Finite Group Databasebeta

← #6687615

Subgroups — #6687615

Order 512.

1962 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×#3226C211yesmaximal, characteristic, complemented
2C2×#3170C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#30910C214yesmaximal, complemented
7#30709C214yesmaximal, complemented
8#30261C211yesmaximal, characteristic, complemented
9#29808C211yesmaximal, characteristic, complemented
10#28750C211yesmaximal, characteristic, complemented
11#28656C211yesmaximal, characteristic, complemented
12#26893C214yesmaximal, complemented
13#26620C214yesmaximal, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18#22247C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3226—28no—
25#3170—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#480C2214yes—
36C2×#474C2214yes—
37C2×#467C2214yes—
38C2×C4×Q16C2214yes—
39C2×#431C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2862C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2550—21no—
48#2540C2212yes—
49#2492C2212yes—
50#2490—21no—
51#2454—21no—
52#2451C2212yes—
53#2448—21no—
54#2446—21no—
55#2442—21no—
56#2439—21no—
57#2429—21no—
58#2427C2212yes—
59#2426—21no—
60#2426C2212yes—
61#2417C2212yes—
62#2414—21no—
63#2409—21no—
64#2407—21no—
65#2367C2212yes—
66#2363—21no—
67#2360C2212yes—
68#2352—21no—
69#2341—21no—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2068C2214yes—
75#2056C2214yes—
76#2042C2214yes—
77#2036C2214yes—
78#2024C2214yes—
79#2015C2214yes—
80#2015C2214yes—
81#2001C2214yes—
82#2000C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1983C2214yes—
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1934C2214yes—
92#1928C2214yes—
93#1923C2212yes—
94#1918C2214yes—
95#1918C2214yes—
96#1916C2212yes—
97#1893C2214yes—
98#1880C2214yes—
99#1877C2214yes—
100#1872C2214yes—
101#1869C2212yes—
102#1863C2214yes—
103#1850C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2312yes—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#532—24no—
119#532—42no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×#127C2311yescharacteristic
131C2×#125—21no—
132C2×#125—21no—
133C2×#124—21no—
134C2×#124C2312yes—
135C2×#124C2312yes—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121—21no—
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4—21no—
155C2×C4×D4D411yescharacteristic
156C2×C4×D4D411yescharacteristic
157C2×C4×D4C2312yes—
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C2×#117—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#500—24no—
166#500D418yescomplemented
167#494—24no—
168#492—42no—
169#487—24no—
170#487—24no—
171#487—42no—
172#486—24no—
173#486—24no—
174#480—216no—
175#474—216no—
176#467—216no—
177C4×Q16—216no—
178#431—24no—
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C4×C8—24no—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200#400—22no—
201#399—22no—
202#398—22no—
203#398—22no—
204#397—22no—
205#396—22no—
206#396—22no—
207#395—22no—
208#394—22no—
209#394—22no—
210#393—22no—
211#392—22no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—22no—
218#391—22no—
219#391C2312yes—
220#391C2312yes—
221#391C2312yes—
222#391C2312yes—
223#390—22no—
224#390—22no—
225#390—22no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#387—22no—
249#387—22no—
250#386—22no—
251#386—22no—
252#385—22no—
253#385—22no—
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#382—21no—
257#382—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—22no—
264#380—22no—
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⋊C4—22no—
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C2×#41—44no—
292C2×#41—44no—
293C2×#41—82no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—22no—
298C22×Q8—44no—
299C22×Q8—44no—
300C22×Q8—82no—
301C22×Q8C2412yes—
302C22×Q8C2412yes—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4C2×D411yescharacteristic
308C22×D4C2412yes—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C2×Q16—28no—
318C2×Q16—44no—
319C2×Q16—44no—
320C2×SD16—44no—
321C2×SD16—44no—
322C2×SD16—44no—
323C22×C8—24no—
324C22×C8—42no—
325C22×C8—42no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C4⋊Q8—24no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—42no—
340C4⋊Q8—44no—
341C4⋊Q8—44no—
342C4⋊Q8C2×D414yes—
343C4⋊Q8C2×D414yes—
344#127—22no—
345#127—22no—
346#125—44no—
347#125—44no—
348#124—44no—
349#124—44no—
350#124—44no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—44no—
354C22⋊Q8—42no—
355C22⋊Q8—42no—
356C22⋊Q8—44no—
357C22⋊Q8—44no—
358C22⋊Q8—44no—
359C22⋊Q8—82no—
360#121—24no—
361#121—42no—
362#121—44no—
363#121—44no—
364#121—44no—
365#121—82no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—42no—
369C4×Q8—42no—
370C4×Q8—44no—
371C4×Q8—44no—
372C4×Q8—82no—
373C4×Q8—82no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—42no—
378C4×D4—44no—
379C4×D4—42no—
380#117—44no—
381#117—44no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
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⋊C4—22no—
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—28no—
457#107C2×D4116yes—
458C4⋊C8—24no—
459C4⋊C8—42no—
460#103—28no—
461#103—28no—
462#103—44no—
463#103—44no—
464#103—44no—
465#102—28no—
466#102—28no—
467#102—44no—
468C22⋊C8—24no—
469C22⋊C8—42no—
470C22⋊C8—42no—
471C4×C8—24no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—22no—
475C4×C8C2×D414yes—
476#95—22no—
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#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496C24—22no—
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499#41—816no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—44no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—44no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—82no—
520C2×Q8—816no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—41no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—82no—
538C2×D4—82no—
539C2×D4—82no—
540C22×C4—22no—
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—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
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×C4#13514yes—
572C22×C4#13714yes—
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×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C2511yescharacteristic
586Q16—416no—
587SD16—88no—
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×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—48no—
600C2×C8C22×D414yes—
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—24no—
610C4⋊C4—24no—
611C4⋊C4—41no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4—82no—
631C4⋊C4—82no—
632C4⋊C4C22×D414yes—
633C4⋊C4C22×D414yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C22⋊C4—82no—
651C22⋊C4—82no—
652C22⋊C4—82no—
653C22⋊C4—82no—
654C42—22no—
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—82no—
671C42—82no—
672C42C22×D412yes—
673C42H(5,𝔽2)12yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×#13512yes—
694C23C2×#13712yes—
695C23C23×D411yescharacteristic
696Q8—48no—
697Q8—48no—
698Q8—44no—
699Q8—44no—
700Q8—44no—
701Q8—44no—
702Q8—88no—
703Q8—84no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—88no—
708D4—84no—
709D4—84no—
710D4—164no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—21no—
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—21no—
742C2×C4—21no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
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—42no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4D4212yes—
771C2×C4D4212yes—
772C2×C4C2×#13512yes—
773C2×C4C2×#13512yes—
774C2×C4C2×#13712yes—
775C2×C4C2×#13712yes—
776C2×C4#57612yes—
777C2×C4#57812yes—
778C2×C4C23×D411yescharacteristic
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4#58512yes—
781C2×C4#58512yes—
782C8—24no—
783C8—42no—
784C8—42no—
785C8—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
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#350011yescharacteristic
810C22C22×#13511yescharacteristic
811C22C22×#13711yescharacteristic
812C22C2×#57611yescharacteristic
813C22C2×#57811yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—44no—
825C4—44no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#327014yes—
832C4#328014yes—
833C4#348712yes—
834C4#356212yes—
835C2—42no—
836C2—42no—
837C2—162no—
838C2#3768311yescharacteristic
839C2#6094711yescharacteristic
840C2#6101411yescharacteristic
841C2C2×#327011yescharacteristic
842C2C2×#328011yescharacteristic
843C2#6252811yescharacteristic
844C2#6253711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
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×#3226C2semidirect
2. C2×#3170C2semidirect
4. #36129C2semidirect
5. #33042C2semidirect
6. #30910C2semidirect
7. #30709C2semidirect
8. #30261C2semidirect
9. #29808C2semidirect
10. #28750C2semidirect
11. #28656C2semidirect
12. #26893C2semidirect
13. #26620C2semidirect
14. #25902C2semidirect
15. #25674C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. #22247C2semidirect
19. #21101C2semidirect
166. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32262
C2×#31702
#361502
#361292
#330422
#309102
#307092
#302612
#298082
#287502
#286562
#268932
#266202
#259022
#256742
#255982
#255972
#222472
#211012