Finite Group Databasebeta

← #97677

Subgroups — #97677

Order 512.

662 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 148 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#34950C211yesmaximal, characteristic
2#9637C211yesmaximal, characteristic
3#8564C212yesmaximal
4C4×Q8⋊C8C212yesmaximal
5#7571C211yesmaximal, characteristic
6#2586—22no—
7#2582C411yescharacteristic
8#2567C412yes—
9#2551C411yescharacteristic
10#2507—22no—
11#2451—22no—
12#2399—22no—
13C4×C4⋊Q8—22no—
14C4×C4⋊Q8C2211yescharacteristic
15#2295—22no—
16C42×Q8C2212yes—
17#1842C2211yescharacteristic
18C4×C4⋊C8C2212yes—
19C42×C8C2211yescharacteristic
20C2×Q8⋊C8—22no—
21C2×Q8⋊C8—22no—
22C2×Q8⋊C8—22no—
23#1279—22no—
24#1279—22no—
25#1272—22no—
26C2×C4⋊Q8—22no—
27C2×C4⋊Q8C2×C411yescharacteristic
28C2×C4×Q8—22no—
29C2×C4×Q8C2×C412yes—
30C2×C4×Q8D412yes—
31C2×C4×Q8D412yes—
32C2×C4×Q8D412yes—
33C2×C4⋊C8—22no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—22no—
36C2×C4×C8—21no—
37C2×C4×C8—22no—
38C2×C4×C8—22no—
39#398—24no—
40#398—22no—
41#398—22no—
42#395—22no—
43#395—24no—
44#395—22no—
45#391—24no—
46#391—22no—
47#391—22no—
48#391D412yes—
49#389—24no—
50#389—22no—
51#389—22no—
52#389—22no—
53#389—22no—
54#389—22no—
55#387—24no—
56#387—24no—
57#384—22no—
58#384C2×C411yescharacteristic
59C4×C4⋊C4—24no—
60C4×C4⋊C4—22no—
61C4×C4⋊C4—22no—
62C4×C4⋊C4—22no—
63C4×C4⋊C4—22no—
64C4×C4⋊C4C2×C412yes—
65C4×C4⋊C4D412yes—
66C4×C4⋊C4D412yes—
67#376—22no—
68C43—22no—
69C43C2311yescharacteristic
70#336—22no—
71Q8⋊C8—28no—
72Q8⋊C8—44no—
73Q8⋊C8—44no—
74C22×Q8—22no—
75C22×Q8C22⋊C412yes—
76C22×Q8C22⋊C412yes—
77C22×C8—41no—
78C22×C8—42no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—22no—
83C4⋊Q8—44no—
84C4⋊Q8—44no—
85C4×Q8—22no—
86C4×Q8—22no—
87C4×Q8—24no—
88C4×Q8—22no—
89C4×Q8—22no—
90C4×Q8—22no—
91C4×Q8—22no—
92C4×Q8—42no—
93C4×Q8—42no—
94C4×Q8—42no—
95C4×Q8—82no—
96C4×Q8—82no—
97C4×Q8SD1614yes—
98C4×Q8Q1614yes—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—24no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4C22⋊C412yes—
110C2×C4⋊C4C22⋊C412yes—
111C2×C4⋊C4C22⋊C412yes—
112C2×C4⋊C4C22⋊C412yes—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—22no—
116C2×C42—22no—
117C2×C42—22no—
118C2×C42—22no—
119C2×C42—22no—
120C2×C42C22×C411yescharacteristic
121C2×C42C2×D412yes—
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D412yes—
125C4⋊C8—24no—
126C4⋊C8—42no—
127C4⋊C8—42no—
128C4⋊C8—42no—
129C4⋊C8—42no—
130C4×C8—24no—
131C4×C8—22no—
132C4×C8—42no—
133C4×C8—41no—
134C4×C8—42no—
135C4×C8—42no—
136#95—22no—
137#95—24no—
138#95—22no—
139#95—24no—
140#95—24no—
141#95—22no—
142#95—22no—
143#95—22no—
144#95—24no—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—48no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—82no—
156C2×Q8#10314yes—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4C2×C22⋊C411yescharacteristic
164C22×C4C2×C22⋊C412yes—
165C22×C4#12011yescharacteristic
166C22×C4#12012yes—
167C22×C4#12011yescharacteristic
168C2×C8—42no—
169C2×C8—44no—
170C2×C8—44no—
171C2×C8—82no—
172C2×C8—82no—
173C2×C8—82no—
174C2×C8—81no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—44no—
182C4⋊C4—42no—
183C4⋊C4—48no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—82no—
191C4⋊C4—84no—
192C4⋊C4—84no—
193C4⋊C4—82no—
194C4⋊C4#10314yes—
195C4⋊C4#10414yes—
196C42—22no—
197C42—22no—
198C42—24no—
199C42—24no—
200C42—21no—
201C42—21no—
202C42—41no—
203C42—44no—
204C42—42no—
205C42—42no—
206C42—42no—
207C42—42no—
208C42—42no—
209C42—42no—
210C42—42no—
211C42—42no—
212C42—82no—
213C42#13111yescharacteristic
214C42#13112yes—
215C42#13111yescharacteristic
216C42C2×SD1612yes—
217C42C2×Q1612yes—
218C42#13712yes—
219C42#13712yes—
220C23#37911yescharacteristic
221Q8—24no—
222Q8—24no—
223Q8—44no—
224Q8—42no—
225Q8—42no—
226Q8—82no—
227Q8—88no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—24no—
234C2×C4—24no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4#40811yescharacteristic
252C2×C4#40811yescharacteristic
253C2×C4#40812yes—
254C2×C4#40812yes—
255C2×C4C2×#10312yes—
256C2×C4#41912yes—
257C2×C4C2×#10412yes—
258C2×C4#42112yes—
259C2×C4#44812yes—
260C2×C4#44812yes—
261C2×C4#45112yes—
262C2×C4#45112yes—
263C2×C4#45311yescharacteristic
264C2×C4#45511yescharacteristic
265C8—44no—
266C8—84no—
267C8—161no—
268C22#178011yescharacteristic
269C22#178712yes—
270C22#178912yes—
271C22#179211yescharacteristic
272C22#179411yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—44no—
278C4—44no—
279C4—41no—
280C4—44no—
281C4—82no—
282C4—82no—
283C4—82no—
284C4#148112yes—
285C4#148512yes—
286C4#149312yes—
287C4#149712yes—
288C4#162311yescharacteristic
289C4#163311yescharacteristic
290C4#164512yes—
291C2#831412yes—
292C2#832011yescharacteristic
293C2#843912yes—
294C2#844011yescharacteristic
295C2#845111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#379
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#349502
#96372
#85642
C4×Q8⋊C82
#75712