Finite Group Databasebeta

← #6583712

Subgroups — #6583712

Order 512.

2020 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3167C211yesmaximal, characteristic, complemented
2C2×#3160C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic, complemented
4#36150C211yesmaximal, characteristic
5#33239C211yesmaximal, characteristic, complemented
6#33207C211yesmaximal, characteristic, complemented
7#33170C211yesmaximal, characteristic, complemented
8#28656C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#27788C214yesmaximal, complemented
11#26481C214yesmaximal, complemented
12#25905C211yesmaximal, characteristic, complemented
13#25904C211yesmaximal, characteristic, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#24777C214yesmaximal, complemented
17#23023C214yesmaximal, complemented
18C4×#498C211yesmaximal, characteristic, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24#3167—28no—
25#3160—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#499C2214yes—
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#492C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#465C2214yes—
37C2×#465C2214yes—
38C2×C4×SD16C2214yes—
39C2×C8×D4C2212yes—
40C2×#427C2214yes—
41C22×C4×C8C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2862C2211yescharacteristic
44#2858C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2540—21no—
50#2536—21no—
51#2490C2212yes—
52#2489—21no—
53#2489C2212yes—
54#2454C2212yes—
55#2453—21no—
56#2453C2212yes—
57#2448—21no—
58#2427—21no—
59#2426—21no—
60#2426—21no—
61#2421—21no—
62#2421—21no—
63#2415—21no—
64#2415C2212yes—
65#2414C2212yes—
66#2407—21no—
67#2367—21no—
68#2363C2212yes—
69#2362—21no—
70#2362C2212yes—
71#2351—21no—
72#2341—21no—
73C4×C4⋊Q8C2211yescharacteristic
74C4×C4⋊Q8C2211yescharacteristic
75C42×D4C2211yescharacteristic
76#2068C2214yes—
77#2067C2214yes—
78#2036C2214yes—
79#2033C2214yes—
80#2026C2214yes—
81#2025C2214yes—
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1968C2214yes—
87#1968C2214yes—
88#1968C2214yes—
89#1957C2211yescharacteristic
90#1956C2211yescharacteristic
91#1941C2214yes—
92#1941C2214yes—
93#1928C2214yes—
94#1925C2214yes—
95#1875C2214yes—
96#1873C2214yes—
97#1863C2214yes—
98#1862C2214yes—
99#1844C2211yescharacteristic
100#1807C2214yes—
101C4×#106C2214yes—
102C8×C4⋊C4C2212yes—
103C4×C4⋊C8C2211yescharacteristic
104C8×C22⋊C4C2212yes—
105C8×C22⋊C4C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C22×#41—21no—
110C22×SD16C2314yes—
111C23×C8C2312yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#533—42no—
119#532—24no—
120#532—42no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×#127C2311yescharacteristic
127C2×#125—21no—
128C2×#125C2312yes—
129C2×#125C2312yes—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8C2312yes—
155C2×C4×D4—21no—
156C2×C4×D4D411yescharacteristic
157C2×C4×D4D411yescharacteristic
158C2×C4×D4C2312yes—
159C2×C4×D4C2311yescharacteristic
160C2×#117—21no—
161C2×#117C2312yes—
162C2×#117C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#500—24no—
166#500—24no—
167#499—216no—
168#498—24no—
169#498D418yescomplemented
170#492—24no—
171#487—24no—
172#487—42no—
173#486—24no—
174#486—42no—
175#465—216no—
176#465—216no—
177C4×SD16—216no—
178C8×D4—28no—
179#427—216no—
180C2×#107C2314yes—
181C2×#107C2314yes—
182C2×#106C2314yes—
183C2×#106C2314yes—
184C2×#106C2314yes—
185C2×C4⋊C8C2312yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C4×C8—24no—
195C2×C4×C8—24no—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2312yes—
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2311yescharacteristic
204#400—22no—
205#400—22no—
206#399—22no—
207#398—22no—
208#397—22no—
209#397—22no—
210#397—22no—
211#396—22no—
212#394—22no—
213#394—22no—
214#394—22no—
215#392—22no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
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—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#388—22no—
254#387—22no—
255#387—22no—
256#386—22no—
257#385—22no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#382—21no—
261#382—21no—
262#382—22no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—22no—
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⋊C4—22no—
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C43C2311yescharacteristic
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8C2412yes—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4C2×D411yescharacteristic
306C22×D4C2412yes—
307C23×C4—22no—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16—28no—
317C22×C8—24no—
318C22×C8—24no—
319C22×C8—24no—
320C22×C8—24no—
321C22×C8—24no—
322C22×C8#4118yescomplemented
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8C2×D414yes—
336C4⋊Q8C2×D414yes—
337#127—22no—
338#127—22no—
339#125—24no—
340#125—24no—
341#125—42no—
342#125—42no—
343#125—44no—
344#124—44no—
345#124—44no—
346#124—82no—
347C22⋊Q8—28no—
348C22⋊Q8—24no—
349C22⋊Q8—42no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356C22⋊Q8—82no—
357#121—28no—
358#121—24no—
359#121—42no—
360#121—44no—
361#121—82no—
362#121—82no—
363C4×Q8—24no—
364C4×Q8—42no—
365C4×Q8—44no—
366C4×Q8—44no—
367C4×Q8—44no—
368C4×Q8—44no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×Q8—82no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—42no—
377C4×D4—44no—
378#117—24no—
379#117—24no—
380#117—42no—
381#117—42no—
382#117—44no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
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⋊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×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#107—28no—
458#106—28no—
459#106—28no—
460#106C2×D4116yes—
461C4⋊C8—24no—
462#103—28no—
463#103—28no—
464#103—44no—
465#102—28no—
466#102—28no—
467#102—44no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C4×C8—24no—
471C4×C8—24no—
472C4×C8—24no—
473C4×C8—24no—
474C4×C8—22no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8C2×D414yes—
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#95—22no—
491#95—22no—
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498C24—22no—
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501#41—816no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—22no—
505C2×Q8—24no—
506C2×Q8—22no—
507C2×Q8—24no—
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×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—24no—
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—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—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—82no—
565C22×C4#13514yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
579C22×C4C2511yescharacteristic
580SD16—416no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—216no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—48no—
591C2×C8C22×D414yes—
592C2×C8C2×#4114yes—
593C2×C8C2×#4114yes—
594C2×C82−1+414yes—
595C4⋊C4—22no—
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—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—82no—
626C4⋊C4—82no—
627C4⋊C4C22×D414yes—
628C4⋊C4C22×D414yes—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—44no—
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—44no—
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—22no—
660C42—21no—
661C42—21no—
662C42—22no—
663C42—44no—
664C42—44no—
665C42—44no—
666C42—44no—
667C42—82no—
668C42#13514yes—
669C42C22×D412yes—
670C42H(5,𝔽2)12yes—
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—
690C23#53212yes—
691C23C2×#13512yes—
692C23C23×D411yescharacteristic
693Q8—48no—
694Q8—48no—
695Q8—44no—
696Q8—44no—
697Q8—84no—
698Q8—84no—
699D4—28no—
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—21no—
713C2×C4—21no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—24no—
724C2×C4—24no—
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—42no—
738C2×C4—42no—
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—88no—
762C2×C4#53212yes—
763C2×C4D4212yes—
764C2×C4D4212yes—
765C2×C4C2×#13512yes—
766C2×C4C2×#13512yes—
767C2×C4C2×#13512yes—
768C2×C4C2×#13512yes—
769C2×C4C2×#13512yes—
770C2×C4#57712yes—
771C2×C4#57712yes—
772C2×C4C23×D411yescharacteristic
773C2×C4C22×#4112yes—
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4C2×2−1+412yes—
776C8—24no—
777C8—42no—
778C8—42no—
779C8#54818yes—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22C2×#53211yescharacteristic
802C22C2×D4211yescharacteristic
803C22#349911yescharacteristic
804C22C22×#13511yescharacteristic
805C22C22×#13511yescharacteristic
806C22C2×#57711yescharacteristic
807C22C2×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—44no—
817C4—41no—
818C4—41no—
819C4—44no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4#328214yes—
826C4#328414yes—
827C4C2×#54812yes—
828C4#351112yes—
829C2—42no—
830C2—42no—
831C2—162no—
832C2#3612211yescharacteristic
833C2#6067311yescharacteristic
834C2#6071211yescharacteristic
835C2C2×#328211yescharacteristic
836C2C2×#328411yescharacteristic
837C2#6247011yescharacteristic
838C2#6247011yescharacteristic
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×#3167C2semidirect
2. C2×#3160C2semidirect
3. #36151C2semidirect
5. #33239C2semidirect
6. #33207C2semidirect
7. #33170C2semidirect
8. #28656C2semidirect
9. #28655C2semidirect
10. #27788C2semidirect
11. #26481C2semidirect
12. #25905C2semidirect
13. #25904C2semidirect
14. #25674C2semidirect
15. #25673C2semidirect
16. #24777C2semidirect
17. #23023C2semidirect
18. C4×#498C2semidirect
19. C4×C8×D4C2semidirect
169. #498D4semidirect
322. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31672
C2×#31602
#361512
#361502
#332392
#332072
#331702
#286562
#286552
#277882
#264812
#259052
#259042
#256742
#256732
#247772
#230232
C4×#4982
C4×C8×D42