Finite Group Databasebeta

← #470106

Subgroups — #470106

Order 512.

930 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1948C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3#15240C211yesmaximal, characteristic
4#13936C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11325C212yesmaximal
7#11268C212yesmaximal
8#11255C211yesmaximal, characteristic
9#11190C212yesmaximal
10#11122C212yesmaximal
11#11077C211yesmaximal, characteristic
12C22×#107C2211yescharacteristic
13C22×#106C2212yes—
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#391C2212yes—
20C2×#384C2211yescharacteristic
21C2×#382C2212yes—
22C2×C4×C4⋊C4C2211yescharacteristic
23#1948—24no—
24#1928—24no—
25C2×#340C2211yescharacteristic
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2212yes—
31C2×#336C2212yes—
32C2×#336C2211yescharacteristic
33#1445—21no—
34#1445—21no—
35#1445—22no—
36#1443—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40#1434—21no—
41#1434—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2311yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C4⋊C4C2311yescharacteristic
54C22×C42—21no—
55C22×C42C2312yes—
56C22×C42C2311yescharacteristic
57C2×#107—22no—
58C2×#107—42no—
59C2×#106—24no—
60C2×#106—42no—
61C2×#106—42no—
62C2×C4⋊C8—24no—
63C2×C4⋊C8—22no—
64C2×#103—22no—
65C2×#103—22no—
66C2×#103—22no—
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—22no—
70C2×#103—42no—
71C2×#103—42no—
72#391—22no—
73#391—22no—
74#391—42no—
75#391—42no—
76#384—22no—
77#384—22no—
78#382—42no—
79#382—42no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4D414yes—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95D411yescharacteristic
96C2×#95D411yescharacteristic
97C2×#95D412yes—
98#340—22no—
99#340—24no—
100#340—42no—
101#340—42no—
102#340—42no—
103#336—24no—
104#336—24no—
105#336—22no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—21no—
115C22×Q8#4112yes—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4C2×D412yes—
123C23×C4C2×D412yes—
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—21no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—21no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—21no—
141C22×C8—21no—
142C22×C8#4112yes—
143C22×C8#4114yes—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
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—44no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4C2×D412yes—
174C2×C4⋊C4C2×D412yes—
175C2×C42—22no—
176C2×C42—22no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—24no—
184C2×C42—82no—
185C2×C42C2×D412yes—
186C2×C42#4112yes—
187#107—44no—
188#106—48no—
189C4⋊C8—28no—
190#103—28no—
191#103—44no—
192#103—48no—
193#95—24no—
194#95—22no—
195#95—22no—
196#95—42no—
197#95—44no—
198#95—44no—
199#95—44no—
200#95—44no—
201#95—44no—
202#95—42no—
203#95—42no—
204#95—42no—
205#95—81no—
206#95—82no—
207#95—82no—
208#95—82no—
209C24C22×D411yescharacteristic
210C2×Q8—22no—
211C2×Q8—24no—
212C2×Q8—24no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×Q8—42no—
216C2×Q8—41no—
217C2×Q8—42no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—42no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
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—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4#12112yes—
283C22×C4#12112yes—
284C22×C4#13512yes—
285C22×C4#13712yes—
286C22×C4C22×D411yescharacteristic
287C22×C4C2×#4111yescharacteristic
288C22×C4C2×#4111yescharacteristic
289C22×C4C2×#4112yes—
290C22×C4C2×#4111yescharacteristic
291C22×C4H(5,𝔽2)12yes—
292C22×C4H(5,𝔽2)12yes—
293C22×C42−1+412yes—
294C22×C42−1+411yescharacteristic
295C22×C42−1+411yescharacteristic
296C2×C8—22no—
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—24no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—84no—
332C4⋊C4—84no—
333C42—22no—
334C42—22no—
335C42—24no—
336C42—42no—
337C42—42no—
338C42—42no—
339C42—42no—
340C42—84no—
341C23C2×#12111yescharacteristic
342C23#53512yes—
343C23#54712yes—
344C23#54711yescharacteristic
345C23#54811yescharacteristic
346C23C2×#13511yescharacteristic
347C23C2×#13711yescharacteristic
348C23#57512yes—
349C23#57712yes—
350C23#57711yescharacteristic
351C23#57811yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—44no—
355Q8—81no—
356Q8—81no—
357Q8—82no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
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—81no—
414C2×C4—81no—
415C2×C4#46414yes—
416C2×C4#52511yescharacteristic
417C2×C4#52511yescharacteristic
418C2×C4#53511yescharacteristic
419C2×C4#53511yescharacteristic
420C2×C4#53611yescharacteristic
421C2×C4#53611yescharacteristic
422C2×C4#53912yes—
423C2×C4#53912yes—
424C2×C4#54012yes—
425C2×C4#54212yes—
426C2×C4#54212yes—
427C2×C4#55112yes—
428C2×C4#55211yescharacteristic
429C2×C4#55212yes—
430C2×C4#55312yes—
431C2×C4#55611yescharacteristic
432C2×C4#56312yes—
433C2×C4#56312yes—
434C8—44no—
435C8—42no—
436C8—81no—
437C22#241311yescharacteristic
438C22#241511yescharacteristic
439C22#261911yescharacteristic
440C22#271812yes—
441C22#272312yes—
442C22C2×#46411yescharacteristic
443C22#304011yescharacteristic
444C22#304211yescharacteristic
445C22#304611yescharacteristic
446C22#321212yes—
447C22#321612yes—
448C22#322112yes—
449C22#322512yes—
450C22#333712yes—
451C22#334211yescharacteristic
452C22#334412yes—
453C22#334812yes—
454C22#335012yes—
455C22#335212yes—
456C22#335611yescharacteristic
457C22#336511yescharacteristic
458C22#337112yes—
459C22#337411yescharacteristic
460C4—24no—
461C4—42no—
462C4—82no—
463C4—82no—
464C4—82no—
465C4—82no—
466C4—82no—
467C4—162no—
468C4—161no—
469C4—162no—
470C4#259811yescharacteristic
471C4#263211yescharacteristic
472C4#263311yescharacteristic
473C4#273812yes—
474C4#277712yes—
475C4#282111yescharacteristic
476C2#1667611yescharacteristic
477C2#2457911yescharacteristic
478C2#2459511yescharacteristic
479C2#2468311yescharacteristic
480C2#2469711yescharacteristic
481C2#2979711yescharacteristic
482C2#2980411yescharacteristic
483C2#3229112yes—
484C2#3229712yes—
485C2#3243612yes—
486C2#3245412yes—
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×#19482
C2×#19282
#152402
#139362
#113572
#113252
#112682
#112552
#111902
#111222
#110772