Finite Group Databasebeta

← #403188

Subgroups — #403188

Order 512.

1166 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2083C212yesmaximal
2C2×#2068C212yesmaximal
3C2×#1947C211yesmaximal, characteristic
4C2×#1928C211yesmaximal, characteristic
5#15199C211yesmaximal, characteristic
6#13818C211yesmaximal, characteristic
7#11357C211yesmaximal, characteristic
8#11322C211yesmaximal, characteristic
9#11077C211yesmaximal, characteristic
10#10932C212yesmaximal
11#10849C212yesmaximal
12C22×#107C2212yes—
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×#103C2211yescharacteristic
17C22×#103C2212yes—
18C22×#103C2211yescharacteristic
19C2×#391C2212yes—
20C2×#391C2211yescharacteristic
21C2×#389C2212yes—
22C2×#384C2211yescharacteristic
23C2×#384C2212yes—
24C2×C4×C4⋊C4C2212yes—
25C2×C4×C4⋊C4C2211yescharacteristic
26#2083—28no—
27#2068—28no—
28#1947—24no—
29#1928—24no—
30C2×#340C2212yes—
31C2×#340C2211yescharacteristic
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2212yes—
37#1444—21no—
38#1444—22no—
39#1444—21no—
40#1436—22no—
41C4⋊#95—21no—
42C4⋊#95C2211yescharacteristic
43C4×#95—21no—
44C4×#95C2211yescharacteristic
45C23×Q8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C23×C8C2312yes—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—22no—
61C22×C42C2311yescharacteristic
62C22×C42C2312yes—
63C2×#107—24no—
64C2×#107—24no—
65C2×#107—24no—
66C2×#107—22no—
67C2×#107—24no—
68C2×C4⋊C8—24no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8—24no—
71C2×C4⋊C8—24no—
72C2×C4⋊C8—42no—
73C2×#103—22no—
74C2×#103—22no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—22no—
79C2×#103—42no—
80C2×#103Q814yes—
81#391—24no—
82#391—22no—
83#391—22no—
84#391—24no—
85#389—24no—
86#389D418yes—
87#384—24no—
88#384—22no—
89#384—22no—
90#384—24no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—24no—
93C4×C4⋊C4—42no—
94C4×C4⋊C4D414yes—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—21no—
101C2×#95—22no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95D411yescharacteristic
105C2×#95D412yes—
106C2×#95D411yescharacteristic
107#340—24no—
108#340—24no—
109#340—24no—
110#340—22no—
111#340—24no—
112#336—24no—
113#336—22no—
114C22×Q8—21no—
115C22×Q8—21no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—22no—
121C22×Q8—21no—
122C22×Q8—22no—
123C22×Q8C2×Q812yes—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4C2×D412yes—
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D412yes—
133C23×C4C2×D411yescharacteristic
134C23×C4C2411yescharacteristic
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—21no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—21no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—21no—
149C22×C8—21no—
150C22×C8C2×Q812yes—
151C22×C8#4114yes—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
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—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—28no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—81no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—81no—
186C2×C4⋊C4C2×D414yes—
187C2×C4⋊C4C2×D412yes—
188C2×C4⋊C4C2×D412yes—
189C2×C4⋊C4C2×D414yes—
190C2×C4⋊C4C2×Q812yes—
191C2×C4⋊C4#4112yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—44no—
200C2×C42—44no—
201C2×C42—82no—
202C2×C42—82no—
203C2×C42C2×D412yes—
204C2×C42C2×D414yes—
205C2×C42#4112yes—
206C2×C42#4114yes—
207#107—48no—
208#107—44no—
209C4⋊C8—28no—
210C4⋊C8—48no—
211#103—28no—
212#103—48no—
213#103—44no—
214#95—24no—
215#95—28no—
216#95—22no—
217#95—24no—
218#95—44no—
219#95—42no—
220#95—44no—
221#95—44no—
222#95—42no—
223#95—42no—
224#95—81no—
225#95Q1614yes—
226C24C22×D411yescharacteristic
227C2×Q8—22no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—42no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—42no—
240C2×Q8—41no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4#12112yes—
296C22×C4#12114yes—
297C22×C4#12114yes—
298C22×C4#12112yes—
299C22×C4C2×Q1612yes—
300C22×C4C2×Q1614yes—
301C22×C4#13712yes—
302C22×C4#13714yes—
303C22×C4C22×D411yescharacteristic
304C22×C4C22×D412yes—
305C22×C4C22×Q811yescharacteristic
306C22×C4C2×#4111yescharacteristic
307C22×C4C2×#4112yes—
308C22×C4C2×#4112yes—
309C22×C4C2×#4111yescharacteristic
310C22×C4H(5,𝔽2)11yescharacteristic
311C22×C42−1+412yes—
312C22×C42−1+411yescharacteristic
313C2×C8—22no—
314C2×C8—24no—
315C2×C8—24no—
316C2×C8—24no—
317C2×C8—24no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—88no—
347C4⋊C4—84no—
348C4⋊C4—88no—
349C4⋊C4—88no—
350C4⋊C4—84no—
351C4⋊C4C22⋊Q814yes—
352C4⋊C4#12714yes—
353C42—22no—
354C42—24no—
355C42—22no—
356C42—24no—
357C42—24no—
358C42—24no—
359C42—24no—
360C42—84no—
361C42—88no—
362C23C2×#12111yescharacteristic
363C23C2×#12112yes—
364C23#54611yescharacteristic
365C23#54712yes—
366C23D4×Q811yescharacteristic
367C23C22×Q1611yescharacteristic
368C23C2×#13711yescharacteristic
369C23C2×#13712yes—
370C23#57611yescharacteristic
371C23#57612yes—
372C23#57711yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—44no—
376Q8—81no—
377Q8—82no—
378Q8—81no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—81no—
434C2×C4—82no—
435C2×C4#46214yes—
436C2×C4#46218yes—
437C2×C4C2×C22⋊Q811yescharacteristic
438C2×C4#52511yescharacteristic
439C2×C4#52912yes—
440C2×C4C2×#12711yescharacteristic
441C2×C4#53211yescharacteristic
442C2×C4#53212yes—
443C2×C4#53312yes—
444C2×C4#53611yescharacteristic
445C2×C4#53711yescharacteristic
446C2×C4#53912yes—
447C2×C4#54112yes—
448C2×C4#54612yes—
449C2×C4#54712yes—
450C2×C4#54812yes—
451C2×C4D4×Q812yes—
452C2×C4#55211yescharacteristic
453C2×C4#55212yes—
454C2×C4#55411yescharacteristic
455C8—44no—
456C8—42no—
457C8—81no—
458C22#241311yescharacteristic
459C22#241711yescharacteristic
460C22#242512yes—
461C22#242912yes—
462C22#285611yescharacteristic
463C22C2×#46211yescharacteristic
464C22C2×#46212yes—
465C22#303911yescharacteristic
466C22#303912yes—
467C22#304111yescharacteristic
468C22#304112yes—
469C22#304511yescharacteristic
470C22#304512yes—
471C22#329911yescharacteristic
472C22#331412yes—
473C22#333311yescharacteristic
474C22#333812yes—
475C22#334412yes—
476C22#334612yes—
477C22#335712yes—
478C22Q8×Q1611yescharacteristic
479C22#338512yes—
480C22#338711yescharacteristic
481C4—24no—
482C4—28no—
483C4—44no—
484C4—42no—
485C4—44no—
486C4—44no—
487C4—82no—
488C4—84no—
489C4—162no—
490C4—161no—
491C4#239611yescharacteristic
492C4#251912yes—
493C4#254011yescharacteristic
494C4#254211yescharacteristic
495C4#255612yes—
496C4#266411yescharacteristic
497C2#1487011yescharacteristic
498C2#2458211yescharacteristic
499C2#2459811yescharacteristic
500C2#2481711yescharacteristic
501C2#2483311yescharacteristic
502C2#2520612yes—
503C2#2522312yes—
504C2#2545512yes—
505C2#2546712yes—
506C2#3316311yescharacteristic
507C2#3316611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ 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×#20832
C2×#20682
C2×#19472
C2×#19282
#151992
#138182
#113572
#113222
#110772
#109322
#108492