Finite Group Databasebeta

← #6549287

Subgroups — #6549287

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36161C211yesmaximal, characteristic
2#34186C211yesmaximal, characteristic
3#29936C211yesmaximal, characteristic, complemented
4#29897C212yesmaximal, complemented
5#27876C211yesmaximal, characteristic, complemented
6#27629C211yesmaximal, characteristic, complemented
7#27605C212yesmaximal, complemented
8#26301C211yesmaximal, characteristic, complemented
9#26301C211yesmaximal, characteristic, complemented
10#26207C212yesmaximal, complemented
11#26135C212yesmaximal, complemented
12#25015C211yesmaximal, characteristic, complemented
13#24970C211yesmaximal, characteristic, complemented
14#24944C212yesmaximal, complemented
15#24942C212yesmaximal, complemented
16#24554C212yesmaximal, complemented
17#23756C211yesmaximal, characteristic, complemented
18#23638C212yesmaximal, complemented
19#22707C211yesmaximal, characteristic, complemented
20#22657C211yesmaximal, characteristic, complemented
21#22490C211yesmaximal, characteristic, complemented
22#22490C211yesmaximal, characteristic, complemented
23D4×C22⋊C8C211yesmaximal, characteristic
24C2×#556C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#485C2212yescomplemented
27C2×C8×D4C2211yescharacteristic
28C2×C8×D4C2211yescharacteristic
29C2×#427C2212yescomplemented
30C22×C22⋊C8C2212yes—
31#2857C2211yescharacteristic
32#2848C2212yes—
33#2547C2211yescharacteristic
34#2538C2211yescharacteristic
35#2485C2212yes—
36#2480—22no—
37#2466—22no—
38#2447—21no—
39#2435—21no—
40#2415C2212yes—
41#2367—21no—
42#2360—21no—
43#2357—21no—
44#2357—21no—
45#2357—22no—
46#2354C2212yes—
47#2354C2211yescharacteristic
48#2354C2212yes—
49#2354C2211yescharacteristic
50#2354C2211yescharacteristic
51#2354C2211yescharacteristic
52#2354C2211yescharacteristic
53#2312—22no—
54#2309—21no—
55C4×C22⋊Q8C2211yescharacteristic
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58#2280C2212yes—
59#2280C2212yes—
60#2280C2212yes—
61#2274—21no—
62#2099C2212yescomplemented
63#2099C2211yescharacteristic, complemented
64#2096C2211yescharacteristic, complemented
65#2084C2211yescharacteristic, complemented
66#2083C2212yescomplemented
67#2077C2211yescharacteristic
68#2077C2212yes—
69#2077C2212yes—
70#2077C2211yescharacteristic
71#2077C2212yescomplemented
72#2077C2212yescomplemented
73#2077C2212yescomplemented
74#2076C2212yes—
75#2076C2212yescomplemented
76#2076C2212yescomplemented
77#2075C2212yes—
78#2075C2212yes—
79#2075C2212yescomplemented
80#2072C2211yescharacteristic, complemented
81#2036C2212yes—
82#2036C2212yescomplemented
83#2035C2211yescharacteristic
84#2035C2211yescharacteristic
85#2035C2212yescomplemented
86#1990C2211yescharacteristic, complemented
87#1990C2211yescharacteristic, complemented
88#1988C2211yescharacteristic, complemented
89#1988C2211yescharacteristic, complemented
90#1954C2211yescharacteristic
91#1954C2211yescharacteristic
92#1947C2211yescharacteristic, complemented
93#1947C2211yescharacteristic, complemented
94#1947C2211yescharacteristic, complemented
95#1947C2211yescharacteristic, complemented
96#1928C2212yescomplemented
97#1921C2212yescomplemented
98#1919C2212yescomplemented
99#1919C2212yescomplemented
100#1892C2212yescomplemented
101#1892C2212yescomplemented
102#1873C2212yescomplemented
103#1873C2212yescomplemented
104#1873C2212yescomplemented
105#1869C2212yes—
106#1869C2212yes—
107#1854C2212yescomplemented
108#1854C2212yescomplemented
109#1854C2212yescomplemented
110#1854C2212yescomplemented
111#1854C2212yescomplemented
112#1854C2212yescomplemented
113#1854C2212yescomplemented
114#1844C2211yescharacteristic, complemented
115#1834C2211yescharacteristic, complemented
116#1825C2212yescomplemented
117#1825C2212yescomplemented
118#1825C2212yescomplemented
119#1825C2212yescomplemented
120#1825C2212yescomplemented
121#1808C2212yescomplemented
122#1807C2212yescomplemented
123#1803C2211yescharacteristic, complemented
124#1803C2211yescharacteristic, complemented
125#1797C2211yescharacteristic
126#1779C2212yes—
127C4×#106C2211yescharacteristic, complemented
128C4×#106C2211yescharacteristic, complemented
129C4×#103C2211yescharacteristic, complemented
130C4×#103C2211yescharacteristic, complemented
131C4×C22⋊C8C2211yescharacteristic
132#1735C2212yescomplemented
133#1735C2212yescomplemented
134#1735C2212yescomplemented
135C23×D4D411yescharacteristic
136C24×C4C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139#556—24no—
140#556—24no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#126—22no—
143C2×#124—21no—
144C2×#124—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2311yescharacteristic
149C2×C4×Q8—21no—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D412yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C2×#117—21no—
161C2×#117C2312yes—
162C2×#117C2312yes—
163C2×#117C2312yes—
164C2×#117C2312yes—
165C2×#117C2312yes—
166C2×#117C2312yes—
167C22×C4⋊C4D411yescharacteristic
168C22×C22⋊C4D412yes—
169C22×C42C2311yescharacteristic
170#485—44no—
171C8×D4—24no—
172C8×D4—24no—
173#427—44no—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#106C2312yes—
179C2×#106C2311yescharacteristic
180C2×#106C2311yescharacteristic
181C2×#106C2311yescharacteristic
182C2×#106C2312yes—
183C2×#106C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×#103C2311yescharacteristic
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2311yescharacteristic
190C2×#103C2311yescharacteristic
191C2×#103C2311yescharacteristic
192C2×C22⋊C8—44no—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2312yes—
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204#397—22no—
205#397—22no—
206#397—22no—
207#396—22no—
208#394—22no—
209#394—22no—
210#391—21no—
211#391—21no—
212#391C2311yescharacteristic
213#390—21no—
214#390—21no—
215#390—22no—
216#390—22no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—21no—
221#389—22no—
222#389—21no—
223#389—21no—
224#389C2312yes—
225#389C2311yescharacteristic
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#387—22no—
238#387—21no—
239#385—22no—
240#385—22no—
241#385—22no—
242#385—21no—
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#384C2311yescharacteristic
246#384C2311yescharacteristic
247#384C2311yescharacteristic
248#382—21no—
249#382—21no—
250#381—22no—
251#381—22no—
252#381—22no—
253#380—21no—
254#380—21no—
255#380—21no—
256#380C2312yes—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#380C2311yescharacteristic
261#380C2311yescharacteristic
262#380C2312yes—
263#380C2312yes—
264#380C2311yescharacteristic
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#379—22no—
270#379—22no—
271#379—22no—
272#379—22no—
273C4×C4⋊C4—22no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
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⋊C4C2312yes—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C22⋊C4—22no—
288C4×C22⋊C4—22no—
289C4×C22⋊C4—22no—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—21no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2312yes—
318#336C2312yes—
319#336C2311yescharacteristic
320#336C2311yescharacteristic
321C25C2×D412yes—
322C22×Q8—21no—
323C22×Q8C2411yescharacteristic
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—42no—
327C22×D4C2×D411yescharacteristic
328C22×D4C2×D412yes—
329C22×D4C2×D411yescharacteristic
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D412yes—
339C23×C4C2×D412yes—
340C23×C4C2×D412yes—
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2412yes—
344C22×C8—24no—
345C22×C8—24no—
346C22×C8—24no—
347C22×C8—42no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8C2411yescharacteristic
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2411yescharacteristic
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358#126—48no—
359#124—44no—
360#124—44no—
361C22⋊Q8—24no—
362C22⋊Q8—24no—
363C22⋊Q8—41no—
364C22⋊Q8—41no—
365C22⋊Q8—44no—
366C22⋊Q8—42no—
367C22⋊Q8—42no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—44no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—28no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4#4114yes—
379C4×D4#4114yes—
380#117—24no—
381#117—24no—
382#117—44no—
383#117—44no—
384#117—42no—
385#117—42no—
386#117—42no—
387#117—42no—
388#117—42no—
389#117—42no—
390#117—42no—
391#117—42no—
392#117—42no—
393#117—42no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
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⋊C4C2×D412yes—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2411yescharacteristic
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2411yescharacteristic
426C2×C22⋊C4—28no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
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⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470#107—42no—
471#107—42no—
472#107—42no—
473#107—42no—
474#106—22no—
475#106—24no—
476#106—41no—
477#106—41no—
478#106—41no—
479#106—42no—
480C4⋊C8—22no—
481C4⋊C8—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103—42no—
486#103—41no—
487#103—42no—
488C22⋊C8—24no—
489C22⋊C8—24no—
490C22⋊C8—22no—
491C22⋊C8—24no—
492C22⋊C8—42no—
493C22⋊C8—42no—
494C22⋊C8—42no—
495C22⋊C8—42no—
496C22⋊C8—41no—
497C4×C8—22no—
498C4×C8—22no—
499#95—21no—
500#95—21no—
501#95—22no—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—21no—
511#95—21no—
512#95—22no—
513#95—21no—
514#95—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520C24—24no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24C22×D412yes—
528C24C22×D412yes—
529C24C22×D411yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—416no—
547C2×D4—42no—
548C2×D4#12314yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4#13514yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2511yescharacteristic
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—21no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—48no—
624C2×C8—84no—
625C2×C8H(5,𝔽2)12yes—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—22no—
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—21no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—81no—
664C4⋊C4—81no—
665C4⋊C4—81no—
666C4⋊C4—82no—
667C4⋊C4#12314yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—44no—
673C22⋊C4—42no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—44no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4#12318yes—
694C42—22no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—44no—
699C42—44no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—82no—
705C42—82no—
706C42—82no—
707C42—82no—
708C42—82no—
709C42C2×#4112yes—
710C42C2×#4112yes—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—48no—
731C23—48no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23C2×#12314yes—
738C23C2×#13512yes—
739C23C23×D411yescharacteristic
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—84no—
745D4—28no—
746D4—48no—
747D4—44no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—82no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×#12312yes—
817C2×C4C2×#12314yes—
818C2×C4C2×#12312yes—
819C2×C4C2×#13512yes—
820C2×C4C2×#13512yes—
821C2×C4#57512yes—
822C2×C4C22×#4111yescharacteristic
823C2×C4C22×#4111yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4#58511yescharacteristic
826C2×C4#58511yescharacteristic
827C2×C4#58511yescharacteristic
828C8—22no—
829C8—42no—
830C8—42no—
831C8—41no—
832C8—41no—
833C8—41no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22C22×#12311yescharacteristic
857C22#348511yescharacteristic
858C22#349611yescharacteristic
859C22C22×#13511yescharacteristic
860C22C2×#57511yescharacteristic
861C22#358411yescharacteristic
862C22#358611yescharacteristic
863C4—22no—
864C4—22no—
865C4—24no—
866C4—41no—
867C4—42no—
868C4—41no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—82no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—82no—
879C4—81no—
880C4—81no—
881C4#309114yes—
882C4#351311yescharacteristic
883C4#351411yescharacteristic
884C4#352111yescharacteristic
885C4#352111yescharacteristic
886C2—44no—
887C2—42no—
888C2—82no—
889C2#3579111yescharacteristic
890C2C2×#309111yescharacteristic
891C2#6052411yescharacteristic
892C2#6170111yescharacteristic
893C2#6174311yescharacteristic
894C2#6224811yescharacteristic
895C2#6230311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29936C2semidirect
4. #29897C2semidirect
5. #27876C2semidirect
6. #27629C2semidirect
7. #27605C2semidirect
8. #26301C2semidirect
9. #26301C2semidirect
10. #26207C2semidirect
11. #26135C2semidirect
12. #25015C2semidirect
13. #24970C2semidirect
14. #24944C2semidirect
15. #24942C2semidirect
16. #24554C2semidirect
17. #23756C2semidirect
18. #23638C2semidirect
19. #22707C2semidirect
20. #22657C2semidirect
21. #22490C2semidirect
22. #22490C2semidirect
26. C2×#485C22semidirect
29. C2×#427C22semidirect
62. #2099C22semidirect
63. #2099C22semidirect
64. #2096C22semidirect
65. #2084C22semidirect
66. #2083C22semidirect
71. #2077C22semidirect
72. #2077C22semidirect
73. #2077C22semidirect
75. #2076C22semidirect
76. #2076C22semidirect
79. #2075C22semidirect
80. #2072C22semidirect
82. #2036C22semidirect
85. #2035C22semidirect
86. #1990C22semidirect
87. #1990C22semidirect
88. #1988C22semidirect
89. #1988C22semidirect
92. #1947C22semidirect
93. #1947C22semidirect
94. #1947C22semidirect
95. #1947C22semidirect
96. #1928C22semidirect
97. #1921C22semidirect
98. #1919C22semidirect
99. #1919C22semidirect
100. #1892C22semidirect
101. #1892C22semidirect
102. #1873C22semidirect
103. #1873C22semidirect
104. #1873C22semidirect
107. #1854C22semidirect
108. #1854C22semidirect
109. #1854C22semidirect
110. #1854C22semidirect
111. #1854C22semidirect
112. #1854C22semidirect
113. #1854C22semidirect
114. #1844C22semidirect
115. #1834C22semidirect
116. #1825C22semidirect
117. #1825C22semidirect
118. #1825C22semidirect
119. #1825C22semidirect
120. #1825C22semidirect
121. #1808C22semidirect
122. #1807C22semidirect
123. #1803C22semidirect
124. #1803C22semidirect
127. C4×#106C22semidirect
128. C4×#106C22semidirect
129. C4×#103C22semidirect
130. C4×#103C22semidirect
132. #1735C22semidirect
133. #1735C22semidirect
134. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#361612
#341862
#299362
#298972
#278762
#276292
#276052
#263012
#262072
#261352
#250152
#249702
#249442
#249422
#245542
#237562
#236382
#227072
#226572
#224902
D4×C22⋊C82