Finite Group Databasebeta

← #6463299

Subgroups — #6463299

Order 512.

1808 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34932C211yesmaximal, characteristic
2#34929C211yesmaximal, characteristic, complemented
3#29045C212yesmaximal, complemented
4#28979C212yesmaximal, complemented
5#28791C211yesmaximal, characteristic, complemented
6#28600C211yesmaximal, characteristic, complemented
7#28400C211yesmaximal, characteristic, complemented
8#28141C211yesmaximal, characteristic
9#28066C212yesmaximal, complemented
10#27813C211yesmaximal, characteristic, complemented
11#27749C211yesmaximal, characteristic, complemented
12#26958C212yesmaximal, complemented
13#25385C211yesmaximal, characteristic
14#25341C211yesmaximal, characteristic, complemented
15#23756C212yesmaximal, complemented
16#23568C212yesmaximal, complemented
17C4×#487C211yesmaximal, characteristic, complemented
18C4×#475C211yesmaximal, characteristic, complemented
19C4×#465C212yesmaximal, complemented
20C4×#461C211yesmaximal, characteristic, complemented
21#21400C212yesmaximal, complemented
22C42×SD16C211yesmaximal, characteristic, complemented
23C4×C8×D4C211yesmaximal, characteristic, complemented
24C2×#533C2212yes—
25C2×#529—21no—
26C2×#487C2211yescharacteristic
27C2×#475C2211yescharacteristic
28C2×#465C2212yes—
29C2×#461C2211yescharacteristic
30C2×C4×SD16C2211yescharacteristic
31C2×C4×SD16C2211yescharacteristic
32C2×C4×SD16C2211yescharacteristic
33C2×C4×SD16C2212yes—
34C2×C8×D4C2211yescharacteristic
35C2×C8×D4C2211yescharacteristic
36C22×C4×C8C2212yes—
37#2556—22no—
38#2553—22no—
39#2552C2211yescharacteristic
40#2551C2211yescharacteristic
41#2547C2211yescharacteristic
42#2546C2211yescharacteristic
43#2542C2211yescharacteristic
44#2542C2211yescharacteristic
45#2538C2211yescharacteristic
46#2537C2211yescharacteristic
47#2506—21no—
48#2496C2212yes—
49#2492C2212yes—
50#2489—21no—
51#2452—21no—
52#2429C2212yes—
53#2427—21no—
54#2422C2212yes—
55#2396—22no—
56#2395—22no—
57C4×C4⋊Q8—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C22⋊Q8—21no—
61C4×C22⋊Q8C2212yes—
62C4×#121C2212yes—
63#2293—21no—
64#2285C2212yes—
65C42×Q8C2211yescharacteristic
66C42×D4C2211yescharacteristic
67C42×D4C2211yescharacteristic
68#2099C2212yes—
69#2096C2212yes—
70#2084C2212yes—
71#2077C2212yes—
72#2077C2212yes—
73#2072C2212yes—
74#2058C2212yes—
75#2043C2212yes—
76#2035C2212yes—
77#2035C2212yes—
78#2035C2212yes—
79#2035C2212yes—
80#2023C2212yes—
81#2013C2212yes—
82#2000C2212yes—
83#2000C2212yes—
84#1990C2212yes—
85#1990C2211yescharacteristic
86#1990C2212yes—
87#1988C2211yescharacteristic
88#1981C2211yescharacteristic
89#1968C2212yes—
90#1956C2211yescharacteristic
91#1956C2212yes—
92#1956C2212yes—
93#1948C2211yescharacteristic
94#1948C2211yescharacteristic
95#1941C2212yes—
96#1934C2212yes—
97#1933C2212yes—
98#1933C2212yes—
99#1933C2212yes—
100#1927C2212yes—
101#1919C2212yes—
102#1893C2212yes—
103#1892C2212yes—
104#1892C2212yes—
105#1892C2212yes—
106#1892C2212yes—
107#1892C2212yes—
108#1877C2212yes—
109#1865C2212yes—
110#1834C2211yescharacteristic
111#1807C2212yes—
112#1803C2211yescharacteristic
113#1802C2211yescharacteristic
114C4×#106C2212yes—
115C4×#106C2211yescharacteristic
116C4×#106C2211yescharacteristic
117C4×#106C2211yescharacteristic
118C8×C4⋊C4C2211yescharacteristic
119C8×C4⋊C4C2211yescharacteristic
120C4×C4⋊C8C2211yescharacteristic
121C4×#103C2212yes—
122C4×#103C2212yes—
123C4×#103C2212yes—
124C4×#103C2211yescharacteristic
125C4×#103C2211yescharacteristic
126C4×#103C2211yescharacteristic
127C4×#103C2212yes—
128C4×#102C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131C8×C22⋊C4C2212yes—
132C8×C22⋊C4C2212yes—
133C4×C22⋊C8C2212yes—
134C42×C8C2211yescharacteristic
135C22×SD16C2311yescharacteristic
136C22×SD16C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139#533—28no—
140#533—44no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146#529—48no—
147C2×#126—22no—
148C2×#125—21no—
149C2×#125—22no—
150C2×#124—21no—
151C2×#123—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×#121—21no—
159C2×#121C2312yes—
160C2×C4×Q8—22no—
161C2×C4×Q8—21no—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2311yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×D4—22no—
167C2×C4×D4D411yescharacteristic
168C2×C4×D4D411yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2311yescharacteristic
173C2×#117—22no—
174C2×#117—22no—
175C22×C42—21no—
176C22×C42C2312yes—
177#487—24no—
178#475—24no—
179#465—28no—
180#461—24no—
181C4×SD16—24no—
182C4×SD16—24no—
183C4×SD16—24no—
184C4×SD16—44no—
185C8×D4—24no—
186C8×D4—24no—
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2311yescharacteristic
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2312yes—
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C4×C8—44no—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2312yes—
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221C2×C4×C8C2311yescharacteristic
222C2×C4×C8C2311yescharacteristic
223#400—22no—
224#400—22no—
225#399—22no—
226#399—22no—
227#398—22no—
228#398—22no—
229#398—22no—
230#397—22no—
231#397—22no—
232#397—22no—
233#396—22no—
234#396—22no—
235#395—22no—
236#394—22no—
237#394—22no—
238#393—22no—
239#391—21no—
240#391—21no—
241#391—22no—
242#391C2312yes—
243#391C2312yes—
244#390—21no—
245#390—21no—
246#390C2312yes—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389—22no—
256#389C2312yes—
257#389C2312yes—
258#389C2312yes—
259#388—22no—
260#388—22no—
261#388—22no—
262#387—22no—
263#387—22no—
264#386—22no—
265#385—22no—
266#385—22no—
267#384—21no—
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#384C2312yes—
271#384C2312yes—
272#382—22no—
273#380—22no—
274#380—21no—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—22no—
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⋊C4D411yescharacteristic
288C4×C4⋊C4D411yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C22⋊C4—22no—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4D412yes—
303C4×C22⋊C4D412yes—
304C4×C22⋊C4C2312yes—
305C43—21no—
306C43C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8C2412yes—
329C22×Q8C2411yescharacteristic
330C22×D4—22no—
331C22×D4C2×D411yescharacteristic
332C22×D4C2411yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4C2×D412yes—
337C23×C4C2×D412yes—
338C23×C4C2412yes—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—24no—
342C2×SD16—22no—
343C2×SD16—24no—
344C2×SD16—42no—
345C22×C8—24no—
346C22×C8—24no—
347C22×C8—24no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8—42no—
351C22×C8C2412yes—
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C4⋊Q8—24no—
358C4⋊Q8—24no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—42no—
364C4⋊Q8—42no—
365C4⋊Q8—44no—
366#126—48no—
367#125—48no—
368#125—44no—
369#124—44no—
370#123—48no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—42no—
375C22⋊Q8—42no—
376C22⋊Q8—42no—
377C22⋊Q8—48no—
378C22⋊Q8—44no—
379C22⋊Q8—44no—
380#121—24no—
381#121—42no—
382#121—44no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—24no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—24no—
389C4×Q8—48no—
390C4×Q8—41no—
391C4×Q8—44no—
392C4×Q8#4114yes—
393C4×D4—24no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—41no—
402C4×D4—48no—
403C4×D4SD1618yescomplemented
404#117—48no—
405#117—48no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
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—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C42—21no—
459C2×C42—24no—
460C2×C42—24no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—44no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D412yes—
474C2×C42C2×D412yes—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#106—22no—
483#106—24no—
484#106—22no—
485#106—22no—
486#106—24no—
487#106—42no—
488C4⋊C8—22no—
489C4⋊C8#4114yes—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—24no—
494#103—24no—
495#103—24no—
496#103—24no—
497#103—24no—
498#103—42no—
499#103—42no—
500#103—42no—
501#103—42no—
502#102—22no—
503#102—22no—
504#102—42no—
505#102#4114yes—
506C22⋊C8—24no—
507C22⋊C8—24no—
508C4×C8—22no—
509C4×C8—22no—
510C4×C8—22no—
511C4×C8—22no—
512C4×C8—24no—
513C4×C8—42no—
514C4×C8—42no—
515C4×C8—41no—
516C4×C8#4114yes—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24—21no—
539C24C22×D412yes—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—44no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—82no—
557C2×Q8C2×#4112yes—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×SD1614yes—
569C2×D4C2×#4112yes—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4C2×SD1618yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2511yescharacteristic
612SD16—28no—
613SD16—48no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—22no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—48no—
629C2×C8—48no—
630C2×C8C2×#4112yes—
631C2×C8C2×#4112yes—
632C2×C8C2×#4112yes—
633C2×C8C2×#4114yes—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C4⋊C4C2×SD1614yes—
676C4⋊C4#13514yes—
677C4⋊C4C2×#4112yes—
678C4⋊C4C2×#4112yes—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—82no—
694C22⋊C4C2×SD1618yes—
695C42—24no—
696C42—24no—
697C42—24no—
698C42—22no—
699C42—22no—
700C42—21no—
701C42—22no—
702C42—22no—
703C42—21no—
704C42—41no—
705C42—42no—
706C42—42no—
707C42—44no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—44no—
712C42—42no—
713C42—42no—
714C42—81no—
715C42C2×SD1614yes—
716C42C2×#4112yes—
717C42C2×#4112yes—
718C42C2×#4112yes—
719C42H(5,𝔽2)12yes—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23C22×SD1614yes—
734C23C23×D411yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—41no—
738Q8—41no—
739Q8—42no—
740Q8—42no—
741Q8—42no—
742Q8—42no—
743Q8—88no—
744Q8—84no—
745D4—28no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—88no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—216no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4#53212yes—
810C2×C4#53212yes—
811C2×C4#54612yes—
812C2×C4#54612yes—
813C2×C4C22×SD1612yes—
814C2×C4C22×SD1614yes—
815C2×C4C22×SD1612yes—
816C2×C4C22×SD1612yes—
817C2×C4C2×#13514yes—
818C2×C4C2×#13512yes—
819C2×C4#57812yes—
820C2×C4C22×#4111yescharacteristic
821C2×C4C22×#4111yescharacteristic
822C2×C4C22×#4111yescharacteristic
823C2×C4C22×#4111yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4#58511yescharacteristic
826C8—22no—
827C8—22no—
828C8—22no—
829C8—24no—
830C8—42no—
831C8—41no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22C2×#53211yescharacteristic
847C22C2×#54611yescharacteristic
848C22D4×#4111yescharacteristic
849C22C23×SD1611yescharacteristic
850C22C22×#13511yescharacteristic
851C22C2×#57811yescharacteristic
852C22#358411yescharacteristic
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—22no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—81no—
864C4—82no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4—82no—
869C4—81no—
870C4—82no—
871C4#316714yes—
872C4#329814yes—
873C4#344411yescharacteristic
874C4#346011yescharacteristic
875C4#348011yescharacteristic
876C4#348111yescharacteristic
877C2—44no—
878C2—82no—
879C2#3488911yescharacteristic
880C2C2×#316711yescharacteristic
881C2#6069611yescharacteristic
882C2C2×#329811yescharacteristic
883C2#6112411yescharacteristic
884C2SD16×#4111yescharacteristic
885C2#6143511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#2537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34929C2semidirect
3. #29045C2semidirect
4. #28979C2semidirect
5. #28791C2semidirect
6. #28600C2semidirect
7. #28400C2semidirect
9. #28066C2semidirect
10. #27813C2semidirect
11. #27749C2semidirect
12. #26958C2semidirect
14. #25341C2semidirect
15. #23756C2semidirect
16. #23568C2semidirect
17. C4×#487C2semidirect
18. C4×#475C2semidirect
19. C4×#465C2semidirect
20. C4×#461C2semidirect
21. #21400C2semidirect
22. C42×SD16C2semidirect
23. C4×C8×D4C2semidirect
403. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
#349322
#349292
#290452
#289792
#287912
#286002
#284002
#281412
#280662
#278132
#277492
#269582
#253852
#253412
#237562
#235682
C4×#4872
C4×#4752
C4×#4652
C4×#4612
#214002
C42×SD162
C4×C8×D42