Finite Group Databasebeta

← #119252

Subgroups — #119252

Order 512.

531 conjugacy classes of subgroups.

The subgroup lattice has 367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21836C211yesmaximal, characteristic
2C2×#1528C211yesmaximal, characteristic
3C2×#1470C211yesmaximal, characteristic
4#8089C211yesmaximal, characteristic
5#7972C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7926C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2283C2211yescharacteristic
15#1991—22no—
16#1989—22no—
17#1824C412yes—
18#1823C412yes—
19#1528—22no—
20#1528—22no—
21C2×#330—22no—
22#1470—22no—
23#1470—22no—
24C2×#324—22no—
25#1302—22no—
26#1288—22no—
27#1283—22no—
28#1282—22no—
29C22×M16—21no—
30C2×#125—21no—
31C2×#125—21no—
32C2×#125—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125D412yes—
41C2×#125D412yes—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C42C2311yescharacteristic
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432D412yes—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C2×C22⋊C8C2×C412yes—
70C2×C22⋊C8D412yes—
71C4×M16—21no—
72C4×M16—21no—
73C4×M16—21no—
74C4×M16D412yes—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97D412yes—
78C2×C4×C8—21no—
79C2×C4×C8—21no—
80C2×C4×C8—21no—
81#383—21no—
82#382—21no—
83#381—21no—
84#380C2×C412yes—
85C4×C4⋊C4—21no—
86C4×C22⋊C4—21no—
87#376—21no—
88#340—24no—
89#340—24no—
90#330—28no—
91#324—28no—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4C22×C411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—24no—
98C2×M16—22no—
99C2×M16—42no—
100C2×M16—41no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—41no—
105C22×C8—41no—
106#125—22no—
107#125—22no—
108#125—22no—
109#125—22no—
110#125—22no—
111#125—22no—
112#125—22no—
113#125—22no—
114#125—41no—
115#125—41no—
116#125—41no—
117#125—41no—
118#125—41no—
119#125—41no—
120#125—41no—
121#125—41no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4C22⋊C412yes—
146C2×C4⋊C4C22⋊C412yes—
147C2×C22⋊C4—22no—
148C2×C42—41no—
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C4⋊C8—22no—
162C4⋊C8—41no—
163C4⋊C8—41no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—41no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177#97—22no—
178#97—22no—
179#97—22no—
180#97—22no—
181#97—41no—
182#97—41no—
183C4×C8—22no—
184C4×C8—41no—
185C4×C8—41no—
186C4×C8—41no—
187C4×C8—41no—
188C4×C8—41no—
189#95—22no—
190#95—41no—
191#95—41no—
192#95—41no—
193C24C4×D411yescharacteristic
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—42no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—82no—
208C22×C4C2×C22⋊C411yescharacteristic
209C22×C4#11711yescharacteristic
210C22×C4#11711yescharacteristic
211C22×C4C4×D411yescharacteristic
212C22×C4C4×D411yescharacteristic
213C22×C4C4×D411yescharacteristic
214C22×C4#12011yescharacteristic
215C22×C4#12111yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12411yescharacteristic
223C22×C4#12411yescharacteristic
224C22×C4#12611yescharacteristic
225C22×C4#12611yescharacteristic
226M16—24no—
227M16—44no—
228M16—42no—
229C2×C8—44no—
230C2×C8—42no—
231C2×C8—44no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—82no—
237C2×C8—82no—
238C2×C8—82no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—44no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—82no—
259C42#12011yescharacteristic
260C42#12111yescharacteristic
261C42#12111yescharacteristic
262C42#12111yescharacteristic
263C42#12111yescharacteristic
264C42#12311yescharacteristic
265C42#12311yescharacteristic
266C42#12311yescharacteristic
267C42#12311yescharacteristic
268C42#12311yescharacteristic
269C42#12311yescharacteristic
270C42#12311yescharacteristic
271C42#12411yescharacteristic
272C42#12411yescharacteristic
273C42#12611yescharacteristic
274C42#12611yescharacteristic
275C23—41no—
276C23—41no—
277C23#38611yescharacteristic
278C23#38811yescharacteristic
279C23#38811yescharacteristic
280C23#44312yes—
281C23#44412yes—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4#38111yescharacteristic
315C2×C4#38611yescharacteristic
316C2×C4#38811yescharacteristic
317C2×C4#38811yescharacteristic
318C2×C4#39411yescharacteristic
319C2×C4#39411yescharacteristic
320C2×C4#39411yescharacteristic
321C2×C4#39411yescharacteristic
322C2×C4#39711yescharacteristic
323C2×C4#39711yescharacteristic
324C2×C4#39711yescharacteristic
325C2×C4#39711yescharacteristic
326C8—44no—
327C8—82no—
328C8—82no—
329C8—82no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#144011yescharacteristic
340C22#187612yes—
341C22#192912yes—
342C22#193711yescharacteristic
343C22#193811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—82no—
357C4—162no—
358C4#183012yes—
359C2—22no—
360C2—22no—
361C2—21no—
362C2—21no—
363C2#1117111yescharacteristic
364C2#1118011yescharacteristic
365C2#1119111yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#218362
C2×#15282
C2×#14702
#80892
#79722
#79322
#79262