Finite Group Databasebeta

← #6815280

Subgroups — #6815280

Order 512.

2003 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#3230C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33239C211yesmaximal, characteristic, complemented
6#31237C214yesmaximal, complemented
7#31197C214yesmaximal, complemented
8#29844C211yesmaximal, characteristic, complemented
9#29842C211yesmaximal, characteristic, complemented
10#28655C211yesmaximal, characteristic, complemented
11#28653C211yesmaximal, characteristic, complemented
12#26793C214yesmaximal, complemented
13#26785C214yesmaximal, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25811C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18C4×#500C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3230—28no—
26#3228—28no—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#492C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#484C2214yes—
37C2×#482C2214yes—
38C2×#477C2214yes—
39C2×#478C2214yes—
40C2×#431C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2545—21no—
49#2536—21no—
50#2491—21no—
51#2491C2212yes—
52#2489—21no—
53#2489C2212yes—
54#2453—21no—
55#2453C2212yes—
56#2452—21no—
57#2452C2212yes—
58#2436—21no—
59#2432—21no—
60#2421—21no—
61#2421—21no—
62#2416—21no—
63#2416C2212yes—
64#2415—21no—
65#2415C2212yes—
66#2362—21no—
67#2362C2212yes—
68#2361—21no—
69#2361C2212yes—
70#2351—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2068C2214yes—
75#2067C2214yes—
76#2067C2214yes—
77#2066C2214yes—
78#2059C2214yes—
79#2058C2214yes—
80#2036C2214yes—
81#2033C2214yes—
82#2000C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1968C2214yes—
89#1968C2214yes—
90#1957C2211yescharacteristic
91#1956C2211yescharacteristic
92#1954C2212yes—
93#1942C2214yes—
94#1939C2212yes—
95#1927C2214yes—
96#1925C2214yes—
97#1923C2212yes—
98#1923C2212yes—
99#1880C2214yes—
100#1877C2214yes—
101#1854C2214yes—
102#1853C2214yes—
103#1845C2211yescharacteristic
104C4×#107C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×SD16C2314yes—
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—42no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2312yes—
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×#127C2311yescharacteristic
130C2×#125—21no—
131C2×#125C2312yes—
132C2×#124—22no—
133C2×#124—21no—
134C2×#124—21no—
135C2×#124—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×#121—22no—
145C2×#121—21no—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121C2312yes—
149C2×#121C2312yes—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8C2312yes—
156C2×C4×D4—22no—
157C2×C4×D4—21no—
158C2×C4×D4D411yescharacteristic
159C2×C4×D4D411yescharacteristic
160C2×C4×D4C2312yes—
161C2×C4×D4C2311yescharacteristic
162C2×#117—21no—
163C2×#117C2312yes—
164C22×C4⋊C4—21no—
165C22×C4⋊C4C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#500—24no—
169#500D418yescomplemented
170#498—24no—
171#498—42no—
172#492—42no—
173#487—24no—
174#487—24no—
175#486—24no—
176#486—24no—
177#484—216no—
178#482—216no—
179#478—216no—
180#477—216no—
181#431—24no—
182#431—24no—
183C2×#107C2314yes—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×#106C2314yes—
187C2×#106C2314yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207#400—22no—
208#400—22no—
209#398—22no—
210#397—22no—
211#397—22no—
212#396—22no—
213#396—22no—
214#394—22no—
215#394—22no—
216#394—22no—
217#393—22no—
218#393—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391C2312yes—
226#391C2312yes—
227#391C2312yes—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#389—22no—
236#389—22no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#387—22no—
254#387—22no—
255#386—22no—
256#386—22no—
257#385—22no—
258#385—22no—
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#382—21no—
262#382—21no—
263#382—22no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—22no—
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4D411yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C43C2311yescharacteristic
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
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—22no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—82no—
303C22×Q8C2412yes—
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×SD16—28no—
319C2×SD16—44no—
320C2×SD16—44no—
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⋊Q8C2×D414yes—
338C4⋊Q8C2×D414yes—
339#127—22no—
340#127—22no—
341#125—24no—
342#125—42no—
343#125—44no—
344#124—44no—
345#124—48no—
346#124—44no—
347#124—82no—
348C22⋊Q8—24no—
349C22⋊Q8—44no—
350C22⋊Q8—42no—
351C22⋊Q8—44no—
352C22⋊Q8—48no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357#121—24no—
358#121—44no—
359#121—42no—
360#121—44no—
361#121—44no—
362#121—48no—
363#121—44no—
364C4×Q8—24no—
365C4×Q8—42no—
366C4×Q8—44no—
367C4×Q8—44no—
368C4×Q8—44no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—42no—
375C4×D4—44no—
376C4×D4—42no—
377C4×D4—48no—
378#117—24no—
379#117—42no—
380#117—44no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—28no—
456#107—44no—
457#107C2×D4116yes—
458#106—28no—
459#106—44no—
460C4⋊C8—24no—
461C4⋊C8—24no—
462C4⋊C8—42no—
463#103—28no—
464#103—28no—
465#103—44no—
466#102—28no—
467#102—28no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C4×C8—24no—
474C4×C8—22no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8—42no—
478C4×C8C2×D414yes—
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#95—22no—
492#95—22no—
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499C24—22no—
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502#41—816no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—44no—
510C2×Q8—44no—
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—42no—
521C2×Q8—82no—
522C2×Q8—816no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—41no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—82no—
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—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
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—82no—
573C22×C4—82no—
574C22×C4#13514yes—
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×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C2511yescharacteristic
588SD16—88no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8C22×D414yes—
600C2×C82−1+414yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—41no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—42no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4C22×D414yes—
634C4⋊C4C22×D414yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—41no—
640C22⋊C4—41no—
641C22⋊C4—44no—
642C22⋊C4—44no—
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—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—22no—
667C42—22no—
668C42—44no—
669C42—44no—
670C42—44no—
671C42—44no—
672C42AGL(1,ℤ/8)14yes—
673C42C22×D412yes—
674C42H(5,𝔽2)12yes—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23C2×#13512yes—
696C23C23×D411yescharacteristic
697Q8—48no—
698Q8—48no—
699Q8—44no—
700Q8—44no—
701Q8—88no—
702Q8—84no—
703Q8—84no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—88no—
708D4—88no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—28no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—21no—
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—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
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—88no—
768C2×C4—88no—
769C2×C4D4212yes—
770C2×C4D4212yes—
771C2×C4C2×#13512yes—
772C2×C4C2×#13512yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4C2×AGL(1,ℤ/8)12yes—
775C2×C4C2×AGL(1,ℤ/8)12yes—
776C2×C4#57712yes—
777C2×C4#57812yes—
778C2×C4C23×D411yescharacteristic
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4C2×2−1+412yes—
781C2×C4#58512yes—
782C8—24no—
783C8—24no—
784C8—42no—
785C8—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22#344911yescharacteristic
808C22C2×D4211yescharacteristic
809C22#349911yescharacteristic
810C22C22×#13511yescharacteristic
811C22C22×AGL(1,ℤ/8)11yescharacteristic
812C22C2×#57711yescharacteristic
813C22C2×#57811yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—44no—
822C4—44no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#327214yes—
832C4#328514yes—
833C4#349712yes—
834C4#356112yes—
835C2—42no—
836C2—81no—
837C2—162no—
838C2#3935611yescharacteristic
839C2#6094611yescharacteristic
840C2#6100811yescharacteristic
841C2C2×#327211yescharacteristic
842C2C2×#328511yescharacteristic
843C2#6247011yescharacteristic
844C2#6247911yescharacteristic
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×#3230C2semidirect
3. #36151C2semidirect
5. #33239C2semidirect
6. #31237C2semidirect
7. #31197C2semidirect
8. #29844C2semidirect
9. #29842C2semidirect
10. #28655C2semidirect
11. #28653C2semidirect
12. #26793C2semidirect
13. #26785C2semidirect
14. #25812C2semidirect
15. #25811C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. C4×#500C2semidirect
19. #21264C2semidirect
169. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#32302
#361512
#361222
#332392
#312372
#311972
#298442
#298422
#286552
#286532
#267932
#267852
#258122
#258112
#255982
#255972
C4×#5002
#212642