Finite Group Databasebeta

← #6472782

Subgroups — #6472782

Order 512.

3107 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36614C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic, complemented
3#32985C211yesmaximal, characteristic, complemented
4#32984C211yesmaximal, characteristic, complemented
5#32981C211yesmaximal, characteristic, complemented
6#32980C211yesmaximal, characteristic, complemented
7#29897C212yesmaximal, complemented
8#29896C212yesmaximal, complemented
9#27605C212yesmaximal, complemented
10#27604C211yesmaximal, characteristic, complemented
11#27602C211yesmaximal, characteristic, complemented
12#24555C212yesmaximal, complemented
13#24554C212yesmaximal, complemented
14#24553C211yesmaximal, characteristic, complemented
15#24552C211yesmaximal, characteristic, complemented
16#24551C211yesmaximal, characteristic, complemented
17#24550C211yesmaximal, characteristic, complemented
18#24008C212yesmaximal, complemented
19#24007C211yesmaximal, characteristic, complemented
20#24004C211yesmaximal, characteristic, complemented
21#21939C212yesmaximal, complemented
22#21760C212yesmaximal, complemented
23C2×#1779C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C2×#525C2211yescharacteristic
27C2×#525C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C2×#484C2211yescharacteristic, complemented
31C2×#481C2211yescharacteristic, complemented
32C2×#485C2212yescomplemented
33C2×#482C2212yescomplemented
34C2×#483C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic, complemented
36C22×C22⋊C8C2212yes—
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2212yes—
40#2849—21no—
41#2849—21no—
42#2849—21no—
43#2848C2211yescharacteristic
44#2848C2211yescharacteristic
45#2848C2211yescharacteristic
46#2848C2211yescharacteristic
47#2847C2211yescharacteristic
48#2847C2211yescharacteristic
49#2847C2211yescharacteristic
50#2847C2211yescharacteristic
51#2846—21no—
52C4×#120—21no—
53C4×#120—21no—
54C4×#120—21no—
55C4×#120—21no—
56#2280—21no—
57#2280—21no—
58#2280—21no—
59#2280—21no—
60#2280C2212yes—
61#2280C2211yescharacteristic
62#2280C2211yescharacteristic
63#2280C2211yescharacteristic
64#2280C2212yes—
65#2280C2212yes—
66#2280C2212yes—
67C2×#381—21no—
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#379—21no—
73C2×C4×C22⋊C4—21no—
74C2×C4×C22⋊C4—21no—
75#2077C2212yescomplemented
76#2077C2212yescomplemented
77#2077C2212yescomplemented
78#2077C2212yescomplemented
79#2076C2212yescomplemented
80#2076C2212yescomplemented
81#2075C2212yescomplemented
82#2075C2212yescomplemented
83#2036C2212yescomplemented
84#2036C2212yescomplemented
85#2035C2212yescomplemented
86#2035C2212yescomplemented
87#2034C2212yescomplemented
88#2034C2212yescomplemented
89#2033C2212yescomplemented
90#2033C2212yescomplemented
91#1893C2212yescomplemented
92#1893C2212yescomplemented
93#1892C2212yescomplemented
94#1892C2212yescomplemented
95#1875C2212yescomplemented
96#1875C2212yescomplemented
97#1875C2212yescomplemented
98#1874C2211yescharacteristic, complemented
99#1874C2211yescharacteristic, complemented
100#1873C2212yescomplemented
101#1873C2212yescomplemented
102#1873C2212yescomplemented
103#1872C2211yescharacteristic, complemented
104#1872C2211yescharacteristic, complemented
105#1854C2212yescomplemented
106#1854C2212yescomplemented
107#1854C2212yescomplemented
108#1854C2212yescomplemented
109#1854C2212yescomplemented
110#1854C2212yescomplemented
111#1854C2212yescomplemented
112#1854C2212yescomplemented
113#1854C2212yescomplemented
114#1854C2212yescomplemented
115#1853C2211yescharacteristic, complemented
116#1853C2211yescharacteristic, complemented
117#1852C2211yescharacteristic, complemented
118#1852C2211yescharacteristic, complemented
119#1825C2212yescomplemented
120#1825C2212yescomplemented
121#1825C2212yescomplemented
122#1825C2212yescomplemented
123#1824C2211yescharacteristic, complemented
124#1824C2211yescharacteristic, complemented
125#1823C2211yescharacteristic, complemented
126#1823C2211yescharacteristic, complemented
127#1808C2212yescomplemented
128#1808C2212yescomplemented
129#1807C2212yescomplemented
130#1807C2212yescomplemented
131#1788C2212yescomplemented
132#1788C2212yescomplemented
133#1779C2211yescharacteristic
134#1779C2211yescharacteristic
135#1779C2212yes—
136#1779C2212yes—
137#1779C2211yescharacteristic
138#1779C2211yescharacteristic
139C26D411yescharacteristic
140C22×#41C2311yescharacteristic
141C24×C4—28no—
142C24×C4—42no—
143C24×C4—42no—
144C24×C4—44no—
145C24×C4D411yescharacteristic
146C24×C4D411yescharacteristic
147C24×C4D411yescharacteristic
148C24×C4D411yescharacteristic
149C24×C4D411yescharacteristic
150C24×C4D411yescharacteristic
151C24×C4D411yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159C23×C8C2312yes—
160C23×C8C2312yes—
161#525—28no—
162#525—42no—
163#525—42no—
164#525—44no—
165C2×#123—21no—
166C2×#123—21no—
167C2×#123—21no—
168C2×C22⋊Q8C2311yescharacteristic
169C2×C22⋊Q8C2311yescharacteristic
170C2×C22⋊Q8C2311yescharacteristic
171C2×C22⋊Q8C2311yescharacteristic
172C2×C22⋊Q8C2311yescharacteristic
173C2×C22⋊Q8C2311yescharacteristic
174C2×#121C2311yescharacteristic
175C2×#121C2311yescharacteristic
176C2×#121C2311yescharacteristic
177C2×#121C2311yescharacteristic
178C2×#121C2311yescharacteristic
179C2×#121C2311yescharacteristic
180C2×#120—21no—
181C2×#120—21no—
182C2×#120—21no—
183C2×#120—21no—
184C2×#120—21no—
185C2×#120—21no—
186C2×#120—21no—
187C2×C4×D4—21no—
188C2×C4×D4—21no—
189C2×C4×D4—21no—
190C2×C4×D4—21no—
191C2×C4×D4—21no—
192C2×C4×D4—21no—
193C2×#117—21no—
194C2×#117—21no—
195C2×#117—21no—
196C2×#117—21no—
197C2×#117—42no—
198C2×#117—42no—
199C2×#117—44no—
200C2×#117C2312yes—
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C22×C22⋊C4—21no—
214C22×C22⋊C4—21no—
215C22×C22⋊C4—21no—
216C22×C22⋊C4—21no—
217C22×C42—21no—
218C22×C42—21no—
219#485—44no—
220#484—42no—
221#483—42no—
222#482—44no—
223#481—42no—
224#480—42no—
225C2×#107C2312yescomplemented
226C2×#107C2312yescomplemented
227C2×#107C2312yescomplemented
228C2×#107C2312yescomplemented
229C2×#106C2312yescomplemented
230C2×#106C2312yescomplemented
231C2×#106C2312yescomplemented
232C2×#106C2312yescomplemented
233C2×#103C2312yescomplemented
234C2×#103C2312yescomplemented
235C2×#103C2312yescomplemented
236C2×#103C2312yescomplemented
237C2×#102C2312yescomplemented
238C2×#102C2312yescomplemented
239C2×#102C2312yescomplemented
240C2×#102C2312yescomplemented
241C2×C22⋊C8—28no—
242C2×C22⋊C8—42no—
243C2×C22⋊C8—42no—
244C2×C22⋊C8—44no—
245C2×C22⋊C8C2311yescharacteristic
246C2×C22⋊C8C2311yescharacteristic
247C2×C22⋊C8C2312yes—
248C2×C22⋊C8C2312yes—
249C2×C22⋊C8C2311yescharacteristic
250C2×C22⋊C8C2311yescharacteristic
251C2×C22⋊C8C2312yes—
252C2×C22⋊C8C2312yes—
253C2×C22⋊C8C2312yes—
254C2×C22⋊C8C2312yes—
255C2×C22⋊C8C2312yes—
256C2×C22⋊C8C2312yes—
257C2×C22⋊C8C2312yes—
258C2×C22⋊C8C2312yes—
259#386—21no—
260#386—21no—
261#386—21no—
262#386—21no—
263#386—21no—
264#386—21no—
265#386—21no—
266#386—21no—
267#386—21no—
268#386—21no—
269#386—21no—
270#386—21no—
271#385—21no—
272#385—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#385—21no—
277#385—21no—
278#385—21no—
279#385—21no—
280#385—21no—
281#385—21no—
282#385—21no—
283#381—21no—
284#381—21no—
285#381—21no—
286#381—22no—
287#381—22no—
288#381—22no—
289#381—22no—
290#380—21no—
291#380—21no—
292#380—21no—
293#380—21no—
294#380—21no—
295#380—21no—
296#380—21no—
297#380—21no—
298#380C2311yescharacteristic
299#380C2311yescharacteristic
300#380C2312yes—
301#380C2312yes—
302#380C2311yescharacteristic
303#380C2311yescharacteristic
304#380C2312yes—
305#380C2312yes—
306#380C2311yescharacteristic
307#380C2311yescharacteristic
308#380C2312yes—
309#380C2312yes—
310#380C2311yescharacteristic
311#380C2311yescharacteristic
312#380C2311yescharacteristic
313#380C2311yescharacteristic
314#380C2311yescharacteristic
315#380C2311yescharacteristic
316#380C2312yes—
317#380C2312yes—
318#379—21no—
319#379—21no—
320#379—21no—
321#379—21no—
322#379—21no—
323#379—21no—
324#379—21no—
325#379—22no—
326#379—22no—
327#379—22no—
328#379—22no—
329C4×C22⋊C4—22no—
330C4×C22⋊C4—22no—
331C4×C22⋊C4—22no—
332C4×C22⋊C4—22no—
333C4×C22⋊C4—22no—
334C4×C22⋊C4—22no—
335C4×C22⋊C4—22no—
336C4×C22⋊C4—22no—
337C4×C22⋊C4—21no—
338C4×C22⋊C4—21no—
339C4×C22⋊C4—21no—
340C4×C22⋊C4—21no—
341C4×C22⋊C4—21no—
342C4×C22⋊C4—21no—
343C2×#95—21no—
344C2×#95—21no—
345C2×#95—21no—
346C2×#95—21no—
347#340C2312yescomplemented
348#340C2312yescomplemented
349#340C2312yescomplemented
350#340C2312yescomplemented
351#340C2312yescomplemented
352#340C2312yescomplemented
353#340C2312yescomplemented
354#340C2312yescomplemented
355#340C2312yescomplemented
356#340C2312yescomplemented
357#340C2312yescomplemented
358#340C2312yescomplemented
359#340C2312yescomplemented
360#340C2312yescomplemented
361#340C2312yescomplemented
362#340C2312yescomplemented
363C25—24no—
364C25—24no—
365C25—42no—
366C25—42no—
367C25—42no—
368C25—42no—
369C25—42no—
370C25C2×D411yescharacteristic
371C25C2×D411yescharacteristic
372C25C2×D411yescharacteristic
373C25C2×D411yescharacteristic
374C25C2×D411yescharacteristic
375C25C2×D411yescharacteristic
376C25C2×D411yescharacteristic
377C2×#41—24no—
378C2×#41—41no—
379C2×#41—41no—
380C2×#41—42no—
381C22×Q8C2411yescharacteristic
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4C2411yescharacteristic
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—42no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—42no—
435C23×C4—41no—
436C23×C4—41no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—432no—
444C23×C4—432no—
445C23×C4C2×D411yescharacteristic
446C23×C4C2×D411yescharacteristic
447C23×C4C2×D411yescharacteristic
448C23×C4C2×D411yescharacteristic
449C23×C4C2×D411yescharacteristic
450C23×C4C2×D411yescharacteristic
451C23×C4C2×D411yescharacteristic
452C23×C4C2×D411yescharacteristic
453C23×C4C2×D411yescharacteristic
454C23×C4C2×D411yescharacteristic
455C23×C4C2×D411yescharacteristic
456C23×C4C2×D411yescharacteristic
457C23×C4C2×D411yescharacteristic
458C23×C4C2×D411yescharacteristic
459C23×C4C2×D411yescharacteristic
460C23×C4C2×D411yescharacteristic
461C23×C4C2×D411yescharacteristic
462C23×C4C2×D411yescharacteristic
463C23×C4C2×D411yescharacteristic
464C23×C4C2×D411yescharacteristic
465C23×C4C2×D411yescharacteristic
466C23×C4#4118yes—
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C22×C8—24no—
475C22×C8—24no—
476C22×C8—42no—
477C22×C8—42no—
478C22×C8—42no—
479C22×C8—42no—
480C22×C8C2412yes—
481C22×C8C2412yes—
482C22×C8C2412yes—
483C22×C8C2412yes—
484#123—44no—
485#123—44no—
486#123—44no—
487C22⋊Q8—24no—
488C22⋊Q8—24no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—24no—
492C22⋊Q8—41no—
493C22⋊Q8—42no—
494C22⋊Q8—41no—
495#121—24no—
496#121—24no—
497#121—22no—
498#121—22no—
499#121—24no—
500#121—41no—
501#121—42no—
502#121—41no—
503#120—44no—
504#120—44no—
505#120—44no—
506#120—44no—
507#120—44no—
508#120—44no—
509#120—44no—
510C4×D4—44no—
511C4×D4—44no—
512C4×D4—44no—
513C4×D4—44no—
514C4×D4—44no—
515C4×D4—44no—
516#117—24no—
517#117—24no—
518#117—24no—
519#117—42no—
520#117—42no—
521#117—42no—
522#117—42no—
523#117—42no—
524#117—42no—
525#117—41no—
526#117—42no—
527#117—41no—
528#117—44no—
529#117—44no—
530#117—44no—
531#117—44no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—42no—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2411yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—44no—
598C2×C22⋊C4—44no—
599C2×C22⋊C4—44no—
600C2×C22⋊C4—44no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4—44no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—44no—
611C2×C42—44no—
612#107—42no—
613#107—42no—
614#107—42no—
615#107—42no—
616#106—42no—
617#106—42no—
618#106—42no—
619#106—42no—
620#103—42no—
621#103—42no—
622#103—42no—
623#103—42no—
624#102—42no—
625#102—42no—
626#102—42no—
627#102—42no—
628C22⋊C8—24no—
629C22⋊C8—24no—
630C22⋊C8—24no—
631C22⋊C8—24no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634C22⋊C8—24no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637C22⋊C8—24no—
638C22⋊C8—42no—
639C22⋊C8—42no—
640C22⋊C8—42no—
641C22⋊C8—42no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—21no—
651#95—21no—
652#95—21no—
653#95—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—41no—
691C24—41no—
692C24—41no—
693C24—41no—
694C24—41no—
695C24—41no—
696C24—41no—
697C24—41no—
698C24—41no—
699C24—41no—
700C24—41no—
701C24—41no—
702C24—41no—
703C24—41no—
704C24—41no—
705C24—41no—
706C24—41no—
707C24—41no—
708C24—41no—
709C24—41no—
710C24—416no—
711C24—416no—
712C24—416no—
713C24—416no—
714C24—416no—
715C24—416no—
716C24—416no—
717C24#12314yes—
718C24#13514yes—
719C24C22×D411yescharacteristic
720C24C22×D411yescharacteristic
721C24C22×D411yescharacteristic
722C24C22×D411yescharacteristic
723C24C22×D411yescharacteristic
724C24C22×D411yescharacteristic
725C24C22×D411yescharacteristic
726#41—84no—
727#41—84no—
728C2×Q8—22no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C22×C4—216no—
758C22×C4—216no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—416no—
863C22×C4—416no—
864C22×C4—416no—
865C22×C4—416no—
866C22×C4—416no—
867C22×C4—416no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—416no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4#12314yes—
887C22×C4#12314yes—
888C22×C4#12314yes—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C2×#4114yes—
897C22×C4C2×#4114yes—
898C22×C4C2×#4114yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C4H(5,𝔽2)14yes—
902C22×C4C2511yescharacteristic
903C2×C8—22no—
904C2×C8—22no—
905C2×C8—22no—
906C2×C8—22no—
907C2×C8—22no—
908C2×C8—22no—
909C2×C8—22no—
910C2×C8—22no—
911C2×C8—22no—
912C2×C8—22no—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—84no—
916C2×C8—84no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—44no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C42—44no—
983C42—44no—
984C42—44no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—44no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—28no—
998C23—28no—
999C23—28no—
1000C23—28no—
1001C23—28no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—28no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—44no—
1037C23—44no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—44no—
1045C23—44no—
1046C23—44no—
1047C23—44no—
1048C23—44no—
1049C23—44no—
1050C23—44no—
1051C23—44no—
1052C23—44no—
1053C23—44no—
1054C23—44no—
1055C23—44no—
1056C23—44no—
1057C23—44no—
1058C23—44no—
1059C23—44no—
1060C23—44no—
1061C23—44no—
1062C23—44no—
1063C23—44no—
1064C23—44no—
1065C23—44no—
1066C23—44no—
1067C23—44no—
1068C23—44no—
1069C23—44no—
1070C23—44no—
1071C23—4128no—
1072C23—44no—
1073C23—44no—
1074C23—44no—
1075C23—44no—
1076C23—44no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23C2×#12312yes—
1085C23C2×#12312yes—
1086C23C2×#12312yes—
1087C23#53412yes—
1088C23#53412yes—
1089C23C2×#13512yes—
1090C23C2×#13512yes—
1091C23C2×#13512yes—
1092C23#57512yes—
1093C23#57512yes—
1094C23#57512yes—
1095C23C23×D411yescharacteristic
1096Q8—42no—
1097Q8—42no—
1098D4—42no—
1099D4—42no—
1100D4—84no—
1101D4—84no—
1102D4—84no—
1103D4—84no—
1104D4—84no—
1105D4—84no—
1106D4—84no—
1107C2×C4—28no—
1108C2×C4—28no—
1109C2×C4—28no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—84no—
1196C2×C4C2×#12312yes—
1197C2×C4C2×#12312yes—
1198C2×C4C2×#12312yes—
1199C2×C4#53412yes—
1200C2×C4#53412yes—
1201C2×C4C22×#4112yes—
1202C2×C4C2×H(5,𝔽2)11yescharacteristic
1203C2×C4C2×H(5,𝔽2)11yescharacteristic
1204C2×C4C2×H(5,𝔽2)12yes—
1205C8—42no—
1206C8—42no—
1207C8—42no—
1208C8—42no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—416no—
1237C22—416no—
1238C22—416no—
1239C22—416no—
1240C22—416no—
1241C22—416no—
1242C22—416no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22#309114yes—
1271C22#319114yes—
1272C22C22×#12311yescharacteristic
1273C22C2×#53411yescharacteristic
1274C22C2×#53411yescharacteristic
1275C22C22×#13511yescharacteristic
1276C22C2×#57511yescharacteristic
1277C22C2×#57511yescharacteristic
1278C22C2×#57511yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—82no—
1287C4—81no—
1288C4—82no—
1289C4—81no—
1290C4—82no—
1291C4—82no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4#349012yes—
1298C4#349012yes—
1299C2—24no—
1300C2—24no—
1301C2—42no—
1302C2—42no—
1303C2—42no—
1304C2—42no—
1305C2—42no—
1306C2—161no—
1307C2#3499211yescharacteristic
1308C2C2×#309111yescharacteristic
1309C2#6051111yescharacteristic
1310C2C2×#319111yescharacteristic
1311C2#6073411yescharacteristic
1312C2#6075211yescharacteristic
1313C2#6075211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36614C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2280C2semidirect
3. #32985C2semidirect
4. #32984C2semidirect
5. #32981C2semidirect
6. #32980C2semidirect
7. #29897C2semidirect
8. #29896C2semidirect
9. #27605C2semidirect
10. #27604C2semidirect
11. #27602C2semidirect
12. #24555C2semidirect
13. #24554C2semidirect
14. #24553C2semidirect
15. #24552C2semidirect
16. #24551C2semidirect
17. #24550C2semidirect
18. #24008C2semidirect
19. #24007C2semidirect
20. #24004C2semidirect
21. #21939C2semidirect
22. #21760C2semidirect
23. C2×#1779C2semidirect
30. C2×#484C22semidirect
31. C2×#481C22semidirect
32. C2×#485C22semidirect
33. C2×#482C22semidirect
34. C2×#483C22semidirect
35. C2×#480C22semidirect
75. #2077C22semidirect
76. #2077C22semidirect
77. #2077C22semidirect
78. #2077C22semidirect
79. #2076C22semidirect
80. #2076C22semidirect
81. #2075C22semidirect
82. #2075C22semidirect
83. #2036C22semidirect
84. #2036C22semidirect
85. #2035C22semidirect
86. #2035C22semidirect
87. #2034C22semidirect
88. #2034C22semidirect
89. #2033C22semidirect
90. #2033C22semidirect
91. #1893C22semidirect
92. #1893C22semidirect
93. #1892C22semidirect
94. #1892C22semidirect
95. #1875C22semidirect
96. #1875C22semidirect
97. #1875C22semidirect
98. #1874C22semidirect
99. #1874C22semidirect
100. #1873C22semidirect
101. #1873C22semidirect
102. #1873C22semidirect
103. #1872C22semidirect
104. #1872C22semidirect
105. #1854C22semidirect
106. #1854C22semidirect
107. #1854C22semidirect
108. #1854C22semidirect
109. #1854C22semidirect
110. #1854C22semidirect
111. #1854C22semidirect
112. #1854C22semidirect
113. #1854C22semidirect
114. #1854C22semidirect
115. #1853C22semidirect
116. #1853C22semidirect
117. #1852C22semidirect
118. #1852C22semidirect
119. #1825C22semidirect
120. #1825C22semidirect
121. #1825C22semidirect
122. #1825C22semidirect
123. #1824C22semidirect
124. #1824C22semidirect
125. #1823C22semidirect
126. #1823C22semidirect
127. #1808C22semidirect
128. #1808C22semidirect
129. #1807C22semidirect
130. #1807C22semidirect
131. #1788C22semidirect
132. #1788C22semidirect
225. C2×#107C23semidirect
226. C2×#107C23semidirect
227. C2×#107C23semidirect
228. C2×#107C23semidirect
229. C2×#106C23semidirect
230. C2×#106C23semidirect
231. C2×#106C23semidirect
232. C2×#106C23semidirect
233. C2×#103C23semidirect
234. C2×#103C23semidirect
235. C2×#103C23semidirect
236. C2×#103C23semidirect
237. C2×#102C23semidirect
238. C2×#102C23semidirect
239. C2×#102C23semidirect
240. C2×#102C23semidirect
347. #340C23semidirect
348. #340C23semidirect
349. #340C23semidirect
350. #340C23semidirect
351. #340C23semidirect
352. #340C23semidirect
353. #340C23semidirect
354. #340C23semidirect
355. #340C23semidirect
356. #340C23semidirect
357. #340C23semidirect
358. #340C23semidirect
359. #340C23semidirect
360. #340C23semidirect
361. #340C23semidirect
362. #340C23semidirect

Maximal subgroups

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

subgroupindex
#366142
C2×#22802
#329852
#329842
#329812
#329802
#298972
#298962
#276052
#276042
#276022
#245552
#245542
#245532
#245522
#245512
#245502
#240082
#240072
#240042
#219392
#217602
C2×#17792