Finite Group Databasebeta

← #375541

Subgroups — #375541

Order 512.

1166 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2C4×#423C211yesmaximal, characteristic
3C4×#423C211yesmaximal, characteristic
4#11204C214yesmaximal
5#10913C214yesmaximal
6#10857C212yesmaximal
7#10857C212yesmaximal
8C22×#125C412yes—
9C2×#423C2212yes—
10C2×#423C2212yes—
11C2×C4×M16C2212yes—
12C2×C4×M16C2212yes—
13#2859—21no—
14#2859—21no—
15#2859—21no—
16#2859—21no—
17#2859—21no—
18#2859—21no—
19#2859—21no—
20#2859—21no—
21C2×#389C412yes—
22C2×#389C412yes—
23C2×#389C2212yes—
24C2×#389C2212yes—
25C2×#384C2211yescharacteristic
26C2×#384C2211yescharacteristic
27C2×#382C412yes—
28C2×C43C2211yescharacteristic
29#1767—21no—
30#1767—21no—
31#1767—21no—
32#1767—21no—
33C4×C4⋊C8—21no—
34C4×C4⋊C8—21no—
35C4×C4⋊C8—21no—
36C4×C4⋊C8—21no—
37C2×#343C2218yes—
38C2×#343C2218yes—
39#1728C2212yes—
40#1728C2212yes—
41C22×M16C2314yes—
42C22×M16C2314yes—
43C2×#125—22no—
44C2×#125—22no—
45C2×#125—22no—
46C2×#125—22no—
47C2×#125—48no—
48C22×C4⋊C4C2×C412yes—
49C22×C4⋊C4C2×C412yes—
50C22×C4⋊C4C2×C414yes—
51C22×C4⋊C4C2×C414yes—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C412yes—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2312yes—
56C22×C42C2×C411yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42C2311yescharacteristic
61C22×C42C2311yescharacteristic
62C22×C42C2311yescharacteristic
63#423—28no—
64#423—24no—
65#423Q818yes—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—22no—
68C2×C4⋊C8—22no—
69C2×C4⋊C8—22no—
70C4×M16—24no—
71C4×M16—24no—
72C4×M16—44no—
73C2×#97—22no—
74C2×#97—22no—
75C2×C4×C8—22no—
76C2×C4×C8—22no—
77#389—22no—
78#389—22no—
79#389—22no—
80#389—22no—
81#389—22no—
82#389—22no—
83#389—22no—
84#389—22no—
85#389—22no—
86#389—22no—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389—22no—
92#389—22no—
93#384—21no—
94#384—21no—
95#384—21no—
96#384—21no—
97#384—21no—
98#384—21no—
99#384—21no—
100#384—21no—
101#382—22no—
102#382—22no—
103#382—22no—
104#382—22no—
105C2×#95C2×C414yes—
106C2×#95C2×C414yes—
107C43D411yescharacteristic
108C43D411yescharacteristic
109C43D411yescharacteristic
110C43D411yescharacteristic
111C43D411yescharacteristic
112C43D411yescharacteristic
113C43D411yescharacteristic
114C43D411yescharacteristic
115#343—216no—
116#343—48no—
117#336—22no—
118#336—22no—
119#336—22no—
120#336—22no—
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C22×C414yes—
128C23×C4C22×C414yes—
129C23×C4C2411yescharacteristic
130C2×M16—24no—
131C2×M16—24no—
132C2×M16—28no—
133C2×M16—24no—
134C2×M16—24no—
135C2×M16—24no—
136C2×M16—28no—
137C2×M16—24no—
138C2×M16C2×Q818yes—
139C2×M16#4118yes—
140C22×C8—24no—
141C22×C8—24no—
142#125—48no—
143#125—48no—
144#125—48no—
145#125—48no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—24no—
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—28no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—48no—
170C2×C4⋊C4—48no—
171C2×C42—24no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—24no—
175C2×C42—24no—
176C2×C42—42no—
177C2×C42—42no—
178C2×C42C22⋊C411yescharacteristic
179C2×C42C22⋊C411yescharacteristic
180C2×C42C22⋊C411yescharacteristic
181C2×C42C22⋊C411yescharacteristic
182C2×C42C22⋊C411yescharacteristic
183C2×C42C22⋊C411yescharacteristic
184C2×C42C22⋊C411yescharacteristic
185C2×C42C22⋊C411yescharacteristic
186C2×C42C22⋊C411yescharacteristic
187C2×C42C22⋊C411yescharacteristic
188C2×C42C22⋊C411yescharacteristic
189C2×C42C22⋊C411yescharacteristic
190C2×C42C22⋊C411yescharacteristic
191C2×C42C22⋊C411yescharacteristic
192C2×C42C22⋊C411yescharacteristic
193C2×C42C22⋊C411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204C2×C42C2×D411yescharacteristic
205C2×C42C2×D411yescharacteristic
206C2×C42C2×Q814yes—
207C2×C42#4114yes—
208C4⋊C8—28no—
209C4⋊C8—28no—
210C4⋊C8—28no—
211C4⋊C8—28no—
212#97—44no—
213#97—44no—
214C4×C8—44no—
215C4×C8—44no—
216#95—24no—
217#95—24no—
218#95—24no—
219#95—24no—
220C24C23×C411yescharacteristic
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—28no—
236C22×C4—28no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—44no—
244C22×C4—44no—
245C22×C4C2×C22⋊C411yescharacteristic
246C22×C4C2×C22⋊C411yescharacteristic
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C2×C22⋊C411yescharacteristic
249C22×C4C2×C22⋊C411yescharacteristic
250C22×C4C2×C22⋊C411yescharacteristic
251C22×C4C2×C22⋊C411yescharacteristic
252C22×C4C2×C22⋊C411yescharacteristic
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C2×C22⋊C411yescharacteristic
255C22×C4C2×C22⋊C411yescharacteristic
256C22×C4C2×C22⋊C411yescharacteristic
257C22×C4C4×Q814yes—
258C22×C4C4×Q814yes—
259C22×C4C22×D411yescharacteristic
260C22×C4C22×D411yescharacteristic
261C22×C4C22×Q812yes—
262C22×C4C2×#4112yes—
263C22×C4C2×#4114yes—
264C22×C4H(5,𝔽2)12yes—
265C22×C42−1+412yes—
266M16—28no—
267M16—28no—
268M16—216no—
269M16—44no—
270M16—44no—
271M16—48no—
272C2×C8—28no—
273C2×C8—28no—
274C2×C8—44no—
275C2×C8—44no—
276C2×C8—44no—
277C2×C8—44no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C4⋊C4—44no—
282C4⋊C4—48no—
283C4⋊C4—48no—
284C4⋊C4—44no—
285C4⋊C4—44no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—44no—
289C4⋊C4—48no—
290C4⋊C4—48no—
291C4⋊C4—44no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4—44no—
295C42—22no—
296C42—22no—
297C42—22no—
298C42—22no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—41no—
316C42—41no—
317C42—41no—
318C42—41no—
319C42#10014yes—
320C42#10114yes—
321C42C22⋊Q814yes—
322C42C22⋊Q814yes—
323C42#12412yes—
324C42#12412yes—
325C42C4⋊Q812yes—
326C42C4⋊Q812yes—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23C22×C22⋊C411yescharacteristic
332C23C2×C4×Q812yes—
333C23C4×#4112yes—
334C23#52012yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—28no—
348C2×C4—28no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—88no—
372C2×C4—88no—
373C2×C4#39112yes—
374C2×C4#39112yes—
375C2×C4#39112yes—
376C2×C4#39112yes—
377C2×C4C2×#10012yes—
378C2×C4C2×#10012yes—
379C2×C4C2×#10012yes—
380C2×C4C2×#10112yes—
381C2×C4C2×#10112yes—
382C2×C4C2×#10112yes—
383C2×C4#41312yes—
384C2×C4#41312yes—
385C2×C4C2×C22⋊Q812yes—
386C2×C4#52512yes—
387C2×C4C2×#12411yescharacteristic
388C2×C4C2×C4⋊Q811yescharacteristic
389C2×C4#53212yes—
390C2×C4#53511yescharacteristic
391C2×C4#53611yescharacteristic
392C2×C4#53712yes—
393C2×C4#55214yes—
394C2×C4#55314yes—
395C2×C4#55414yes—
396C2×C4#55714yes—
397C8—48no—
398C8—48no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22C2×#39111yescharacteristic
406C22#229711yescharacteristic
407C22#231111yescharacteristic
408C22#237014yes—
409C22C22×#10011yescharacteristic
410C22C22×#10111yescharacteristic
411C22C2×#41311yescharacteristic
412C22C2×#41311yescharacteristic
413C4—22no—
414C4—22no—
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—84no—
424C4—84no—
425C4#199714yes—
426C4#199814yes—
427C4#256212yes—
428C4#256512yes—
429C4#256612yes—
430C4#258412yes—
431C2—24no—
432C2#1416011yescharacteristic
433C2C2×#199711yescharacteristic
434C2C2×#199811yescharacteristic
435C2#2142411yescharacteristic
436C2#2142511yescharacteristic
437C2#2187811yescharacteristic
438C2#2187911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ 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×#28592
C4×#4232
#112042
#109132
#108572