Finite Group Databasebeta

← #102464

Subgroups — #102464

Order 512.

496 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 94 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#33149C211yesmaximal, characteristic
2#33147C211yesmaximal, characteristic
3#30187C211yesmaximal, characteristic
4#11346C211yesmaximal, characteristic
5#7668C211yesmaximal, characteristic
6#7667C211yesmaximal, characteristic
7#7020C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9#2857C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#2100—21no—
12#2072—21no—
13#2043—21no—
14#2024—21no—
15#1988—21no—
16#1987—21no—
17#1948—21no—
18#1947—21no—
19#1921—22no—
20#1919—22no—
21#1892—22no—
22#1853—21no—
23#1852—21no—
24#1824—21no—
25#1824—21no—
26#1797C2211yescharacteristic
27#1797C2211yescharacteristic
28C2×#336—22no—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1272—22no—
32#1271—22no—
33C23×C8—21no—
34C23×C8D412yes—
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×C22⋊Q8—21no—
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C42—21no—
42C22×C42C2311yescharacteristic
43C2×#107—22no—
44C2×#106—22no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×#103—22no—
48C2×#103—22no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51#391—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#384D411yescharacteristic
58#384D411yescharacteristic
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C2×#95—21no—
68#340—22no—
69#340—22no—
70#340—22no—
71#340—22no—
72#340—22no—
73#340—22no—
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—44no—
81#336D412yes—
82#336D412yes—
83C22×Q8—21no—
84C22×Q8—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4#4111yescharacteristic
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—22no—
96C22×C8—42no—
97C22×C8—42no—
98C22×C8—41no—
99C22×C8—42no—
100C22×C8—41no—
101C22×C8—42no—
102C4⋊Q8—42no—
103C4⋊Q8—42no—
104C22⋊Q8—42no—
105C22⋊Q8—42no—
106C22⋊Q8—82no—
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—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—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4Q1612yes—
128C2×C22⋊C4—41no—
129C2×C22⋊C4—41no—
130C2×C42—42no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139#107—44no—
140#106—44no—
141C4⋊C8—42no—
142C4⋊C8—42no—
143#103—82no—
144#103—82no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155C24#12111yescharacteristic
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—42no—
161C2×Q8—81no—
162C2×Q8—81no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—41no—
176C22×C4—42no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—42no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4#12011yescharacteristic
186C22×C4#12011yescharacteristic
187C22×C4#12011yescharacteristic
188C22×C4#12111yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4#12711yescharacteristic
191C22×C4C2×Q1611yescharacteristic
192C22×C4#13512yes—
193C22×C4#13511yescharacteristic
194C22×C4#13712yes—
195C22×C4#13711yescharacteristic
196C22×C4#13711yescharacteristic
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—44no—
203C2×C8—44no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—81no—
210C2×C8—82no—
211C2×C8—81no—
212C2×C8—82no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C4⋊C4—82no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C22⋊C4—82no—
236C22⋊C4—82no—
237C42—22no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—82no—
242C42—81no—
243C42—81no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23#39211yescharacteristic
249C23#46412yes—
250C23#46711yescharacteristic
251C23#47011yescharacteristic
252C23#47112yes—
253Q8—82no—
254Q8—82no—
255Q8—162no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4#45111yescharacteristic
300C2×C4#45111yescharacteristic
301C2×C4#45211yescharacteristic
302C2×C4#45211yescharacteristic
303C2×C4#45212yes—
304C2×C4#45311yescharacteristic
305C2×C4#45411yescharacteristic
306C2×C4#45812yes—
307C2×C4#49511yescharacteristic
308C2×C4#49711yescharacteristic
309C8—82no—
310C8—82no—
311C8—82no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—22no—
321C22#168412yes—
322C22#170412yes—
323C22#200111yescharacteristic
324C22#200611yescharacteristic
325C22#201011yescharacteristic
326C22#201511yescharacteristic
327C22#201711yescharacteristic
328C22#201911yescharacteristic
329C22#202211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—82no—
339C4—82no—
340C4—161no—
341C4—161no—
342C4—161no—
343C4—161no—
344C4#161512yes—
345C4#161812yes—
346C2—22no—
347C2—22no—
348C2#996911yescharacteristic
349C2#997811yescharacteristic
350C2#1002711yescharacteristic
351C2#1003511yescharacteristic
352C2#1025811yescharacteristic
353C2#1027711yescharacteristic
354C2#1032511yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C22×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
#331492
#331472
#301872
#113462
#76682
#76672
#70202