Finite Group Databasebeta

← #6579395

Subgroups — #6579395

Order 512.

2104 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3139C211yesmaximal, characteristic, complemented
2C2×#3131C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33238C211yesmaximal, characteristic, complemented
6#33048C211yesmaximal, characteristic, complemented
7#33043C211yesmaximal, characteristic, complemented
8#28750C211yesmaximal, characteristic, complemented
9#28717C211yesmaximal, characteristic, complemented
10#27781C214yesmaximal, complemented
11#27275C214yesmaximal, complemented
12#27267C214yesmaximal, complemented
13#25905C211yesmaximal, characteristic, complemented
14#25904C211yesmaximal, characteristic, complemented
15#25857C211yesmaximal, characteristic, complemented
16#25856C211yesmaximal, characteristic, complemented
17#22426C214yesmaximal, complemented
18#21647C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#548C2212yes—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3139—28no—
26C2×#491C2214yes—
27#3131—28no—
28C2×#488C2214yes—
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#435C2212yes—
39C2×#419C2214yes—
40C2×#416C2214yes—
41C2×C4×M16C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2868C2211yescharacteristic
44#2858C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2552C2212yes—
50#2545C2212yes—
51#2542—21no—
52#2538—21no—
53#2491—21no—
54#2491—21no—
55#2452—21no—
56#2452—21no—
57#2441C2212yes—
58#2441C2212yes—
59#2436C2212yes—
60#2432C2212yes—
61#2429—21no—
62#2429—21no—
63#2423—21no—
64#2423—21no—
65#2416—21no—
66#2416—21no—
67#2365—21no—
68#2361—21no—
69#2361—21no—
70#2354C2212yes—
71Q8×C4⋊C4—21no—
72C4×C4⋊Q8C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C42×D4C2211yescharacteristic
75#2072C2214yes—
76#2043C2214yes—
77#2042C2214yes—
78#2042C2214yes—
79#2026C2214yes—
80#2025C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1983C2214yes—
85#1959C2214yes—
86#1959C2214yes—
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1936C2214yes—
91#1935C2214yes—
92#1933C2214yes—
93#1895C2214yes—
94#1892C2214yes—
95#1875C2214yes—
96#1873C2214yes—
97#1834C2211yescharacteristic
98#1803C2214yes—
99#1788C2214yes—
100#1787C2214yes—
101#1771C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41C2312yes—
110C23×Q8C2312yes—
111C22×M16C2312yes—
112C23×C8C2312yes—
113#548—216no—
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—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×#127C2311yescharacteristic
133C2×#125C2312yes—
134C2×#125C2312yes—
135C2×#124—22no—
136C2×#124C2312yes—
137C2×#124C2312yes—
138C2×#124C2312yes—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8C2312yes—
147C2×#121—22no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121—21no—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2312yes—
159C2×C4×D4—22no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4D411yescharacteristic
163C2×C4×D4D411yescharacteristic
164C2×C4×D4C2311yescharacteristic
165C2×#117C2312yes—
166C2×#117C2312yes—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#491—216no—
172#488—216no—
173#487—24no—
174#487—24no—
175#487—24no—
176#487—24no—
177#487—42no—
178#487D418yescomplemented
179#486—24no—
180#486—24no—
181#486—42no—
182#435—28no—
183C2×C4⋊C8C2312yes—
184#419—216no—
185#416—216no—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C4×M16—24no—
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×#97C2312yes—
204C2×C4×C8—24no—
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2312yes—
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210#399—22no—
211#399—22no—
212#398—22no—
213#398—22no—
214#396—22no—
215#396—22no—
216#396—22no—
217#396—22no—
218#394—22no—
219#394—22no—
220#393—22no—
221#393—22no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391C2312yes—
226#391C2312yes—
227#390—22no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390—21no—
233#390—21no—
234#390C2312yes—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—22no—
244#389—22no—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#387—22no—
253#387—22no—
254#386—22no—
255#386—22no—
256#385—22no—
257#385—22no—
258#384—22no—
259#384—21no—
260#384—21no—
261#384C2311yescharacteristic
262#384C2311yescharacteristic
263#384C2312yes—
264#384C2312yes—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380C2312yes—
270#380C2312yes—
271C4×C4⋊C4—22no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4D411yescharacteristic
276C4×C4⋊C4D411yescharacteristic
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
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—24no—
294C2×#41—28no—
295C2×#41—42no—
296C2×#41—44no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—24no—
302C22×Q8—28no—
303C22×Q8—42no—
304C22×Q8—44no—
305C22×Q8C2412yes—
306C22×Q8C2412yes—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—21no—
310C22×D4—21no—
311C22×D4C2×D411yescharacteristic
312C22×D4C2412yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—42no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—42no—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—44no—
341C4⋊Q8—44no—
342C4⋊Q8—42no—
343C4⋊Q8—44no—
344C4⋊Q8—82no—
345C4⋊Q8C2×D414yes—
346C4⋊Q8C2×D414yes—
347#127—22no—
348#127—22no—
349#125—24no—
350#125—24no—
351#125—42no—
352#125—42no—
353#124—24no—
354#124—28no—
355#124—42no—
356#124—44no—
357#124—48no—
358C22⋊Q8—28no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363C22⋊Q8—48no—
364C22⋊Q8—82no—
365C22⋊Q8—82no—
366#121—28no—
367#121—44no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—48no—
372C4×Q8—28no—
373C4×Q8—44no—
374C4×Q8—44no—
375C4×Q8—44no—
376C4×Q8—44no—
377C4×Q8—44no—
378C4×D4—44no—
379C4×D4—44no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—48no—
383C4×D4#4118yes—
384#117—24no—
385#117—24no—
386#117—42no—
387#117—42no—
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—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C4⋊C8—24no—
466#103—28no—
467#103—28no—
468#103—28no—
469#103—28no—
470#103—44no—
471#103—44no—
472#103—44no—
473#103C2×D4116yes—
474#102—28no—
475#102—28no—
476#102—44no—
477#102—44no—
478C22⋊C8—24no—
479C22⋊C8—24no—
480#97—24no—
481#97—24no—
482#97—42no—
483C4×C8—24no—
484C4×C8—22no—
485C4×C8—22no—
486C4×C8—22no—
487C4×C8C2×D414yes—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502#95C2×D411yescharacteristic
503#95C2×D411yescharacteristic
504C24—22no—
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507#41—416no—
508#41—88no—
509C2×Q8—24no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—22no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—44no—
518C2×Q8—416no—
519C2×Q8—44no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—82no—
529C2×Q8—88no—
530C2×Q8C22×D414yes—
531C2×D4—22no—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—82no—
549C2×D4#12414yes—
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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—82no—
580C22×C4—82no—
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×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2511yescharacteristic
596M16—48no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—48no—
609C2×C8C22×D414yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—24no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C4⋊C4#12414yes—
646C4⋊C4C22×D414yes—
647C22⋊C4—41no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4#12414yes—
666C22⋊C4#12414yes—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—22no—
680C42—44no—
681C42—44no—
682C42—44no—
683C42—44no—
684C42C22×D412yes—
685C42C2×#4114yes—
686C42H(5,𝔽2)12yes—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23C2×#12412yes—
707C23C2×#12412yes—
708C23C23×D411yescharacteristic
709Q8—28no—
710Q8—44no—
711Q8—48no—
712Q8—44no—
713Q8—44no—
714Q8—88no—
715Q8—84no—
716Q8—84no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—88no—
721D4—88no—
722D4—84no—
723D4—84no—
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—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—88no—
780C2×C4—88no—
781C2×C4C2×#12412yes—
782C2×C4C2×#12412yes—
783C2×C4C2×#12412yes—
784C2×C4C2×#12412yes—
785C2×C4D4212yes—
786C2×C4D4212yes—
787C2×C4#57512yes—
788C2×C4#57512yes—
789C2×C4#57712yes—
790C2×C4#57812yes—
791C2×C4C23×D411yescharacteristic
792C2×C4C22×#4112yes—
793C2×C4C2×H(5,𝔽2)11yescharacteristic
794C2×C4#58512yes—
795C8—24no—
796C8—42no—
797C8—42no—
798C8—42no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22C22×#12411yescharacteristic
821C22C2×D4211yescharacteristic
822C22#350011yescharacteristic
823C22C2×#57511yescharacteristic
824C22C2×#57511yescharacteristic
825C22C2×#57711yescharacteristic
826C22C2×#57811yescharacteristic
827C4—22no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—44no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—44no—
837C4—41no—
838C4—41no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4#326914yes—
845C4#327114yes—
846C4D4×#4112yes—
847C4#351412yes—
848C2—42no—
849C2—42no—
850C2—162no—
851C2D4×#12411yescharacteristic
852C2#6061811yescharacteristic
853C2#6062311yescharacteristic
854C2C2×#326911yescharacteristic
855C2C2×#327111yescharacteristic
856C2#6254311yescharacteristic
857C2#6254511yescharacteristic
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×#3139C2semidirect
2. C2×#3131C2semidirect
3. #36134C2semidirect
5. #33238C2semidirect
6. #33048C2semidirect
7. #33043C2semidirect
8. #28750C2semidirect
9. #28717C2semidirect
10. #27781C2semidirect
11. #27275C2semidirect
12. #27267C2semidirect
13. #25905C2semidirect
14. #25904C2semidirect
15. #25857C2semidirect
16. #25856C2semidirect
17. #22426C2semidirect
18. #21647C2semidirect
19. C4×#435C2semidirect
178. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31392
C2×#31312
#361342
#361222
#332382
#330482
#330432
#287502
#287172
#277812
#272752
#272672
#259052
#259042
#258572
#258562
#224262
#216472
C4×#4352