Finite Group Databasebeta

← #379711

Subgroups — #379711

Order 512.

908 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#400C211yesmaximal, characteristic
2#11255C212yesmaximal
3#11202C211yesmaximal, characteristic
4#10877C212yesmaximal
5#10874C212yesmaximal
6#10835C211yesmaximal, characteristic
7#10798C212yesmaximal
8#10797C212yesmaximal
9#10696C212yesmaximal
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×#97C2212yes—
13C22×#97C2211yescharacteristic
14C22×C4×C8C2212yes—
15C2×#400C411yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×#336C2212yes—
19C2×#336C2212yes—
20C2×#336C2212yes—
21C2×#336C2212yes—
22C2×#336C2212yes—
23C2×#336C2212yes—
24C2×#336C2212yes—
25C2×#336C2212yes—
26C2×#336C2211yescharacteristic
27C2×#336C2212yes—
28C2×#336C2212yes—
29#1445C411yescharacteristic
30#1443C412yes—
31#1442C411yescharacteristic
32#1442C412yes—
33#1441C411yescharacteristic
34C4×#95C2212yes—
35C4×#95C2211yescharacteristic
36C4×#95C2212yes—
37C23×C8C2312yes—
38C23×C8C2312yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C4⋊C4C2×C411yescharacteristic
43C22×C4⋊C4C2×C411yescharacteristic
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C42C2312yes—
46C22×C42C2312yes—
47C22×C42C2311yescharacteristic
48C22×C42C2311yescharacteristic
49C22×C42C2311yescharacteristic
50C2×C4⋊C8—24no—
51C2×C4⋊C8—22no—
52C2×C4⋊C8—41no—
53C2×C4⋊C8—41no—
54C2×C4⋊C8—41no—
55C2×#97—24no—
56C2×#97—24no—
57C2×#97—41no—
58C2×#97—41no—
59C2×#97—42no—
60C2×#97Q814yes—
61C2×C4×C8—24no—
62C2×C4×C8—24no—
63C2×C4×C8—42no—
64#400—24no—
65C4×C4⋊C4—41no—
66C4×C4⋊C4—41no—
67C4×C4⋊C4—41no—
68C4×C4⋊C4—41no—
69C2×#95C2×C411yescharacteristic
70C2×#95C2×C412yes—
71C2×#95C2×C412yes—
72C2×#95C2×C412yes—
73C2×#95C2×C412yes—
74C2×#95C2×C412yes—
75C2×#95C2×C412yes—
76C2×#95C2×C411yescharacteristic
77C2×#95C2×C412yes—
78C2×#95C2×C412yes—
79C2×#95C2×C412yes—
80C2×#95C2×C412yes—
81C2×#95C2×C411yescharacteristic
82C2×#95C2×C411yescharacteristic
83#336—24no—
84#336—24no—
85#336—24no—
86#336—24no—
87#336—24no—
88#336—24no—
89#336—24no—
90#336—24no—
91#336—41no—
92#336—42no—
93#336—42no—
94C23×C4C22×C411yescharacteristic
95C23×C4C22×C411yescharacteristic
96C23×C4C22×C412yes—
97C23×C4C22×C412yes—
98C23×C4C22×C411yescharacteristic
99C23×C4C22×C411yescharacteristic
100C23×C4C22×C411yescharacteristic
101C23×C4C22×C412yes—
102C23×C4C22×C412yes—
103C23×C4C22×C411yescharacteristic
104C23×C4C2411yescharacteristic
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8C2×Q814yes—
129C22×C8#4114yes—
130C22×C8#4114yes—
131C22×C8#4114yes—
132C22×C8#4114yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4M1614yes—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—21no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42—21no—
167C2×C42—22no—
168C2×C42C2×Q812yes—
169C2×C42#4112yes—
170C4⋊C8—44no—
171C4⋊C8—44no—
172#97—44no—
173#97—48no—
174C4×C8—48no—
175#95—24no—
176#95—22no—
177#95—24no—
178#95—24no—
179#95—24no—
180#95—24no—
181#95—42no—
182#95—41no—
183#95—42no—
184#95—42no—
185#95—42no—
186#95—41no—
187#95—41no—
188#95—42no—
189C24C23×C411yescharacteristic
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4C4×Q812yes—
245C22×C4C4×Q812yes—
246C22×C4C2×M1614yes—
247C22×C4C2×M1612yes—
248C22×C4#13114yes—
249C22×C4#13112yes—
250C22×C4C22×Q811yescharacteristic
251C22×C4C2×#4112yes—
252C22×C4C2×#4112yes—
253C22×C4C2×#4111yescharacteristic
254C22×C4C2×#4112yes—
255C22×C4C2×#4112yes—
256C22×C4H(5,𝔽2)11yescharacteristic
257C22×C4H(5,𝔽2)11yescharacteristic
258C22×C4H(5,𝔽2)11yescharacteristic
259C22×C42−1+411yescharacteristic
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—24no—
264C2×C8—24no—
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8#12518yes—
288C4⋊C4—44no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4—44no—
292C42—22no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—42no—
297C42—42no—
298C42—41no—
299C42—42no—
300C42—41no—
301C42—42no—
302C42—42no—
303C42—42no—
304C42—42no—
305C42—42no—
306C42—42no—
307C42—42no—
308C42—41no—
309C42—41no—
310C23C2×C4×Q811yescharacteristic
311C23C4×#4112yes—
312C23C4×#4112yes—
313C23#51811yescharacteristic
314C23#52011yescharacteristic
315C23C22×M1611yescharacteristic
316C23C2×#13112yes—
317C23C2×#13111yescharacteristic
318C23#56812yes—
319C23#56811yescharacteristic
320C23#56811yescharacteristic
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
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—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4C2×#12512yes—
382C2×C4#52912yes—
383C2×C4#52912yes—
384C2×C4#53312yes—
385C2×C4#53811yescharacteristic
386C2×C4#53911yescharacteristic
387C2×C4#54311yescharacteristic
388C2×C4#54411yescharacteristic
389C2×C4#55112yes—
390C2×C4#55112yes—
391C2×C4#55111yescharacteristic
392C2×C4#55212yes—
393C2×C4#55312yes—
394C2×C4#55312yes—
395C2×C4#55511yescharacteristic
396C2×C4#55511yescharacteristic
397C2×C4#55612yes—
398C2×C4#55911yescharacteristic
399C8—28no—
400C8—44no—
401C8—44no—
402C8—82no—
403C22C4×#12512yes—
404C22#232911yescharacteristic
405C22#237211yescharacteristic
406C22#237312yes—
407C22#237411yescharacteristic
408C22#296211yescharacteristic
409C22#296212yes—
410C22Q8×M1611yescharacteristic
411C22#296512yes—
412C22#296612yes—
413C22#296712yes—
414C22#296712yes—
415C22#296812yes—
416C22#296812yes—
417C22#296912yes—
418C22#297012yes—
419C22#297311yescharacteristic
420C22#297611yescharacteristic
421C22#297711yescharacteristic
422C22#298011yescharacteristic
423C22#299111yescharacteristic
424C22#299312yes—
425C22#299511yescharacteristic
426C4—42no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—44no—
431C4—44no—
432C4—81no—
433C4—81no—
434C4—82no—
435C4—82no—
436C4#256912yes—
437C4#257111yescharacteristic
438C4#257211yescharacteristic
439C4#257312yes—
440C4#259311yescharacteristic
441C4#261211yescharacteristic
442C2#1425411yescharacteristic
443C2#2167412yes—
444C2#2167812yes—
445C2#2228911yescharacteristic
446C2#2229011yescharacteristic
447C2#2327311yescharacteristic
448C2#2327411yescharacteristic
449C2#2328412yes—
450C2#2328512yes—
451C2#2329611yescharacteristic
452C2#2329711yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socle, prime radicalC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ 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
C4×#4002
#112552
#112022
#108772
#108742
#108352
#107982
#107972
#106962