Finite Group Databasebeta

← #103978

Subgroups — #103978

Order 512.

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

normal subgroups only

This group has 461 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#29272C211yesmaximal, characteristic
2#28284C211yesmaximal, characteristic
3#28161C211yesmaximal, characteristic
4#9874C211yesmaximal, characteristic
5#7591C211yesmaximal, characteristic
6#7588C211yesmaximal, characteristic
7#7040C211yesmaximal, characteristic
8C2×#477—21no—
9C2×#462—21no—
10C4×C4⋊Q8C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2099—21no—
14#2072—21no—
15#2068—22no—
16#2057—21no—
17#2016—21no—
18#1988—21no—
19#1981—21no—
20#1947—21no—
21#1947—21no—
22#1918—22no—
23#1878—22no—
24#1842C2211yescharacteristic
25#1831C2211yescharacteristic
26#1831C2211yescharacteristic
27#1803—21no—
28#1803—21no—
29#1744C2211yescharacteristic
30#1279—22no—
31#1271—22no—
32#1271—22no—
33C22×Q16—22no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40#477—42no—
41#477—42no—
42#462—42no—
43#462—42no—
44C2×#107—22no—
45C2×#107—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8D412yes—
51C2×#103—22no—
52C2×#103—22no—
53C2×#103—22no—
54C2×#103—22no—
55C2×C4×C8—21no—
56#391—21no—
57#391—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389—21no—
65#384D411yescharacteristic
66#384D411yescharacteristic
67#384D411yescharacteristic
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C43C2311yescharacteristic
75#340—22no—
76#340—22no—
77#340—22no—
78#340—22no—
79#340—22no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336D412yes—
85#336D412yes—
86C22×Q8—21no—
87C22×Q8—21no—
88C22×Q8—21no—
89C2×Q16—44no—
90C2×Q16—44no—
91C2×Q16—82no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—41no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8—21no—
99C4⋊Q8—21no—
100C4⋊Q8—21no—
101C4⋊Q8—21no—
102C4⋊Q8—42no—
103C4⋊Q8D812yes—
104C4⋊Q8Q1612yescomplemented
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
113C4×Q8—82no—
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—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142#107—44no—
143#107—44no—
144C4⋊C8—42no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153#103—44no—
154#103—44no—
155#103—82no—
156#103—82no—
157C4×C8—22no—
158C4×C8—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4#12011yescharacteristic
188C22×C4#12011yescharacteristic
189C22×C4#12011yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12111yescharacteristic
193C22×C4#12711yescharacteristic
194Q16—88no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—81no—
206C2×C8—81no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4—82no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C42—21no—
237C42—21no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—82no—
243C42—81no—
244C42—81no—
245C42—81no—
246C42—81no—
247C42C2×D811yescharacteristic
248C42C2×Q1611yescharacteristic
249C42#13511yescharacteristic
250C42#13511yescharacteristic
251C42AGL(1,ℤ/8)11yescharacteristic
252C42AGL(1,ℤ/8)11yescharacteristic
253C42#13711yescharacteristic
254C42#13711yescharacteristic
255C23#39211yescharacteristic
256Q8—42no—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260Q8—42no—
261Q8—81no—
262Q8—81no—
263Q8—82no—
264Q8—81no—
265Q8—81no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—81no—
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#44711yescharacteristic
298C2×C4#44711yescharacteristic
299C2×C4#44911yescharacteristic
300C2×C4#44911yescharacteristic
301C2×C4#45111yescharacteristic
302C2×C4#45111yescharacteristic
303C2×C4#45211yescharacteristic
304C2×C4#45211yescharacteristic
305C2×C4#45511yescharacteristic
306C2×C4#45611yescharacteristic
307C2×C4#46611yescharacteristic
308C2×C4#46711yescharacteristic
309C2×C4#46911yescharacteristic
310C2×C4#47011yescharacteristic
311C2×C4#47312yes—
312C8—82no—
313C8—82no—
314C8—82no—
315C8—82no—
316C22#199911yescharacteristic
317C22#200111yescharacteristic
318C22#200711yescharacteristic
319C22#200811yescharacteristic
320C22#200911yescharacteristic
321C22#201011yescharacteristic
322C22#202011yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4—82no—
336C4—161no—
337C4—161no—
338C4—161no—
339C4#164111yescharacteristic
340C4#164411yescharacteristic
341C4#164911yescharacteristic
342C4#165211yescharacteristic
343C2#999611yescharacteristic
344C2#1000311yescharacteristic
345C2#1003111yescharacteristic
346C2#1018311yescharacteristic
347C2#1018511yescharacteristic
348C2#1021511yescharacteristic
349C2#1023311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
104. C4⋊Q8Q16semidirect

Maximal subgroups

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

subgroupindex
#292722
#282842
#281612
#98742
#75912
#75882
#70402