Finite Group Databasebeta

← #97507

Subgroups — #97507

Order 512.

620 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic
2#9870C211yesmaximal, characteristic
3#9637C211yesmaximal, characteristic
4#9637C211yesmaximal, characteristic
5#8587C211yesmaximal, characteristic
6#8587C211yesmaximal, characteristic
7#8586C211yesmaximal, characteristic
8#2806C414yes—
9#2584—22no—
10#2582—22no—
11#2567—21no—
12#2552—21no—
13#2552—21no—
14#2507—22no—
15#2369—21no—
16#2365—21no—
17Q8×C4⋊C4—21no—
18C4×C4⋊Q8C2211yescharacteristic
19C4×C4⋊Q8C2211yescharacteristic
20C4×C4⋊Q8C2211yescharacteristic
21#1842C2211yescharacteristic
22#1842C2211yescharacteristic
23#1842C2211yescharacteristic
24C42×C8C2211yescharacteristic
25C2×#333—21no—
26C2×#333—21no—
27C2×#332—21no—
28C2×Q8⋊C8—22no—
29C2×Q8⋊C8—22no—
30#1296—21no—
31#1296—21no—
32#1296—21no—
33#1279—22no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×#125—22no—
38C2×C4×Q8—22no—
39C2×C4×Q8—21no—
40C2×C4×Q8D412yes—
41C2×C4×Q8D412yes—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
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#398—24no—
55#398—24no—
56#398—24no—
57#395—24no—
58#391—22no—
59#391—24no—
60#391—21no—
61#391C2×C412yes—
62#391C2×C412yes—
63#389—22no—
64#389—22no—
65#389—24no—
66#389—22no—
67#389—22no—
68#389—22no—
69#389—24no—
70#389—21no—
71#389—21no—
72#389—21no—
73#389—21no—
74#389—21no—
75#389C2×C412yes—
76#387—24no—
77#384—22no—
78#384—22no—
79#384D411yescharacteristic
80#384D411yescharacteristic
81#384D411yescharacteristic
82C4×C4⋊C4—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4D412yes—
90C43C2311yescharacteristic
91#333—42no—
92#333—42no—
93#332—42no—
94Q8⋊C8—44no—
95Q8⋊C8—44no—
96C22×Q8—21no—
97C22×Q8C22⋊C412yes—
98C22×Q8C22⋊C412yes—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—21no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8SD1612yes—
112C4⋊Q8SD1612yes—
113C4⋊Q8Q1612yes—
114C4⋊Q8Q1612yes—
115#125—82no—
116#125—82no—
117C4×Q8—42no—
118C4×Q8—42no—
119C4×Q8—42no—
120C4×Q8—42no—
121C4×Q8—41no—
122C4×Q8—41no—
123C4×Q8—41no—
124C4×Q8—41no—
125C4×Q8—82no—
126C4×Q8—82no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4C22⋊C412yes—
146C2×C4⋊C4C22⋊C412yes—
147C2×C4⋊C4C22⋊C412yes—
148C2×C4⋊C4C22⋊C412yes—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—24no—
153C2×C42C22×C411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C4⋊C8—42no—
161C4⋊C8—42no—
162C4⋊C8—42no—
163C4⋊C8—41no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4×C8—22no—
176C4×C8—22no—
177C4×C8—22no—
178C4×C8—41no—
179C4×C8—41no—
180C4×C8—41no—
181#95—24no—
182#95—24no—
183#95—24no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—22no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—42no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8#10314yes—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4C2×C22⋊C411yescharacteristic
211C22×C4C2×C22⋊C411yescharacteristic
212C22×C4C2×C22⋊C411yescharacteristic
213C22×C4#12011yescharacteristic
214C22×C4#12011yescharacteristic
215C22×C4#12011yescharacteristic
216C22×C4#12011yescharacteristic
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—82no—
258C4⋊C4—82no—
259C4⋊C4—84no—
260C4⋊C4—84no—
261C4⋊C4—84no—
262C4⋊C4—84no—
263C4⋊C4#10314yes—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—41no—
271C42—42no—
272C42—42no—
273C42—42no—
274C42—42no—
275C42—42no—
276C42—42no—
277C42—84no—
278C42C2×SD1611yescharacteristic
279C42C2×SD1611yescharacteristic
280C42C2×Q1611yescharacteristic
281C42C2×Q1611yescharacteristic
282C42#13511yescharacteristic
283C42#13511yescharacteristic
284C42AGL(1,ℤ/8)11yescharacteristic
285C42#13711yescharacteristic
286C42#13711yescharacteristic
287C42#13711yescharacteristic
288C42#13711yescharacteristic
289C42#13711yescharacteristic
290C23#37911yescharacteristic
291Q8—44no—
292Q8—44no—
293Q8—42no—
294Q8—42no—
295Q8—42no—
296Q8—42no—
297Q8—82no—
298Q8—82no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4C2×#10311yescharacteristic
327C2×C4C2×#10311yescharacteristic
328C2×C4#41611yescharacteristic
329C2×C4#41711yescharacteristic
330C2×C4#41911yescharacteristic
331C2×C4#41911yescharacteristic
332C2×C4#44811yescharacteristic
333C2×C4#44811yescharacteristic
334C2×C4#44811yescharacteristic
335C2×C4#44811yescharacteristic
336C2×C4#44911yescharacteristic
337C2×C4#44911yescharacteristic
338C2×C4#45111yescharacteristic
339C2×C4#45111yescharacteristic
340C2×C4#45111yescharacteristic
341C2×C4#45111yescharacteristic
342C2×C4#45211yescharacteristic
343C2×C4#45211yescharacteristic
344C2×C4#45311yescharacteristic
345C2×C4#45311yescharacteristic
346C2×C4#45411yescharacteristic
347C2×C4#45511yescharacteristic
348C2×C4#45511yescharacteristic
349C2×C4#45611yescharacteristic
350C8—44no—
351C8—161no—
352C8—161no—
353C8—161no—
354C22#178711yescharacteristic
355C22#178711yescharacteristic
356C22#178811yescharacteristic
357C22#179111yescharacteristic
358C22#179211yescharacteristic
359C22#179211yescharacteristic
360C22#179311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—44no—
368C4—41no—
369C4—44no—
370C4—82no—
371C4—82no—
372C4—82no—
373C4—82no—
374C4#162211yescharacteristic
375C4#162311yescharacteristic
376C4#162611yescharacteristic
377C4#163211yescharacteristic
378C4#163311yescharacteristic
379C4#163611yescharacteristic
380C4#164311yescharacteristic
381C4#164411yescharacteristic
382C4#164511yescharacteristic
383C4#164511yescharacteristic
384C4#164811yescharacteristic
385C4#165311yescharacteristic
386C2#835511yescharacteristic
387C2#835611yescharacteristic
388C2#835811yescharacteristic
389C2#844811yescharacteristic
390C2#845011yescharacteristic
391C2#845111yescharacteristic
392C2#853211yescharacteristic
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
#598712
#98702
#96372
#85872
#85862