Finite Group Databasebeta

← #416842

Subgroups — #416842

Order 512.

960 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1834C211yesmaximal, characteristic
2C2×#1768C211yesmaximal, characteristic
3#14277C211yesmaximal, characteristic
4#14277C211yesmaximal, characteristic
5#11293C212yesmaximal
6#11292C212yesmaximal
7#11228C212yesmaximal
8#11227C212yesmaximal
9#10843C211yesmaximal, characteristic
10#10843C211yesmaximal, characteristic
11#10842C211yesmaximal, characteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×#97C2211yescharacteristic
15C22×C4×C8C2211yescharacteristic
16C2×#389C2212yes—
17C2×#389C2212yes—
18C2×#384C2211yescharacteristic
19C2×#384C2211yescharacteristic
20C2×#382C2211yescharacteristic
21C2×#382C2211yescharacteristic
22C2×#376C2211yescharacteristic
23#1834—24no—
24#1768—24no—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#336C2211yescharacteristic
34C2×#336C2211yescharacteristic
35#1444—21no—
36#1444—21no—
37#1444—21no—
38#1444—21no—
39#1442—21no—
40#1442—21no—
41#1442—21no—
42#1442—21no—
43C4⋊#95C2212yes—
44C4⋊#95C2212yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C23×C8C2311yescharacteristic
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4C2312yes—
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2312yes—
59C22×C42C2311yescharacteristic
60C22×C42C2311yescharacteristic
61C22×C42C2311yescharacteristic
62C2×C4⋊C8—22no—
63C2×C4⋊C8—22no—
64C2×C4⋊C8—22no—
65C2×C4⋊C8—22no—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—22no—
68C2×#97—22no—
69C2×#97—22no—
70C2×#97—22no—
71C2×C4×C8—22no—
72C2×C4×C8—22no—
73C2×C4×C8D414yes—
74#389—24no—
75#389—24no—
76#389—42no—
77#389—42no—
78#384—22no—
79#384—22no—
80#384—22no—
81#384—22no—
82#382—22no—
83#382—22no—
84#382Q814yes—
85#382Q814yes—
86#376—22no—
87#376—22no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95D411yescharacteristic
99C2×#95D411yescharacteristic
100C2×#95D411yescharacteristic
101C2×#95D411yescharacteristic
102#340—24no—
103#340—24no—
104#340—24no—
105#340—24no—
106#340—42no—
107#340—42no—
108#340—42no—
109#340—42no—
110#336—22no—
111#336—22no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C23×C4C2411yescharacteristic
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—21no—
128C22×C8—21no—
129C22×C8—21no—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—21no—
133C22×C8—21no—
134C22×C8—21no—
135C22×C8—21no—
136C22×C8—21no—
137C22×C8—21no—
138C22×C8—21no—
139C22×C8—21no—
140C22×C8—21no—
141C22×C8—21no—
142C22×C8—21no—
143C22×C8—21no—
144C22×C8—21no—
145C22×C8—21no—
146C22×C8—21no—
147C22×C8C2×D412yes—
148C22×C8C2×D412yes—
149C22×C8#4112yes—
150C22×C8#4112yes—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4—82no—
187C2×C4⋊C4C2×Q814yes—
188C2×C4⋊C4C2×Q814yes—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42C2×D412yes—
200C2×C42C2×Q812yes—
201C2×C42C2×Q812yes—
202C2×C42#4112yes—
203C2×C42#4112yes—
204C2×C42#4112yes—
205C2×C42#4112yes—
206C2×C42#4112yes—
207C4⋊C8—28no—
208C4⋊C8—28no—
209#97—44no—
210C4×C8—28no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—24no—
216#95—24no—
217#95—24no—
218#95—24no—
219#95—44no—
220#95—44no—
221#95—82no—
222#95—82no—
223#95—82no—
224#95—82no—
225C24C22×D411yescharacteristic
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4#12112yes—
277C22×C4#12112yes—
278C22×C4C22⋊Q812yes—
279C22×C4C22⋊Q812yes—
280C22×C4C22⋊Q812yes—
281C22×C4C22⋊Q812yes—
282C22×C4#12412yes—
283C22×C4#12412yes—
284C22×C4C22×D411yescharacteristic
285C22×C4C22×Q811yescharacteristic
286C22×C4C22×Q811yescharacteristic
287C22×C4C2×#4111yescharacteristic
288C22×C4C2×#4111yescharacteristic
289C22×C4C2×#4111yescharacteristic
290C22×C4C2×#4111yescharacteristic
291C22×C4C2×#4111yescharacteristic
292C22×C4C2×#4111yescharacteristic
293C22×C4C2×#4111yescharacteristic
294C22×C4H(5,𝔽2)11yescharacteristic
295C22×C4H(5,𝔽2)11yescharacteristic
296C22×C42−1+411yescharacteristic
297C22×C42−1+411yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—84no—
343C4⋊C4—84no—
344C4⋊C4—84no—
345C4⋊C4—84no—
346C4⋊C4—88no—
347C4⋊C4—88no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42#12314yes—
357C42#12514yes—
358C42#12514yes—
359C42C4⋊Q814yes—
360C23C2×#12111yescharacteristic
361C23C2×C22⋊Q811yescharacteristic
362C23C2×C22⋊Q811yescharacteristic
363C23C2×#12411yescharacteristic
364C23#53211yescharacteristic
365C23#53511yescharacteristic
366C23#53611yescharacteristic
367C23#57612yes—
368C23#57712yes—
369C23#57712yes—
370C23#57812yes—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4#39814yes—
428C2×C4#39814yes—
429C2×C4C2×#12311yescharacteristic
430C2×C4#52511yescharacteristic
431C2×C4#52511yescharacteristic
432C2×C4C2×#12511yescharacteristic
433C2×C4C2×#12511yescharacteristic
434C2×C4#52911yescharacteristic
435C2×C4#52911yescharacteristic
436C2×C4C2×C4⋊Q811yescharacteristic
437C2×C4#53711yescharacteristic
438C2×C4#53711yescharacteristic
439C2×C4#54211yescharacteristic
440C2×C4#54211yescharacteristic
441C2×C4#55211yescharacteristic
442C2×C4#55211yescharacteristic
443C2×C4#55311yescharacteristic
444C2×C4#55311yescharacteristic
445C2×C4#55411yescharacteristic
446C2×C4#55411yescharacteristic
447C2×C4#55411yescharacteristic
448C2×C4#55411yescharacteristic
449C2×C4#55511yescharacteristic
450C2×C4#55511yescharacteristic
451C2×C4#55611yescharacteristic
452C2×C4#55611yescharacteristic
453C2×C4#55711yescharacteristic
454C2×C4#55711yescharacteristic
455C2×C4#55711yescharacteristic
456C2×C4#55711yescharacteristic
457C8—42no—
458C8—42no—
459C8—42no—
460C8—42no—
461C22C2×#39811yescharacteristic
462C22#256311yescharacteristic
463C22#256511yescharacteristic
464C22#256611yescharacteristic
465C22#256811yescharacteristic
466C22#262011yescharacteristic
467C22#285011yescharacteristic
468C22#305711yescharacteristic
469C22#305711yescharacteristic
470C22#305811yescharacteristic
471C22#305911yescharacteristic
472C22#308312yes—
473C22#308312yes—
474C22#308412yes—
475C22#308412yes—
476C22#313612yes—
477C22#313712yes—
478C22#317812yes—
479C22#317912yes—
480C22#322412yes—
481C22#322512yes—
482C22#324112yes—
483C22#324212yes—
484C4—24no—
485C4—24no—
486C4—42no—
487C4—42no—
488C4—84no—
489C4—81no—
490C4—81no—
491C4—84no—
492C4—162no—
493C4—162no—
494C4#248511yescharacteristic
495C4#248511yescharacteristic
496C4#250811yescharacteristic
497C4#250811yescharacteristic
498C4#250911yescharacteristic
499C4#250911yescharacteristic
500C4#258411yescharacteristic
501C4#258411yescharacteristic
502C2#1523411yescharacteristic
503C2#2366711yescharacteristic
504C2#2366811yescharacteristic
505C2#2915112yes—
506C2#2918812yes—
507C2#2920312yes—
508C2#2922812yes—
509C2#2984711yescharacteristic
510C2#2984811yescharacteristic
511C2#3304511yescharacteristic
512C2#3304611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#18342
C2×#17682
#142772
#112932
#112922
#112282
#112272
#108432
#108422