Finite Group Databasebeta

← #6816656

Subgroups — #6816656

Order 512.

2088 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3227C211yesmaximal, characteristic, complemented
2C2×#3226C211yesmaximal, characteristic, complemented
3#36149C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33314C211yesmaximal, characteristic, complemented
6#31104C214yesmaximal, complemented
7#31096C214yesmaximal, complemented
8#29878C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28716C211yesmaximal, characteristic, complemented
11#28688C211yesmaximal, characteristic, complemented
12#26058C214yesmaximal, complemented
13#25813C211yesmaximal, characteristic, complemented
14#25811C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25671C211yesmaximal, characteristic, complemented
17#25022C214yesmaximal, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×D4×Q8—21no—
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3227—28no—
26#3226—28no—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#481C2214yes—
37C2×#480C2214yes—
38C2×#476C2214yes—
39C2×#474C2214yes—
40C2×#431C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2868C2211yescharacteristic
43#2862C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2551—21no—
49#2551C2212yes—
50#2546—21no—
51#2535C2212yes—
52#2447—21no—
53#2447—21no—
54#2440—21no—
55#2440—21no—
56#2440C2212yes—
57#2440C2212yes—
58#2434—21no—
59#2434—21no—
60#2427—21no—
61#2427—21no—
62#2420C2212yes—
63#2420C2212yes—
64#2407—21no—
65#2407—21no—
66#2349C2212yes—
67D4×C4⋊C4—21no—
68D4×C4⋊C4C2212yes—
69#2339—21no—
70#2339—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2088C2214yes—
75#2087C2214yes—
76#2085C2214yes—
77#2077C2214yes—
78#2076C2214yes—
79#2071C2214yes—
80#2058C2214yes—
81#2057C2214yes—
82#2034C2214yes—
83#2033C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1955C2212yes—
91#1949C2214yes—
92#1940C2212yes—
93#1936C2214yes—
94#1924C2212yes—
95#1924C2212yes—
96#1864C2214yes—
97#1862C2214yes—
98#1853C2214yes—
99#1852C2214yes—
100#1847C2214yes—
101#1847C2214yes—
102#1834C2211yescharacteristic
103#1802C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105#1762C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41—21no—
110C22×#41—21no—
111C23×Q8—21no—
112C23×Q8—21no—
113D4×Q8—48no—
114#532—24no—
115#532—24no—
116#532—42no—
117#532—42no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—42no—
128C2×C4⋊Q8—42no—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×C4⋊Q8C2312yes—
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×#127C2311yescharacteristic
137C2×#124—21no—
138C2×#124—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—22no—
144C2×C22⋊Q8—22no—
145C2×#121—21no—
146C2×#121—21no—
147C2×#121C2312yes—
148C2×#121C2312yes—
149C2×C4×Q8—21no—
150C2×C4×D4—22no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4D411yescharacteristic
156C2×C4×D4D411yescharacteristic
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×C4×D4C2311yescharacteristic
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#500—24no—
168#500—24no—
169#500—42no—
170#498—24no—
171#498—24no—
172#498—42no—
173#486—24no—
174#486—24no—
175#486D418yescomplemented
176#481—216no—
177#480—216no—
178#476—216no—
179#474—216no—
180#431—24no—
181#431—24no—
182C2×#107C2314yes—
183C2×#107C2314yes—
184C2×#107C2314yes—
185C2×#106C2314yes—
186C2×#106C2314yes—
187C2×#106C2314yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205#398—22no—
206#398—22no—
207#397—22no—
208#397—22no—
209#397—22no—
210#395—22no—
211#395—22no—
212#395—22no—
213#395—22no—
214#394—22no—
215#394—22no—
216#392—22no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#390—21no—
227#390—21no—
228#390C2312yes—
229#389—22no—
230#389—22no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#386—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#385—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#384—21no—
252#384—21no—
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#384C2312yes—
256#384C2312yes—
257#382C2312yes—
258#382C2312yes—
259#381—22no—
260#381—22no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C2×#95—22no—
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—44no—
296C2×#41—82no—
297C2×#41—82no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—21no—
302C22×Q8—21no—
303C22×Q8—22no—
304C22×Q8—22no—
305C22×Q8—44no—
306C22×Q8—44no—
307C22×Q8—44no—
308C22×Q8—44no—
309C22×Q8—82no—
310C22×Q8—82no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4C2×D411yescharacteristic
316C22×D4C2412yes—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C4⋊Q8—24no—
333C4⋊Q8—24no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—42no—
344C4⋊Q8—42no—
345C4⋊Q8—44no—
346C4⋊Q8—44no—
347C4⋊Q8—44no—
348C4⋊Q8—44no—
349C4⋊Q8—44no—
350C4⋊Q8—48no—
351C4⋊Q8—82no—
352C4⋊Q8C2×D414yes—
353#127—22no—
354#127C2×D414yes—
355#124—44no—
356#124—44no—
357C22⋊Q8—48no—
358C22⋊Q8—48no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—82no—
362C22⋊Q8—82no—
363#121—24no—
364#121—24no—
365#121—42no—
366#121—42no—
367#121—44no—
368#121—44no—
369C4×Q8—44no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—28no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—44no—
379C4×D4—44no—
380C4×D4—48no—
381C4×D4—82no—
382C4×D4—82no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—28no—
457#107—28no—
458#107—44no—
459#106—28no—
460#106—28no—
461#106—44no—
462C4⋊C8—24no—
463C4⋊C8—24no—
464C4⋊C8—24no—
465#102—28no—
466#102—28no—
467#102—28no—
468#102C2×D4116yes—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473#97—24no—
474#97—24no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8C2×D414yes—
479#95—22no—
480#95—22no—
481#95—22no—
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#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499C24—22no—
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502#41—816no—
503#41—816no—
504C2×Q8—24no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—82no—
524C2×Q8—82no—
525C2×Q8—816no—
526C2×Q8—816no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—22no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4C22×D414yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4AGL(1,ℤ/8)14yes—
587C22×C4#13714yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2511yescharacteristic
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8C22×D414yes—
612C2×C82−1+414yes—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C4⋊C4C22×D414yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—22no—
680C42—44no—
681C42C22×D412yes—
682C42H(5,𝔽2)12yes—
683C422−1+414yes—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—24no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23C2×AGL(1,ℤ/8)12yes—
704C23C2×#13712yes—
705C23C23×D411yescharacteristic
706Q8—48no—
707Q8—88no—
708Q8—88no—
709Q8—84no—
710Q8—84no—
711Q8—84no—
712Q8—84no—
713D4—28no—
714D4—28no—
715D4—48no—
716D4—48no—
717D4—44no—
718D4—88no—
719D4—88no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—88no—
776C2×C4—88no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4—164no—
780C2×C4#53612yes—
781C2×C4#53612yes—
782C2×C4D4212yes—
783C2×C4D4212yes—
784C2×C4C2×AGL(1,ℤ/8)12yes—
785C2×C4C2×AGL(1,ℤ/8)12yes—
786C2×C4C2×#13712yes—
787C2×C4C2×#13712yes—
788C2×C4#57612yes—
789C2×C4#57712yes—
790C2×C4C23×D411yescharacteristic
791C2×C4C2×H(5,𝔽2)11yescharacteristic
792C2×C4C2×2−1+412yes—
793C2×C4C2×2−1+412yes—
794C8—24no—
795C8—24no—
796C8—42no—
797C8—42no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22C2×#53611yescharacteristic
820C22C2×D4211yescharacteristic
821C22#349911yescharacteristic
822C22C22×AGL(1,ℤ/8)11yescharacteristic
823C22C22×#13711yescharacteristic
824C22C2×#57611yescharacteristic
825C22C2×#57711yescharacteristic
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—44no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4#326414yes—
844C4#326614yes—
845C4#349912yes—
846C4#355212yes—
847C2—42no—
848C2—42no—
849C2—84no—
850C2#3936011yescharacteristic
851C2#6086011yescharacteristic
852C2#6087711yescharacteristic
853C2C2×#326411yescharacteristic
854C2C2×#326611yescharacteristic
855C2#6247711yescharacteristic
856C2#6248011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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
1. C2×#3227C2semidirect
2. C2×#3226C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33314C2semidirect
6. #31104C2semidirect
7. #31096C2semidirect
8. #29878C2semidirect
9. #29877C2semidirect
10. #28716C2semidirect
11. #28688C2semidirect
12. #26058C2semidirect
13. #25813C2semidirect
14. #25811C2semidirect
15. #25673C2semidirect
16. #25671C2semidirect
17. #25022C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect
175. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32272
C2×#32262
#361492
D4×C4⋊Q82
#333142
#311042
#310962
#298782
#298772
#287162
#286882
#260582
#258132
#258112
#256732
#256712
#250222
#216462
#212652