Finite Group Databasebeta

← #99176

Subgroups — #99176

Order 512.

592 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 112 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#13807C211yesmaximal, characteristic
2#8557C211yesmaximal, characteristic
3C4×#323C211yesmaximal, characteristic
4#7028C212yesmaximal, complemented
5#7024C212yesmaximal, complemented
6C2×#381C411yescharacteristic
7C2×C4×C22⋊C4C411yescharacteristic
8C2×C4×C22⋊C4C2211yescharacteristic
9#1797C2212yes—
10C4×C22⋊C8C2212yes—
11C2×#323—21no—
12C2×#323—21no—
13#1437—21no—
14#1437—21no—
15#1434—21no—
16#1434C411yescharacteristic
17#1434C2211yescharacteristic
18C4×#95—21no—
19C4×#95C411yescharacteristic
20C4×#95C2211yescharacteristic
21#1280—21no—
22#1280—21no—
23C24×C4C2×C411yescharacteristic
24C22×C22⋊C4—21no—
25C22×C22⋊C4—21no—
26C22×C22⋊C4D411yescharacteristic
27C22×C22⋊C4D411yescharacteristic
28C22×C42—21no—
29C22×C42—21no—
30C22×C42—21no—
31C22×C42C2×C411yescharacteristic
32C22×C42C2311yescharacteristic
33C2×C4⋊C8—22no—
34C2×C22⋊C8—22no—
35C2×C22⋊C8—22no—
36C2×C4×C8—22no—
37#381—22no—
38#381—22no—
39C4×C22⋊C4—22no—
40C4×C22⋊C4—22no—
41C4×C22⋊C4—22no—
42C4×C22⋊C4C814yescomplemented
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95C2×C411yescharacteristic
51C2×#95C2×C411yescharacteristic
52C2×#95C2×C411yescharacteristic
53C2×#95C2×C411yescharacteristic
54C2×#95D411yescharacteristic
55C2×#95D411yescharacteristic
56#336—22no—
57#336—22no—
58#323—24no—
59#323—42no—
60C25C22⋊C411yescharacteristic
61C23×C4—21no—
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—81no—
70C23×C4—81no—
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C2×C812yes—
75C23×C4M1612yes—
76C23×C4C22×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4C2×D411yescharacteristic
79C22×C8—42no—
80C22×C8—42no—
81C2×C22⋊C4—24no—
82C2×C22⋊C4—22no—
83C2×C22⋊C4—22no—
84C2×C22⋊C4—22no—
85C2×C22⋊C4—22no—
86C2×C22⋊C4—21no—
87C2×C22⋊C4—21no—
88C2×C22⋊C4—24no—
89C2×C22⋊C4—41no—
90C2×C22⋊C4—42no—
91C2×C22⋊C4—42no—
92C2×C22⋊C4—81no—
93C2×C22⋊C4—81no—
94C2×C42—24no—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—42no—
98C2×C42—42no—
99C2×C42—42no—
100C2×C42—41no—
101C2×C42—41no—
102C2×C42—81no—
103C2×C42—81no—
104C2×C42—81no—
105C2×C42—81no—
106C2×C42—81no—
107C2×C42—81no—
108C2×C42#4112yes—
109C2×C42#4112yes—
110C4⋊C8—82no—
111C22⋊C8—24no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114C22⋊C8—42no—
115C4×C8—82no—
116#95—24no—
117#95—22no—
118#95—22no—
119#95—21no—
120#95—21no—
121#95—21no—
122#95—21no—
123#95—42no—
124#95—42no—
125#95—42no—
126#95—42no—
127#95—81no—
128#95—81no—
129#95C2×C812yes—
130#95C2×C812yes—
131#95M1612yes—
132#95M1612yes—
133C24—21no—
134C24—21no—
135C24—21no—
136C24—21no—
137C24—21no—
138C24—21no—
139C24—41no—
140C24—41no—
141C24—41no—
142C24—41no—
143C24C22⋊C812yes—
144C24C2×C22⋊C411yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
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—81no—
199C22×C4—81no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4—82no—
203C22×C4—82no—
204C22×C4—82no—
205C22×C4—82no—
206C22×C4C22⋊C812yes—
207C22×C4#10412yes—
208C22×C4#11711yescharacteristic
209C22×C4#11711yescharacteristic
210C22×C4#12312yes—
211C22×C4#12312yes—
212C22×C4C22×C811yescharacteristic
213C22×C4C2×M1611yescharacteristic
214C22×C4C2×M1611yescharacteristic
215C22×C4C2×M1611yescharacteristic
216C22×C4#13512yes—
217C22×C4AGL(1,ℤ/8)11yescharacteristic
218C22×C4#13711yescharacteristic
219C2×C8—44no—
220C2×C8—82no—
221C2×C8—82no—
222C2×C8—82no—
223C2×C8—82no—
224C2×C8—82no—
225C22⋊C4—44no—
226C22⋊C4—48no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—84no—
230C42—42no—
231C42—42no—
232C42—81no—
233C42—81no—
234C42—84no—
235C42—82no—
236C42—82no—
237C42—84no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23—81no—
264C23—81no—
265C23#38111yescharacteristic
266C23C2×C22⋊C811yescharacteristic
267C23#40711yescharacteristic
268C23#41611yescharacteristic
269C23#41711yescharacteristic
270C23C2×#10411yescharacteristic
271C23#42111yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
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—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
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#43111yescharacteristic
338C2×C4#43111yescharacteristic
339C2×C4#43211yescharacteristic
340C2×C4#43211yescharacteristic
341C2×C4#48212yes—
342C2×C4#48512yes—
343C8—84no—
344C8—162no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—82no—
361C22—82no—
362C22—82no—
363C22—82no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22#147611yescharacteristic
369C22#147711yescharacteristic
370C22#148811yescharacteristic
371C22#148911yescharacteristic
372C22#181711yescharacteristic
373C22#182511yescharacteristic
374C22#182611yescharacteristic
375C22#182711yescharacteristic
376C22#182711yescharacteristic
377C22#182811yescharacteristic
378C22#182911yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—22no—
384C4—22no—
385C4—44no—
386C4—42no—
387C4—42no—
388C4—42no—
389C4—82no—
390C4—82no—
391C4—82no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—21no—
396C2—21no—
397C2—82no—
398C2#870811yescharacteristic
399C2#873011yescharacteristic
400C2#873411yescharacteristic
401C2#876211yescharacteristic
402C2#877011yescharacteristic
403C2#877311yescharacteristic
404C2#877911yescharacteristic
subgroupG/H
center, socleC23#381
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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
4. #7028C2semidirect
5. #7024C2semidirect
42. C4×C22⋊C4C8semidirect

Maximal subgroups

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

subgroupindex
#138072
#85572
C4×#3232
#70282
#70242