Finite Group Databasebeta

← #100595

Subgroups — #100595

Order 512.

466 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 106 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#29864C211yesmaximal, characteristic
2#22652C211yesmaximal, characteristic
3#9705C211yesmaximal, characteristic, complemented
4#9692C211yesmaximal, characteristic, complemented
5#7574C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic, complemented
7#7022C211yesmaximal, characteristic, complemented
8C2×#474—21no—
9C2×#435—21no—
10C2×#424—21no—
11#2868C2211yescharacteristic
12#2293C2211yescharacteristic
13#2083—21no—
14#2083C412yes—
15#2071—21no—
16#2071C412yes—
17#1988—21no—
18#1940—21no—
19#1851—21no—
20#1850—21no—
21#1842C2211yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1798—21no—
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C2×#332—21no—
28C2×#332—21no—
29C2×#332—21no—
30C2×#332—21no—
31#1271—21no—
32#1270—21no—
33C22×M16—21no—
34C23×C8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4×D4D411yescharacteristic
39C2×#117—21no—
40#474—42no—
41#474—42no—
42#435—42no—
43#435—42no—
44C2×#107—22no—
45#424—42no—
46#424—42no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53C2×C4⋊C8—21no—
54C2×C4⋊C8D411yescharacteristic
55C2×C4⋊C8D411yescharacteristic
56C2×C4⋊C8D411yescharacteristic
57C2×C4⋊C8D411yescharacteristic
58C2×#102—22no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C2×#97—21no—
62C2×C4×C8—21no—
63#390C2×C411yescharacteristic
64#390D411yescharacteristic
65#389C2×C411yescharacteristic
66#389D411yescharacteristic
67#388—21no—
68#388—21no—
69#384—21no—
70#384—21no—
71#384—21no—
72#384C2×C412yes—
73C4×C4⋊C4D411yescharacteristic
74C4×C22⋊C4—21no—
75C43C2311yescharacteristic
76#340—22no—
77#340—22no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336C2×C412yes—
86#332—42no—
87#332—42no—
88#332—42no—
89#332—42no—
90C22×Q8—41no—
91C22×D4C22⋊C411yescharacteristic
92C23×C4—21no—
93C2×M16—42no—
94C2×M16—42no—
95C2×M16—81no—
96C22×C8—21no—
97C22×C8—22no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—42no—
102C22×C8—42no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—81no—
106C4⋊Q8—41no—
107C4⋊Q8—41no—
108C4⋊Q8—41no—
109C4⋊Q8—41no—
110C4⋊Q8—41no—
111C4⋊Q8—41no—
112C4⋊Q8—41no—
113C4⋊Q8—41no—
114C4⋊Q8—41no—
115C4⋊Q8—41no—
116C4⋊Q8—41no—
117C4⋊Q8—41no—
118C4×D4—21no—
119C4×D4—21no—
120C4×D4D812yes—
121C4×D4SD1612yes—
122#117—41no—
123#117—41no—
124#117—41no—
125#117—41no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4C22⋊C411yescharacteristic
135C2×C4⋊C4C22⋊C411yescharacteristic
136C2×C4⋊C4C22⋊C411yescharacteristic
137C2×C22⋊C4—21no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C42—21no—
143C2×C42C22×C411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150#107—44no—
151C4⋊C8—22no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C4⋊C8—42no—
159C4⋊C8—42no—
160C4⋊C8—41no—
161C4⋊C8—41no—
162C4⋊C8—41no—
163C4⋊C8—41no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8D812yes—
169#102—44no—
170C22⋊C8—42no—
171C22⋊C8—42no—
172#97—41no—
173#97—41no—
174C4×C8—81no—
175#95—21no—
176#95—21no—
177#95—21no—
178C24—21no—
179C2×Q8—81no—
180C2×Q8—81no—
181C2×Q8—81no—
182C2×Q8—81no—
183C2×Q8—81no—
184C2×Q8—81no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4#10212yes—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4C2×C22⋊C411yescharacteristic
200C22×C4C4×D411yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4#12011yescharacteristic
203C22×C4#12111yescharacteristic
204C22×C4#12111yescharacteristic
205C22×C4#12311yescharacteristic
206M16—84no—
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—84no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4#10212yes—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—81no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42C2×D811yescharacteristic
268C42C2×D811yescharacteristic
269C42C2×SD1611yescharacteristic
270C42#13511yescharacteristic
271C42AGL(1,ℤ/8)11yescharacteristic
272C42AGL(1,ℤ/8)11yescharacteristic
273C42AGL(1,ℤ/8)11yescharacteristic
274C42#13711yescharacteristic
275C23—22no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#38611yescharacteristic
283Q8—161no—
284Q8—161no—
285Q8—161no—
286Q8—161no—
287D4—42no—
288D4—81no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4C2×#10211yescharacteristic
319C2×C4#41711yescharacteristic
320C2×C4C4×D811yescharacteristic
321C2×C4#44211yescharacteristic
322C2×C4#44711yescharacteristic
323C2×C4#44711yescharacteristic
324C2×C4#44811yescharacteristic
325C2×C4#44911yescharacteristic
326C2×C4#45311yescharacteristic
327C2×C4#45411yescharacteristic
328C2×C4#45911yescharacteristic
329C2×C4#46311yescharacteristic
330C2×C4#47111yescharacteristic
331C2×C4#47311yescharacteristic
332C2×C4#48011yescharacteristic
333C2×C4#48111yescharacteristic
334C8—42no—
335C8—82no—
336C8—82no—
337C8—81no—
338C8—81no—
339C8—81no—
340C8—161no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#187411yescharacteristic
349C22#187911yescharacteristic
350C22#188311yescharacteristic
351C22#190211yescharacteristic
352C22#190811yescharacteristic
353C22#190911yescharacteristic
354C22#191511yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—162no—
370C4#161911yescharacteristic
371C4#162211yescharacteristic
372C4#162511yescharacteristic
373C4#162711yescharacteristic
374C2—82no—
375C2#897711yescharacteristic
376C2#917111yescharacteristic
377C2#919511yescharacteristic
378C2#927111yescharacteristic
379C2#929111yescharacteristic
380C2#933911yescharacteristic
381C2#937711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #9705C2semidirect
4. #9692C2semidirect
6. #7040C2semidirect
7. #7022C2semidirect

Maximal subgroups

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

subgroupindex
#298642
#226522
#97052
#96922
#75742
#70402
#70222