Finite Group Databasebeta

← #7024418

Subgroups — #7024418

Order 512.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59771C211yesmaximal, characteristic, complemented
2#59148C211yesmaximal, characteristic, complemented
3#32639C211yesmaximal, characteristic, complemented
4#32622C211yesmaximal, characteristic, complemented
5#32101C211yesmaximal, characteristic, complemented
6#32092C211yesmaximal, characteristic, complemented
7#31969C211yesmaximal, characteristic, complemented
8#31155C211yesmaximal, characteristic, complemented
9#30899C211yesmaximal, characteristic, complemented
10#30879C211yesmaximal, characteristic, complemented
11#29245C211yesmaximal, characteristic, complemented
12#27281C211yesmaximal, characteristic, complemented
13#27277C211yesmaximal, characteristic, complemented
14#26901C211yesmaximal, characteristic, complemented
15#26762C211yesmaximal, characteristic, complemented
16#26710C211yesmaximal, characteristic, complemented
17#26176C211yesmaximal, characteristic, complemented
18#25979C211yesmaximal, characteristic, complemented
19#25974C211yesmaximal, characteristic, complemented
20#25661C211yesmaximal, characteristic, complemented
21#25273C211yesmaximal, characteristic, complemented
22#25101C211yesmaximal, characteristic
23#25099C211yesmaximal, characteristic, complemented
24#24737C211yesmaximal, characteristic, complemented
25#24215C211yesmaximal, characteristic
26#24197C211yesmaximal, characteristic, complemented
27#23506C211yesmaximal, characteristic, complemented
28#22885C211yesmaximal, characteristic, complemented
29#22868C211yesmaximal, characteristic
30#22297C211yesmaximal, characteristic, complemented
31#22191C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#487C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#461C2211yescharacteristic, complemented
43C2×#448C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic, complemented
47C2×#419C2211yescharacteristic
48C2×#419C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×#418C2211yescharacteristic
51#2804—21no—
52#2780—21no—
53#2715—21no—
54#2700—21no—
55#2592C2211yescharacteristic
56#2589—21no—
57#2587—21no—
58#2580C2211yescharacteristic, complemented
59#2547C2211yescharacteristic
60#2546C2211yescharacteristic, complemented
61#2545C2211yescharacteristic
62#2545C2211yescharacteristic
63#2521—21no—
64#2509C2211yescharacteristic, complemented
65#2509C2211yescharacteristic, complemented
66#2492—21no—
67#2480—21no—
68#2480—21no—
69#2474—21no—
70#2452—21no—
71#2452C2211yescharacteristic, complemented
72#2452C2211yescharacteristic, complemented
73#2450—21no—
74#2448C2211yescharacteristic
75#2447C2211yescharacteristic
76#2439C2211yescharacteristic
77#2439C2211yescharacteristic
78#2437—21no—
79#2435C2211yescharacteristic
80#2434C2211yescharacteristic
81#2369C2211yescharacteristic, complemented
82#2368—21no—
83#2367C2211yescharacteristic
84#2363C2211yescharacteristic
85#2363C2211yescharacteristic
86#2349C2211yescharacteristic, complemented
87#2342—21no—
88Q8×C22⋊C4C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90C4×C22⋊Q8C2211yescharacteristic
91C4×C22⋊Q8C2211yescharacteristic
92C4×#121C2211yescharacteristic
93#2296C2211yescharacteristic
94#2097C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2055C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2024C2211yescharacteristic, complemented
127#2024C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2013C2211yescharacteristic, complemented
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#1985C2211yescharacteristic, complemented
135#1985C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic
139#1981C2211yescharacteristic, complemented
140#1973C2211yescharacteristic, complemented
141#1970C2211yescharacteristic
142#1960C2211yescharacteristic, complemented
143#1958C2211yescharacteristic
144#1939C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1895C2211yescharacteristic
167#1894C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1877C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1809C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1797C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1763C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#556—42no—
213#556—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—42no—
224C2×#124—42no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8D411yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#489—42no—
255#487—42no—
256#477—42no—
257#476—42no—
258#468—24no—
259#463—42no—
260#463—42no—
261#463—42no—
262#461—42no—
263#448—24no—
264#447—24no—
265#442—42no—
266C4×SD16—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#419—42no—
281#419—42no—
282#418—42no—
283#418—42no—
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391D411yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389—21no—
383#389—21no—
384#389—21no—
385#389D411yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387D411yescharacteristic
417#387D411yescharacteristic
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385D411yescharacteristic
437#385D411yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380D411yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C2×#95—21no—
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8C2×D411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—82no—
571#126—44no—
572#126—44no—
573#124—22no—
574#124—22no—
575#124—22no—
576#124—22no—
577#124—22no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—44no—
586#124—44no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—42no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—82no—
593#121—22no—
594#121#4114yes—
595C4×Q8—22no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—82no—
614#117—22no—
615#117—44no—
616#117—41no—
617#117—41no—
618#117—41no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—41no—
725#107—41no—
726#107—41no—
727#106—22no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776#97—41no—
777#97—41no—
778C4×C8—41no—
779C4×C8—41no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—41no—
851C2×Q8—41no—
852C2×Q8—41no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—44no—
857C2×Q8—44no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—82no—
865C2×Q8—82no—
866C2×Q8H(5,𝔽2)12yes—
867C2×D4—24no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4C2×#4112yes—
894C2×D4H(5,𝔽2)12yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C2×#4112yes—
950C22×C42−1+412yes—
951C22×C4C2511yescharacteristic
952SD16—44no—
953SD16—82no—
954SD16—82no—
955D8—44no—
956D8—82no—
957M16—82no—
958M16—82no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4C2×#4112yes—
1033C4⋊C4H(5,𝔽2)12yes—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—22no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—41no—
1088C42—41no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—22no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23#54812yes—
1133C23C23×D411yescharacteristic
1134Q8—22no—
1135Q8—22no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—84no—
1147Q8—82no—
1148Q8—162no—
1149Q8—162no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—22no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—84no—
1163D4—84no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—82no—
1245C2×C4—82no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4#54812yes—
1253C2×C4#57512yes—
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×2−1+411yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22C2×#54811yescharacteristic
1298C22#348411yescharacteristic
1299C22#348811yescharacteristic
1300C22C2×#57511yescharacteristic
1301C22#358411yescharacteristic
1302C22#358511yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4#351311yescharacteristic
1331C4#351911yescharacteristic
1332C4#353511yescharacteristic
1333C4#353611yescharacteristic
1334C2—42no—
1335C2—82no—
1336C2—82no—
1337C2—161no—
1338C2#4310311yescharacteristic
1339C2#6132311yescharacteristic
1340C2#6134311yescharacteristic
1341C2#6159011yescharacteristic
1342C2#6162711yescharacteristic
1343C2#6199211yescharacteristic
1344C2#6208711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59771C2semidirect
2. #59148C2semidirect
3. #32639C2semidirect
4. #32622C2semidirect
5. #32101C2semidirect
6. #32092C2semidirect
7. #31969C2semidirect
8. #31155C2semidirect
9. #30899C2semidirect
10. #30879C2semidirect
11. #29245C2semidirect
12. #27281C2semidirect
13. #27277C2semidirect
14. #26901C2semidirect
15. #26762C2semidirect
16. #26710C2semidirect
17. #26176C2semidirect
18. #25979C2semidirect
19. #25974C2semidirect
20. #25661C2semidirect
21. #25273C2semidirect
23. #25099C2semidirect
24. #24737C2semidirect
26. #24197C2semidirect
27. #23506C2semidirect
28. #22885C2semidirect
30. #22297C2semidirect
31. #22191C2semidirect
35. C2×#487C22semidirect
36. C2×#477C22semidirect
42. C2×#461C22semidirect
46. C2×C4×SD16C22semidirect
58. #2580C22semidirect
60. #2546C22semidirect
64. #2509C22semidirect
65. #2509C22semidirect
71. #2452C22semidirect
72. #2452C22semidirect
81. #2369C22semidirect
86. #2349C22semidirect
94. #2097C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2074C22semidirect
100. #2068C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
108. #2055C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
126. #2024C22semidirect
127. #2024C22semidirect
130. #2013C22semidirect
134. #1985C22semidirect
135. #1985C22semidirect
139. #1981C22semidirect
140. #1973C22semidirect
142. #1960C22semidirect
144. #1939C22semidirect
145. #1939C22semidirect
148. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
156. #1926C22semidirect
158. #1921C22semidirect
159. #1920C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
173. #1877C22semidirect
174. #1877C22semidirect
175. #1877C22semidirect
178. #1865C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
187. #1862C22semidirect
193. #1805C22semidirect
198. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#597712
#591482
#326392
#326222
#321012
#320922
#319692
#311552
#308992
#308792
#292452
#272812
#272772
#269012
#267622
#267102
#261762
#259792
#259742
#256612
#252732
#251012
#250992
#247372
#242152
#241972
#235062
#228852
#228682
#222972
#221912