Finite Group Databasebeta

← #215607

Subgroups — #215607

Order 512.

838 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2863C211yesmaximal, characteristic
2#20777C211yesmaximal, characteristic
3#20777C211yesmaximal, characteristic
4#9880C214yesmaximal
5#9879C212yesmaximal
6#9878C212yesmaximal
7#8705C214yesmaximal
8#2863—21no—
9#2863—21no—
10#2863—21no—
11#2863—21no—
12#2863—21no—
13#2863—21no—
14#2863—21no—
15#2863—21no—
16C2×#391C411yescharacteristic
17C2×#391C411yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#389C411yescharacteristic
20C2×#389C411yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#387C412yes—
23C2×#387C412yes—
24C2×#387C2212yes—
25C2×#383C2212yes—
26C2×C43C2211yescharacteristic
27#1839—21no—
28#1839—21no—
29#1831—21no—
30#1831—21no—
31#1817C2212yes—
32#1817C2212yes—
33#1797C2212yes—
34#1797C2212yes—
35C4×C4⋊C8—21no—
36C4×C4⋊C8—21no—
37C4×C22⋊C8C2212yes—
38C4×C22⋊C8C2212yes—
39#1744—21no—
40#1744—21no—
41#1280C2218yes—
42#1280C2218yes—
43C23×Q8C2×C411yescharacteristic
44C22×C4⋊C4C2×C412yes—
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4C2×C412yes—
47C22×C4⋊C4C2×C412yes—
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C42C2×C411yescharacteristic
51C22×C42C2×C411yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C2×C4⋊C8—22no—
58C2×C4⋊C8—22no—
59C2×C22⋊C8C2314yes—
60C2×C22⋊C8C2314yes—
61C2×C4×C8—22no—
62C2×C4×C8—22no—
63#391—21no—
64#391—21no—
65#391—21no—
66#391—21no—
67#391—21no—
68#391—21no—
69#391—21no—
70#391—21no—
71#391—21no—
72#391—21no—
73#391—21no—
74#391—21no—
75#389—21no—
76#389—21no—
77#389—21no—
78#389—21no—
79#389—21no—
80#389—21no—
81#389—21no—
82#389—21no—
83#389—21no—
84#389—21no—
85#389—21no—
86#389—21no—
87#387—22no—
88#387—22no—
89#387—22no—
90#387—22no—
91#387—22no—
92#387—22no—
93#387—22no—
94#387—22no—
95#387—22no—
96#387—22no—
97#387—22no—
98#387—22no—
99#383—22no—
100#383—22no—
101#383—22no—
102#383—22no—
103C2×#95C2×C412yes—
104C2×#95C2×C412yes—
105C2×#95C2×C412yes—
106C2×#95C2×C412yes—
107C2×#95C2×C412yes—
108C2×#95C2×C412yes—
109C2×#95C2×C412yes—
110C2×#95C2312yes—
111C2×#95C2312yes—
112C43D411yescharacteristic
113C43D411yescharacteristic
114C43D411yescharacteristic
115C43D411yescharacteristic
116C43D411yescharacteristic
117C43D411yescharacteristic
118C43D411yescharacteristic
119C43D411yescharacteristic
120#336—22no—
121#336—22no—
122#336—22no—
123#336—22no—
124#336—22no—
125#336—22no—
126#336—22no—
127#336—22no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—24no—
131C22×Q8—42no—
132C22×Q8—42no—
133C23×C4C22×C411yescharacteristic
134C23×C4C22×C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C22×C411yescharacteristic
137C23×C4C22×C412yes—
138C23×C4C22×C412yes—
139C23×C4C22×C412yes—
140C23×C4C22×C412yes—
141C23×C4C22×C411yescharacteristic
142C23×C4C22×C411yescharacteristic
143C23×C4C2411yescharacteristic
144C22×C8—24no—
145C22×C8—24no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—28no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—44no—
164C2×C42—24no—
165C2×C42—24no—
166C2×C42—24no—
167C2×C42—42no—
168C2×C42—42no—
169C2×C42—42no—
170C2×C42—42no—
171C2×C42C22⋊C411yescharacteristic
172C2×C42C22⋊C411yescharacteristic
173C2×C42C22⋊C411yescharacteristic
174C2×C42C22⋊C411yescharacteristic
175C2×C42C22⋊C411yescharacteristic
176C2×C42C22⋊C411yescharacteristic
177C2×C42C22⋊C411yescharacteristic
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×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C4⋊C8—44no—
200C4⋊C8—44no—
201C22⋊C8—28no—
202C22⋊C8—28no—
203C4×C8—44no—
204C4×C8—44no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95—22no—
209#95—22no—
210#95—22no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—22no—
223C24C23×C411yescharacteristic
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—88no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
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—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C411yescharacteristic
268C22×C4C2×C22⋊C411yescharacteristic
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C22⋊C411yescharacteristic
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C22⋊C411yescharacteristic
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4#13114yes—
278C22×C4#13114yes—
279C22×C4C22×D411yescharacteristic
280C22×C4C22×D411yescharacteristic
281C22×C42−1+414yes—
282C2×C8—44no—
283C2×C8—44no—
284C2×C8—44no—
285C2×C8—44no—
286C2×C8—44no—
287C2×C8—44no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—44no—
291C4⋊C4—44no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—44no—
297C4⋊C4—42no—
298C4⋊C4—44no—
299C4⋊C4—42no—
300C42—22no—
301C42—22no—
302C42—22no—
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—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C42—41no—
323C42—41no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42—41no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23C22×C22⋊C411yescharacteristic
333C23#51912yes—
334C23C2×#13112yes—
335C23C2×#13112yes—
336Q8—84no—
337Q8—84no—
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—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—28no—
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—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—84no—
390C2×C4—84no—
391C2×C4—84no—
392C2×C4—84no—
393C2×C4#40812yes—
394C2×C4#40812yes—
395C2×C4#40812yes—
396C2×C4#40812yes—
397C2×C4#41012yes—
398C2×C4#41012yes—
399C2×C4#41312yes—
400C2×C4#41312yes—
401C2×C4#53612yes—
402C2×C4#53612yes—
403C8—84no—
404C8—84no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22#231011yescharacteristic
412C22C2×#40811yescharacteristic
413C22C2×#40811yescharacteristic
414C22C2×#41011yescharacteristic
415C22C2×#41011yescharacteristic
416C22C2×#41311yescharacteristic
417C22C2×#41311yescharacteristic
418C22#298614yes—
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—82no—
433C4—82no—
434C4—82no—
435C4—82no—
436C4#147314yes—
437C2—24no—
438C2C2×#147311yescharacteristic
439C2#1738011yescharacteristic
440C2#1738211yescharacteristic
441C2#1738311yescharacteristic
442C2#2181911yescharacteristic
443C2#2182611yescharacteristic
444C2#2183111yescharacteristic
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 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#28632
#207772
#98802
#98792
#98782
#87052