Finite Group Databasebeta

← #100518

Subgroups — #100518

Order 512.

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

normal subgroups only

This group has 381 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#33200C211yesmaximal, characteristic
2#22832C211yesmaximal, characteristic
3#8566C211yesmaximal, characteristic
4#7663C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#479—21no—
9#2859C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1989—21no—
12#1984—21no—
13#1949—21no—
14#1948C411yescharacteristic
15#1947C411yescharacteristic
16#1917—22no—
17#1842C2211yescharacteristic
18#1839—21no—
19#1831C2211yescharacteristic
20#1831C2211yescharacteristic
21#1805—21no—
22#1803C411yescharacteristic
23#1803C411yescharacteristic
24#1770—21no—
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1745—21no—
28C2×Q8⋊C8—21no—
29#1279—21no—
30#1271—22no—
31#1271—21no—
32#1271—21no—
33C2×#125—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37#479—42no—
38#479—42no—
39C2×#107—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8C2×C411yescharacteristic
48C2×C4⋊C8C2×C411yescharacteristic
49C2×#103—21no—
50C2×#103—21no—
51C2×#97—22no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#382—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4C2×C411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C43—21no—
68C43C2311yescharacteristic
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#336—22no—
74#336—22no—
75#336—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81#336D411yescharacteristic
82#336D411yescharacteristic
83Q8⋊C8—42no—
84C22×Q8C22⋊C411yescharacteristic
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—22no—
90C22×C8—41no—
91C22×C8—41no—
92#125—41no—
93#125—41no—
94#125—41no—
95#125—41no—
96C4×Q8—22no—
97C4×Q8—21no—
98C4×Q8—21no—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—41no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
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⋊C4—41no—
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42C22×C411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133#107—42no—
134#106—42no—
135C4⋊C8—22no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—42no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148#103—42no—
149#103—42no—
150#97—44no—
151C4×C8—41no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—41no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—41no—
159#95—41no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8#10112yes—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4C2×C22⋊C411yescharacteristic
173C22×C4C4×D411yescharacteristic
174C22×C4C4×D411yescharacteristic
175C22×C4#12011yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12311yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—42no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—42no—
232C42—42no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—81no—
240C42#13511yescharacteristic
241C42#13511yescharacteristic
242C42AGL(1,ℤ/8)11yescharacteristic
243C42AGL(1,ℤ/8)11yescharacteristic
244C42AGL(1,ℤ/8)11yescharacteristic
245C42#13711yescharacteristic
246C42#13711yescharacteristic
247C42#13711yescharacteristic
248C23#38611yescharacteristic
249Q8—22no—
250Q8—22no—
251Q8—41no—
252Q8—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4C2×#10111yescharacteristic
285C2×C4#41311yescharacteristic
286C2×C4#41611yescharacteristic
287C2×C4#41711yescharacteristic
288C2×C4#41811yescharacteristic
289C2×C4#41911yescharacteristic
290C2×C4#44311yescharacteristic
291C2×C4#44411yescharacteristic
292C2×C4#44911yescharacteristic
293C2×C4#44911yescharacteristic
294C2×C4#46811yescharacteristic
295C2×C4#46811yescharacteristic
296C2×C4#47011yescharacteristic
297C2×C4#47011yescharacteristic
298C2×C4#48211yescharacteristic
299C2×C4#48211yescharacteristic
300C8—42no—
301C8—81no—
302C8—82no—
303C8—82no—
304C8—81no—
305C8—81no—
306C8—161no—
307C22#187511yescharacteristic
308C22#187611yescharacteristic
309C22#188111yescharacteristic
310C22#189411yescharacteristic
311C22#190111yescharacteristic
312C22#190511yescharacteristic
313C22#190611yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—161no—
330C4—161no—
331C4#155211yescharacteristic
332C4#155411yescharacteristic
333C4#155611yescharacteristic
334C4#155711yescharacteristic
335C2#899611yescharacteristic
336C2#914011yescharacteristic
337C2#918211yescharacteristic
338C2#920911yescharacteristic
339C2#924611yescharacteristic
340C2#930811yescharacteristic
341C2#935211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332002
#228322
#85662
#76632
#76602
#70402
#70312