Finite Group Databasebeta

← #6396471

Subgroups — #6396471

Order 512.

2096 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3213C211yesmaximal, characteristic
2#34398C211yesmaximal, characteristic, complemented
3#34377C211yesmaximal, characteristic, complemented
4#23104C212yesmaximal, complemented
5#23098C212yesmaximal, complemented
6#23005C212yesmaximal, complemented
7#22999C212yesmaximal, complemented
8#22875C212yesmaximal, complemented
9#22870C212yesmaximal, complemented
10#22858C212yesmaximal, complemented
11#22855C212yesmaximal, complemented
12#22279C212yesmaximal, complemented
13#22233C212yesmaximal, complemented
14#21986C211yesmaximal, characteristic, complemented
15#21704C212yesmaximal, complemented
16#21654C212yesmaximal, complemented
17#21401C211yesmaximal, characteristic, complemented
18C2×#1958C211yesmaximal, characteristic, complemented
19#20476C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×#124C2211yescharacteristic
22#3213C4116yescomplemented
23C2×#496C2212yes—
24C2×#489C2212yes—
25C2×#463C2212yes—
26C2×#463C2212yes—
27C2×#448C2212yes—
28C2×#447C2212yes—
29C2×#442C2212yes—
30C2×#440C2212yescomplemented
31C2×C4×SD16C2212yescomplemented
32C2×C4×D8C2212yes—
33C2×#432C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic
39#2379—21no—
40#2379—21no—
41#2379—21no—
42#2379—21no—
43#2367C2212yes—
44#2367C2212yes—
45#2361C2212yes—
46#2361C2212yes—
47#2357C2212yescomplemented
48#2349C2212yescomplemented
49#2342—22no—
50Q8×C22⋊C4C2212yes—
51#2339—22no—
52D4×C22⋊C4C2212yes—
53#2337—22no—
54#2331C2212yescomplemented
55#2328C2212yescomplemented
56#2326C2212yes—
57#2326C2212yes—
58#2325—21no—
59#2325—21no—
60#2318—22no—
61#2315—21no—
62#2312—21no—
63#2285C2211yescharacteristic
64#2283C2211yescharacteristic
65C2×#382C2211yescharacteristic
66#1990C2211yescharacteristic, complemented
67#1990C2211yescharacteristic, complemented
68#1973C2212yescomplemented
69#1972C2212yes—
70#1970C2212yes—
71#1968C2212yescomplemented
72#1958C2212yes—
73#1958C2212yes—
74#1958C2212yes—
75#1958C2212yes—
76#1957C2211yescharacteristic, complemented
77#1957C2211yescharacteristic, complemented
78#1949C2212yescomplemented
79#1949C2212yescomplemented
80#1936C2212yes—
81#1935C2212yescomplemented
82#1934C2212yes—
83#1933C2212yescomplemented
84#1928C2212yescomplemented
85#1927C2212yescomplemented
86#1926C2212yes—
87#1925C2212yes—
88#1893C2212yes—
89#1893C2212yes—
90#1880C2212yescomplemented
91#1880C2212yescomplemented
92#1879C2212yes—
93#1879C2212yes—
94#1879C2212yes—
95#1879C2212yes—
96#1877C2212yescomplemented
97#1877C2212yescomplemented
98#1865C2212yescomplemented
99#1864C2212yes—
100#1863C2212yescomplemented
101#1862C2212yes—
102#1853C2212yes—
103#1852C2212yes—
104#1847C2212yescomplemented
105#1836C2212yescomplemented
106#1770C2211yescharacteristic, complemented
107#1770C2211yescharacteristic, complemented
108C8×C4⋊C4C2211yescharacteristic, complemented
109C8×C4⋊C4C2211yescharacteristic, complemented
110#1763C2212yescomplemented
111#1762C2212yes—
112C4×#103C2212yescomplemented
113C4×#102C2212yes—
114C4×#102C2212yescomplemented
115C4×#102C2212yescomplemented
116#1752C2212yes—
117C8×C22⋊C4C2212yes—
118#1746C2212yescomplemented
119#1726C2212yescomplemented
120C22×#41—21no—
121C23×Q8C2311yescharacteristic
122C23×D4C2311yescharacteristic
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125C22×D8C2312yes—
126C22×D8C2312yes—
127C23×C8C2311yescharacteristic
128C23×C8C2311yescharacteristic
129#532—24no—
130#532C2×C418yescomplemented
131C2×C4⋊Q8C2311yescharacteristic
132C2×#127C2311yescharacteristic
133C2×#124—21no—
134C2×#124—21no—
135C2×#124—21no—
136C2×#124—24no—
137C2×#124C2×C418yescomplemented
138C2×#124C2312yes—
139C2×#124C2312yes—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2312yes—
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—21no—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×C4×D4C2312yes—
150C2×C4×D4C2312yes—
151C2×C4×D4C2312yes—
152C2×#117—21no—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—22no—
158C22×C42C2311yescharacteristic
159#496C2×C4116yescomplemented
160#489C2×C4116yescomplemented
161#463C2×C4116yescomplemented
162#463C2×C4116yescomplemented
163#448C2×C4116yescomplemented
164#447C2×C4116yescomplemented
165#442—44no—
166#440—44no—
167C4×SD16—44no—
168C4×D8—44no—
169#432C2×C418yescomplemented
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×#103—42no—
177C2×#103—42no—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#102—42no—
185C2×#102—42no—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×C22⋊C8C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×C4×C8—24no—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207#391—22no—
208#391—22no—
209#391—22no—
210#391—22no—
211#391C2312yes—
212#391C2312yes—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#387—22no—
232#387—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#385—22no—
242#385—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#383D412yes—
254#382—21no—
255#382—21no—
256#382—21no—
257#382D411yescharacteristic
258#382D411yescharacteristic
259#382C2312yes—
260#382C2312yes—
261#381—22no—
262#381D412yes—
263#380—21no—
264#380—22no—
265#380—22no—
266#380D411yescharacteristic
267#380D411yescharacteristic
268#380C2312yes—
269#379—22no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4—22no—
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4C2312yes—
281#376C2312yes—
282C2×#95—21no—
283C2×#95—21no—
284C2×#95—22no—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297C25—21no—
298C2×#41—28no—
299C2×#41—82no—
300C2×#41—82no—
301C22×Q8—21no—
302C22×Q8—21no—
303C22×Q8—22no—
304C22×Q8—41no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8—41no—
308C22×Q8C22×C414yes—
309C22×Q8C2412yes—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—22no—
315C22×D4—41no—
316C22×D4—41no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4C22×C414yes—
320C22×D4C2412yes—
321C22×D4C2412yes—
322C23×C4—21no—
323C23×C4—22no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—42no—
334C2×SD16—42no—
335C2×SD16—42no—
336C2×SD16—42no—
337C2×SD16C22×C418yes—
338C2×SD16C22×C418yes—
339C2×D8—42no—
340C2×D8—42no—
341C2×D8—42no—
342C2×D8—42no—
343C2×D8C22×C418yes—
344C2×D8C22×C418yes—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—41no—
350C22×C8—41no—
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2412yes—
354C22×C8C2412yes—
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C4⋊Q8—22no—
358C4⋊Q8C22×C414yes—
359#127—22no—
360#127C22×C414yes—
361#124—28no—
362#124—28no—
363#124—28no—
364#124—24no—
365#124—24no—
366#124C22×C418yes—
367#124C22×C418yes—
368#121—28no—
369#121—24no—
370#121C22×C418yes—
371C4×Q8—42no—
372C4×Q8—42no—
373C4×Q8—42no—
374C4×Q8—42no—
375C4×D4—28no—
376C4×D4—24no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—84no—
386C4×D4—84no—
387C4×D4C22×C418yes—
388#117—82no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—84no—
435C2×C22⋊C4C2×D412yes—
436C2×C22⋊C4C2×D412yes—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42C22×C414yes—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42#4114yes—
446C2×C42C2412yes—
447C2×C42C2412yes—
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—42no—
451#107—42no—
452#106—42no—
453#106—42no—
454C4⋊C8C22×C414yes—
455C4⋊C8C22×C414yes—
456#103—24no—
457#103—24no—
458#103—42no—
459#103—42no—
460#103C22×C418yes—
461#103C22×C418yes—
462#102—24no—
463#102—24no—
464#102—24no—
465#102—24no—
466#102—42no—
467#102—42no—
468#102—42no—
469#102—42no—
470#102C22×C418yes—
471#102C22×C418yes—
472C22⋊C8C22×C418yes—
473#97—24no—
474#97—42no—
475#97C22×C418yes—
476C4×C8—24no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—42no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95C2×D412yes—
497#95C2×D412yes—
498#95C2×D412yes—
499#95C2×D412yes—
500#95C2×D412yes—
501#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504C24—22no—
505C24—22no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—81no—
510C24—81no—
511C24—81no—
512C24—81no—
513C24C22×D411yescharacteristic
514#41—816no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—81no—
525C2×Q8—81no—
526C2×Q8—81no—
527C2×Q8—81no—
528C2×Q8—82no—
529C2×Q8—82no—
530C2×Q8C23×C414yes—
531C2×D4—28no—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4C23×C414yes—
558C2×D4C23×C414yes—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C4×D414yes—
598C22×C4C4×D414yes—
599C22×C4C23×C412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C2×#4112yes—
610C22×C4C2511yescharacteristic
611SD16—48no—
612SD16—48no—
613D8—48no—
614D8—48no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—22no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—44no—
630C2×C8—44no—
631C2×C8C23×C414yes—
632C2×C8C23×C414yes—
633C2×C8H(5,𝔽2)12yes—
634C2×C8H(5,𝔽2)12yes—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—81no—
650C4⋊C4—81no—
651C4⋊C4—81no—
652C4⋊C4—81no—
653C4⋊C4—81no—
654C4⋊C4—81no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4C23×C414yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—44no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—82no—
686C42—82no—
687C42—82no—
688C42—82no—
689C42—82no—
690C42C4×D414yes—
691C42C4×D414yes—
692C42C23×C412yes—
693C42C23×C412yes—
694C42C2×#4112yes—
695C42C2×#4112yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—24no—
701C23—24no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—48no—
715C23—84no—
716C23—84no—
717C23—162no—
718C23—162no—
719C23—162no—
720C23—162no—
721C23C2×C4×D412yes—
722C23#57612yes—
723C23#57712yes—
724C23C23×D411yescharacteristic
725Q8—24no—
726Q8—24no—
727Q8—42no—
728Q8—42no—
729Q8—84no—
730Q8—84no—
731D4—24no—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—416no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—84no—
741D4—84no—
742D4—84no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—28no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—88no—
790C2×C4—84no—
791C2×C4—164no—
792C2×C4—164no—
793C2×C4—164no—
794C2×C4—164no—
795C2×C4—162no—
796C2×C4—162no—
797C2×C4C2×C4×D412yes—
798C2×C4C2×C4×D412yes—
799C2×C4C2×C4×D412yes—
800C2×C4C2×C4×D412yes—
801C2×C4C2×C4×D412yes—
802C2×C4C24×C411yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4C2×H(5,𝔽2)11yescharacteristic
805C2×C4C2×H(5,𝔽2)11yescharacteristic
806C2×C4#58511yescharacteristic
807C2×C4#58511yescharacteristic
808C8—24no—
809C8—24no—
810C8—22no—
811C8—22no—
812C8—41no—
813C8—41no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—168no—
835C22#294614yes—
836C22C22×C4×D411yescharacteristic
837C22#349811yescharacteristic
838C22#350011yescharacteristic
839C22C2×#57611yescharacteristic
840C22C2×#57711yescharacteristic
841C22#358411yescharacteristic
842C22#358411yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—42no—
849C4—42no—
850C4—44no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4C4×H(5,𝔽2)11yescharacteristic
859C4C4×H(5,𝔽2)11yescharacteristic
860C4#349411yescharacteristic
861C4#349411yescharacteristic
862C2—24no—
863C2—84no—
864C2—84no—
865C2#3427511yescharacteristic
866C2C2×#294611yescharacteristic
867C2#6016111yescharacteristic
868C2#6243511yescharacteristic
869C2#6243611yescharacteristic
870C2#6255711yescharacteristic
871C2#6255811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3213C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34398C2semidirect
3. #34377C2semidirect
4. #23104C2semidirect
5. #23098C2semidirect
6. #23005C2semidirect
7. #22999C2semidirect
8. #22875C2semidirect
9. #22870C2semidirect
10. #22858C2semidirect
11. #22855C2semidirect
12. #22279C2semidirect
13. #22233C2semidirect
14. #21986C2semidirect
15. #21704C2semidirect
16. #21654C2semidirect
17. #21401C2semidirect
18. C2×#1958C2semidirect
19. #20476C2semidirect
22. #3213C4semidirect
30. C2×#440C22semidirect
31. C2×C4×SD16C22semidirect
47. #2357C22semidirect
48. #2349C22semidirect
54. #2331C22semidirect
55. #2328C22semidirect
66. #1990C22semidirect
67. #1990C22semidirect
68. #1973C22semidirect
71. #1968C22semidirect
76. #1957C22semidirect
77. #1957C22semidirect
78. #1949C22semidirect
79. #1949C22semidirect
81. #1935C22semidirect
83. #1933C22semidirect
84. #1928C22semidirect
85. #1927C22semidirect
90. #1880C22semidirect
91. #1880C22semidirect
96. #1877C22semidirect
97. #1877C22semidirect
98. #1865C22semidirect
100. #1863C22semidirect
104. #1847C22semidirect
105. #1836C22semidirect
106. #1770C22semidirect
107. #1770C22semidirect
108. C8×C4⋊C4C22semidirect
109. C8×C4⋊C4C22semidirect
110. #1763C22semidirect
112. C4×#103C22semidirect
114. C4×#102C22semidirect
115. C4×#102C22semidirect
118. #1746C22semidirect
119. #1726C22semidirect
130. #532C2×C4semidirect
137. C2×#124C2×C4semidirect
159. #496C2×C4semidirect
160. #489C2×C4semidirect
161. #463C2×C4semidirect
162. #463C2×C4semidirect
163. #448C2×C4semidirect
164. #447C2×C4semidirect
169. #432C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32132
#343982
#343772
#231042
#230982
#230052
#229992
#228752
#228702
#228582
#228552
#222792
#222332
#219862
#217042
#216542
#214012
C2×#19582
#204762