Finite Group Databasebeta

← #6684012

Subgroups — #6684012

Order 512.

2001 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33048C211yesmaximal, characteristic, complemented
6#30967C214yesmaximal, complemented
7#30796C214yesmaximal, complemented
8#30276C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26364C214yesmaximal, complemented
13#26157C214yesmaximal, complemented
14#25905C211yesmaximal, characteristic, complemented
15#25813C211yesmaximal, characteristic, complemented
16#25812C211yesmaximal, characteristic, complemented
17#25673C211yesmaximal, characteristic, complemented
18#22246C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3228—28no—
26#3165—28no—
27C2×#501C2214yes—
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#500C2211yescharacteristic
31C2×#500C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#482C2214yes—
38C2×#478C2214yes—
39C2×#431C2211yescharacteristic
40C2×#428C2214yes—
41C2×C4×M16C2211yescharacteristic
42#2868C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2552C2212yes—
49#2545—21no—
50#2542—21no—
51#2538—21no—
52#2491—21no—
53#2491C2212yes—
54#2452—21no—
55#2452C2212yes—
56#2441C2212yes—
57#2441C2212yes—
58#2436—21no—
59#2432—21no—
60#2429—21no—
61#2429—21no—
62#2423—21no—
63#2423—21no—
64#2416—21no—
65#2416C2212yes—
66#2365—21no—
67#2361—21no—
68#2361C2212yes—
69#2354C2212yes—
70Q8×C4⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2093C2214yes—
75#2093C2214yes—
76#2087C2214yes—
77#2083C2214yes—
78#2076C2214yes—
79#2065C2214yes—
80#2059C2214yes—
81#2057C2214yes—
82#2033C2214yes—
83#2025C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1957C2211yescharacteristic
90#1947C2214yes—
91#1936C2214yes—
92#1926C2214yes—
93#1924C2212yes—
94#1920C2214yes—
95#1919C2214yes—
96#1917C2212yes—
97#1895C2214yes—
98#1875C2214yes—
99#1870C2212yes—
100#1862C2214yes—
101#1854C2214yes—
102#1852C2214yes—
103#1851C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×M16C2312yes—
112#548—48no—
113#533—24no—
114#533—24no—
115#533—42no—
116#533—42no—
117#532—24no—
118#532—42no—
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⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×#127C2311yescharacteristic
132C2×#125C2312yes—
133C2×#125C2312yes—
134C2×#124—22no—
135C2×#124—21no—
136C2×#124—21no—
137C2×#124—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—22no—
146C2×#121—22no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121C2312yes—
151C2×#121C2312yes—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4D411yescharacteristic
161C2×C4×D4D411yescharacteristic
162C2×C4×D4C2312yes—
163C2×C4×D4C2311yescharacteristic
164C2×#117C2312yes—
165C2×#117C2312yes—
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#501—216no—
171#500—24no—
172#500—24no—
173#500—24no—
174#500—42no—
175#498—24no—
176#498D418yescomplemented
177#486—24no—
178#486—24no—
179#486—42no—
180#482—216no—
181#478—216no—
182#431—24no—
183#428—216no—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×#107C2314yes—
187C2×#107C2314yes—
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#399—22no—
207#398—22no—
208#398—22no—
209#396—22no—
210#396—22no—
211#396—22no—
212#396—22no—
213#394—22no—
214#394—22no—
215#393—22no—
216#393—22no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#390—22no—
223#390—21no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390C2312yes—
228#390C2312yes—
229#390C2312yes—
230#389—22no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—22no—
237#389—22no—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#387—22no—
248#387—22no—
249#386—22no—
250#386—22no—
251#385—22no—
252#385—22no—
253#384—22no—
254#384—21no—
255#384—21no—
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#384C2312yes—
259#384C2312yes—
260#380—21no—
261#380—21no—
262#380—21no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
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—44no—
302C22×Q8—44no—
303C22×Q8—82no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C2×D411yescharacteristic
309C22×D4C2412yes—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C4⋊Q8—24no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—42no—
335C4⋊Q8—44no—
336C4⋊Q8—44no—
337C4⋊Q8—44no—
338C4⋊Q8—82no—
339C4⋊Q8C2×D414yes—
340C4⋊Q8C2×D414yes—
341#127—22no—
342#127—22no—
343#125—24no—
344#125—24no—
345#125—42no—
346#125—42no—
347#124—44no—
348#124—48no—
349#124—44no—
350#124—82no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—48no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8—82no—
358C22⋊Q8—82no—
359#121—28no—
360#121—24no—
361#121—42no—
362#121—44no—
363#121—44no—
364#121—44no—
365#121—48no—
366C4×Q8—44no—
367C4×Q8—44no—
368C4×Q8—44no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×Q8—44no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—42no—
376C4×D4—44no—
377C4×D4—42no—
378C4×D4—48no—
379#117—24no—
380#117—24no—
381#117—42no—
382#117—42no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
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—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
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⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461#107—28no—
462#107—28no—
463#107—28no—
464#107—44no—
465#106—28no—
466#106C2×D4116yes—
467C4⋊C8—24no—
468C4⋊C8—24no—
469#102—28no—
470#102—28no—
471#102—28no—
472#102—44no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C22⋊C8—24no—
476#97—24no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—22no—
480C4×C8C2×D414yes—
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—42no—
506C2×Q8—42no—
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—82no—
519C2×Q8—816no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—41no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—82no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
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—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C42−1+414yes—
584C22×C4C2511yescharacteristic
585M16—216no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8C22×D414yes—
597C2×C82−1+414yes—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—41no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—82no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4C22×D414yes—
636C4⋊C4C22×D414yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—41no—
642C22⋊C4—41no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—82no—
654C22⋊C4—82no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—22no—
669C42—22no—
670C42—44no—
671C42—44no—
672C42—44no—
673C42—44no—
674C42AGL(1,ℤ/8)14yes—
675C42C22×D412yes—
676C42H(5,𝔽2)12yes—
677C23—21no—
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—
698C23C23×D411yescharacteristic
699Q8—48no—
700Q8—48no—
701Q8—88no—
702Q8—84no—
703Q8—84no—
704Q8—84no—
705D4—44no—
706D4—44no—
707D4—44no—
708D4—88no—
709D4—88no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—21no—
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—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
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—88no—
769C2×C4—88no—
770C2×C4#53612yes—
771C2×C4D4212yes—
772C2×C4D4212yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4C2×AGL(1,ℤ/8)12yes—
775C2×C4C2×AGL(1,ℤ/8)12yes—
776C2×C4#57512yes—
777C2×C4#57612yes—
778C2×C4#57812yes—
779C2×C4C23×D411yescharacteristic
780C2×C4C2×H(5,𝔽2)11yescharacteristic
781C2×C4C2×2−1+412yes—
782C2×C4C2×2−1+412yes—
783C8—24no—
784C8—24no—
785C8—42no—
786C8—42no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22C2×#53611yescharacteristic
809C22C2×D4211yescharacteristic
810C22#349911yescharacteristic
811C22C22×AGL(1,ℤ/8)11yescharacteristic
812C22C2×#57511yescharacteristic
813C22C2×#57611yescharacteristic
814C22C2×#57811yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—44no—
823C4—41no—
824C4—41no—
825C4—44no—
826C4—41no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#326914yes—
833C4#327414yes—
834C4#348612yes—
835C4#355212yes—
836C2—42no—
837C2—81no—
838C2—162no—
839C2#3767511yescharacteristic
840C2#6086411yescharacteristic
841C2#6088011yescharacteristic
842C2C2×#326911yescharacteristic
843C2C2×#327411yescharacteristic
844C2#6247911yescharacteristic
845C2#6248111yescharacteristic
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×#3228C2semidirect
2. C2×#3165C2semidirect
3. #36134C2semidirect
5. #33048C2semidirect
6. #30967C2semidirect
7. #30796C2semidirect
8. #30276C2semidirect
9. #29878C2semidirect
10. #28689C2semidirect
11. #28654C2semidirect
12. #26364C2semidirect
13. #26157C2semidirect
14. #25905C2semidirect
15. #25813C2semidirect
16. #25812C2semidirect
17. #25673C2semidirect
18. #22246C2semidirect
19. #21102C2semidirect
176. #498D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#31652
#361342
#361222
#330482
#309672
#307962
#302762
#298782
#286892
#286542
#263642
#261572
#259052
#258132
#258122
#256732
#222462
#211022