Finite Group Databasebeta

← #6686425

Subgroups — #6686425

Order 512.

1973 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3227C211yesmaximal, characteristic, complemented
2C2×#3182C211yesmaximal, characteristic, complemented
3#36149C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33210C211yesmaximal, characteristic, complemented
6#30685C214yesmaximal, complemented
7#30583C214yesmaximal, complemented
8#30281C211yesmaximal, characteristic, complemented
9#29844C211yesmaximal, characteristic, complemented
10#28688C211yesmaximal, characteristic, complemented
11#28613C211yesmaximal, characteristic, complemented
12#26567C214yesmaximal, complemented
13#26396C214yesmaximal, complemented
14#25813C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18#22220C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3227—28no—
25#3182—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#492C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#481C2214yes—
36C2×#476C2214yes—
37C2×#468C2214yes—
38C2×#440C2214yes—
39C2×#431C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550—21no—
48#2535C2212yes—
49#2492C2212yes—
50#2451C2212yes—
51#2447—21no—
52#2447—21no—
53#2446—21no—
54#2442—21no—
55#2439—21no—
56#2429—21no—
57#2427—21no—
58#2427—21no—
59#2420C2212yes—
60#2420C2212yes—
61#2417C2212yes—
62#2409—21no—
63#2407—21no—
64#2407—21no—
65#2360C2212yes—
66#2352—21no—
67#2349C2212yes—
68Q8×C22⋊C4—21no—
69#2339—21no—
70#2339—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2097C2214yes—
75#2097C2214yes—
76#2085C2214yes—
77#2068C2214yes—
78#2057C2214yes—
79#2055C2214yes—
80#2036C2214yes—
81#2035C2214yes—
82#2033C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1949C2214yes—
91#1943C2214yes—
92#1925C2214yes—
93#1924C2212yes—
94#1917C2212yes—
95#1877C2214yes—
96#1877C2214yes—
97#1870C2212yes—
98#1865C2214yes—
99#1862C2214yes—
100#1862C2214yes—
101#1852C2214yes—
102#1851C2212yes—
103#1845C2211yescharacteristic
104#1809C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C22×#41—21no—
111C23×Q8—21no—
112C22×SD16C2314yes—
113C22×M16C2312yes—
114#533—24no—
115#533—42no—
116#532—24no—
117#532—24no—
118#532—42no—
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⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×#127C2311yescharacteristic
131C2×#125—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⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8C2312yes—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4D411yescharacteristic
152C2×C4×D4D411yescharacteristic
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#500—24no—
163#500—42no—
164#498—24no—
165#498—24no—
166#492—24no—
167#487—24no—
168#487—42no—
169#486—24no—
170#486D418yescomplemented
171#481—216no—
172#476—216no—
173#468—216no—
174#440—216no—
175#431—24no—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—24no—
193C2×#97C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#398—22no—
200#398—22no—
201#397—22no—
202#397—22no—
203#397—22no—
204#396—22no—
205#395—22no—
206#394—22no—
207#394—22no—
208#393—22no—
209#392—22no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
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—21no—
226#390—21no—
227#390C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—22no—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#387—22no—
241#387—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#382—21no—
253#382—21no—
254#382C2312yes—
255#382C2312yes—
256#381—22no—
257#381—22no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—22no—
264#380—22no—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4D411yescharacteristic
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
280C2×#95—22no—
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—44no—
294C2×#41—44no—
295C2×#41—82no—
296C2×#41—82no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—22no—
302C22×Q8—44no—
303C22×Q8—44no—
304C22×Q8—82no—
305C22×Q8C2412yes—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C2×D411yescharacteristic
311C22×D4C2412yes—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C2×SD16—28no—
323C2×SD16—28no—
324C2×SD16—44no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—42no—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C4⋊Q8—24no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—42no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8C2×D414yes—
346#127—22no—
347#127C2×D414yes—
348#125—44no—
349#124—44no—
350#124—44no—
351C22⋊Q8—24no—
352C22⋊Q8—44no—
353C22⋊Q8—42no—
354C22⋊Q8—44no—
355C22⋊Q8—82no—
356C22⋊Q8—82no—
357C22⋊Q8—82no—
358#121—24no—
359#121—24no—
360#121—42no—
361#121—42no—
362#121—44no—
363#121—44no—
364C4×Q8—24no—
365C4×Q8—42no—
366C4×Q8—44no—
367C4×Q8—82no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—44no—
372C4×D4—42no—
373C4×D4—42no—
374C4×D4—42no—
375C4×D4—42no—
376C4×D4—44no—
377C4×D4—44no—
378C4×D4—82no—
379C4×D4—82no—
380#117—44no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
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—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
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⋊C4—22no—
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—28no—
450#107—44no—
451#107—44no—
452#106—28no—
453#106—28no—
454C4⋊C8—24no—
455C4⋊C8—24no—
456#103—28no—
457#103—44no—
458#103—44no—
459#102—28no—
460#102—44no—
461#102C2×D4116yes—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—42no—
465#97—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8C2×D414yes—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
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—
498#41—816no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—44no—
505C2×Q8—44no—
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—82no—
518C2×Q8—816no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—22no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—82no—
536C2×D4—82no—
537C2×D4C22×D414yes—
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—22no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4#13714yes—
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×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C2511yescharacteristic
590SD16—416no—
591M16—48no—
592C2×C8—22no—
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×C8C22×D414yes—
603C2×C82−1+414yes—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—41no—
616C4⋊C4—41no—
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—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—82no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4C22×D414yes—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—41no—
641C22⋊C4—41no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
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—82no—
670C42C22×D412yes—
671C42H(5,𝔽2)12yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—24no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C2×#13712yes—
693C23C23×D411yescharacteristic
694Q8—48no—
695Q8—44no—
696Q8—44no—
697Q8—88no—
698Q8—84no—
699Q8—84no—
700Q8—84no—
701D4—28no—
702D4—44no—
703D4—48no—
704D4—48no—
705D4—44no—
706D4—88no—
707D4—88no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—28no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
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—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—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
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—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—88no—
767C2×C4—88no—
768C2×C4—88no—
769C2×C4—164no—
770C2×C4D4212yes—
771C2×C4D4212yes—
772C2×C4C2×#13712yes—
773C2×C4C2×#13712yes—
774C2×C4#57512yes—
775C2×C4#57612yes—
776C2×C4#57712yes—
777C2×C4C23×D411yescharacteristic
778C2×C4C2×H(5,𝔽2)11yescharacteristic
779C2×C4C2×2−1+412yes—
780C2×C4#58512yes—
781C8—24no—
782C8—24no—
783C8—42no—
784C8—42no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—44no—
797C22—41no—
798C22—41no—
799C22—44no—
800C22—41no—
801C22—44no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22#344911yescharacteristic
807C22C2×D4211yescharacteristic
808C22#349911yescharacteristic
809C22C22×#13711yescharacteristic
810C22C2×#57511yescharacteristic
811C22C2×#57611yescharacteristic
812C22C2×#57711yescharacteristic
813C4—22no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—44no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4#326614yes—
831C4#327314yes—
832C4#348912yes—
833C4#355412yes—
834C2—42no—
835C2—81no—
836C2—84no—
837C2#3768011yescharacteristic
838C2#6096611yescharacteristic
839C2#6100611yescharacteristic
840C2C2×#326611yescharacteristic
841C2C2×#327311yescharacteristic
842C2#6248011yescharacteristic
843C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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×#3182C2semidirect
4. #36129C2semidirect
5. #33210C2semidirect
6. #30685C2semidirect
7. #30583C2semidirect
8. #30281C2semidirect
9. #29844C2semidirect
10. #28688C2semidirect
11. #28613C2semidirect
12. #26567C2semidirect
13. #26396C2semidirect
14. #25813C2semidirect
15. #25673C2semidirect
16. #25672C2semidirect
17. #25597C2semidirect
18. #22220C2semidirect
19. #21102C2semidirect
170. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32272
C2×#31822
#361492
#361292
#332102
#306852
#305832
#302812
#298442
#286882
#286132
#265672
#263962
#258132
#256732
#256722
#255972
#222202
#211022