Finite Group Databasebeta

← #6684007

Subgroups — #6684007

Order 512.

2058 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3226C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33048C211yesmaximal, characteristic, complemented
6#30962C214yesmaximal, complemented
7#30797C214yesmaximal, complemented
8#30277C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26357C214yesmaximal, complemented
13#26142C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25811C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22248C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×D4×Q8—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3226—28no—
26#3165—28no—
27C2×#501C2214yes—
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#500C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#480C2214yes—
38C2×#474C2214yes—
39C2×#431C2211yescharacteristic
40C2×#428C2214yes—
41C2×C4×M16C2211yescharacteristic
42#2868C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2551—21no—
49#2551C2212yes—
50#2546—21no—
51#2540—21no—
52#2490C2212yes—
53#2454C2212yes—
54#2448—21no—
55#2440—21no—
56#2440—21no—
57#2440C2212yes—
58#2440C2212yes—
59#2434—21no—
60#2434—21no—
61#2427—21no—
62#2426—21no—
63#2426—21no—
64#2414C2212yes—
65#2407—21no—
66#2367—21no—
67#2363C2212yes—
68D4×C4⋊C4—21no—
69D4×C4⋊C4C2212yes—
70#2341—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2094C2214yes—
75#2094C2214yes—
76#2088C2214yes—
77#2083C2214yes—
78#2077C2214yes—
79#2065C2214yes—
80#2059C2214yes—
81#2058C2214yes—
82#2033C2214yes—
83#2023C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1947C2214yes—
91#1936C2214yes—
92#1926C2214yes—
93#1924C2212yes—
94#1921C2214yes—
95#1921C2214yes—
96#1917C2212yes—
97#1895C2214yes—
98#1874C2214yes—
99#1870C2212yes—
100#1862C2214yes—
101#1854C2214yes—
102#1853C2214yes—
103#1851C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C23×Q8—21no—
112C22×M16C2312yes—
113D4×Q8—48no—
114#533—24no—
115#533—42no—
116#532—24no—
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⋊Q8C2312yes—
133C2×C4⋊Q8C2312yes—
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2311yescharacteristic
136C2×#127C2311yescharacteristic
137C2×#125C2312yes—
138C2×#124—21no—
139C2×#124—21no—
140C2×#124—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—22no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×D4—22no—
158C2×C4×D4—21no—
159C2×C4×D4D411yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4C2312yes—
162C2×C4×D4C2311yescharacteristic
163C2×#117C2312yes—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#501—216no—
171#500—24no—
172#500—24no—
173#500D418yescomplemented
174#498—24no—
175#498—24no—
176#498—42no—
177#486—24no—
178#486—24no—
179#486—42no—
180#480—216no—
181#474—216no—
182#431—24no—
183#428—216no—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×#107C2314yes—
187C2×#106C2314yes—
188C2×#106C2314yes—
189C2×#106C2314yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C4×M16—24no—
200C2×#97C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205#399—22no—
206#398—22no—
207#398—22no—
208#397—22no—
209#396—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#390—22no—
223#390—22no—
224#390—22no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#389—22no—
233#389—22no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#386—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#384—21no—
254#384—21no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2312yes—
258#384C2312yes—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4D411yescharacteristic
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C22⋊C4—22no—
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4C2311yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C43C2311yescharacteristic
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—82no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—44no—
303C22×Q8—44no—
304C22×Q8—44no—
305C22×Q8—44no—
306C22×Q8—82no—
307C22×Q8—82no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4C2×D411yescharacteristic
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—24no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C4⋊Q8—24no—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—42no—
341C4⋊Q8—42no—
342C4⋊Q8—44no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8—44no—
346C4⋊Q8—44no—
347C4⋊Q8—48no—
348C4⋊Q8—82no—
349C4⋊Q8C2×D414yes—
350C4⋊Q8C2×D414yes—
351#127—22no—
352#127—22no—
353#125—24no—
354#125—42no—
355#124—44no—
356#124—44no—
357#124—82no—
358C22⋊Q8—48no—
359C22⋊Q8—48no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363C22⋊Q8—44no—
364C22⋊Q8—82no—
365#121—28no—
366#121—24no—
367#121—42no—
368#121—44no—
369#121—82no—
370#121—82no—
371C4×Q8—44no—
372C4×Q8—44no—
373C4×Q8—44no—
374C4×Q8—82no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—42no—
380C4×D4—44no—
381C4×D4—48no—
382#117—24no—
383#117—42no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
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—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463#107—28no—
464#107—28no—
465#107C2×D4116yes—
466#106—28no—
467#106—28no—
468#106—44no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471#102—28no—
472#102—28no—
473#102—28no—
474#102—44no—
475C22⋊C8—24no—
476C22⋊C8—24no—
477C22⋊C8—24no—
478#97—24no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8C2×D414yes—
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—
503C2×Q8—24no—
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—82no—
523C2×Q8—82no—
524C2×Q8—816no—
525C2×Q8—816no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4AGL(1,ℤ/8)14yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C42−1+414yes—
593C22×C4C2511yescharacteristic
594M16—216no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8C22×D414yes—
606C2×C82−1+414yes—
607C4⋊C4—22no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4C22×D414yes—
645C4⋊C4C22×D414yes—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—22no—
677C42—22no—
678C42—44no—
679C42—44no—
680C42—82no—
681C42#13714yes—
682C42C22×D412yes—
683C42H(5,𝔽2)12yes—
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—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23#53612yes—
704C23C2×AGL(1,ℤ/8)12yes—
705C23C23×D411yescharacteristic
706Q8—48no—
707Q8—48no—
708Q8—88no—
709Q8—88no—
710Q8—84no—
711Q8—84no—
712Q8—84no—
713D4—28no—
714D4—44no—
715D4—44no—
716D4—88no—
717D4—84no—
718D4—84no—
719D4—164no—
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—24no—
729C2×C4—28no—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—24no—
738C2×C4—24no—
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—21no—
750C2×C4—21no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
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#53612yes—
779C2×C4D4212yes—
780C2×C4D4212yes—
781C2×C4C2×AGL(1,ℤ/8)12yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×#13712yes—
784C2×C4C2×#13712yes—
785C2×C4C2×#13712yes—
786C2×C4#57612yes—
787C2×C4#57712yes—
788C2×C4C23×D411yescharacteristic
789C2×C4C2×H(5,𝔽2)11yescharacteristic
790C2×C4C2×2−1+412yes—
791C2×C4C2×2−1+412yes—
792C8—24no—
793C8—24no—
794C8—42no—
795C8—42no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22C2×#53611yescharacteristic
818C22C2×D4211yescharacteristic
819C22#349911yescharacteristic
820C22C22×AGL(1,ℤ/8)11yescharacteristic
821C22C22×#13711yescharacteristic
822C22C2×#57611yescharacteristic
823C22C2×#57711yescharacteristic
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—44no—
832C4—44no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4#326414yes—
842C4#327814yes—
843C4#348612yes—
844C4#355212yes—
845C2—42no—
846C2—42no—
847C2—162no—
848C2#3767511yescharacteristic
849C2#6086011yescharacteristic
850C2#6087711yescharacteristic
851C2C2×#326411yescharacteristic
852C2C2×#327811yescharacteristic
853C2#6247711yescharacteristic
854C2#6248011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
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×#3226C2semidirect
2. C2×#3165C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33048C2semidirect
6. #30962C2semidirect
7. #30797C2semidirect
8. #30277C2semidirect
9. #29877C2semidirect
10. #28689C2semidirect
11. #28654C2semidirect
12. #26357C2semidirect
13. #26142C2semidirect
14. #25903C2semidirect
15. #25812C2semidirect
16. #25811C2semidirect
17. #25673C2semidirect
18. #22248C2semidirect
19. #21102C2semidirect
173. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32262
C2×#31652
#361502
D4×C4⋊Q82
#330482
#309622
#307972
#302772
#298772
#286892
#286542
#263572
#261422
#259032
#258122
#258112
#256732
#222482
#211022