Finite Group Databasebeta

← #98227

Subgroups — #98227

Order 512.

601 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36598C211yesmaximal, characteristic
2#9898C211yesmaximal, characteristic
3#9692C211yesmaximal, characteristic
4#8587C211yesmaximal, characteristic
5#8564C211yesmaximal, characteristic
6#8564C211yesmaximal, characteristic
7#7571C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9#2862—21no—
10#2582C412yes—
11#2571—21no—
12#2570—22no—
13#2568—21no—
14#2511—22no—
15#2446—22no—
16#2365—21no—
17#2355—21no—
18#2355C412yes—
19C4×C4⋊Q8—21no—
20C4×C4⋊Q8C2211yescharacteristic
21C42×Q8C2211yescharacteristic
22#1842C2211yescharacteristic
23#1842C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C2×#333—21no—
27C2×#332—22no—
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30#1296—21no—
31#1296—22no—
32#1279—21no—
33#1279—21no—
34#1272—22no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8D411yescharacteristic
38C2×C4⋊Q8D412yes—
39C2×C4×Q8—22no—
40C2×C4×Q8C2×C412yes—
41C2×C4×Q8C2×C411yescharacteristic
42C2×C4×Q8D411yescharacteristic
43C2×C4×Q8D411yescharacteristic
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54#400—24no—
55#400—24no—
56#398—24no—
57#391—22no—
58#391—22no—
59#391—22no—
60#391—22no—
61#391—22no—
62#391—22no—
63#391D412yes—
64#389—22no—
65#389—22no—
66#389—22no—
67#389—21no—
68#389—21no—
69#387—24no—
70#387—24no—
71#387—24no—
72#384—21no—
73#384—21no—
74#384C2×C412yes—
75#384D411yescharacteristic
76#384D412yes—
77#382—22no—
78#382—22no—
79#382—22no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4C2×C411yescharacteristic
89C4×C4⋊C4D411yescharacteristic
90C4×C4⋊C4D411yescharacteristic
91C43—21no—
92C43C2311yescharacteristic
93#336—21no—
94#336—21no—
95#333—42no—
96#332—44no—
97Q8⋊C8—42no—
98Q8⋊C8—42no—
99C22×Q8—22no—
100C22×Q8C22⋊C411yescharacteristic
101C22×Q8C22⋊C412yes—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—42no—
111C4⋊Q8—42no—
112C4⋊Q8—41no—
113C4⋊Q8—41no—
114C4⋊Q8—41no—
115C4⋊Q8—41no—
116C4⋊Q8—41no—
117C4⋊Q8—41no—
118C4⋊Q8—41no—
119C4⋊Q8—41no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—21no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—42no—
129C4×Q8—42no—
130C4×Q8—82no—
131C4×Q8—82no—
132C4×Q8SD1612yes—
133C4×Q8Q1612yes—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4C22⋊C411yescharacteristic
149C2×C4⋊C4C22⋊C411yescharacteristic
150C2×C4⋊C4C22⋊C411yescharacteristic
151C2×C4⋊C4C22⋊C412yes—
152C2×C4⋊C4C22⋊C414yes—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—22no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—24no—
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—42no—
173C4⋊C8—42no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4×C8—41no—
183C4×C8—41no—
184C4×C8—41no—
185C4×C8—41no—
186#95—24no—
187#95—24no—
188#95—24no—
189#95—24no—
190#95—24no—
191#95—24no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—22no—
196#95—22no—
197C2×Q8—21no—
198C2×Q8—21no—
199C2×Q8—21no—
200C2×Q8—21no—
201C2×Q8—22no—
202C2×Q8—21no—
203C2×Q8—22no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8#10312yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4C2×C22⋊C411yescharacteristic
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C2×C22⋊C411yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12011yescharacteristic
226C22×C4#12011yescharacteristic
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—81no—
230C2×C8—81no—
231C2×C8—81no—
232C2×C8—81no—
233C2×C8—81no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—82no—
269C4⋊C4—84no—
270C4⋊C4#10312yes—
271C42—21no—
272C42—21no—
273C42—22no—
274C42—22no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—41no—
280C42—42no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C42—41no—
290C42—84no—
291C42C2×SD1611yescharacteristic
292C42C2×Q1611yescharacteristic
293C42#13511yescharacteristic
294C42#13511yescharacteristic
295C42#13511yescharacteristic
296C42#13511yescharacteristic
297C42AGL(1,ℤ/8)11yescharacteristic
298C42AGL(1,ℤ/8)11yescharacteristic
299C42#13711yescharacteristic
300C42#13711yescharacteristic
301C42#13711yescharacteristic
302C42#13711yescharacteristic
303C23#37911yescharacteristic
304Q8—22no—
305Q8—22no—
306Q8—41no—
307Q8—41no—
308Q8—82no—
309Q8—82no—
310Q8—82no—
311Q8—82no—
312Q8—82no—
313Q8—82no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4#41311yescharacteristic
345C2×C4#41311yescharacteristic
346C2×C4C2×#10311yescharacteristic
347C2×C4#41611yescharacteristic
348C2×C4#41611yescharacteristic
349C2×C4#41711yescharacteristic
350C2×C4#41711yescharacteristic
351C2×C4#41911yescharacteristic
352C2×C4#44811yescharacteristic
353C2×C4#44811yescharacteristic
354C2×C4#44911yescharacteristic
355C2×C4#44911yescharacteristic
356C2×C4#44911yescharacteristic
357C2×C4#44911yescharacteristic
358C2×C4#45111yescharacteristic
359C2×C4#45111yescharacteristic
360C2×C4#45211yescharacteristic
361C2×C4#45211yescharacteristic
362C2×C4#45211yescharacteristic
363C2×C4#45211yescharacteristic
364C2×C4#45311yescharacteristic
365C2×C4#45411yescharacteristic
366C2×C4#45511yescharacteristic
367C2×C4#45611yescharacteristic
368C8—82no—
369C8—82no—
370C8—161no—
371C8—161no—
372C22#178511yescharacteristic
373C22#178711yescharacteristic
374C22#178811yescharacteristic
375C22#178811yescharacteristic
376C22#179211yescharacteristic
377C22#179311yescharacteristic
378C22#179611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—42no—
387C4—42no—
388C4—81no—
389C4—82no—
390C4—82no—
391C4—81no—
392C4—84no—
393C4#154211yescharacteristic
394C4#155011yescharacteristic
395C4#155411yescharacteristic
396C4#155911yescharacteristic
397C4#162011yescharacteristic
398C4#162611yescharacteristic
399C4#163011yescharacteristic
400C4#163611yescharacteristic
401C4#164011yescharacteristic
402C4#164011yescharacteristic
403C4#164811yescharacteristic
404C4#165311yescharacteristic
405C2#834311yescharacteristic
406C2#838911yescharacteristic
407C2#842511yescharacteristic
408C2#842711yescharacteristic
409C2#844511yescharacteristic
410C2#844811yescharacteristic
411C2#847011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#379
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#365982
#98982
#96922
#85872
#85642
#75712