Finite Group Databasebeta

← #6683986

Subgroups — #6683986

Order 512.

2214 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3226C211yesmaximal, characteristic, complemented
2C22×#500C211yesmaximal, characteristic, complemented
3#36122C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#30946C214yesmaximal, complemented
7#30773C214yesmaximal, complemented
8#30276C211yesmaximal, characteristic, complemented
9#29876C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28655C211yesmaximal, characteristic, complemented
12#26336C214yesmaximal, complemented
13#26126C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25813C211yesmaximal, characteristic, complemented
16#25813C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22247C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×D4×Q8—21no—
21C2×#548—21no—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26#3226—28no—
27C2×#500—28no—
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#500C2214yes—
31C2×#500C2211yescharacteristic
32C2×#500C2211yescharacteristic
33C2×#500C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#480C2214yes—
39C2×#474C2214yes—
40C2×#431C2211yescharacteristic
41C22×#107C2214yes—
42C22×C4×C8C2211yescharacteristic
43#2868C2211yescharacteristic
44#2858C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2551—21no—
50#2551C2212yes—
51#2546—21no—
52#2545—21no—
53#2491—21no—
54#2491C2212yes—
55#2452—21no—
56#2452C2212yes—
57#2440—21no—
58#2440—21no—
59#2440C2212yes—
60#2440C2212yes—
61#2436—21no—
62#2434—21no—
63#2434—21no—
64#2432—21no—
65#2416—21no—
66#2416C2212yes—
67#2361—21no—
68#2361C2212yes—
69D4×C4⋊C4—21no—
70D4×C4⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2093C2214yes—
75#2093C2214yes—
76#2086C2214yes—
77#2083C2214yes—
78#2075C2214yes—
79#2067C2214yes—
80#2057C2214yes—
81#2057C2214yes—
82#2033C2214yes—
83#2023C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1947C2214yes—
91#1934C2214yes—
92#1925C2214yes—
93#1923C2212yes—
94#1918C2214yes—
95#1918C2214yes—
96#1916C2212yes—
97#1893C2214yes—
98#1874C2214yes—
99#1869C2212yes—
100#1862C2214yes—
101#1852C2214yes—
102#1852C2214yes—
103#1850C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C23×Q8—21no—
112C23×Q8—21no—
113C23×C8C2312yes—
114D4×Q8—48no—
115#548—48no—
116#532—24no—
117#532—42no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—21no—
128C2×C4⋊Q8—21no—
129C2×C4⋊Q8—21no—
130C2×C4⋊Q8—42no—
131C2×C4⋊Q8—42no—
132C2×C4⋊Q8—42no—
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2311yescharacteristic
136C2×C4⋊Q8C2312yes—
137C2×C4⋊Q8C2312yes—
138C2×C4⋊Q8C2312yes—
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×#127C2311yescharacteristic
142C2×#124—22no—
143C2×#124—21no—
144C2×#124—21no—
145C2×#124—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×#121—22no—
153C2×#121—21no—
154C2×#121—21no—
155C2×#121—21no—
156C2×#121C2312yes—
157C2×#121C2312yes—
158C2×C4×Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4—21no—
163C2×C4×D4D411yescharacteristic
164C2×C4×D4D411yescharacteristic
165C2×C4×D4C2312yes—
166C2×C4×D4C2311yescharacteristic
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#500—24no—
176#500—24no—
177#500—24no—
178#500—216no—
179#500—24no—
180#500—42no—
181#500D418yescomplemented
182#486—24no—
183#486—24no—
184#486—42no—
185#480—216no—
186#474—216no—
187#431—24no—
188C2×#107—216no—
189C2×#107C2314yes—
190C2×#107C2314yes—
191C2×#107C2314yes—
192C2×#107C2314yes—
193C2×#107C2314yes—
194C2×#107C2314yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C4×C8—24no—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210#398—22no—
211#398—22no—
212#396—22no—
213#396—22no—
214#395—22no—
215#395—22no—
216#395—22no—
217#395—22no—
218#394—22no—
219#394—22no—
220#393—22no—
221#393—22no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390C2312yes—
232#390C2312yes—
233#390C2312yes—
234#389—22no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#388—22no—
247#388—22no—
248#386—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#384—21no—
257#384—21no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2312yes—
261#384C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—44no—
305C22×Q8—44no—
306C22×Q8—44no—
307C22×Q8—44no—
308C22×Q8—44no—
309C22×Q8—44no—
310C22×Q8—82no—
311C22×Q8—82no—
312C22×Q8—82no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C2×D411yescharacteristic
318C22×D4C2412yes—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C22×C8—24no—
330C22×C8—24no—
331C22×C8—24no—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—24no—
337C4⋊Q8—24no—
338C4⋊Q8—24no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—42no—
348C4⋊Q8—42no—
349C4⋊Q8—42no—
350C4⋊Q8—44no—
351C4⋊Q8—44no—
352C4⋊Q8—44no—
353C4⋊Q8—44no—
354C4⋊Q8—44no—
355C4⋊Q8—44no—
356C4⋊Q8—48no—
357C4⋊Q8—44no—
358C4⋊Q8—82no—
359C4⋊Q8C2×D414yes—
360C4⋊Q8C2×D414yes—
361#127—22no—
362#127—22no—
363#124—44no—
364#124—48no—
365#124—44no—
366#124—82no—
367C22⋊Q8—44no—
368C22⋊Q8—44no—
369C22⋊Q8—44no—
370C22⋊Q8—48no—
371C22⋊Q8—48no—
372C22⋊Q8—48no—
373#121—28no—
374#121—24no—
375#121—42no—
376#121—44no—
377#121—48no—
378#121—44no—
379#121—44no—
380C4×Q8—44no—
381C4×Q8—44no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—24no—
385C4×D4—42no—
386C4×D4—44no—
387C4×D4—48no—
388C4×D4—48no—
389C4×D4D818yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—44no—
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D411yescharacteristic
449C2×C22⋊C4C2×D411yescharacteristic
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470#107—28no—
471#107—28no—
472#107—28no—
473#107—28no—
474#107—44no—
475#107C2×D4116yes—
476C4⋊C8—24no—
477C4⋊C8—24no—
478#102—28no—
479#102—28no—
480#102—28no—
481#102—44no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C4×C8—24no—
486C4×C8—22no—
487C4×C8—22no—
488C4×C8—22no—
489C4×C8C2×D414yes—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502#95C2×D411yescharacteristic
503#95C2×D411yescharacteristic
504#95C2×D411yescharacteristic
505#95C2×D411yescharacteristic
506C24—22no—
507C24C22×D411yescharacteristic
508C24C22×D411yescharacteristic
509#41—816no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—44no—
521C2×Q8—42no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—82no—
534C2×Q8—816no—
535C2×Q8—816no—
536C2×Q8—816no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—82no—
555C2×D4C2×D814yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4C2×D814yes—
592C22×C4C2×D814yes—
593C22×C4#13714yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
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×C42−1+414yes—
607C22×C4C2511yescharacteristic
608C2×C8—216no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8C22×D414yes—
620C2×C82−1+414yes—
621C4⋊C4—22no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—42no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4C2×D814yes—
658C4⋊C4C22×D414yes—
659C4⋊C4C22×D414yes—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4C2×D814yes—
677C22⋊C4C2×D814yes—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—22no—
690C42—22no—
691C42—44no—
692C42—44no—
693C42C2×D814yes—
694C42C22×D412yes—
695C42H(5,𝔽2)12yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23#53612yes—
714C23C22×D812yes—
715C23C22×D812yes—
716C23C2×#13712yes—
717C23C23×D411yescharacteristic
718Q8—48no—
719Q8—48no—
720Q8—88no—
721Q8—88no—
722Q8—88no—
723Q8—84no—
724Q8—84no—
725Q8—84no—
726D4—28no—
727D4—44no—
728D4—44no—
729D4—88no—
730D4—88no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
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—24no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—88no—
787C2×C4—88no—
788C2×C4—88no—
789C2×C4—88no—
790C2×C4#53612yes—
791C2×C4D4212yes—
792C2×C4D4212yes—
793C2×C4C22×D812yes—
794C2×C4C22×D812yes—
795C2×C4C22×D812yes—
796C2×C4C22×D812yes—
797C2×C4C22×D812yes—
798C2×C4C2×#13712yes—
799C2×C4C2×#13712yes—
800C2×C4#57612yes—
801C2×C4#57812yes—
802C2×C4C23×D411yescharacteristic
803C2×C4C2×H(5,𝔽2)11yescharacteristic
804C2×C4C2×2−1+412yes—
805C2×C4C2×2−1+412yes—
806C8—24no—
807C8—24no—
808C8—42no—
809C8—42no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22#322614yescomplemented
831C22C2×#53611yescharacteristic
832C22C2×D4211yescharacteristic
833C22#349911yescharacteristic
834C22C23×D811yescharacteristic
835C22C22×#13711yescharacteristic
836C22C2×#57611yescharacteristic
837C22C2×#57811yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—44no—
848C4—44no—
849C4—41no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4#327014yes—
856C4D4×D814yes—
857C4#348612yes—
858C4#355212yes—
859C2—24no—
860C2—42no—
861C2—162no—
862C2#3767511yescharacteristic
863C2C2×#322611yescharacteristic
864C2#6088011yescharacteristic
865C2C2×#327011yescharacteristic
866C2C2×D4×D811yescharacteristic
867C2#6247111yescharacteristic
868C2#6248011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
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. C22×#500C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33042C2semidirect
6. #30946C2semidirect
7. #30773C2semidirect
8. #30276C2semidirect
9. #29876C2semidirect
10. #28689C2semidirect
11. #28655C2semidirect
12. #26336C2semidirect
13. #26126C2semidirect
14. #25903C2semidirect
15. #25813C2semidirect
16. #25813C2semidirect
17. #25673C2semidirect
18. #22247C2semidirect
19. #21101C2semidirect
181. #500D4semidirect
830. C22#3226semidirect

Maximal subgroups

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

subgroupindex
C2×#32262
C22×#5002
#361222
D4×C4⋊Q82
#330422
#309462
#307732
#302762
#298762
#286892
#286552
#263362
#261262
#259032
#258132
#256732
#222472
#211012