Finite Group Databasebeta

← #99679

Subgroups — #99679

Order 512.

406 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 102 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#23816C211yesmaximal, characteristic
2#23152C211yesmaximal, characteristic
3#9868C211yesmaximal, characteristic
4#9868C211yesmaximal, characteristic
5C4×#332C211yesmaximal, characteristic
6#7027C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#446—21no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100C411yescharacteristic
12#2100C411yescharacteristic
13#2072—21no—
14#2043C411yescharacteristic
15#2043C411yescharacteristic
16#2024—21no—
17#1985—21no—
18#1940—21no—
19#1917—21no—
20#1916—21no—
21#1771—21no—
22#1767C2211yescharacteristic
23#1767C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C4×#103—21no—
28#1744C2211yescharacteristic
29C2×#332—21no—
30#1296—21no—
31#1279—21no—
32#1279—21no—
33#1279—21no—
34#1279—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39#446—42no—
40#446—42no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×#103—21no—
53C2×#97—21no—
54C2×#97—21no—
55C2×#97—21no—
56C2×C4×C8—21no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60#391—21no—
61#391—21no—
62#389—21no—
63#389—21no—
64#389—21no—
65#389C2×C411yescharacteristic
66#389C2×C411yescharacteristic
67#384C2×C411yescharacteristic
68#384D411yescharacteristic
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4D411yescharacteristic
73C4×C4⋊C4D411yescharacteristic
74C43C2311yescharacteristic
75#340—21no—
76#340—21no—
77#340—21no—
78#340—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336C2×C411yescharacteristic
89#336C2×C411yescharacteristic
90#332—24no—
91C22×Q8—21no—
92C22×Q8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101C4⋊Q8—22no—
102C4⋊Q8—41no—
103C4⋊Q8—42no—
104C4×Q8—41no—
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
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—41no—
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42C22×C411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—42no—
148C4⋊C8—42no—
149C4⋊C8SD1612yes—
150C4⋊C8Q1612yes—
151#103—42no—
152#103—42no—
153#103—42no—
154#103—42no—
155#97—42no—
156#97—41no—
157#97—41no—
158#97—41no—
159#97—41no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—42no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—41no—
167#95—21no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—41no—
172#95—41no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—81no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4C2×C22⋊C411yescharacteristic
190C22×C4C4×D411yescharacteristic
191C22×C4C4×D411yescharacteristic
192C22×C4#12011yescharacteristic
193C22×C4#12111yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12311yescharacteristic
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C4⋊C4—21no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—42no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4#10412yes—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—81no—
256C42—81no—
257C42C2×SD1611yescharacteristic
258C42C2×Q1611yescharacteristic
259C42#13511yescharacteristic
260C42#13511yescharacteristic
261C42AGL(1,ℤ/8)11yescharacteristic
262C42#13711yescharacteristic
263C42#13711yescharacteristic
264C42#13711yescharacteristic
265C23#38611yescharacteristic
266Q8—42no—
267Q8—42no—
268Q8—82no—
269Q8—82no—
270Q8—81no—
271Q8—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C2×#10411yescharacteristic
304C2×C4#42111yescharacteristic
305C2×C4C4×SD1611yescharacteristic
306C2×C4C4×Q1611yescharacteristic
307C2×C4#44011yescharacteristic
308C2×C4#44111yescharacteristic
309C2×C4#45011yescharacteristic
310C2×C4#45111yescharacteristic
311C2×C4#45211yescharacteristic
312C2×C4#45211yescharacteristic
313C2×C4#45411yescharacteristic
314C2×C4#45411yescharacteristic
315C2×C4#46111yescharacteristic
316C2×C4#46211yescharacteristic
317C2×C4#46311yescharacteristic
318C2×C4#46411yescharacteristic
319C8—42no—
320C8—42no—
321C8—81no—
322C8—81no—
323C8—82no—
324C8—82no—
325C8—81no—
326C8—81no—
327C22#187111yescharacteristic
328C22#187711yescharacteristic
329C22#187811yescharacteristic
330C22#188111yescharacteristic
331C22#188111yescharacteristic
332C22#188811yescharacteristic
333C22#189111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—42no—
345C4—41no—
346C4—81no—
347C4—82no—
348C4—81no—
349C4—81no—
350C4—161no—
351C4#163511yescharacteristic
352C4#163611yescharacteristic
353C4#163711yescharacteristic
354C4#163811yescharacteristic
355C2#898911yescharacteristic
356C2#899011yescharacteristic
357C2#900811yescharacteristic
358C2#903211yescharacteristic
359C2#904711yescharacteristic
360C2#904811yescharacteristic
361C2#906511yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#238162
#231522
#98682
C4×#3322
#70272