Finite Group Databasebeta

← #120895

Subgroups — #120895

Order 512.

449 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21975C211yesmaximal, characteristic
2#10856C211yesmaximal, characteristic
3#8128C211yesmaximal, characteristic
4#8093C211yesmaximal, characteristic
5#8092C211yesmaximal, characteristic
6#8081C211yesmaximal, characteristic
7#7941C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1939—21no—
16#1939—21no—
17#1851—22no—
18#1843—21no—
19#1832—21no—
20C2×#344—22no—
21#1309—22no—
22#1303—22no—
23#1303—21no—
24#1303—21no—
25#1301—21no—
26#1301—21no—
27#1284C414yes—
28C22×M16—21no—
29C22×M16D412yes—
30C2×#117—21no—
31C22×C42C2311yescharacteristic
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#423—21no—
45#423—21no—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423D412yes—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—22no—
58C2×C4⋊C8—22no—
59C2×C4⋊C8D411yescharacteristic
60C2×C4⋊C8D411yescharacteristic
61C2×C4⋊C8Q812yes—
62#407—21no—
63#407C2×C412yes—
64C2×C22⋊C8—21no—
65C4×M16—21no—
66C4×M16—21no—
67C2×C4×C8—21no—
68#383Q812yes—
69#382—21no—
70#381C2×C412yes—
71#380—21no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C4×C4⋊C4D411yescharacteristic
75C4×C4⋊C4D411yescharacteristic
76C4×C22⋊C4—21no—
77C4×C22⋊C4—21no—
78C4×C22⋊C4C2×C412yes—
79#376—21no—
80#376—21no—
81C43—21no—
82#344—44no—
83#336—22no—
84#336—22no—
85C23×C4C22×C411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4#4111yescharacteristic
88C2×M16—22no—
89C2×M16—22no—
90C2×M16—22no—
91C2×M16—22no—
92C2×M16—42no—
93C2×M16—42no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—42no—
97C2×M16—42no—
98C22×C8—22no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—22no—
102#117—22no—
103#117—22no—
104#117—41no—
105#117—41no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—41no—
109C2×C22⋊C4—22no—
110C2×C22⋊C4—22no—
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—22no—
114C2×C42—41no—
115C2×C42—41no—
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×Q811yescharacteristic
120C2×C42C2×Q811yescharacteristic
121C2×C42#4111yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125C2×C42#4111yescharacteristic
126C2×C42#4111yescharacteristic
127C2×C42#4111yescharacteristic
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—21no—
134C4⋊C8—21no—
135C4⋊C8—22no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—82no—
145C4⋊C8—82no—
146C22⋊C8—22no—
147C22⋊C8—22no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152#97—41no—
153#97—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—41no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162#95—41no—
163#95C4⋊C412yes—
164#95C4⋊C412yes—
165C24C4×D411yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—81no—
175C22×C4C2×C4⋊C411yescharacteristic
176C22×C4#11711yescharacteristic
177C22×C4#11711yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4C4×Q811yescharacteristic
181C22×C4#12011yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4C22⋊Q811yescharacteristic
184C22×C4C22⋊Q811yescharacteristic
185C22×C4C22⋊Q811yescharacteristic
186C22×C4#12311yescharacteristic
187C22×C4#12311yescharacteristic
188C22×C4#12311yescharacteristic
189C22×C4#12411yescharacteristic
190C22×C4#12511yescharacteristic
191C22×C4#12611yescharacteristic
192C22×C4#12611yescharacteristic
193M16—44no—
194M16—82no—
195M16—81no—
196M16—81no—
197M16—82no—
198M16—82no—
199M16—82no—
200C2×C8—44no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—42no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C22⋊C4—24no—
218C22⋊C4—42no—
219C22⋊C4—82no—
220C42—42no—
221C42—42no—
222C42—41no—
223C42—41no—
224C42—41no—
225C42—41no—
226C42—82no—
227C42—82no—
228C42#12111yescharacteristic
229C42#12111yescharacteristic
230C42C22⋊Q811yescharacteristic
231C42C22⋊Q811yescharacteristic
232C42#12311yescharacteristic
233C42#12311yescharacteristic
234C42#12411yescharacteristic
235C42#12411yescharacteristic
236C42#12411yescharacteristic
237C42#12511yescharacteristic
238C42#12511yescharacteristic
239C42#12511yescharacteristic
240C42#12511yescharacteristic
241C42#12611yescharacteristic
242C42#12611yescharacteristic
243C42C4⋊Q811yescharacteristic
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23#38511yescharacteristic
249C23#38711yescharacteristic
250C23#38811yescharacteristic
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4#38211yescharacteristic
283C2×C4#38711yescharacteristic
284C2×C4#38811yescharacteristic
285C2×C4#38911yescharacteristic
286C2×C4#39311yescharacteristic
287C2×C4#39411yescharacteristic
288C2×C4#39711yescharacteristic
289C2×C4#39811yescharacteristic
290C2×C4#39811yescharacteristic
291C2×C4#40011yescharacteristic
292C2×C4#40011yescharacteristic
293C2×C4#40011yescharacteristic
294C2×C4#45311yescharacteristic
295C2×C4#45411yescharacteristic
296C2×C4#45511yescharacteristic
297C2×C4#45611yescharacteristic
298C8—82no—
299C8—82no—
300C8—82no—
301C8—81no—
302C8—82no—
303C8—81no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—81no—
313C22—81no—
314C22#144211yescharacteristic
315C22#185911yescharacteristic
316C22#186011yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—82no—
328C4—84no—
329C4#202711yescharacteristic
330C4#202811yescharacteristic
331C4#203711yescharacteristic
332C4#203811yescharacteristic
333C4#208012yes—
334C2—21no—
335C2—21no—
336C2—41no—
337C2—41no—
338C2#1127611yescharacteristic
339C2#1128011yescharacteristic
340C2#1128111yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1442
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#219752
#108562
#81282
#80932
#80922
#80812
#79412