Finite Group Databasebeta

← #119017

Subgroups — #119017

Order 512.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21838C211yesmaximal, characteristic
2C2×#1998C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4#8042C211yesmaximal, characteristic
5#8028C211yesmaximal, characteristic
6C2×#1291C211yesmaximal, characteristic
7#7876C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2285C2211yescharacteristic
15#1998—22no—
16#1998C414yescomplemented
17#1992—22no—
18#1989—22no—
19#1824—21no—
20#1823—21no—
21C2×#343—21no—
22C2×#343—21no—
23#1528—22no—
24#1528—22no—
25C2×#330—22no—
26#1296—22no—
27#1295—22no—
28#1291—22no—
29#1277—22no—
30C22×M16—21no—
31C22×M16—21no—
32C22×M16—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125C2×C412yes—
44C2×#125D412yes—
45C2×#117—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4D411yescharacteristic
49C22×C4⋊C4D411yescharacteristic
50C22×C42C2311yescharacteristic
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432D412yes—
59#423—21no—
60#423—21no—
61#423—21no—
62#423C2×C412yes—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8D412yes—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C4×M16—21no—
70C4×M16—21no—
71C4×M16—21no—
72C4×M16—21no—
73C4×M16—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16C2×C412yes—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97D412yes—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83#384D412yes—
84#382—21no—
85#380—21no—
86#380—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89#343—24no—
90#343—24no—
91#340—24no—
92#340—24no—
93#330—28no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—24no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—44no—
103C2×M16—42no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—44no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114#125—22no—
115#125—22no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—22no—
120#125—22no—
121#125—22no—
122#125—41no—
123#125—41no—
124#125—41no—
125#125—41no—
126#125—41no—
127#125—41no—
128#125—41no—
129#125—41no—
130#117—82no—
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—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4C22⋊C412yes—
157C2×C4⋊C4C22⋊C412yes—
158C2×C22⋊C4—41no—
159C2×C42—41no—
160C2×C42C22×C411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C22⋊C8—22no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184#97—22no—
185#97—22no—
186#97—22no—
187#97—22no—
188#97—41no—
189#97—41no—
190#97—41no—
191#97—41no—
192C4×C8—22no—
193C4×C8—41no—
194C4×C8—41no—
195C4×C8—41no—
196#95—41no—
197#95—41no—
198C24#12311yescharacteristic
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—82no—
214C22×C4C2×C22⋊C411yescharacteristic
215C22×C4#11711yescharacteristic
216C22×C4#11711yescharacteristic
217C22×C4#12011yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12311yescharacteristic
223C22×C4#12311yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12411yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12611yescharacteristic
231C22×C4#12611yescharacteristic
232M16—24no—
233M16—42no—
234M16—44no—
235M16—44no—
236M16—44no—
237M16—44no—
238M16—82no—
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—44no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—82no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—82no—
271C4⋊C4—82no—
272C22⋊C4—82no—
273C42—82no—
274C42C4×D411yescharacteristic
275C42C4×D411yescharacteristic
276C42C4×D411yescharacteristic
277C42C4×D411yescharacteristic
278C42#12011yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42#12111yescharacteristic
283C42#12311yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C42#12411yescharacteristic
287C42#12411yescharacteristic
288C42#12611yescharacteristic
289C42#12611yescharacteristic
290C23—21no—
291C23—21no—
292C23—22no—
293C23—22no—
294C23#38111yescharacteristic
295C23#39411yescharacteristic
296C23#39711yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4#38611yescharacteristic
331C2×C4#38611yescharacteristic
332C2×C4#38811yescharacteristic
333C2×C4#38811yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#38811yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39711yescharacteristic
340C2×C4#39711yescharacteristic
341C2×C4#39711yescharacteristic
342C2×C4#45412yes—
343C2×C4#45612yes—
344C8—44no—
345C8—44no—
346C8—82no—
347C8—82no—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22#144011yescharacteristic
358C22#203812yes—
359C22#204811yescharacteristic
360C22#204911yescharacteristic
361C22#205012yes—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—162no—
375C4#188611yescharacteristic
376C4#188811yescharacteristic
377C4#203812yes—
378C2—41no—
379C2—41no—
380C2#1049712yes—
381C2#1049912yes—
382C2#1115111yescharacteristic
383C2#1115211yescharacteristic
384C2#1116211yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
16. #1998C4semidirect

Maximal subgroups

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

subgroupindex
#218382
C2×#19982
C2×#15282
#80422
#80282
C2×#12912
#78762