Finite Group Databasebeta

← #6620096

Subgroups — #6620096

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36463C211yesmaximal, characteristic
2C4×D4×Q8C211yesmaximal, characteristic, complemented
3#33031C211yesmaximal, characteristic, complemented
4#33003C212yesmaximal, complemented
5#29467C212yesmaximal, complemented
6#29411C212yesmaximal, complemented
7#29257C211yesmaximal, characteristic, complemented
8#28614C211yesmaximal, characteristic, complemented
9#27225C212yesmaximal, complemented
10#26727C212yesmaximal, complemented
11#26550C212yesmaximal, complemented
12#26300C211yesmaximal, characteristic, complemented
13#26230C211yesmaximal, characteristic
14#25888C211yesmaximal, characteristic, complemented
15#25756C211yesmaximal, characteristic
16#24894C212yesmaximal, complemented
17#23217C211yesmaximal, characteristic, complemented
18#23182C211yesmaximal, characteristic, complemented
19#22997C211yesmaximal, characteristic, complemented
20#22965C211yesmaximal, characteristic, complemented
21#22835C211yesmaximal, characteristic, complemented
22C4×#479C211yesmaximal, characteristic, complemented
23C4×#448C212yesmaximal, complemented
24C2×D4×Q8C2211yescharacteristic
25C22×C4×Q8C2212yes—
26C2×#492C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#480C2212yes—
29C2×#479C2211yescharacteristic
30C2×#477C2211yescharacteristic
31C2×#460C2211yescharacteristic
32C2×#448C2212yes—
33C2×#448C2212yes—
34C2×C4×SD16C2212yes—
35C2×C4×SD16C2212yes—
36#2858C2211yescharacteristic
37#2854C2212yes—
38#2563C2211yescharacteristic
39#2557—22no—
40#2541C2211yescharacteristic
41#2513—21no—
42#2490C2212yes—
43#2459—22no—
44#2445—21no—
45#2420C2212yes—
46#2369C2211yescharacteristic
47#2366—21no—
48#2366C2211yescharacteristic
49#2365—21no—
50#2365C2211yescharacteristic
51#2360—22no—
52#2360C2212yes—
53#2357—21no—
54Q8×C4⋊C4C2211yescharacteristic
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2211yescharacteristic
57Q8×C22⋊C4C2212yes—
58C4×C4⋊Q8—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#125C2211yescharacteristic
61C4×C22⋊Q8—22no—
62C4×C22⋊Q8C2212yes—
63C4×#121C2212yes—
64C42×Q8C2211yescharacteristic
65C42×D4—21no—
66C42×D4C2211yescharacteristic
67#2097C2212yes—
68#2077C2212yes—
69#2077C2212yes—
70#2055C2212yes—
71#2055C2212yes—
72#2036C2212yes—
73#2036C2212yes—
74#2033C2212yes—
75#2033C2212yes—
76#2026C2212yes—
77#2000C2212yes—
78#2000C2212yes—
79#1990C2211yescharacteristic
80#1989C2211yescharacteristic
81#1987C2211yescharacteristic
82#1982C2211yescharacteristic
83#1981C2211yescharacteristic
84#1981C2211yescharacteristic
85#1968C2212yes—
86#1957C2211yescharacteristic
87#1954C2211yescharacteristic
88#1954C2211yescharacteristic
89#1949C2211yescharacteristic
90#1948C2211yescharacteristic
91#1947C2211yescharacteristic
92#1942C2212yes—
93#1934C2212yes—
94#1933C2212yes—
95#1928C2212yes—
96#1925C2212yes—
97#1925C2212yes—
98#1923C2212yes—
99#1923C2212yes—
100#1921C2212yes—
101#1920C2211yescharacteristic
102#1918C2211yescharacteristic
103#1880C2212yes—
104#1880C2212yes—
105#1880C2212yes—
106#1880C2212yes—
107#1880C2212yes—
108#1880C2212yes—
109#1877C2212yes—
110#1874C2212yes—
111#1865C2212yes—
112#1865C2211yescharacteristic
113#1864C2212yes—
114#1863C2212yes—
115#1863C2212yes—
116#1863C2211yescharacteristic
117#1863C2212yes—
118#1853C2212yes—
119#1831C2211yescharacteristic
120#1823C2212yes—
121#1817C2212yes—
122#1805C2211yescharacteristic
123#1787C2212yes—
124#1787C2212yes—
125C4×#107C2211yescharacteristic
126C4×#106C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128C8×C4⋊C4C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C4×#103C2212yes—
132C4×#103C2212yes—
133C4×#103C2211yescharacteristic
134C4×C22⋊C8C2212yes—
135C23×Q8C2312yes—
136C22×SD16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139D4×Q8—24no—
140D4×Q8—24no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127—21no—
145C2×#127C2311yescharacteristic
146C2×#125C2311yescharacteristic
147C2×#124—21no—
148C2×#124—21no—
149C2×#123—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8C2312yes—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×C4×Q8—22no—
155C2×C4×Q8—22no—
156C2×C4×Q8—44no—
157C2×C4×Q8—44no—
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2312yes—
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4—22no—
167C2×C4×D4—21no—
168C2×C4×D4D411yescharacteristic
169C2×C4×D4D411yescharacteristic
170C2×C4×D4C2312yes—
171C2×C4×D4C2311yescharacteristic
172C22×C4⋊C4—22no—
173C22×C4⋊C4C2312yes—
174C22×C42—22no—
175C22×C42C2312yes—
176#492—24no—
177#487—24no—
178#480—44no—
179#479—24no—
180#477—24no—
181#460—24no—
182#448—28no—
183#448—44no—
184C4×SD16—44no—
185C4×SD16—44no—
186C2×#107C2312yes—
187C2×#107C2311yescharacteristic
188C2×#107C2311yescharacteristic
189C2×#107C2312yes—
190C2×#106C2311yescharacteristic
191C2×#106C2311yescharacteristic
192C2×#106C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221#397—22no—
222#397—22no—
223#394—22no—
224#394—22no—
225#393—22no—
226#392—22no—
227#391—22no—
228#391—22no—
229#391—22no—
230#391C2312yes—
231#391C2312yes—
232#390—21no—
233#390—21no—
234#390—21no—
235#390—22no—
236#390—21no—
237#390—21no—
238#390C2312yes—
239#390C2312yes—
240#390C2312yes—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—22no—
247#389—22no—
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#387—21no—
257#387—21no—
258#387—22no—
259#387—22no—
260#387—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#384—21no—
269#384C2311yescharacteristic
270#382—21no—
271#382C2311yescharacteristic
272#381—22no—
273#380—22no—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4D411yescharacteristic
289C4×C4⋊C4D411yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4D412yes—
302C4×C22⋊C4D412yes—
303C4×C22⋊C4C2312yes—
304C43—21no—
305C43C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#336C2311yescharacteristic
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2311yescharacteristic
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8C2412yes—
335C22×Q8C2411yescharacteristic
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C2×D411yescharacteristic
341C22×D4C2412yes—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4C2×D412yes—
346C23×C4C2×D412yes—
347C23×C4C2412yes—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—24no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16—42no—
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2411yescharacteristic
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—28no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8#4114yes—
368#127—22no—
369#127—22no—
370#127—44no—
371#125—22no—
372#125—41no—
373#124—82no—
374#124—82no—
375#123—84no—
376C22⋊Q8—216no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379#121—24no—
380#121—42no—
381#121—42no—
382#121—42no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—42no—
393C4×Q8—41no—
394C4×Q8—48no—
395C4×Q8—48no—
396C4×Q8#4114yes—
397C4×D4—28no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—42no—
403C4×D4—42no—
404C4×D4—44no—
405C4×D4—44no—
406C4×D4—84no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—48no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C22⋊C4—22no—
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—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—48no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—24no—
483#107—22no—
484#107—22no—
485#107—42no—
486#106—22no—
487#106—22no—
488#106—42no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—41no—
493#103—24no—
494#103—22no—
495#103—24no—
496#103—24no—
497#103—22no—
498#103—22no—
499#103—24no—
500#103—42no—
501#103—42no—
502#103—42no—
503#103#4114yes—
504#102—24no—
505#102—24no—
506#102—42no—
507#102—42no—
508#102—42no—
509C22⋊C8—24no—
510C22⋊C8—42no—
511C22⋊C8—42no—
512C22⋊C8—42no—
513C4×C8—22no—
514C4×C8—22no—
515C4×C8—42no—
516C4×C8—42no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—21no—
529#95—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—21no—
535#95—22no—
536#95C2×D412yes—
537#95C2×D412yes—
538#95C2×D412yes—
539C24—22no—
540C24C22×D412yes—
541C2×Q8—28no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—48no—
553C2×Q8—48no—
554C2×Q8—48no—
555C2×Q8—48no—
556C2×Q8—42no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8C2×#4114yes—
560C2×Q8C2×#4112yes—
561C2×Q8C2×#4112yes—
562C2×Q8H(5,𝔽2)12yes—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—82no—
581C2×D4—82no—
582C2×D4—82no—
583C2×D4#13514yes—
584C22×C4—21no—
585C22×C4—28no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2511yescharacteristic
626SD16—48no—
627SD16—48no—
628SD16—84no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—21no—
646C2×C8C2×#4112yes—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4#13714yes—
684C4⋊C4C2×#4112yes—
685C4⋊C4C2×#4112yes—
686C4⋊C4H(5,𝔽2)12yes—
687C22⋊C4—28no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C42—24no—
704C42—24no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—22no—
710C42—22no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—42no—
715C42—42no—
716C42—41no—
717C42—44no—
718C42—44no—
719C42—42no—
720C42—44no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—81no—
726C42—82no—
727C42C2×#4112yes—
728C42C2×#4112yes—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23C2×#13514yes—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—24no—
748Q8—24no—
749Q8—416no—
750Q8—42no—
751Q8—42no—
752Q8—162no—
753Q8#55914yes—
754D4—28no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—88no—
760D4—84no—
761D4—162no—
762D4—164no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—48no—
792C2×C4—416no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—84no—
824C2×C4—88no—
825C2×C4—164no—
826C2×C4#52512yes—
827C2×C4#52512yes—
828C2×C4C2×#13512yes—
829C2×C4C2×#13714yes—
830C2×C4C2×#13712yes—
831C2×C4#57712yes—
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4#58511yescharacteristic
838C8—22no—
839C8—42no—
840C8—41no—
841C8—42no—
842C8—41no—
843C8—41no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22C2×#52511yescharacteristic
859C22D4×#4111yescharacteristic
860C22#348411yescharacteristic
861C22C22×#13511yescharacteristic
862C22C22×#13711yescharacteristic
863C22C2×#57711yescharacteristic
864C22#358511yescharacteristic
865C4—24no—
866C4—22no—
867C4—24no—
868C4—22no—
869C4—41no—
870C4—42no—
871C4—44no—
872C4—42no—
873C4—41no—
874C4—42no—
875C4—42no—
876C4—41no—
877C4—42no—
878C4—81no—
879C4—82no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—81no—
884C4#310814yes—
885C4C2×#55911yescharacteristic
886C4#348111yescharacteristic
887C4#350611yescharacteristic
888C4#351311yescharacteristic
889C2—44no—
890C2—162no—
891C2#3644111yescharacteristic
892C2C2×#310811yescharacteristic
893C2#6059311yescharacteristic
894C2#6143211yescharacteristic
895C2#6146911yescharacteristic
896C2#6156711yescharacteristic
897C2#6159311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2541C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×D4×Q8C2semidirect
3. #33031C2semidirect
4. #33003C2semidirect
5. #29467C2semidirect
6. #29411C2semidirect
7. #29257C2semidirect
8. #28614C2semidirect
9. #27225C2semidirect
10. #26727C2semidirect
11. #26550C2semidirect
12. #26300C2semidirect
14. #25888C2semidirect
16. #24894C2semidirect
17. #23217C2semidirect
18. #23182C2semidirect
19. #22997C2semidirect
20. #22965C2semidirect
21. #22835C2semidirect
22. C4×#479C2semidirect
23. C4×#448C2semidirect

Maximal subgroups

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

subgroupindex
#364632
C4×D4×Q82
#330312
#330032
#294672
#294112
#292572
#286142
#272252
#267272
#265502
#263002
#262302
#258882
#257562
#248942
#232172
#231822
#229972
#229652
#228352
C4×#4792
C4×#4482