Finite Group Databasebeta

← #6684786

Subgroups — #6684786

Order 512.

2163 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×#3210C211yesmaximal, characteristic, complemented
2C22×#487C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33170C211yesmaximal, characteristic, complemented
6#30881C214yesmaximal, complemented
7#30520C214yesmaximal, complemented
8#30261C211yesmaximal, characteristic, complemented
9#29845C211yesmaximal, characteristic, complemented
10#28750C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#25903C211yesmaximal, characteristic, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25722C211yesmaximal, characteristic, complemented
15#25600C211yesmaximal, characteristic, complemented
16#25086C214yesmaximal, complemented
17#24431C214yesmaximal, complemented
18#22218C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#548C2212yes—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3210—28no—
26C2×#494C2211yescharacteristic
27C2×#494C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487—28no—
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2214yes—
34C2×#487C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#465C2214yes—
38C2×#464C2214yes—
39C2×#452C2214yes—
40C2×#451C2214yes—
41C2×#431C2211yescharacteristic
42C22×#103C2214yes—
43C22×C4×C8C2211yescharacteristic
44#2862C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2550—21no—
51#2545C2212yes—
52#2492C2212yes—
53#2491—21no—
54#2491—21no—
55#2452—21no—
56#2452—21no—
57#2451C2212yes—
58#2446—21no—
59#2442—21no—
60#2439—21no—
61#2436C2212yes—
62#2432C2212yes—
63#2429—21no—
64#2417C2212yes—
65#2416—21no—
66#2416—21no—
67#2409—21no—
68#2361—21no—
69#2361—21no—
70#2360C2212yes—
71#2352—21no—
72Q8×C22⋊C4—21no—
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C42×D4C2211yescharacteristic
76#2066C2214yes—
77#2056C2214yes—
78#2042C2214yes—
79#2042C2214yes—
80#2035C2214yes—
81#2023C2214yes—
82#2016C2214yes—
83#2015C2214yes—
84#2015C2214yes—
85#2001C2214yes—
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1983C2214yes—
89#1968C2214yes—
90#1957C2211yescharacteristic
91#1956C2211yescharacteristic
92#1956C2211yescharacteristic
93#1956C2211yescharacteristic
94#1927C2214yes—
95#1923C2212yes—
96#1916C2212yes—
97#1878C2214yes—
98#1878C2214yes—
99#1874C2214yes—
100#1869C2212yes—
101#1865C2214yes—
102#1850C2212yes—
103#1844C2211yescharacteristic
104#1788C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41C2312yes—
110C23×Q8—21no—
111C23×Q8C2312yes—
112C22×Q16C2314yes—
113C22×Q16C2314yes—
114C22×SD16C2314yes—
115C23×C8C2312yes—
116#548—48no—
117#533—24no—
118#533—42no—
119#532—24no—
120#532—42no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—24no—
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⋊Q8C2312yes—
132C2×C4⋊Q8C2311yescharacteristic
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×#127C2311yescharacteristic
137C2×#125—21no—
138C2×#124—22no—
139C2×#124C2312yes—
140C2×#124C2312yes—
141C2×#124C2312yes—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—22no—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2312yes—
148C2×#121—22no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121—21no—
152C2×#121—21no—
153C2×#121C2312yes—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2312yes—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D411yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×#117—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#494—24no—
172#494—42no—
173#492—24no—
174#487—24no—
175#487—24no—
176#487—216no—
177#487—24no—
178#487D418yescomplemented
179#486—24no—
180#486—42no—
181#465—48no—
182#464—216no—
183#452—216no—
184#451—48no—
185#431—24no—
186C2×#106C2314yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×#103—216no—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C4×C8—24no—
204C2×C4×C8C2312yes—
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209#400—22no—
210#398—22no—
211#398—22no—
212#396—22no—
213#396—22no—
214#396—22no—
215#395—22no—
216#394—22no—
217#394—22no—
218#393—22no—
219#393—22no—
220#393—22no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—22no—
226#391—22no—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#390—21no—
233#390—21no—
234#390—21no—
235#390—21no—
236#390—21no—
237#390—21no—
238#390C2312yes—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—22no—
248#389C2312yes—
249#389C2312yes—
250#388—22no—
251#388—22no—
252#388—22no—
253#387—22no—
254#387—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#384C2311yescharacteristic
262#384C2311yescharacteristic
263#382—21no—
264#382—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—22no—
271#380C2312yes—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4D411yescharacteristic
276C4×C4⋊C4D411yescharacteristic
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C22⋊C4—22no—
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4D411yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C4×C22⋊C4C2311yescharacteristic
286C43C2311yescharacteristic
287#340C2314yes—
288#340C2314yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294C2×#41—24no—
295C2×#41—42no—
296C2×#41—44no—
297C2×#41—44no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—24no—
303C22×Q8—28no—
304C22×Q8—42no—
305C22×Q8—44no—
306C22×Q8—44no—
307C22×Q8—44no—
308C22×Q8—82no—
309C22×Q8C2412yes—
310C22×Q8C2412yes—
311C22×Q8C2412yes—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4C2×D411yescharacteristic
317C22×D4C2412yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C2×Q16—28no—
328C2×Q16—44no—
329C2×Q16—44no—
330C2×Q16—44no—
331C2×Q16—44no—
332C2×Q16—44no—
333C2×SD16—28no—
334C2×SD16—44no—
335C2×SD16—44no—
336C22×C8—24no—
337C22×C8—24no—
338C22×C8—42no—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C4⋊Q8—24no—
344C4⋊Q8—24no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—42no—
354C4⋊Q8—44no—
355C4⋊Q8—44no—
356C4⋊Q8—44no—
357C4⋊Q8—42no—
358C4⋊Q8—44no—
359C4⋊Q8C2×D414yes—
360C4⋊Q8C2×D414yes—
361#127—22no—
362#127—22no—
363#125—44no—
364#124—24no—
365#124—42no—
366#124—44no—
367#124—44no—
368#124—48no—
369C22⋊Q8—28no—
370C22⋊Q8—24no—
371C22⋊Q8—42no—
372C22⋊Q8—44no—
373C22⋊Q8—48no—
374C22⋊Q8—44no—
375C22⋊Q8—82no—
376#121—28no—
377#121—44no—
378#121—44no—
379#121—48no—
380#121—44no—
381#121—44no—
382C4×Q8—24no—
383C4×Q8—42no—
384C4×Q8—44no—
385C4×Q8—44no—
386C4×Q8—82no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—44no—
391C4×D4—44no—
392C4×D4—48no—
393#117—44no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
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⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468#106—44no—
469C4⋊C8—24no—
470C4⋊C8—42no—
471#103—28no—
472#103—28no—
473#103—28no—
474#103—44no—
475#103—44no—
476#103—44no—
477#103C2×D4116yes—
478#102—28no—
479#102—44no—
480#102—44no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—42no—
484C4×C8—24no—
485C4×C8—22no—
486C4×C8—22no—
487C4×C8—22no—
488C4×C8C2×D414yes—
489#95—22no—
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#95—22no—
501#95—22no—
502#95—22no—
503#95C2×D411yescharacteristic
504#95C2×D411yescharacteristic
505#95C2×D411yescharacteristic
506#95C2×D411yescharacteristic
507#95C2×D411yescharacteristic
508#95C2×D411yescharacteristic
509C24—22no—
510C24C22×D411yescharacteristic
511C24C22×D411yescharacteristic
512#41—88no—
513#41—88no—
514C2×Q8—24no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—24no—
519C2×Q8—24no—
520C2×Q8—24no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—416no—
529C2×Q8—44no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×Q8—88no—
539C2×Q8—816no—
540C2×Q8C22×D414yes—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—82no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4#13514yes—
594C22×C4#13714yes—
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×C4C22×D411yescharacteristic
607C22×C4H(5,𝔽2)14yes—
608C22×C4C2511yescharacteristic
609Q16—88no—
610Q16—88no—
611SD16—88no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—48no—
624C2×C8C22×D414yes—
625C4⋊C4—22no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4C22×D414yes—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—44no—
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—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—22no—
689C42—22no—
690C42—44no—
691C42—44no—
692C42—82no—
693C42C22×D412yes—
694C42H(5,𝔽2)12yes—
695C23—21no—
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#53512yes—
714C23C2×#13512yes—
715C23C2×#13712yes—
716C23C23×D411yescharacteristic
717Q8—28no—
718Q8—48no—
719Q8—44no—
720Q8—44no—
721Q8—44no—
722Q8—44no—
723Q8—44no—
724Q8—88no—
725Q8—88no—
726Q8—84no—
727D4—44no—
728D4—44no—
729D4—44no—
730D4—88no—
731D4—88no—
732D4—84no—
733D4—84no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—21no—
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—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
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—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—88no—
791C2×C4—88no—
792C2×C4—88no—
793C2×C4#53512yes—
794C2×C4D4212yes—
795C2×C4D4212yes—
796C2×C4C2×#13512yes—
797C2×C4C2×#13512yes—
798C2×C4C2×#13712yes—
799C2×C4C2×#13712yes—
800C2×C4#57712yes—
801C2×C4#57812yes—
802C2×C4C23×D411yescharacteristic
803C2×C4C2×H(5,𝔽2)12yes—
804C2×C4C2×H(5,𝔽2)11yescharacteristic
805C2×C4#58512yes—
806C8—24no—
807C8—42no—
808C8—42no—
809C8—42no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22#321014yescomplemented
831C22C2×#53511yescharacteristic
832C22C2×D4211yescharacteristic
833C22#350011yescharacteristic
834C22C22×#13511yescharacteristic
835C22C22×#13711yescharacteristic
836C22C2×#57711yescharacteristic
837C22C2×#57811yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—41no—
842C4—44no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—44no—
849C4—41no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4#327014yes—
856C4#328214yes—
857C4#348812yes—
858C4#355812yes—
859C2—24no—
860C2—81no—
861C2—162no—
862C2#3767711yescharacteristic
863C2C2×#321011yescharacteristic
864C2#6082411yescharacteristic
865C2C2×#327011yescharacteristic
866C2C2×#328211yescharacteristic
867C2#6252811yescharacteristic
868C2#6254211yescharacteristic
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×#3210C2semidirect
2. C22×#487C2semidirect
3. #36129C2semidirect
5. #33170C2semidirect
6. #30881C2semidirect
7. #30520C2semidirect
8. #30261C2semidirect
9. #29845C2semidirect
10. #28750C2semidirect
11. #28616C2semidirect
12. #25903C2semidirect
13. #25857C2semidirect
14. #25722C2semidirect
15. #25600C2semidirect
16. #25086C2semidirect
17. #24431C2semidirect
18. #22218C2semidirect
19. #21101C2semidirect
178. #487D4semidirect
830. C22#3210semidirect

Maximal subgroups

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

subgroupindex
C2×#32102
C22×#4872
#361292
#361222
#331702
#308812
#305202
#302612
#298452
#287502
#286162
#259032
#258572
#257222
#256002
#250862
#244312
#222182
#211012