Finite Group Databasebeta

← #100540

Subgroups — #100540

Order 512.

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

normal subgroups only

This group has 418 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#33153C211yesmaximal, characteristic
2#20754C211yesmaximal, characteristic
3#8708C211yesmaximal, characteristic
4#7687C211yesmaximal, characteristic
5#7665C211yesmaximal, characteristic
6#7045C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C2×#424—21no—
9#2857C2211yescharacteristic
10C4×#117C2211yescharacteristic
11#1987C411yescharacteristic
12#1987C411yescharacteristic
13#1948C411yescharacteristic
14#1947C411yescharacteristic
15#1919—21no—
16#1918—21no—
17#1854—21no—
18#1832—22no—
19#1831—22no—
20#1825—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24#1729—21no—
25#1728C2211yescharacteristic
26C2×#336C2211yescharacteristic
27#1279—21no—
28#1279—21no—
29#1272—22no—
30#1271—22no—
31C22×M16—21no—
32C23×C8—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C22⋊Q8—21no—
35C2×#117D411yescharacteristic
36C2×#117D411yescharacteristic
37C22×C42C2311yescharacteristic
38C2×#107—21no—
39C2×#106—21no—
40#424—42no—
41#424—42no—
42C2×C4⋊C8—24no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8C2×C411yescharacteristic
45C2×C4⋊C8C2×C411yescharacteristic
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#389—21no—
52#389—21no—
53#384C2×C411yescharacteristic
54#380—21no—
55#380—21no—
56C4×C4⋊C4C2×C411yescharacteristic
57C4×C4⋊C4C2×C411yescharacteristic
58C4×C4⋊C4D411yescharacteristic
59C4×C4⋊C4D411yescharacteristic
60C4×C22⋊C4—21no—
61C4×C22⋊C4—21no—
62#376—21no—
63C43—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#336—24no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336D412yes—
77#336D412yes—
78C22×Q8—21no—
79C23×C4C2×D411yescharacteristic
80C23×C4#4111yescharacteristic
81C23×C4#4111yescharacteristic
82C2×M16—41no—
83C2×M16—41no—
84C2×M16—41no—
85C2×M16—41no—
86C2×M16—41no—
87C2×M16—41no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C22⋊Q8—81no—
103C22⋊Q8—81no—
104#117—21no—
105#117—21no—
106#117—41no—
107#117—41no—
108#117SD1612yes—
109#117Q1612yes—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C22⋊C4—21no—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—41no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135#107—42no—
136#106—42no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—48no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C22⋊C8—22no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—81no—
147C4×C8—41no—
148C4×C8—41no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—41no—
154#95—41no—
155C24#12311yescharacteristic
156C2×Q8—42no—
157C2×Q8—81no—
158C2×Q8—81no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C2×C22⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4C2×SD1611yescharacteristic
184C22×C4C2×Q1611yescharacteristic
185C22×C4AGL(1,ℤ/8)11yescharacteristic
186C22×C4#13711yescharacteristic
187M16—81no—
188M16—81no—
189M16—81no—
190M16—81no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—81no—
205C2×C8—81no—
206C2×C8—81no—
207C2×C8—81no—
208C2×C8—81no—
209C2×C8—81no—
210C2×C8—81no—
211C2×C8—81no—
212C2×C8—81no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4—81no—
229C4⋊C4#10312yes—
230C4⋊C4#10312yes—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—22no—
240C42—22no—
241C42—41no—
242C42—41no—
243C42—42no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—81no—
249C42—81no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#38611yescharacteristic
257C23#48311yescharacteristic
258C23#48411yescharacteristic
259Q8—162no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
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—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4#41011yescharacteristic
303C2×C4#41011yescharacteristic
304C2×C4C2×#10311yescharacteristic
305C2×C4#41711yescharacteristic
306C2×C4#42111yescharacteristic
307C2×C4#42111yescharacteristic
308C2×C4#44311yescharacteristic
309C2×C4#44411yescharacteristic
310C2×C4#45011yescharacteristic
311C2×C4#45111yescharacteristic
312C2×C4#47111yescharacteristic
313C2×C4#47211yescharacteristic
314C8—82no—
315C8—82no—
316C8—82no—
317C8—81no—
318C8—81no—
319C8—161no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#187211yescharacteristic
331C22#187611yescharacteristic
332C22#188111yescharacteristic
333C22#189711yescharacteristic
334C22#189911yescharacteristic
335C22#190211yescharacteristic
336C22#190711yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—42no—
345C4—41no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4—161no—
350C4—161no—
351C4#151211yescharacteristic
352C4#151211yescharacteristic
353C4#151811yescharacteristic
354C4#151811yescharacteristic
355C2—41no—
356C2—41no—
357C2#899311yescharacteristic
358C2#915211yescharacteristic
359C2#916711yescharacteristic
360C2#921311yescharacteristic
361C2#924011yescharacteristic
362C2#931411yescharacteristic
363C2#934811yescharacteristic
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
#331532
#207542
#87082
#76872
#76652
#70452
#70292