Finite Group Databasebeta

← #136205

Subgroups — #136205

Order 512.

483 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 483 conjugacy classes of subgroups — too many to draw. Only its 88 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#14590C211yesmaximal, characteristic
2C2×#1346C211yesmaximal, characteristic
3#11296C211yesmaximal, characteristic
4#9027C211yesmaximal, characteristic
5#8857C211yesmaximal, characteristic
6#7251C211yesmaximal, characteristic
7#7189C211yesmaximal, characteristic
8C2×#398C2211yescharacteristic
9#2316C2211yescharacteristic
10C2×#387—21no—
11#1853—21no—
12#1823—21no—
13C2×#343C2211yescharacteristic
14#1736—21no—
15C2×#339—21no—
16C2×#324C2211yescharacteristic
17C2×#324C2211yescharacteristic
18#1443—21no—
19#1443—21no—
20#1441C2211yescharacteristic
21#1436—21no—
22#1436—21no—
23#1436—21no—
24C4⋊#95C2211yescharacteristic
25#1346C414yescomplemented
26#1294—21no—
27#1294—21no—
28C22×M16—21no—
29C2×#117—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4D411yescharacteristic
32C22×C4⋊C4D411yescharacteristic
33C22×C4⋊C4D411yescharacteristic
34C22×C4⋊C4C2311yescharacteristic
35C22×C42—21no—
36C22×C42D411yescharacteristic
37C2×#106—41no—
38C2×C22⋊C8—21no—
39C2×C22⋊C8—21no—
40#398—21no—
41#398—21no—
42#398C2×C412yes—
43#398Q812yes—
44#389—41no—
45#389—41no—
46#387—42no—
47#387—42no—
48#380—21no—
49#380—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95D411yescharacteristic
63C2×#95D411yescharacteristic
64#343—21no—
65#343C2×C412yes—
66#340—41no—
67#340—41no—
68#340—41no—
69#340—41no—
70#340—41no—
71#339—42no—
72#324—21no—
73#324—21no—
74#324—21no—
75#324C2×C412yes—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C2×M16—22no—
86C2×M16—41no—
87C2×M16—41no—
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C22×C8—41no—
92C22×C8—41no—
93C22×C8—41no—
94#117—41no—
95#117—41no—
96#117—41no—
97#117—41no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4C4⋊C412yes—
121C2×C4⋊C4SD1612yes—
122C2×C4⋊C4C22×C411yescharacteristic
123C2×C4⋊C4C2×Q811yescharacteristic
124C2×C4⋊C4#4111yescharacteristic
125C2×C4⋊C4#4111yescharacteristic
126C2×C22⋊C4—41no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—42no—
133C2×C42—81no—
134C2×C42—81no—
135#106—82no—
136C22⋊C8—22no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140#95—22no—
141#95—22no—
142#95—21no—
143#95—41no—
144#95—42no—
145#95—42no—
146#95—42no—
147#95—42no—
148#95—42no—
149#95—42no—
150#95—42no—
151#95—42no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—81no—
157#95—81no—
158#95C4⋊C412yes—
159C24#12011yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
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—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4C2×C4⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C22⋊Q811yescharacteristic
220C22×C4C22⋊Q811yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4C2×SD1611yescharacteristic
223C22×C4#13511yescharacteristic
224C22×C4AGL(1,ℤ/8)11yescharacteristic
225C22×C4AGL(1,ℤ/8)11yescharacteristic
226M16—42no—
227M16—42no—
228M16—81no—
229M16—81no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—81no—
233C2×C8—81no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C22⋊C4—81no—
262C22⋊C4—81no—
263C42—42no—
264C42—81no—
265C42—81no—
266C42—81no—
267C42—84no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23#38511yescharacteristic
273C23#44911yescharacteristic
274C23#45011yescharacteristic
275C23#45411yescharacteristic
276C23#45511yescharacteristic
277C23B(4,𝔽2)11yescharacteristic
278C23#45811yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
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—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
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—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4C4×SD1611yescharacteristic
354C2×C4#44211yescharacteristic
355C2×C4#47611yescharacteristic
356C2×C4#47811yescharacteristic
357C8—82no—
358C8—82no—
359C8—161no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22#159711yescharacteristic
373C22#160111yescharacteristic
374C22#161211yescharacteristic
375C22#161611yescharacteristic
376C22#186011yescharacteristic
377C22#186411yescharacteristic
378C22#186711yescharacteristic
379C22#219711yescharacteristic
380C22#219811yescharacteristic
381C22#220311yescharacteristic
382C22#220311yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—82no—
392C4—82no—
393C4—82no—
394C4—82no—
395C4—82no—
396C4—161no—
397C4—161no—
398C4—161no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2#887011yescharacteristic
404C2#1214211yescharacteristic
405C2#1214311yescharacteristic
406C2#1220911yescharacteristic
407C2#1221011yescharacteristic
408C2#1295911yescharacteristic
409C2#1297111yescharacteristic
subgroupG/H
center, socleC23B(4,𝔽2)
commutatorC2×C4⋊C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24#120
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
25. #1346C4semidirect

Maximal subgroups

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

subgroupindex
#145902
C2×#13462
#112962
#90272
#88572
#72512
#71892