Finite Group Databasebeta

← #101281

Subgroups — #101281

Order 512.

439 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 439 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23658C211yesmaximal, characteristic
2#21957C211yesmaximal, characteristic
3#8724C211yesmaximal, characteristic
4#8723C211yesmaximal, characteristic
5#7598C211yesmaximal, characteristic
6#7045C211yesmaximal, characteristic
7#7045C211yesmaximal, characteristic
8C2×#433—21no—
9C2×#428—21no—
10#2296C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2084—21no—
13#2084C412yes—
14#2083—21no—
15#2083C412yes—
16#1940—21no—
17#1940—21no—
18#1939—21no—
19#1939—21no—
20#1798—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1736—21no—
26#1728C2211yescharacteristic
27#1296—21no—
28#1296—21no—
29#1296—21no—
30#1296—21no—
31#1271—21no—
32#1271—21no—
33C22×M16—21no—
34C2×#117D411yescharacteristic
35C2×#117D411yescharacteristic
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C42C2311yescharacteristic
40#433—42no—
41#433—42no—
42#428—42no—
43#428—42no—
44C2×#107—22no—
45C2×#106—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8D411yescharacteristic
53C2×C4⋊C8D411yescharacteristic
54C2×C4⋊C8D411yescharacteristic
55C2×C4⋊C8D411yescharacteristic
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×#97—21no—
61C2×C4×C8—21no—
62#389C2×C411yescharacteristic
63#389C2×C411yescharacteristic
64#389D411yescharacteristic
65#389D411yescharacteristic
66#385—21no—
67#385—21no—
68#384—21no—
69#384—21no—
70#384—21no—
71#384C2×C412yes—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336C2×C412yes—
84C23×C4—41no—
85C23×C4C2×D411yescharacteristic
86C23×C4#4111yescharacteristic
87C23×C4#4111yescharacteristic
88C2×M16—22no—
89C2×M16—22no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C22×C8—22no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101#117—21no—
102#117—21no—
103#117—41no—
104#117—41no—
105#117D812yes—
106#117SD1612yes—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4—81no—
123C2×C4⋊C4—81no—
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138#107—44no—
139#106—44no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—42no—
145C4⋊C8—42no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—81no—
151C4⋊C8—81no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—81no—
157C22⋊C8—81no—
158#97—42no—
159C4×C8—42no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164C24#12311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—42no—
182C22×C4—82no—
183C22×C4—82no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4C2×C22⋊C411yescharacteristic
187C22×C4C4×D411yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4#12011yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4C2×D811yescharacteristic
193C22×C4C2×SD1611yescharacteristic
194C22×C4AGL(1,ℤ/8)11yescharacteristic
195C22×C4#13711yescharacteristic
196M16—42no—
197M16—42no—
198M16—42no—
199M16—42no—
200C2×C8—24no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—81no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C2×C8—81no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—82no—
234C4⋊C4—82no—
235C4⋊C4—82no—
236C4⋊C4—81no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4#10212yes—
241C4⋊C4#10212yes—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—81no—
245C42—22no—
246C42—22no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23#38611yescharacteristic
262C23#48011yescharacteristic
263C23#48111yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—162no—
304C2×C4—162no—
305C2×C4C2×#10211yescharacteristic
306C2×C4#41711yescharacteristic
307C2×C4#44711yescharacteristic
308C2×C4#44811yescharacteristic
309C2×C4#45611yescharacteristic
310C2×C4#45611yescharacteristic
311C2×C4#45811yescharacteristic
312C2×C4#45811yescharacteristic
313C2×C4#47111yescharacteristic
314C2×C4#47111yescharacteristic
315C2×C4#47211yescharacteristic
316C2×C4#47311yescharacteristic
317C8—44no—
318C8—81no—
319C8—81no—
320C8—81no—
321C8—81no—
322C8—161no—
323C8—161no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#187411yescharacteristic
335C22#188611yescharacteristic
336C22#189011yescharacteristic
337C22#190211yescharacteristic
338C22#190311yescharacteristic
339C22#190711yescharacteristic
340C22#190811yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—42no—
350C4—42no—
351C4—81no—
352C4—81no—
353C4—162no—
354C4#161011yescharacteristic
355C4#161011yescharacteristic
356C4#161111yescharacteristic
357C4#161111yescharacteristic
358C2—41no—
359C2—41no—
360C2#902711yescharacteristic
361C2#917111yescharacteristic
362C2#917311yescharacteristic
363C2#942011yescharacteristic
364C2#943411yescharacteristic
365C2#952111yescharacteristic
366C2#952211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#236582
#219572
#87242
#87232
#75982
#70452