Finite Group Databasebeta

← #119645

Subgroups — #119645

Order 512.

978 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C2×#1463C211yesmaximal, characteristic
2#13923C211yesmaximal, characteristic
3#13776C211yesmaximal, characteristic
4C2×#1297C212yesmaximal
5#8019C212yesmaximal
6C23×C4⋊C4C2211yescharacteristic
7C2×#407C2212yes—
8C2×#381—21no—
9C2×#380C2211yescharacteristic
10C2×C4×C22⋊C4C2211yescharacteristic
11C2×C4×C22⋊C4C2212yes—
12#1463—24no—
13C2×#324—22no—
14#1441C412yescomplemented
15#1441C412yescomplemented
16#1436—24no—
17#1436—22no—
18C22⋊#95—21no—
19C22⋊#95—21no—
20C22⋊#95—21no—
21#1297—24no—
22#1294—24no—
23C24×C4D411yescharacteristic
24C24×C4D411yescharacteristic
25C24×C4C2311yescharacteristic
26C22×M16—22no—
27C22×C4⋊C4—22no—
28C22×C4⋊C4—22no—
29C22×C4⋊C4—22no—
30C22×C4⋊C4—22no—
31C22×C4⋊C4—22no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4C2×C412yes—
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4D412yes—
37C22×C22⋊C4—21no—
38C22×C22⋊C4—22no—
39C22×C22⋊C4—21no—
40C22×C42—21no—
41C22×C42—22no—
42#407—22no—
43#407—22no—
44#407—22no—
45#407D414yes—
46C2×C22⋊C8—22no—
47C2×C22⋊C8—22no—
48#381—28no—
49#380—22no—
50#380—22no—
51C4×C22⋊C4—22no—
52C4×C22⋊C4—22no—
53C4×C22⋊C4—22no—
54C4×C22⋊C4—22no—
55C4×C22⋊C4—22no—
56C4×C22⋊C4—22no—
57C2×#95—24no—
58C2×#95—22no—
59C2×#95—22no—
60C2×#95—21no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95C2×C412yes—
66C2×#95D414yes—
67#324—28no—
68C25C2×D411yescharacteristic
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—24no—
72C23×C4—22no—
73C23×C4—24no—
74C23×C4—21no—
75C23×C4—22no—
76C23×C4—22no—
77C23×C4—22no—
78C23×C4—22no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—42no—
83C23×C4—81no—
84C23×C4—81no—
85C23×C4—81no—
86C23×C4—81no—
87C23×C4C22⋊C412yes—
88C23×C4C22⋊C412yes—
89C23×C4C22×C411yescharacteristic
90C23×C4C2×D412yes—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D412yes—
93C23×C4#4112yes—
94C23×C4#4112yes—
95C23×C4#4112yes—
96C23×C4#4112yes—
97C2×M16—24no—
98C2×M16—42no—
99C2×M16—82no—
100C2×M16—82no—
101C22×C8—42no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—24no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4—81no—
122C2×C22⋊C4—24no—
123C2×C22⋊C4—28no—
124C2×C22⋊C4—44no—
125C2×C22⋊C4—42no—
126C2×C22⋊C4—42no—
127C2×C22⋊C4—42no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—44no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C42—41no—
133C2×C42—42no—
134C2×C42—41no—
135C2×C42—42no—
136C2×C42—81no—
137C2×C42—81no—
138C2×C42—82no—
139C2×C42—82no—
140C22⋊C8—24no—
141C22⋊C8—24no—
142C22⋊C8—42no—
143C22⋊C8—42no—
144#95—216no—
145#95—24no—
146#95—24no—
147#95—24no—
148#95—44no—
149#95—44no—
150#95—42no—
151#95—82no—
152#95—82no—
153#95—82no—
154#95—82no—
155C24—22no—
156C24—22no—
157C24—22no—
158C24—22no—
159C24—41no—
160C24—41no—
161C24C2×C22⋊C411yescharacteristic
162C24#12011yescharacteristic
163C24#12112yes—
164C24#12311yescharacteristic
165C24#12312yes—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—28no—
175C22×C4—24no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—48no—
188C22×C4—48no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—44no—
198C22×C4—44no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—44no—
203C22×C4—42no—
204C22×C4—44no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—44no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—82no—
220C22×C4—82no—
221C22×C4—82no—
222C22×C4—82no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—84no—
226C22×C4—84no—
227C22×C4#10414yes—
228C22×C4#11711yescharacteristic
229C22×C4#11711yescharacteristic
230C22×C4C4×D412yes—
231C22×C4C4×D412yes—
232C22×C4#12011yescharacteristic
233C22×C4#12112yes—
234C22×C4#12112yes—
235C22×C4#12112yes—
236C22×C4#12312yes—
237C22×C4#12312yes—
238C22×C4#12312yes—
239C22×C4#12311yescharacteristic
240C22×C4#12412yes—
241C22×C4#12412yes—
242C22×C4#12612yes—
243C22×C4#12612yes—
244M16—84no—
245M16—84no—
246C2×C8—44no—
247C2×C8—82no—
248C2×C8—82no—
249C4⋊C4—44no—
250C4⋊C4—44no—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4—82no—
254C4⋊C4—82no—
255C22⋊C4—48no—
256C22⋊C4—48no—
257C22⋊C4—48no—
258C22⋊C4—82no—
259C22⋊C4—82no—
260C42—82no—
261C42—84no—
262C42—82no—
263C42—84no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—24no—
273C23—24no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—24no—
281C23—24no—
282C23—42no—
283C23—42no—
284C23—44no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23#38111yescharacteristic
289C23#38611yescharacteristic
290C23#38611yescharacteristic
291C23#39412yes—
292C23#39712yes—
293C23C2×#10412yes—
294C23#42112yes—
295C23#45412yes—
296C23#45612yes—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—48no—
319C2×C4—48no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—48no—
326C2×C4—48no—
327C2×C4—44no—
328C2×C4—48no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—84no—
336C2×C4—82no—
337C2×C4—84no—
338C2×C4—82no—
339C2×C4—84no—
340C2×C4—84no—
341C2×C4—84no—
342C2×C4—82no—
343C2×C4—84no—
344C2×C4—82no—
345C2×C4—84no—
346C2×C4—84no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4#38812yes—
354C2×C4#38812yes—
355C2×C4#39412yes—
356C2×C4#39712yes—
357C8—84no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—48no—
376C22—48no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22#144011yescharacteristic
382C22#182612yes—
383C22#187112yes—
384C22#188611yescharacteristic
385C22#188811yescharacteristic
386C22#189611yescharacteristic
387C22#189711yescharacteristic
388C22#191311yescharacteristic
389C22#191311yescharacteristic
390C22#203814yes—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—44no—
396C4—84no—
397C4—88no—
398C4—82no—
399C4—161no—
400C4—161no—
401C2—22no—
402C2—24no—
403C2—22no—
404C2—42no—
405C2#940811yescharacteristic
406C2#941011yescharacteristic
407C2#941211yescharacteristic
408C2#941411yescharacteristic
409C2#1116211yescharacteristic
410C2#1117211yescharacteristic
411C2#1120111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
14. #1441C4semidirect
15. #1441C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14632
#139232
#137762
C2×#12972
#80192