Finite Group Databasebeta

← #119882

Subgroups — #119882

Order 512.

543 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21844C211yesmaximal, characteristic
2#21837C211yesmaximal, characteristic
3#17385C211yesmaximal, characteristic
4#8066C211yesmaximal, characteristic
5#7941C211yesmaximal, characteristic
6#7866C211yesmaximal, characteristic
7#7857C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1994—22no—
16#1991—22no—
17#1988C412yescomplemented
18#1987C412yescomplemented
19#1986—22no—
20#1826—22no—
21#1825—22no—
22#1472—22no—
23#1470—22no—
24#1461—22no—
25#1299—22no—
26#1284—22no—
27#1276—22no—
28#1274—22no—
29#533—21no—
30#533—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37C2×C4⋊Q8C2×C411yescharacteristic
38C2×C4⋊Q8C2×C411yescharacteristic
39C2×#125D412yes—
40C2×C22⋊Q8—21no—
41C2×C22⋊Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×#117—21no—
45C2×#117D412yes—
46C22×C42C2311yescharacteristic
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431D412yes—
63#423—21no—
64#423—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8C2×C412yes—
67#407—21no—
68#407D412yes—
69C2×C22⋊C8—21no—
70C2×C22⋊C8—21no—
71C4×M16—21no—
72C4×M16D412yes—
73C2×C4×C8—21no—
74C2×C4×C8—21no—
75#383—21no—
76#382—21no—
77#381—21no—
78#380—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4C2×C412yes—
82C4×C22⋊C4—21no—
83C4×C22⋊C4—21no—
84C4×C22⋊C4—21no—
85#376—21no—
86#376—21no—
87C43D412yes—
88#340—24no—
89#340—24no—
90#339—28no—
91#324—28no—
92C22×Q8—21no—
93C22×Q8—21no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—22no—
98C2×M16—22no—
99C22×C8—22no—
100C22×C8—41no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—21no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109#125—22no—
110#125—22no—
111#125—22no—
112#125—22no—
113C22⋊Q8—41no—
114C22⋊Q8—41no—
115C22⋊Q8—41no—
116C22⋊Q8—41no—
117C22⋊Q8—41no—
118C22⋊Q8—41no—
119C22⋊Q8—41no—
120C22⋊Q8—41no—
121C4×Q8—41no—
122C4×Q8—41no—
123C4×Q8—41no—
124C4×Q8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129#117—24no—
130#117—22no—
131#117—22no—
132#117—22no—
133#117—22no—
134#117—42no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4C22⋊C412yes—
142C2×C4⋊C4C22⋊C412yes—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42C22×C411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—41no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179#97—22no—
180#97—41no—
181C4×C8—22no—
182C4×C8—22no—
183C4×C8—41no—
184C4×C8—41no—
185C4×C8—41no—
186C4×C8—41no—
187#95—22no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193C24#12111yescharacteristic
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—82no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—81no—
209C22×C4C2×C22⋊C411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4C4×D411yescharacteristic
212C22×C4#12011yescharacteristic
213C22×C4#12011yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4#12111yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12311yescharacteristic
223C22×C4#12411yescharacteristic
224C22×C4#12411yescharacteristic
225C22×C4#12611yescharacteristic
226C22×C4#12611yescharacteristic
227M16—44no—
228M16—82no—
229C2×C8—44no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—82no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—44no—
240C4⋊C4—44no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—82no—
253C42—24no—
254C42—42no—
255C42—44no—
256C42—42no—
257C42—42no—
258C42—42no—
259C42—42no—
260C42—82no—
261C42#11711yescharacteristic
262C42#11711yescharacteristic
263C42C4×D411yescharacteristic
264C42C4×D411yescharacteristic
265C42#12111yescharacteristic
266C42#12111yescharacteristic
267C42#12111yescharacteristic
268C42#12111yescharacteristic
269C42#12311yescharacteristic
270C42#12311yescharacteristic
271C42#12311yescharacteristic
272C42#12311yescharacteristic
273C42#12411yescharacteristic
274C42#12411yescharacteristic
275C42#12611yescharacteristic
276C42#12611yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23#38611yescharacteristic
281C23#39411yescharacteristic
282C23#39711yescharacteristic
283Q8—82no—
284Q8—82no—
285Q8—82no—
286Q8—81no—
287Q8—81no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4#38111yescharacteristic
318C2×C4#38611yescharacteristic
319C2×C4#38811yescharacteristic
320C2×C4#38811yescharacteristic
321C2×C4#38811yescharacteristic
322C2×C4#38811yescharacteristic
323C2×C4#39411yescharacteristic
324C2×C4#39411yescharacteristic
325C2×C4#39411yescharacteristic
326C2×C4#39711yescharacteristic
327C2×C4#39711yescharacteristic
328C2×C4#39711yescharacteristic
329C2×C4#44312yes—
330C2×C4#44412yes—
331C8—82no—
332C8—82no—
333C8—82no—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—82no—
344C22#144011yescharacteristic
345C22#187612yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—84no—
356C4—82no—
357C4—82no—
358C4—162no—
359C4#191212yes—
360C4#192912yes—
361C4#193711yescharacteristic
362C4#193811yescharacteristic
363C2—22no—
364C2—41no—
365C2—41no—
366C2#1115611yescharacteristic
367C2#1118011yescharacteristic
368C2#1119111yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
17. #1988C4semidirect
18. #1987C4semidirect

Maximal subgroups

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

subgroupindex
#218442
#218372
#173852
#80662
#79412
#78662
#78572