Finite Group Databasebeta

← #100388

Subgroups — #100388

Order 512.

654 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 116 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#33108C211yesmaximal, characteristic
2#13821C211yesmaximal, characteristic
3#9909C211yesmaximal, characteristic
4#9885C211yesmaximal, characteristic
5#8706C211yesmaximal, characteristic
6#7039C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8C2×#483—21no—
9#2857C2211yescharacteristic
10C2×#389—21no—
11C2×C4×C4⋊C4—21no—
12C2×C4×C4⋊C4—21no—
13C2×C4×C4⋊C4C2211yescharacteristic
14#1981C412yescomplemented
15#1948C412yescomplemented
16#1927—22no—
17#1872—21no—
18#1797C2211yescharacteristic
19#1797C2211yescharacteristic
20C4×C22⋊C8C2211yescharacteristic
21#1436—22no—
22C4⋊#95C2211yescharacteristic
23#1434—21no—
24C4×#95C2211yescharacteristic
25#1294—22no—
26#1294—21no—
27#1294—21no—
28#1279—22no—
29C2×C4⋊Q8C2×C411yescharacteristic
30C2×C22⋊Q8—21no—
31C22×C4⋊C4—22no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4D411yescharacteristic
34C22×C4⋊C4D411yescharacteristic
35C22×C42—21no—
36C22×C42—21no—
37C22×C42—22no—
38C22×C42C2311yescharacteristic
39#483—42no—
40#483—42no—
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8C2×C412yes—
44C2×#103—22no—
45C2×#103—22no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#389—28no—
52#389—21no—
53#389—21no—
54#384C2×C411yescharacteristic
55#380—21no—
56#380—21no—
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C4×C4⋊C4—42no—
60C4×C4⋊C4—42no—
61C4×C4⋊C4—42no—
62C4×C4⋊C4—42no—
63C4×C4⋊C4C2×C412yes—
64C4×C4⋊C4D412yes—
65C2×#95—22no—
66C2×#95—21no—
67C2×#95—22no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95D411yescharacteristic
71C2×#95D411yescharacteristic
72C2×#95D412yes—
73#340—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77C22×Q8—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—22no—
82C23×C4—21no—
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C22×C8—22no—
87C22×C8—41no—
88C22×C8—41no—
89C4⋊Q8—42no—
90C22⋊Q8—41no—
91C22⋊Q8—41no—
92C22⋊Q8—41no—
93C22⋊Q8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—24no—
99C2×C4⋊C4—24no—
100C2×C4⋊C4—28no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—42no—
107C2×C4⋊C4—44no—
108C2×C4⋊C4—44no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4C22⋊C412yes—
113C2×C4⋊C4C22⋊C412yes—
114C2×C4⋊C4D812yes—
115C2×C4⋊C4SD1612yes—
116C2×C22⋊C4—41no—
117C2×C42—24no—
118C2×C42—22no—
119C2×C42—22no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—41no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—44no—
129C2×C42—44no—
130C2×C42—82no—
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42#4111yescharacteristic
134C2×C42#4111yescharacteristic
135#106—44no—
136C4⋊C8—42no—
137C4⋊C8—42no—
138#103—44no—
139#103—44no—
140C22⋊C8—22no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C4×C8—42no—
147#95—28no—
148#95—22no—
149#95—22no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—42no—
154#95—42no—
155#95—44no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95SD1612yes—
161C24#12011yescharacteristic
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—42no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—42no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4C2×C22⋊C411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4C4×D411yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4C2×D811yescharacteristic
216C22×C4C2×SD1611yescharacteristic
217C22×C4C2×SD1611yescharacteristic
218C22×C4#13511yescharacteristic
219C22×C4AGL(1,ℤ/8)11yescharacteristic
220C22×C4AGL(1,ℤ/8)11yescharacteristic
221C22×C4#13711yescharacteristic
222C22×C4#13711yescharacteristic
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—81no—
228C2×C8—81no—
229C2×C8—81no—
230C2×C8—81no—
231C2×C8—81no—
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—44no—
238C4⋊C4—44no—
239C4⋊C4—416no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4#10214yes—
249C4⋊C4#10414yes—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C42—22no—
253C42—22no—
254C42—41no—
255C42—41no—
256C42—44no—
257C42—44no—
258C42—42no—
259C42—42no—
260C42—42no—
261C42—42no—
262C42—88no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23#38611yescharacteristic
268C23#44711yescharacteristic
269C23#44811yescharacteristic
270C23#45011yescharacteristic
271C23#45211yescharacteristic
272C23#45511yescharacteristic
273C23#45611yescharacteristic
274Q8—82no—
275Q8—82no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—82no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#41012yes—
338C2×C4C2×#10211yescharacteristic
339C2×C4#41711yescharacteristic
340C2×C4C2×#10412yes—
341C2×C4C4×SD1611yescharacteristic
342C2×C4#44011yescharacteristic
343C2×C4#46111yescharacteristic
344C2×C4#46311yescharacteristic
345C2×C4#48011yescharacteristic
346C2×C4#48111yescharacteristic
347C8—82no—
348C8—82no—
349C8—161no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22#163911yescharacteristic
363C22#164311yescharacteristic
364C22#164711yescharacteristic
365C22#165111yescharacteristic
366C22#187411yescharacteristic
367C22#187711yescharacteristic
368C22#188211yescharacteristic
369C22#189611yescharacteristic
370C22#189911yescharacteristic
371C22#190511yescharacteristic
372C22#190611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—44no—
381C4—44no—
382C4—41no—
383C4—41no—
384C4—84no—
385C4—82no—
386C4—161no—
387C4—161no—
388C4#150212yes—
389C4#150912yes—
390C2—21no—
391C2—21no—
392C2—21no—
393C2—21no—
394C2#898511yescharacteristic
395C2#914811yescharacteristic
396C2#918011yescharacteristic
397C2#923111yescharacteristic
398C2#925611yescharacteristic
399C2#932411yescharacteristic
400C2#936211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
14. #1981C4semidirect
15. #1948C4semidirect

Maximal subgroups

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

subgroupindex
#331082
#138212
#99092
#98852
#87062
#70392
#70282