Finite Group Databasebeta

← #99192

Subgroups — #99192

Order 512.

514 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 92 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#13947C211yesmaximal, characteristic
2#8557C211yesmaximal, characteristic
3C4×#323C211yesmaximal, characteristic
4#7028C212yesmaximal, complemented
5#7024C212yesmaximal, complemented
6C2×C4×C22⋊C4C2211yescharacteristic
7#1797C2212yes—
8C4×C22⋊C8C2212yes—
9C2×#323—21no—
10C2×#323—21no—
11#1443—21no—
12#1440—21no—
13#1437—21no—
14#1434—21no—
15#1434C411yescharacteristic
16#1434C411yescharacteristic
17#1434C2211yescharacteristic
18C22⋊#95C411yescharacteristic
19C22⋊#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×C42C2×C411yescharacteristic
30C22×C42C2311yescharacteristic
31C2×C4⋊C8—22no—
32C2×C22⋊C8—22no—
33C2×C22⋊C8—22no—
34C2×C4×C8—22no—
35C4×C22⋊C4—22no—
36C4×C22⋊C4—22no—
37C2×#95—21no—
38C2×#95—21no—
39C2×#95—21no—
40C2×#95—21no—
41C2×#95—21no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95C2×C411yescharacteristic
47C2×#95C2×C411yescharacteristic
48C2×#95C2×C411yescharacteristic
49C2×#95C2×C411yescharacteristic
50C2×#95D411yescharacteristic
51C2×#95D411yescharacteristic
52#336—22no—
53#336—22no—
54#323—24no—
55#323—42no—
56C25C22⋊C411yescharacteristic
57C23×C4—21no—
58C23×C4—21no—
59C23×C4—21no—
60C23×C4—21no—
61C23×C4—22no—
62C23×C4—22no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—81no—
66C23×C4—81no—
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22×C411yescharacteristic
71C23×C4C2×D411yescharacteristic
72C23×C4C2×D411yescharacteristic
73C22×C8—42no—
74C22×C8—42no—
75C2×C22⋊C4—22no—
76C2×C22⋊C4—22no—
77C2×C22⋊C4—22no—
78C2×C22⋊C4—22no—
79C2×C22⋊C4—21no—
80C2×C22⋊C4—21no—
81C2×C22⋊C4—41no—
82C2×C22⋊C4—42no—
83C2×C22⋊C4—42no—
84C2×C22⋊C4—42no—
85C2×C22⋊C4—42no—
86C2×C22⋊C4—81no—
87C2×C22⋊C4—81no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—42no—
91C2×C42—41no—
92C2×C42—41no—
93C2×C42—81no—
94C2×C42—81no—
95C2×C42—81no—
96C2×C42#4112yes—
97C2×C42#4112yes—
98C4⋊C8—82no—
99C22⋊C8—24no—
100C22⋊C8—42no—
101C22⋊C8—42no—
102C22⋊C8—42no—
103C4×C8—82no—
104#95—22no—
105#95—22no—
106#95—22no—
107#95—22no—
108#95—22no—
109#95—22no—
110#95—42no—
111#95—42no—
112#95—42no—
113#95—42no—
114#95—81no—
115#95—81no—
116#95—81no—
117#95—81no—
118#95—81no—
119C24—21no—
120C24—21no—
121C24—21no—
122C24—21no—
123C24—21no—
124C24—21no—
125C24—41no—
126C24—41no—
127C24—41no—
128C24—41no—
129C24#10412yes—
130C24C2×C22⋊C411yescharacteristic
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—42no—
163C22×C4—42no—
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—81no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—84no—
189C22×C4—84no—
190C22×C4#11711yescharacteristic
191C22×C4#11711yescharacteristic
192C22×C4#12312yes—
193C22×C4#12312yes—
194C22×C4#13112yes—
195C22×C4#13112yes—
196C22×C4#13512yes—
197C22×C4AGL(1,ℤ/8)11yescharacteristic
198C22×C4#13711yescharacteristic
199C2×C8—44no—
200C2×C8—82no—
201C2×C8—82no—
202C2×C8—82no—
203C2×C8—82no—
204C2×C8—82no—
205C22⋊C4—44no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—84no—
209C22⋊C4—84no—
210C42—42no—
211C42—42no—
212C42—81no—
213C42—81no—
214C42—82no—
215C42—82no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—81no—
236C23—81no—
237C23—81no—
238C23—81no—
239C23—81no—
240C23—81no—
241C23—81no—
242C23—81no—
243C23#38111yescharacteristic
244C23#40811yescharacteristic
245C23#40811yescharacteristic
246C23#41611yescharacteristic
247C23#41711yescharacteristic
248C23C2×#10411yescharacteristic
249C23#42111yescharacteristic
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—84no—
280C2×C4—84no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4#43312yes—
312C2×C4#43312yes—
313C2×C4#48212yes—
314C2×C4#48512yes—
315C8—84no—
316C8—162no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#148211yescharacteristic
341C22#148311yescharacteristic
342C22#149411yescharacteristic
343C22#149511yescharacteristic
344C22#181811yescharacteristic
345C22#182511yescharacteristic
346C22#182611yescharacteristic
347C22#182711yescharacteristic
348C22#182711yescharacteristic
349C22#182811yescharacteristic
350C22#182911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—42no—
356C4—82no—
357C4—82no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—161no—
362C4—161no—
363C2—21no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—82no—
368C2#871111yescharacteristic
369C2#873211yescharacteristic
370C2#873611yescharacteristic
371C2#876211yescharacteristic
372C2#877011yescharacteristic
373C2#877311yescharacteristic
374C2#877611yescharacteristic
subgroupG/H
center, socleC23#381
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC25C22⋊C4
LCSG ▷ C23×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

Maximal subgroups

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

subgroupindex
#139472
#85572
C4×#3232
#70282
#70242