Finite Group Databasebeta

← #6684782

Subgroups — #6684782

Order 512.

2318 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3206C211yesmaximal, characteristic, complemented
2C22×#487C211yesmaximal, characteristic, complemented
3#36122C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33170C211yesmaximal, characteristic, complemented
6#30878C214yesmaximal, complemented
7#30522C214yesmaximal, complemented
8#30263C211yesmaximal, characteristic, complemented
9#29845C211yesmaximal, characteristic, complemented
10#28748C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#25902C211yesmaximal, characteristic, complemented
13#25856C211yesmaximal, characteristic, complemented
14#25718C211yesmaximal, characteristic, complemented
15#25597C211yesmaximal, characteristic, complemented
16#25078C214yesmaximal, complemented
17#24429C214yesmaximal, complemented
18#22218C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×D4×Q8C2212yes—
21C2×#548—21no—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26#3206—28no—
27C2×#492C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487—28no—
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2214yes—
35C2×#487C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#465C2214yes—
39C2×#461C2214yes—
40C2×#448C2214yes—
41C2×#448C2214yes—
42C2×#431C2211yescharacteristic
43C22×#103C2214yes—
44C22×C4×C8C2211yescharacteristic
45#2868C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2856C2211yescharacteristic
51#2551—21no—
52#2551—21no—
53#2546C2212yes—
54#2545—21no—
55#2491—21no—
56#2491C2212yes—
57#2452—21no—
58#2452C2212yes—
59#2440—21no—
60#2440—21no—
61#2440—21no—
62#2440—21no—
63#2436—21no—
64#2434C2212yes—
65#2434C2212yes—
66#2432—21no—
67#2416—21no—
68#2416C2212yes—
69#2361—21no—
70#2361C2212yes—
71D4×C4⋊C4—21no—
72D4×C4⋊C4—21no—
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C42×D4C2211yescharacteristic
76#2066C2214yes—
77#2055C2214yes—
78#2043C2214yes—
79#2043C2214yes—
80#2035C2214yes—
81#2024C2214yes—
82#2013C2214yes—
83#2013C2214yes—
84#2013C2214yes—
85#2000C2214yes—
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1981C2214yes—
89#1968C2214yes—
90#1957C2211yescharacteristic
91#1956C2211yescharacteristic
92#1956C2211yescharacteristic
93#1956C2211yescharacteristic
94#1927C2214yes—
95#1923C2212yes—
96#1916C2212yes—
97#1880C2214yes—
98#1877C2214yes—
99#1872C2214yes—
100#1869C2212yes—
101#1865C2214yes—
102#1850C2212yes—
103#1844C2211yescharacteristic
104#1787C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C23×Q8C2312yes—
112C23×Q8C2312yes—
113C22×SD16C2314yes—
114C22×SD16C2314yes—
115C22×SD16C2314yes—
116C23×C8C2312yes—
117D4×Q8—48no—
118#548—48no—
119#532—24no—
120#532—42no—
121C2×C4⋊Q8—22no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8—24no—
124C2×C4⋊Q8—24no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—21no—
128C2×C4⋊Q8—21no—
129C2×C4⋊Q8—21no—
130C2×C4⋊Q8—21no—
131C2×C4⋊Q8—42no—
132C2×C4⋊Q8—42no—
133C2×C4⋊Q8—42no—
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2311yescharacteristic
136C2×C4⋊Q8C2312yes—
137C2×C4⋊Q8C2312yes—
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2312yes—
140C2×C4⋊Q8C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2312yes—
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127C2311yescharacteristic
145C2×#124—22no—
146C2×#124—21no—
147C2×#124—21no—
148C2×#124—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8C2312yes—
154C2×C22⋊Q8C2312yes—
155C2×#121—22no—
156C2×#121—21no—
157C2×#121—21no—
158C2×#121—21no—
159C2×#121C2312yes—
160C2×#121C2312yes—
161C2×C4×Q8—21no—
162C2×C4×Q8C2312yes—
163C2×C4×D4—22no—
164C2×C4×D4—22no—
165C2×C4×D4—21no—
166C2×C4×D4D411yescharacteristic
167C2×C4×D4D411yescharacteristic
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#492—24no—
179#492—24no—
180#492—42no—
181#487—24no—
182#487—24no—
183#487—24no—
184#487—216no—
185#487—24no—
186#487—42no—
187#487D418yescomplemented
188#465—48no—
189#461—216no—
190#448—216no—
191#448—48no—
192#431—24no—
193C2×#106C2314yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×#103—216no—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#103C2314yes—
200C2×#103C2314yes—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#103C2314yes—
205C2×#103C2314yes—
206C2×#102C2314yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C4×C8—24no—
211C2×C4×C8C2312yes—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216#398—22no—
217#398—22no—
218#396—22no—
219#396—22no—
220#395—22no—
221#395—22no—
222#395—22no—
223#395—22no—
224#394—22no—
225#394—22no—
226#393—22no—
227#393—22no—
228#391—21no—
229#391—21no—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#390—21no—
234#390—21no—
235#390—21no—
236#390—21no—
237#390C2312yes—
238#390C2312yes—
239#390C2312yes—
240#389—22no—
241#389—22no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#388—22no—
254#386—22no—
255#386—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384—21no—
263#384—21no—
264#384—21no—
265#384—21no—
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#380—21no—
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380C2312yes—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4D411yescharacteristic
278C4×C4⋊C4D411yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4D411yescharacteristic
284C4×C22⋊C4D411yescharacteristic
285C4×C22⋊C4C2311yescharacteristic
286C4×C22⋊C4C2311yescharacteristic
287C43C2311yescharacteristic
288#340C2314yes—
289#340C2314yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295C2×#41—44no—
296C2×#41—44no—
297C2×#41—82no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—24no—
304C22×Q8—24no—
305C22×Q8—28no—
306C22×Q8—42no—
307C22×Q8—42no—
308C22×Q8—44no—
309C22×Q8—44no—
310C22×Q8—44no—
311C22×Q8—44no—
312C22×Q8—44no—
313C22×Q8—82no—
314C22×Q8C2412yes—
315C22×Q8C2412yes—
316C22×Q8C2412yes—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4C2×D411yescharacteristic
322C22×D4C2412yes—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—28no—
334C2×SD16—28no—
335C2×SD16—44no—
336C2×SD16—44no—
337C2×SD16—44no—
338C2×SD16—44no—
339C2×SD16—44no—
340C2×SD16—44no—
341C2×SD16—44no—
342C22×C8—24no—
343C22×C8—24no—
344C22×C8—42no—
345C22×C8C2412yes—
346C22×C8C2412yes—
347C22×C8C2412yes—
348C22×C8C2412yes—
349C4⋊Q8—24no—
350C4⋊Q8—24no—
351C4⋊Q8—24no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8—42no—
361C4⋊Q8—44no—
362C4⋊Q8—44no—
363C4⋊Q8—44no—
364C4⋊Q8—44no—
365C4⋊Q8—44no—
366C4⋊Q8—42no—
367C4⋊Q8—42no—
368C4⋊Q8—44no—
369C4⋊Q8—44no—
370C4⋊Q8—44no—
371C4⋊Q8—48no—
372C4⋊Q8C2×D414yes—
373C4⋊Q8C2×D414yes—
374#127—22no—
375#127—22no—
376#124—44no—
377#124—48no—
378#124—44no—
379#124—82no—
380C22⋊Q8—28no—
381C22⋊Q8—48no—
382C22⋊Q8—48no—
383C22⋊Q8—44no—
384C22⋊Q8—44no—
385C22⋊Q8—48no—
386#121—28no—
387#121—24no—
388#121—42no—
389#121—44no—
390#121—48no—
391#121—44no—
392#121—44no—
393C4×Q8—44no—
394C4×Q8—44no—
395C4×D4—24no—
396C4×D4—24no—
397C4×D4—24no—
398C4×D4—42no—
399C4×D4—44no—
400C4×D4—48no—
401C4×D4—48no—
402C4×D4SD1618yescomplemented
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#106—44no—
482C4⋊C8—24no—
483C4⋊C8—42no—
484#103—28no—
485#103—28no—
486#103—28no—
487#103—28no—
488#103—44no—
489#103—44no—
490#103—44no—
491#103—44no—
492#103C2×D4116yes—
493#102—44no—
494C22⋊C8—24no—
495C22⋊C8—24no—
496C22⋊C8—42no—
497C4×C8—24no—
498C4×C8—22no—
499C4×C8—22no—
500C4×C8—22no—
501C4×C8C2×D414yes—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95C2×D411yescharacteristic
513#95C2×D411yescharacteristic
514#95C2×D411yescharacteristic
515#95C2×D411yescharacteristic
516#95C2×D411yescharacteristic
517#95C2×D411yescharacteristic
518C24—22no—
519C24C22×D411yescharacteristic
520C24C22×D411yescharacteristic
521#41—816no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—24no—
527C2×Q8—22no—
528C2×Q8—24no—
529C2×Q8—24no—
530C2×Q8—22no—
531C2×Q8—24no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—416no—
539C2×Q8—44no—
540C2×Q8—42no—
541C2×Q8—42no—
542C2×Q8—44no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—82no—
547C2×Q8—82no—
548C2×Q8—82no—
549C2×Q8—88no—
550C2×Q8—816no—
551C2×Q8—88no—
552C2×Q8—88no—
553C2×Q8C22×D414yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—82no—
572C2×D4C2×SD1614yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4C2×SD1614yes—
609C22×C4C2×SD1614yes—
610C22×C4#13714yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4H(5,𝔽2)14yes—
624C22×C4C2511yescharacteristic
625SD16—88no—
626SD16—88no—
627SD16—88no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—48no—
640C2×C8C22×D414yes—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4C2×SD1614yes—
676C4⋊C4C22×D414yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—44no—
682C22⋊C4—44no—
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⋊C4C2×SD1614yes—
694C22⋊C4C2×SD1614yes—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—22no—
707C42—22no—
708C42—44no—
709C42—44no—
710C42C2×SD1614yes—
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—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23#53512yes—
731C23C22×SD1612yes—
732C23C22×SD1612yes—
733C23C2×#13712yes—
734C23C23×D411yescharacteristic
735Q8—28no—
736Q8—48no—
737Q8—44no—
738Q8—44no—
739Q8—44no—
740Q8—44no—
741Q8—44no—
742Q8—88no—
743Q8—88no—
744Q8—88no—
745Q8—84no—
746D4—28no—
747D4—44no—
748D4—44no—
749D4—88no—
750D4—88no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
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—21no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4#53512yes—
811C2×C4D4212yes—
812C2×C4D4212yes—
813C2×C4C22×SD1612yes—
814C2×C4C22×SD1612yes—
815C2×C4C22×SD1612yes—
816C2×C4C22×SD1612yes—
817C2×C4C22×SD1612yes—
818C2×C4C2×#13712yes—
819C2×C4C2×#13712yes—
820C2×C4#57712yes—
821C2×C4#57812yes—
822C2×C4C23×D411yescharacteristic
823C2×C4C2×H(5,𝔽2)12yes—
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4#58512yes—
826C8—24no—
827C8—42no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22#320614yescomplemented
851C22C2×#53511yescharacteristic
852C22C2×D4211yescharacteristic
853C22#350011yescharacteristic
854C22C23×SD1611yescharacteristic
855C22C22×#13711yescharacteristic
856C22C2×#57711yescharacteristic
857C22C2×#57811yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—41no—
865C4—44no—
866C4—41no—
867C4—41no—
868C4—44no—
869C4—41no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4#327014yes—
876C4D4×SD1614yes—
877C4#348812yes—
878C4#355812yes—
879C2—24no—
880C2—42no—
881C2—162no—
882C2#3767711yescharacteristic
883C2C2×#320611yescharacteristic
884C2#6082411yescharacteristic
885C2C2×#327011yescharacteristic
886C2C2×D4×SD1611yescharacteristic
887C2#6252611yescharacteristic
888C2#6254011yescharacteristic
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×#3206C2semidirect
2. C22×#487C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33170C2semidirect
6. #30878C2semidirect
7. #30522C2semidirect
8. #30263C2semidirect
9. #29845C2semidirect
10. #28748C2semidirect
11. #28614C2semidirect
12. #25902C2semidirect
13. #25856C2semidirect
14. #25718C2semidirect
15. #25597C2semidirect
16. #25078C2semidirect
17. #24429C2semidirect
18. #22218C2semidirect
19. #21101C2semidirect
187. #487D4semidirect
402. C4×D4SD16semidirect
850. C22#3206semidirect

Maximal subgroups

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

subgroupindex
C2×#32062
C22×#4872
#361222
D4×C4⋊Q82
#331702
#308782
#305222
#302632
#298452
#287482
#286142
#259022
#258562
#257182
#255972
#250782
#244292
#222182
#211012