Finite Group Databasebeta

← #7562856

Subgroups — #7562856

Order 512.

1834 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3339C211yesmaximal, characteristic, complemented
2C2×#3164C211yesmaximal, characteristic, complemented
3#45159C212yesmaximal, complemented
4#30804C212yesmaximal, complemented
5#30791C212yesmaximal, complemented
6#28704C211yesmaximal, characteristic, complemented
7#28528C211yesmaximal, characteristic, complemented
8#27791C211yesmaximal, characteristic, complemented
9#27790C211yesmaximal, characteristic, complemented
10#26152C212yesmaximal, complemented
11#26143C212yesmaximal, complemented
12#26067C211yesmaximal, characteristic, complemented
13#26064C211yesmaximal, characteristic, complemented
14#25714C212yesmaximal, complemented
15#25466C212yesmaximal, complemented
16#24780C211yesmaximal, characteristic, complemented
17#24778C211yesmaximal, characteristic, complemented
18#24309C212yesmaximal, complemented
19#23160C211yesmaximal, characteristic, complemented
20#22656C211yesmaximal, characteristic, complemented
21#22656C211yesmaximal, characteristic, complemented
22#21524C211yesmaximal, characteristic, complemented
23#21491C211yesmaximal, characteristic, complemented
24C2×#553C2212yes—
25C2×#544C2212yes—
26#3339—28no—
27#3164—28no—
28C2×#501C2212yes—
29C2×#501C2212yes—
30C2×#500C2211yescharacteristic
31C2×#500C2211yescharacteristic
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#481C2212yes—
35C2×#482C2212yes—
36C2×#478C2212yes—
37C2×#476C2212yes—
38C2×#466C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C2×C8×D4C2211yescharacteristic
44C2×C8×D4C2211yescharacteristic
45C2×#428C2212yes—
46C2×#427C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C22×#107C2211yescharacteristic
49C22×#107C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2716—22no—
52#2707—22no—
53#2696—22no—
54#2676—22no—
55#2563C2212yes—
56#2560—22no—
57#2547C2212yes—
58#2491—22no—
59#2491C2212yes—
60#2490C2212yes—
61#2460—22no—
62#2442C2212yes—
63#2439C2212yes—
64#2427—22no—
65#2416C2212yes—
66#2414C2212yes—
67#2392C2211yescharacteristic
68#2370C2212yes—
69#2352C2212yes—
70#2352C2212yes—
71#2324C2212yes—
72#2092C2212yes—
73#2092C2212yes—
74#2085C2212yes—
75#2085C2212yes—
76#2075C2212yes—
77#2075C2212yes—
78#2067C2212yes—
79#2065C2212yes—
80#2059C2212yes—
81#2058C2212yes—
82#2034C2212yes—
83#2034C2212yes—
84#2033C2212yes—
85#2033C2212yes—
86#2025C2212yes—
87#2023C2212yes—
88#1989C2212yes—
89#1988C2212yes—
90#1970C2211yescharacteristic
91#1970C2211yescharacteristic
92#1970C2211yescharacteristic
93#1955C2211yescharacteristic
94#1949C2212yes—
95#1949C2212yes—
96#1942C2211yescharacteristic
97#1942C2211yescharacteristic
98#1942C2211yescharacteristic
99#1940C2211yescharacteristic
100#1936C2212yes—
101#1926C2212yes—
102#1925C2212yes—
103#1924C2211yescharacteristic
104#1924C2211yescharacteristic
105#1920C2212yes—
106#1919C2212yes—
107#1895C2212yes—
108#1875C2212yes—
109#1874C2212yes—
110#1870C2211yescharacteristic
111#1870C2211yescharacteristic
112#1854C2212yes—
113#1854C2212yes—
114#1854C2212yes—
115#1853C2212yes—
116#1853C2212yes—
117#1853C2212yes—
118#1846C2211yescharacteristic
119#1846C2211yescharacteristic
120#1808C2211yescharacteristic
121#1808C2211yescharacteristic
122#1808C2211yescharacteristic
123#1808C2211yescharacteristic
124#1808C2211yescharacteristic
125#1798C2211yescharacteristic
126C4×#107C2211yescharacteristic
127C4×#107C2211yescharacteristic
128C4×#107C2211yescharacteristic
129C8×C4⋊C4C2211yescharacteristic
130#1762C2212yes—
131C8×C22⋊C4C2211yescharacteristic
132C8×C22⋊C4C2211yescharacteristic
133C22×D8C2311yescharacteristic
134C22×M16C2311yescharacteristic
135C23×C8C2311yescharacteristic
136C23×C8C2311yescharacteristic
137C23×C8C2311yescharacteristic
138#553—28no—
139#553—44no—
140#544—28no—
141#544—44no—
142C2×C4⋊Q8—22no—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2312yes—
145C2×#126—22no—
146C2×#125—22no—
147C2×#125C2312yes—
148C2×#125C2312yes—
149C2×#124—22no—
150C2×#124—22no—
151C2×#123—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—22no—
154C2×#121—22no—
155C2×#121—22no—
156C2×#121C2312yes—
157C2×#121C2312yes—
158C2×#121C2312yes—
159C2×C4×D4—22no—
160C2×C4×D4C2312yes—
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×#117C2312yes—
165C2×#117C2312yes—
166C2×#117C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169#501—28no—
170#501—28no—
171#500—24no—
172#500—24no—
173#499—24no—
174#499D418yescomplemented
175#482—28no—
176#481—28no—
177#478—28no—
178#476—44no—
179#466—24no—
180#466—24no—
181#466—24no—
182C4×D8—24no—
183C8×D4—24no—
184C8×D4—24no—
185C8×D4—24no—
186#428—28no—
187#427—24no—
188#427—24no—
189C2×#107—24no—
190C2×#107—24no—
191C2×#107C2312yes—
192C2×#107C2311yescharacteristic
193C2×#107C2311yescharacteristic
194C2×#107C2311yescharacteristic
195C2×#107C2311yescharacteristic
196C2×#107C2311yescharacteristic
197C2×#107C2312yes—
198C2×#107C2312yes—
199C2×#107C2312yes—
200C2×#107C2311yescharacteristic
201C2×#107C2311yescharacteristic
202C2×#106C2312yes—
203C2×#106C2312yes—
204C2×#106C2312yes—
205C2×#106C2312yes—
206C2×#106C2312yes—
207C2×#106C2312yes—
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2311yescharacteristic
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2312yes—
217C2×#102C2312yes—
218C2×#102C2312yes—
219C2×C22⋊C8C2311yescharacteristic
220C2×C22⋊C8C2311yescharacteristic
221C2×C22⋊C8C2311yescharacteristic
222C2×C22⋊C8C2311yescharacteristic
223C2×C22⋊C8C2311yescharacteristic
224C2×C22⋊C8C2311yescharacteristic
225C2×C22⋊C8C2311yescharacteristic
226C2×C22⋊C8C2311yescharacteristic
227#405—24no—
228C2×#97C2311yescharacteristic
229C2×#97C2311yescharacteristic
230C2×C4×C8C2311yescharacteristic
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233C2×C4×C8C2311yescharacteristic
234#400—22no—
235#398—22no—
236#398D411yescharacteristic
237#397—22no—
238#397—22no—
239#397—22no—
240#397D411yescharacteristic
241#396—22no—
242#396—22no—
243#396D411yescharacteristic
244#396D411yescharacteristic
245#394—22no—
246#394—22no—
247#394—22no—
248#394—22no—
249#394D411yescharacteristic
250#394D411yescharacteristic
251#394D411yescharacteristic
252#393—22no—
253#393—22no—
254#393—22no—
255#393—22no—
256#392—22no—
257#392D411yescharacteristic
258#391—22no—
259#391—22no—
260#390—22no—
261#390—22no—
262#390—22no—
263#390C2312yes—
264#390C2312yes—
265#390C2312yes—
266#389—22no—
267#389C2312yes—
268#389C2312yes—
269#389C2312yes—
270#388—22no—
271#388—22no—
272#388—22no—
273#388—22no—
274#388—22no—
275#388—22no—
276#387—22no—
277#387—22no—
278#387—22no—
279#387—22no—
280#387—22no—
281#386—22no—
282#386—22no—
283#386—22no—
284#386—22no—
285#385—22no—
286#385—22no—
287#382C2312yes—
288#382C2312yes—
289#380—22no—
290#380—22no—
291#380—22no—
292#380C2312yes—
293#380C2312yes—
294#380C2312yes—
295#380C2312yes—
296#380C2312yes—
297C4×C4⋊C4—22no—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2311yescharacteristic
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4C2311yescharacteristic
305C4×C22⋊C4C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#336C2311yescharacteristic
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2311yescharacteristic
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323C22×Q8—22no—
324C22×Q8—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4C2×D411yescharacteristic
329C22×D4C2×D411yescharacteristic
330C22×D4C2×D411yescharacteristic
331C22×D4C2412yes—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4C2411yescharacteristic
336C23×C4C2411yescharacteristic
337C23×C4C2411yescharacteristic
338C2×D8—22no—
339C2×D8—22no—
340C2×D8—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8#4114yes—
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C4⋊Q8—24no—
362C4⋊Q8—24no—
363C4⋊Q8—24no—
364C4⋊Q8—42no—
365C4⋊Q8—48no—
366#126—48no—
367#125—24no—
368#125—24no—
369#125—42no—
370#125—48no—
371#125C2×D418yes—
372#124—84no—
373#124—84no—
374#123—48no—
375C22⋊Q8—48no—
376C22⋊Q8—48no—
377#121—24no—
378#121—24no—
379#121—24no—
380#121—24no—
381#121—42no—
382#121—42no—
383#121—48no—
384#121—84no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4—48no—
394#117—22no—
395#117—22no—
396#117—24no—
397#117—24no—
398#117—42no—
399#117—42no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D411yescharacteristic
449C2×C22⋊C4C2×D411yescharacteristic
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D411yescharacteristic
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#107—22no—
468#107—22no—
469#107—22no—
470#107—24no—
471#107—22no—
472#107—22no—
473#107—24no—
474#107—24no—
475#107—24no—
476#107C2×D414yes—
477#107C2×D414yes—
478#106—24no—
479#106—24no—
480#106—24no—
481#106—42no—
482#106—42no—
483#106C2×D418yes—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488#102—24no—
489#102—24no—
490#102—24no—
491#102—24no—
492#102—24no—
493#102—42no—
494#102—42no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503#97—22no—
504#97—22no—
505C4×C8—22no—
506C4×C8—22no—
507C4×C8—22no—
508C4×C8C2×D414yes—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
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#95C2×D411yescharacteristic
525#95C2×D411yescharacteristic
526#95C2×D411yescharacteristic
527#95C2×D411yescharacteristic
528#95C2×D411yescharacteristic
529#95C2×D411yescharacteristic
530C24—22no—
531C24C22×D411yescharacteristic
532C24C22×D411yescharacteristic
533C24C22×D411yescharacteristic
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×Q8—82no—
539C2×Q8—82no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—82no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C2×#4112yes—
608C22×C42−1+412yes—
609C22×C4C2511yescharacteristic
610D8—44no—
611M16—28no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—28no—
619C2×C8—21no—
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—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8—44no—
633C2×C8C22×D412yes—
634C2×C8C22×D412yes—
635C2×C8C2×#4112yes—
636C2×C8C2×#4112yes—
637C2×C82−1+412yes—
638C2×C82−1+412yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4C22×D414yes—
670C4⋊C4C22×D414yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—44no—
707C42—44no—
708C42—82no—
709C42—82no—
710C42—82no—
711C42C22×D412yes—
712C42H(5,𝔽2)12yes—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23#54712yes—
740C23#57612yes—
741C23C23×D411yescharacteristic
742Q8—164no—
743Q8—164no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—88no—
752D4—164no—
753D4—164no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—164no—
818C2×C4—164no—
819C2×C4—164no—
820C2×C4D4212yes—
821C2×C4D4212yes—
822C2×C4#54712yes—
823C2×C4C23×D411yescharacteristic
824C2×C4C22×#4111yescharacteristic
825C2×C4C2×H(5,𝔽2)11yescharacteristic
826C2×C4C2×2−1+411yescharacteristic
827C2×C4C2×2−1+411yescharacteristic
828C2×C4C2×2−1+411yescharacteristic
829C8—22no—
830C8—22no—
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8#54814yes—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22C2×D4211yescharacteristic
866C22C2×#54711yescharacteristic
867C22#349911yescharacteristic
868C22C2×#57611yescharacteristic
869C22#358411yescharacteristic
870C22#358411yescharacteristic
871C22#358411yescharacteristic
872C4—22no—
873C4—22no—
874C4—22no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—44no—
881C4—41no—
882C4—44no—
883C4—41no—
884C4—41no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4C2×#54811yescharacteristic
891C4#348611yescharacteristic
892C4#351111yescharacteristic
893C4#355211yescharacteristic
894C2—42no—
895C2—42no—
896C2—81no—
897C2—162no—
898C2#5912511yescharacteristic
899C2#6105611yescharacteristic
900C2#6109011yescharacteristic
901C2#6126111yescharacteristic
902C2#6126211yescharacteristic
903C2#6249011yescharacteristic
904C2#6249211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3339C2semidirect
2. C2×#3164C2semidirect
3. #45159C2semidirect
4. #30804C2semidirect
5. #30791C2semidirect
6. #28704C2semidirect
7. #28528C2semidirect
8. #27791C2semidirect
9. #27790C2semidirect
10. #26152C2semidirect
11. #26143C2semidirect
12. #26067C2semidirect
13. #26064C2semidirect
14. #25714C2semidirect
15. #25466C2semidirect
16. #24780C2semidirect
17. #24778C2semidirect
18. #24309C2semidirect
19. #23160C2semidirect
20. #22656C2semidirect
21. #22656C2semidirect
22. #21524C2semidirect
23. #21491C2semidirect
174. #499D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33392
C2×#31642
#451592
#308042
#307912
#287042
#285282
#277912
#277902
#261522
#261432
#260672
#260642
#257142
#254662
#247802
#247782
#243092
#231602
#226562
#215242
#214912