no—
492#102—24no—
493#102—24no—
494#102—24no—
495#102—24no—
496#102—42no—
497#102—42no—
498#102C2×Q818yes—
499#102C2×Q818yes—
500#97—24no—
501#97—42no—
502C4×C8—24no—
503C4×C8—41no—
504C4×C8—41no—
505C4×C8—41no—
506C4×C8—41no—
507C4×C8—42no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529#95C2×D412yes—
530C24—22no—
531C24—24no—
532C24—42no—
533C24—42no—
534C24—81no—
535C24—81no—
536C24—81no—
537C24—81no—
538C24C22×D411yescharacteristic
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—81no—
544C2×Q8—81no—
545C2×D4—28no—
546C2×D4—24no—
547C2×D4—28no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—42no—
554C2×D4—44no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4C22×Q814yes—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×Q812yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C42−1+412yes—
605C22×C4C2511yescharacteristic
606M16—28no—
607M16—28no—
608C2×C8—28no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—22no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—44no—
624C2×C8C22×Q812yes—
625C2×C8C22×Q812yes—
626C2×C8C2×#4114yes—
627C2×C8C2×#4114yes—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
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—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—81no—
668C4⋊C4—81no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4C22×Q814yes—
681C4⋊C4C2×#4112yes—
682C4⋊C4C2×#4112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—22no—
700C42—22no—
701C42—24no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—22no—
707C42—21no—
708C42—21no—
709C42—22no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—82no—
714C42—82no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—48no—
727C23—84no—
728C23—84no—
729C23—162no—
730C23—162no—
731C23—162no—
732C23—162no—
733C23#53212yes—
734C23#54612yes—
735C23D4×Q812yes—
736C23C23×D411yescharacteristic
737Q8—84no—
738Q8—84no—
739D4—24no—
740D4—24no—
741D4—42no—
742D4—42no—
743D4—48no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—164no—
803C2×C4—164no—
804C2×C4—162no—
805C2×C4—162no—
806C2×C4#53212yes—
807C2×C4#53314yes—
808C2×C4#53914yes—
809C2×C4#54612yes—
810C2×C4D4×Q812yes—
811C2×C4#55214yes—
812C2×C4#55414yes—
813C2×C4#57612yes—
814C2×C4#57712yes—
815C2×C4C23×Q811yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C8—24no—
822C8—24no—
823C8—22no—
824C8—22no—
825C8—41no—
826C8—41no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—168no—
841C22#255614yes—
842C22C2×#53211yescharacteristic
843C22C2×#54611yescharacteristic
844C22C2×D4×Q811yescharacteristic
845C22C2×#57611yescharacteristic
846C22C2×#57711yescharacteristic
847C22#358411yescharacteristic
848C22#358411yescharacteristic
849C4—22no—
850C4—22no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—41no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—82no—
863C4—81no—
864C4—81no—
865C4—82no—
866C4—81no—
867C4—81no—
868C4#255614yes—
869C4C2×#53311yescharacteristic
870C4C2×#53911yescharacteristic
871C4C2×#55211yescharacteristic
872C4C2×#55411yescharacteristic
873C2—24no—
874C2—84no—
875C2C2×#255611yescharacteristic
876C2#6072211yescharacteristic
877C2#6072411yescharacteristic
878C2#6117111yescharacteristic
879C2#6117211yescharacteristic
880C2#6137011yescharacteristic
881C2#6137111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35585C2semidirect
3. #28974C2semidirect
4. #28973C2semidirect
5. #28968C2semidirect
6. #28967C2semidirect
7. #28950C2semidirect
8. #28949C2semidirect
9. #28944C2semidirect
10. #28943C2semidirect
12. #23671C2semidirect
14. #23554C2semidirect
15. #21318C2semidirect
16. #21160C2semidirect
17. #21160C2semidirect
20. #21036C2semidirect
22. #20435C2semidirect
44. #2509C22semidirect
46. #2508C22semidirect
48. #2507C22semidirect
50. #2506C22semidirect
73. #2088C22semidirect
74. #2088C22semidirect
75. #2087C22semidirect
76. #2086C22semidirect
81. #2059C22semidirect
82. #2059C22semidirect
83. #2058C22semidirect
84. #2057C22semidirect
85. #1991C22semidirect
86. #1991C22semidirect
87. #1991C22semidirect
88. #1991C22semidirect
89. #1990C22semidirect
90. #1990C22semidirect
91. #1990C22semidirect
92. #1990C22semidirect
93. #1944C22semidirect
94. #1944C22semidirect
95. #1943C22semidirect
96. #1943C22semidirect
97. #1942C22semidirect
98. #1942C22semidirect
99. #1941C22semidirect
100. #1941C22semidirect
109. #1921C22semidirect
110. #1920C22semidirect
111. #1919C22semidirect
112. #1918C22semidirect
117. #1771C22semidirect
118. #1771C22semidirect
119. C8×C4⋊C4C22semidirect
120. C8×C4⋊C4C22semidirect
191. C2×#102Q8semidirect

Maximal subgroups

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

subgroupindex
#355852
#355152
#289742
#289732
#289682
#289672
#289502
#289492
#289442
#289432
#237312
#236712
#236142
#235542
#213182
#211602
#210892
C2×#19342
#210362
#208762
#204352
#204162