Finite Group Databasebeta

← #101840

Subgroups — #101840

Order 512.

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

normal subgroups only

This group has 397 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#29219C211yesmaximal, characteristic
2#23152C211yesmaximal, characteristic
3#9705C211yesmaximal, characteristic
4#9705C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7022C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#446—21no—
9#2868C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2099—21no—
12#2099—21no—
13#1990C412yes—
14#1988—21no—
15#1988—21no—
16#1985—21no—
17#1940—21no—
18#1917—21no—
19#1916—21no—
20#1834C412yes—
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1771—21no—
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C2×#332—21no—
28C2×#332—21no—
29C2×#332—21no—
30C2×#332—21no—
31#1271—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C4×Q8—21no—
38#446—42no—
39#446—42no—
40C2×C4⋊C8—21no—
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×#97—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×C4×C8—21no—
53C2×C4×C8C2×C412yes—
54#391—21no—
55#389—21no—
56#389D411yescharacteristic
57#389D411yescharacteristic
58#384—21no—
59#384—21no—
60#384—21no—
61#384C2×C412yes—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—22no—
68#340—22no—
69#340—22no—
70#340—22no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#332—42no—
83#332—42no—
84#332—42no—
85#332—42no—
86C22×Q8—21no—
87C22×Q8—41no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—22no—
96C4⋊Q8—41no—
97C4⋊Q8—42no—
98C4⋊Q8—42no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—41no—
103C4⋊Q8—41no—
104C4⋊Q8—41no—
105C4⋊Q8—41no—
106C4⋊Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C42—21no—
127C2×C42—21no—
128C2×C42C22×C411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42#4111yescharacteristic
134C2×C42#4111yescharacteristic
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—42no—
144C4⋊C8—42no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8D812yes—
150C4⋊C8SD1612yes—
151#97—42no—
152#97—41no—
153#97—41no—
154#97—41no—
155#97—41no—
156C4×C8—42no—
157C4×C8—42no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—81no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—81no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—42no—
177C22×C4C2×C22⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12311yescharacteristic
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C2×C8—81no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—44no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—81no—
223C4⋊C4—82no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4#10112yes—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42C2×D811yescharacteristic
241C42C2×SD1611yescharacteristic
242C42#13511yescharacteristic
243C42#13511yescharacteristic
244C42AGL(1,ℤ/8)11yescharacteristic
245C42AGL(1,ℤ/8)11yescharacteristic
246C42AGL(1,ℤ/8)11yescharacteristic
247C42#13711yescharacteristic
248C23#38611yescharacteristic
249Q8—82no—
250Q8—82no—
251Q8—161no—
252Q8—161no—
253Q8—161no—
254Q8—161no—
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—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
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—41no—
279C2×C4—41no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4C2×#10111yescharacteristic
284C2×C4#41311yescharacteristic
285C2×C4C4×D811yescharacteristic
286C2×C4C4×SD1611yescharacteristic
287C2×C4#44011yescharacteristic
288C2×C4#44211yescharacteristic
289C2×C4#44711yescharacteristic
290C2×C4#44811yescharacteristic
291C2×C4#44911yescharacteristic
292C2×C4#44911yescharacteristic
293C2×C4#45411yescharacteristic
294C2×C4#45411yescharacteristic
295C2×C4#45911yescharacteristic
296C2×C4#46011yescharacteristic
297C2×C4#46311yescharacteristic
298C2×C4#46411yescharacteristic
299C8—42no—
300C8—42no—
301C8—82no—
302C8—81no—
303C8—81no—
304C8—161no—
305C8—161no—
306C22#187911yescharacteristic
307C22#188011yescharacteristic
308C22#188811yescharacteristic
309C22#190111yescharacteristic
310C22#190211yescharacteristic
311C22#190211yescharacteristic
312C22#190911yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—41no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—162no—
329C4#162511yescharacteristic
330C4#162611yescharacteristic
331C4#162711yescharacteristic
332C4#162811yescharacteristic
333C2#906211yescharacteristic
334C2#925111yescharacteristic
335C2#925211yescharacteristic
336C2#929111yescharacteristic
337C2#929211yescharacteristic
338C2#942211yescharacteristic
339C2#945611yescharacteristic
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
#292192
#231522
#97052
#76522
#70222