Finite Group Databasebeta

← #219183

Subgroups — #219183

Order 512.

510 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23816C211yesmaximal, characteristic
2#22311C211yesmaximal, characteristic
3#22242C211yesmaximal, characteristic
4#9877C211yesmaximal, characteristic
5#9647C211yesmaximal, characteristic
6#9548C212yesmaximal
7#9547C212yesmaximal
8#8850C212yesmaximal
9#8848C212yesmaximal
10#8811C211yesmaximal, characteristic
11#8134C211yesmaximal, characteristic
12C2×#446C2212yes—
13C4×C4⋊Q8C2211yescharacteristic
14C4×C4⋊Q8C2211yescharacteristic
15#2100C412yes—
16#2072C412yes—
17#2043C412yes—
18#2024C412yes—
19#1985—22no—
20#1984C2212yes—
21#1939C2212yes—
22#1917—22no—
23#1917—22no—
24#1917—22no—
25#1831C2211yescharacteristic
26#1831C2211yescharacteristic
27#1770C2212yes—
28C4×#103C2212yes—
29C4×#103C2212yes—
30#1744C2211yescharacteristic
31#1744C2211yescharacteristic
32C4×#97C2211yescharacteristic
33C2×#335C2212yes—
34C2×#334C2212yes—
35C2×Q8⋊C8C2212yes—
36C2×Q8⋊C8C2212yes—
37#1279C2212yes—
38#1279C2212yes—
39#1273C2211yescharacteristic
40#1273C2211yescharacteristic
41#1273C2211yescharacteristic
42#1273C2211yescharacteristic
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×C4⋊Q8C2×C411yescharacteristic
45C2×C4×Q8—21no—
46C2×C4×Q8C2312yes—
47#446—42no—
48#446—42no—
49C2×C4⋊C8—22no—
50C2×C4⋊C8—22no—
51C2×C4⋊C8C2312yes—
52C2×C4⋊C8C2312yes—
53C2×#103C2×C412yes—
54C2×#103C2×C412yes—
55C2×#103C2×C412yes—
56C2×#103C2×C412yes—
57C2×#97—22no—
58C2×#97—21no—
59C2×#97—21no—
60C2×#97—22no—
61C2×C4×C8C2311yescharacteristic
62C2×C4×C8C2311yescharacteristic
63C2×C4×C8C2311yescharacteristic
64C2×C4×C8C2311yescharacteristic
65C2×C4×C8C2311yescharacteristic
66C2×C4×C8C2311yescharacteristic
67#391—21no—
68#391C2×C412yes—
69#389—21no—
70#389—21no—
71#389—21no—
72#389C2×C412yes—
73#384C2×C411yescharacteristic
74#384C2×C411yescharacteristic
75C4×C4⋊C4—21no—
76C4×C4⋊C4—21no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4C2312yes—
79C43C2311yescharacteristic
80#340C2×C412yes—
81#340C2×C412yes—
82#340C2×C412yes—
83#340C2×C412yes—
84#336—24no—
85#336—22no—
86#336—22no—
87#336—21no—
88#336—21no—
89#336—21no—
90#336—21no—
91#336C2×C412yes—
92#336C2×C412yes—
93#336D412yes—
94#336D412yes—
95#335—42no—
96#334—42no—
97Q8⋊C8—42no—
98Q8⋊C8—42no—
99C22×Q8—21no—
100C22×Q8C22×C412yes—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8C22×C412yes—
106C22×C8C22×C412yes—
107C22×C8C2×D412yes—
108C22×C8C2×D412yes—
109C4⋊Q8—42no—
110C4⋊Q8—42no—
111C4×Q8—22no—
112C4×Q8—22no—
113C4×Q8—22no—
114C4×Q8—22no—
115C4×Q8—82no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4C22×C412yes—
126C2×C4⋊C4C22×C412yes—
127C2×C4⋊C4C22×C412yes—
128C2×C42—22no—
129C2×C42—22no—
130C2×C42C22×C411yescharacteristic
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42C2411yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—44no—
142C4⋊C8—82no—
143#103—42no—
144#103—42no—
145#103—42no—
146#103—42no—
147#97—42no—
148#97—42no—
149#97—44no—
150#97—82no—
151C4×C8—21no—
152C4×C8—21no—
153C4×C8—21no—
154C4×C8—21no—
155C4×C8—21no—
156C4×C8—21no—
157C4×C8—21no—
158C4×C8—21no—
159C4×C8—21no—
160C4×C8—21no—
161C4×C8—21no—
162C4×C8—21no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—42no—
174C2×Q8—81no—
175C2×Q8—81no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4C4×D411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4C4×D411yescharacteristic
184C22×C4C23×C411yescharacteristic
185C22×C4C22×D411yescharacteristic
186C22×C4C2×#4111yescharacteristic
187C2×C8—22no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4—82no—
226C4⋊C4—81no—
227C42—22no—
228C42—22no—
229C42—22no—
230C42—22no—
231C42—41no—
232C42—41no—
233C42—42no—
234C42—42no—
235C42—42no—
236C42—42no—
237C42H(5,𝔽2)11yescharacteristic
238C42H(5,𝔽2)11yescharacteristic
239C422−1+411yescharacteristic
240C422−1+411yescharacteristic
241C23C2×C4×D411yescharacteristic
242Q8—42no—
243Q8—42no—
244Q8—42no—
245Q8—42no—
246Q8—84no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
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—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4#52011yescharacteristic
274C2×C4#52011yescharacteristic
275C2×C4#53511yescharacteristic
276C2×C4#53611yescharacteristic
277C2×C4#54211yescharacteristic
278C2×C4#54211yescharacteristic
279C2×C4#56812yes—
280C2×C4#56812yes—
281C2×C4#57712yes—
282C2×C4#57812yes—
283C8—42no—
284C8—42no—
285C8—42no—
286C8—42no—
287C8—42no—
288C8—42no—
289C8—82no—
290C8—82no—
291C22#232611yescharacteristic
292C22#293011yescharacteristic
293C22#293011yescharacteristic
294C22#294911yescharacteristic
295C22#295011yescharacteristic
296C22#295611yescharacteristic
297C22#295611yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4—82no—
306C4—82no—
307C4—82no—
308C4#299512yes—
309C4#299512yes—
310C4#322512yes—
311C4#324212yes—
312C2#1795111yescharacteristic
313C2#1795211yescharacteristic
314C2#1795311yescharacteristic
315C2#1795311yescharacteristic
316C2#2221511yescharacteristic
317C2#2222911yescharacteristic
318C2#2223711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socle, prime radicalC23C2×C4×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ #1744 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#238162
#223112
#222422
#98772
#96472
#95482
#95472
#88502
#88482
#88112
#81342