Finite Group Databasebeta

← #6684006

Subgroups — #6684006

Order 512.

2040 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3227C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33048C211yesmaximal, characteristic, complemented
6#30974C214yesmaximal, complemented
7#30791C214yesmaximal, complemented
8#30278C211yesmaximal, characteristic, complemented
9#29876C211yesmaximal, characteristic, complemented
10#28688C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26354C214yesmaximal, complemented
13#26143C214yesmaximal, complemented
14#25905C211yesmaximal, characteristic, complemented
15#25811C211yesmaximal, characteristic, complemented
16#25811C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22246C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3227—28no—
26#3165—28no—
27C2×#501C2214yes—
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#481C2214yes—
38C2×#476C2214yes—
39C2×#431C2211yescharacteristic
40C2×#428C2214yes—
41C2×C4×M16C2211yescharacteristic
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2550C2212yes—
49#2545—21no—
50#2492—21no—
51#2491—21no—
52#2491C2212yes—
53#2452—21no—
54#2452C2212yes—
55#2451—21no—
56#2446—21no—
57#2442C2212yes—
58#2439C2212yes—
59#2436—21no—
60#2432—21no—
61#2429—21no—
62#2417—21no—
63#2416—21no—
64#2416C2212yes—
65#2409—21no—
66#2361—21no—
67#2361C2212yes—
68#2360—21no—
69#2352C2212yes—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2092C2214yes—
75#2092C2214yes—
76#2086C2214yes—
77#2085C2214yes—
78#2075C2214yes—
79#2065C2214yes—
80#2058C2214yes—
81#2058C2214yes—
82#2033C2214yes—
83#2025C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1949C2214yes—
91#1936C2214yes—
92#1926C2214yes—
93#1924C2212yes—
94#1920C2214yes—
95#1919C2214yes—
96#1917C2212yes—
97#1895C2214yes—
98#1875C2214yes—
99#1870C2212yes—
100#1862C2214yes—
101#1853C2214yes—
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—
113#548—48no—
114#533—24no—
115#533—42no—
116#532—24no—
117#532—42no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2312yes—
130C2×C4⋊Q8C2312yes—
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×#127C2311yescharacteristic
134C2×#125C2312yes—
135C2×#124—22no—
136C2×#124—21no—
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—21no—
144C2×C22⋊Q8—22no—
145C2×#121—22no—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121C2312yes—
150C2×#121C2312yes—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×D4—22no—
156C2×C4×D4—21no—
157C2×C4×D4D411yescharacteristic
158C2×C4×D4D411yescharacteristic
159C2×C4×D4C2312yes—
160C2×C4×D4C2311yescharacteristic
161C2×#117C2312yes—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#501—216no—
169#500—24no—
170#500—24no—
171#498—24no—
172#498—24no—
173#498—42no—
174#498D418yescomplemented
175#486—24no—
176#486—24no—
177#486—42no—
178#481—216no—
179#476—216no—
180#431—24no—
181#428—216no—
182C2×#107C2314yes—
183C2×#107C2314yes—
184C2×#106C2314yes—
185C2×#106C2314yes—
186C2×#106C2314yes—
187C2×#106C2314yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C4×M16—24no—
198C2×#97C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203#400—22no—
204#398—22no—
205#398—22no—
206#396—22no—
207#396—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#394—22no—
212#393—22no—
213#393—22no—
214#393—22no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—22no—
225#391—22no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2312yes—
232#390C2312yes—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—22no—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#387—22no—
248#387—22no—
249#386—22no—
250#386—22no—
251#386—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#382C2312yes—
258#382C2312yes—
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⋊Q8C2×D414yes—
347C4⋊Q8C2×D414yes—
348#127—22no—
349#127—22no—
350#125—24no—
351#125—42no—
352#124—44no—
353#124—44no—
354#124—48no—
355#124—82no—
356C22⋊Q8—44no—
357C22⋊Q8—48no—
358C22⋊Q8—44no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—82no—
362#121—28no—
363#121—24no—
364#121—42no—
365#121—44no—
366#121—44no—
367#121—44no—
368#121—48no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×Q8—44no—
372C4×Q8—82no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—42no—
377C4×D4—44no—
378C4×D4—42no—
379C4×D4—48no—
380#117—24no—
381#117—42no—
382C2×C4⋊C4—21no—
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—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
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—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—28no—
458#107—28no—
459#106—28no—
460#106—28no—
461#106—44no—
462#106C2×D4116yes—
463C4⋊C8—24no—
464C4⋊C8—24no—
465#102—28no—
466#102—28no—
467#102—28no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472#97—24no—
473C4×C8—22no—
474C4×C8—22no—
475C4×C8—22no—
476C4×C8C2×D414yes—
477#95—22no—
478#95—22no—
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#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497C24—22no—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500#41—816no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—82no—
521C2×Q8—82no—
522C2×Q8—816no—
523C2×Q8—816no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—41no—
531C2×D4—44no—
532C2×D4—44no—
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—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
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—22no—
558C22×C4—22no—
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—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4AGL(1,ℤ/8)14yes—
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
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×C42−1+414yes—
591C22×C4C2511yescharacteristic
592M16—216no—
593C2×C8—22no—
594C2×C8—22no—
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×C8C22×D414yes—
604C2×C82−1+414yes—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—41no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—82no—
637C4⋊C4—82no—
638C4⋊C4C22×D414yes—
639C4⋊C4C22×D414yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—41no—
645C22⋊C4—41no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—22no—
672C42—22no—
673C42—44no—
674C42—44no—
675C42—82no—
676C42C22×D412yes—
677C42H(5,𝔽2)12yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#53612yes—
698C23C2×AGL(1,ℤ/8)12yes—
699C23C23×D411yescharacteristic
700Q8—48no—
701Q8—48no—
702Q8—88no—
703Q8—88no—
704Q8—84no—
705Q8—84no—
706Q8—84no—
707D4—44no—
708D4—44no—
709D4—44no—
710D4—88no—
711D4—88no—
712D4—84no—
713D4—84no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—24no—
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—24no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
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—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
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—88no—
772C2×C4—88no—
773C2×C4—88no—
774C2×C4#53612yes—
775C2×C4D4212yes—
776C2×C4D4212yes—
777C2×C4C2×AGL(1,ℤ/8)12yes—
778C2×C4C2×AGL(1,ℤ/8)12yes—
779C2×C4#57512yes—
780C2×C4#57712yes—
781C2×C4#57712yes—
782C2×C4C23×D411yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×2−1+412yes—
785C2×C4C2×2−1+412yes—
786C8—24no—
787C8—24no—
788C8—42no—
789C8—42no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22C2×#53611yescharacteristic
812C22C2×D4211yescharacteristic
813C22#349911yescharacteristic
814C22C22×AGL(1,ℤ/8)11yescharacteristic
815C22C2×#57511yescharacteristic
816C22C2×#57711yescharacteristic
817C22C2×#57711yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—44no—
825C4—41no—
826C4—41no—
827C4—44no—
828C4—41no—
829C4—41no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4#326514yes—
836C4#327514yes—
837C4#348612yes—
838C4#355212yes—
839C2—42no—
840C2—42no—
841C2—162no—
842C2#3767511yescharacteristic
843C2#6086411yescharacteristic
844C2#6088111yescharacteristic
845C2C2×#326511yescharacteristic
846C2C2×#327511yescharacteristic
847C2#6247711yescharacteristic
848C2#6248311yescharacteristic
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×#3227C2semidirect
2. C2×#3165C2semidirect
3. #36129C2semidirect
5. #33048C2semidirect
6. #30974C2semidirect
7. #30791C2semidirect
8. #30278C2semidirect
9. #29876C2semidirect
10. #28688C2semidirect
11. #28654C2semidirect
12. #26354C2semidirect
13. #26143C2semidirect
14. #25905C2semidirect
15. #25811C2semidirect
16. #25811C2semidirect
17. #25673C2semidirect
18. #22246C2semidirect
19. #21102C2semidirect
174. #498D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32272
C2×#31652
#361292
#361222
#330482
#309742
#307912
#302782
#298762
#286882
#286542
#263542
#261432
#259052
#258112
#256732
#222462
#211022