Finite Group Databasebeta

← #6815279

Subgroups — #6815279

Order 512.

1923 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3226C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33239C211yesmaximal, characteristic, complemented
6#31235C214yesmaximal, complemented
7#31194C214yesmaximal, complemented
8#29844C211yesmaximal, characteristic, complemented
9#29842C211yesmaximal, characteristic, complemented
10#28656C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26799C214yesmaximal, complemented
13#26791C214yesmaximal, 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×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3231—28no—
25#3226—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#492C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#485C2214yes—
36C2×#480C2214yes—
37C2×#479C2214yes—
38C2×#474C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2550—21no—
48#2540—21no—
49#2492C2212yes—
50#2490C2212yes—
51#2454C2212yes—
52#2451C2212yes—
53#2448—21no—
54#2446—21no—
55#2442—21no—
56#2439—21no—
57#2429—21no—
58#2427—21no—
59#2426—21no—
60#2426—21no—
61#2417C2212yes—
62#2414C2212yes—
63#2409—21no—
64#2407—21no—
65#2367—21no—
66#2363C2212yes—
67#2360C2212yes—
68#2352—21no—
69#2341—21no—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2068C2214yes—
75#2068C2214yes—
76#2067C2214yes—
77#2065C2214yes—
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#1928C2214yes—
96#1926C2214yes—
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#533—24no—
113#533—24no—
114#533—42no—
115#533—42no—
116#532—24no—
117#532—42no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125—21no—
130C2×#125C2312yes—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×#121—21no—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121C2312yes—
145C2×#121C2312yes—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8C2312yes—
152C2×C4×D4—21no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C2×#117C2312yes—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#500—24no—
164#500D418yescomplemented
165#498—24no—
166#498—42no—
167#492—42no—
168#487—24no—
169#487—24no—
170#486—24no—
171#486—24no—
172#485—216no—
173#480—216no—
174#479—216no—
175#474—216no—
176#431—24no—
177#431—24no—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200C2×C4×C8C2312yes—
201C2×C4×C8C2311yescharacteristic
202#400—22no—
203#399—22no—
204#398—22no—
205#398—22no—
206#397—22no—
207#396—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#394—22no—
212#393—22no—
213#392—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—22no—
221#391—22no—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#390—22no—
226#390—22no—
227#390—22no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#387—22no—
251#387—22no—
252#386—22no—
253#386—22no—
254#385—22no—
255#385—22no—
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#382—21no—
259#382—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—22no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4—22no—
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C43C2311yescharacteristic
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
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—21no—
298C22×Q8—22no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—82no—
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×SD16—28no—
318C2×SD16—44no—
319C2×SD16—44no—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C4⋊Q8—24no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—42no—
334C4⋊Q8—44no—
335C4⋊Q8—44no—
336C4⋊Q8C2×D414yes—
337C4⋊Q8C2×D414yes—
338#127—22no—
339#127—22no—
340#125—24no—
341#125—42no—
342#125—44no—
343#124—44no—
344#124—44no—
345#124—82no—
346C22⋊Q8—24no—
347C22⋊Q8—44no—
348C22⋊Q8—42no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—82no—
353C22⋊Q8—82no—
354#121—24no—
355#121—44no—
356#121—42no—
357#121—44no—
358#121—82no—
359#121—82no—
360C4×Q8—24no—
361C4×Q8—42no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×Q8—44no—
365C4×Q8—82no—
366C4×Q8—82no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—42no—
371C4×D4—44no—
372C4×D4—42no—
373#117—24no—
374#117—42no—
375#117—44no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—28no—
451#107—44no—
452#107C2×D4116yes—
453#106—28no—
454#106—44no—
455C4⋊C8—24no—
456C4⋊C8—24no—
457C4⋊C8—42no—
458#103—28no—
459#103—28no—
460#103—44no—
461#102—28no—
462#102—28no—
463#102—44no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C4×C8—24no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—42no—
473C4×C8C2×D414yes—
474#95—22no—
475#95—22no—
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#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494C24—22no—
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497#41—816no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—44no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—44no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—82no—
517C2×Q8—816no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—41no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—82no—
535C2×D4—82no—
536C2×D4—82no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
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—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4#13514yes—
570C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
583SD16—88no—
584C2×C8—22no—
585C2×C8—22no—
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×C8C22×D414yes—
595C2×C82−1+414yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—41no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—82no—
625C4⋊C4—82no—
626C4⋊C4—82no—
627C4⋊C4—82no—
628C4⋊C4C22×D414yes—
629C4⋊C4C22×D414yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—22no—
662C42—22no—
663C42—44no—
664C42—44no—
665C42—82no—
666C42—82no—
667C42#13714yes—
668C42C22×D412yes—
669C42H(5,𝔽2)12yes—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23C2×#13512yes—
691C23C23×D411yescharacteristic
692Q8—48no—
693Q8—48no—
694Q8—44no—
695Q8—44no—
696Q8—88no—
697Q8—84no—
698Q8—84no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—88no—
703D4—84no—
704D4—84no—
705D4—164no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—28no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
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—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
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—88no—
763C2×C4—88no—
764C2×C4D4212yes—
765C2×C4D4212yes—
766C2×C4C2×#13512yes—
767C2×C4C2×#13512yes—
768C2×C4C2×#13712yes—
769C2×C4C2×#13712yes—
770C2×C4C2×#13712yes—
771C2×C4#57612yes—
772C2×C4#57712yes—
773C2×C4C23×D411yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4C2×2−1+412yes—
776C2×C4#58512yes—
777C8—24no—
778C8—24no—
779C8—42no—
780C8—42no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22#344911yescharacteristic
803C22C2×D4211yescharacteristic
804C22#349911yescharacteristic
805C22C22×#13511yescharacteristic
806C22C22×#13711yescharacteristic
807C22C2×#57611yescharacteristic
808C22C2×#57711yescharacteristic
809C4—22no—
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—44no—
818C4—44no—
819C4—41no—
820C4—41no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4#327814yes—
827C4#328014yes—
828C4#349712yes—
829C4#356112yes—
830C2—42no—
831C2—81no—
832C2—162no—
833C2#3935611yescharacteristic
834C2#6094711yescharacteristic
835C2#6100611yescharacteristic
836C2C2×#327811yescharacteristic
837C2C2×#328011yescharacteristic
838C2#6247011yescharacteristic
839C2#6248011yescharacteristic
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×#3231C2semidirect
2. C2×#3226C2semidirect
4. #36129C2semidirect
5. #33239C2semidirect
6. #31235C2semidirect
7. #31194C2semidirect
8. #29844C2semidirect
9. #29842C2semidirect
10. #28656C2semidirect
11. #28654C2semidirect
12. #26799C2semidirect
13. #26791C2semidirect
14. #25812C2semidirect
15. #25811C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. C4×#500C2semidirect
19. #21264C2semidirect
164. #500D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32262
#361502
#361292
#332392
#312352
#311942
#298442
#298422
#286562
#286542
#267992
#267912
#258122
#258112
#255982
#255972
C4×#5002
#212642