Finite Group Databasebeta

← #103699

Subgroups — #103699

Order 512.

481 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 481 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29286C211yesmaximal, characteristic
2#28717C211yesmaximal, characteristic
3#28687C211yesmaximal, characteristic
4#9692C211yesmaximal, characteristic
5#9673C211yesmaximal, characteristic
6#7570C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#498—21no—
9C2×#487—21no—
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2086—22no—
14#2084—22no—
15#2072—22no—
16#1990—21no—
17#1990—21no—
18#1988—21no—
19#1988—21no—
20#1948—22no—
21#1947—21no—
22#1947—21no—
23#1842C2211yescharacteristic
24#1803—22no—
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28C2×#332—22no—
29C2×Q8⋊C8—22no—
30#1271—22no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38#498—42no—
39#498—42no—
40#487—42no—
41#487—42no—
42C2×#107—22no—
43C2×#106—24no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D412yes—
49C2×C4⋊C8D412yes—
50C2×#103—24no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384D411yescharacteristic
64#384D411yescharacteristic
65#384D412yes—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C43C2311yescharacteristic
71#340—24no—
72#340—24no—
73#340—22no—
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336D412yes—
79#332—44no—
80Q8⋊C8—44no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—41no—
84C22×C8—22no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—41no—
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—21no—
93C4⋊Q8—21no—
94C4⋊Q8—42no—
95C4⋊Q8—42no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—41no—
103C4⋊Q8—41no—
104C4⋊Q8SD1612yes—
105C4⋊Q8SD1612yes—
106C4×Q8—42no—
107C4×Q8—42no—
108C4×Q8—42no—
109C4×Q8—42no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42#4111yescharacteristic
137#107—82no—
138#106—48no—
139C4⋊C8—24no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—42no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149#103—48no—
150C4×C8—41no—
151C4×C8—41no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—42no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—81no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—81no—
172C2×Q8—81no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4#12011yescharacteristic
179C22×C4#12011yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12711yescharacteristic
185C2×C8—24no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—81no—
196C2×C8—81no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—81no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C42—21no—
228C42—21no—
229C42—22no—
230C42—22no—
231C42—41no—
232C42—82no—
233C42—82no—
234C42C2×SD1611yescharacteristic
235C42C2×SD1611yescharacteristic
236C42#13511yescharacteristic
237C42#13511yescharacteristic
238C42#13512yes—
239C42AGL(1,ℤ/8)11yescharacteristic
240C42AGL(1,ℤ/8)11yescharacteristic
241C42AGL(1,ℤ/8)12yes—
242C42#13711yescharacteristic
243C42#13711yescharacteristic
244C23#39211yescharacteristic
245Q8—44no—
246Q8—44no—
247Q8—82no—
248Q8—82no—
249Q8—161no—
250Q8—161no—
251Q8—161no—
252Q8—161no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4#44811yescharacteristic
278C2×C4#44811yescharacteristic
279C2×C4#44911yescharacteristic
280C2×C4#44911yescharacteristic
281C2×C4#44912yes—
282C2×C4#45011yescharacteristic
283C2×C4#45011yescharacteristic
284C2×C4#45211yescharacteristic
285C2×C4#45211yescharacteristic
286C2×C4#45311yescharacteristic
287C2×C4#45411yescharacteristic
288C2×C4#45612yes—
289C2×C4#46312yes—
290C2×C4#46511yescharacteristic
291C2×C4#46511yescharacteristic
292C2×C4#46811yescharacteristic
293C2×C4#46811yescharacteristic
294C2×C4#47312yes—
295C2×C4#49511yescharacteristic
296C2×C4#49611yescharacteristic
297C8—44no—
298C8—82no—
299C8—82no—
300C8—82no—
301C22#200011yescharacteristic
302C22#200011yescharacteristic
303C22#200511yescharacteristic
304C22#200611yescharacteristic
305C22#200911yescharacteristic
306C22#201211yescharacteristic
307C22#202011yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—41no—
315C4—82no—
316C4—82no—
317C4—161no—
318C4—161no—
319C4—162no—
320C4#162011yescharacteristic
321C4#162311yescharacteristic
322C4#162611yescharacteristic
323C4#162611yescharacteristic
324C4#165212yes—
325C4#165412yes—
326C4#167912yes—
327C4#169912yes—
328C2#1007411yescharacteristic
329C2#1011711yescharacteristic
330C2#1018711yescharacteristic
331C2#1020011yescharacteristic
332C2#1023011yescharacteristic
333C2#1025111yescharacteristic
334C2#1027011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ 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
#292862
#287172
#286872
#96922
#96732
#75702
#70312