Finite Group Databasebeta

← #100684

Subgroups — #100684

Order 512.

389 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 90 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#29971C211yesmaximal, characteristic
2#21958C211yesmaximal, characteristic
3#7725C211yesmaximal, characteristic
4#7667C211yesmaximal, characteristic
5#7579C211yesmaximal, characteristic
6#7044C211yesmaximal, characteristic
7#7020C211yesmaximal, characteristic
8C2×#433—21no—
9#2857C2211yescharacteristic
10#2296C2211yescharacteristic
11#2099C411yescharacteristic
12#2099C411yescharacteristic
13#2088—21no—
14#2087—21no—
15#2058C411yescharacteristic
16#2057C411yescharacteristic
17#1940—21no—
18#1940—21no—
19#1939—21no—
20#1939—21no—
21#1854—21no—
22#1825—21no—
23#1817C2211yescharacteristic
24#1798—21no—
25#1797C2211yescharacteristic
26#1797C2211yescharacteristic
27#1797C2211yescharacteristic
28C2×#336C2211yescharacteristic
29#1272—21no—
30#1272—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C23×C8—21no—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×#117D411yescharacteristic
39C2×#117D411yescharacteristic
40C22×C42C2311yescharacteristic
41#433—42no—
42#433—42no—
43C2×#107—21no—
44C2×#106—21no—
45C2×C4⋊C8—21no—
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×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×#97—21no—
57C2×C4×C8—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389C2×C411yescharacteristic
62#389C2×C411yescharacteristic
63#389D411yescharacteristic
64#389D411yescharacteristic
65#385—21no—
66#385—21no—
67#384C2×C411yescharacteristic
68#380—21no—
69#380—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#340—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#336D411yescharacteristic
89#336D411yescharacteristic
90C22×Q8—21no—
91C23×C4C2×D411yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—22no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—81no—
105C22×C8—81no—
106C4⋊Q8—81no—
107C22⋊Q8—82no—
108#117—21no—
109#117—21no—
110#117—81no—
111#117SD1612yes—
112#117Q1612yes—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C22⋊C4—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—41no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—81no—
133C2×C42C22×C411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137#107—81no—
138#106—81no—
139C4⋊C8—42no—
140C4⋊C8—42no—
141C4⋊C8—81no—
142C4⋊C8—81no—
143C4⋊C8—81no—
144C4⋊C8—81no—
145C4⋊C8—81no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—81no—
153#97—42no—
154C4×C8—42no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—21no—
159#95—41no—
160#95—41no—
161C24#12311yescharacteristic
162C2×Q8—42no—
163C2×Q8—81no—
164C2×Q8—81no—
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—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4C2×C22⋊C411yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4C4×D411yescharacteristic
184C22×C4#12011yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4C2×SD1611yescharacteristic
188C22×C4C2×Q1611yescharacteristic
189C22×C4AGL(1,ℤ/8)11yescharacteristic
190C22×C4#13711yescharacteristic
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—81no—
211C2×C8—82no—
212C2×C8—81no—
213C2×C8—82no—
214C2×C8—81no—
215C2×C8—81no—
216C2×C8—81no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—82no—
235C4⋊C4#10312yes—
236C4⋊C4#10312yes—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—81no—
240C22⋊C4—82no—
241C42—22no—
242C42—22no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23#38611yescharacteristic
256C23#48311yescharacteristic
257C23#48411yescharacteristic
258Q8—162no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
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—41no—
293C2×C4—82no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C2×#10311yescharacteristic
301C2×C4#41711yescharacteristic
302C2×C4#44311yescharacteristic
303C2×C4#44411yescharacteristic
304C2×C4#45011yescharacteristic
305C2×C4#45111yescharacteristic
306C2×C4#47111yescharacteristic
307C2×C4#47311yescharacteristic
308C8—81no—
309C8—81no—
310C8—81no—
311C8—81no—
312C8—81no—
313C8—81no—
314C8—82no—
315C8—161no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22#187211yescharacteristic
327C22#187611yescharacteristic
328C22#188111yescharacteristic
329C22#190311yescharacteristic
330C22#190811yescharacteristic
331C22#191211yescharacteristic
332C22#191311yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—42no—
345C4—81no—
346C4—81no—
347C4—161no—
348C4—161no—
349C2—41no—
350C2—41no—
351C2#899311yescharacteristic
352C2#916911yescharacteristic
353C2#920011yescharacteristic
354C2#926311yescharacteristic
355C2#928411yescharacteristic
356C2#933211yescharacteristic
357C2#937411yescharacteristic
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
#299712
#219582
#77252
#76672
#75792
#70442
#70202