Finite Group Databasebeta

← #100884

Subgroups — #100884

Order 512.

473 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 80 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#27956C211yesmaximal, characteristic
2#14477C211yesmaximal, characteristic
3#9888C211yesmaximal, characteristic
4#9683C211yesmaximal, characteristic
5#8719C211yesmaximal, characteristic
6#7036C211yesmaximal, characteristic
7#7036C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#382C2211yescharacteristic
10#2085—22no—
11#1993C412yescomplemented
12#1853—21no—
13#1852—21no—
14#1847C412yescomplemented
15#1749C2211yescharacteristic
16#1749C2211yescharacteristic
17#1749C2211yescharacteristic
18C2×#328—21no—
19C2×#328—21no—
20#1443—21no—
21#1442—21no—
22#1441—21no—
23#1436—21no—
24#1436—21no—
25#1434—21no—
26#1434C2211yescharacteristic
27#1434C2211yescharacteristic
28#1295—22no—
29#1294—21no—
30#1294—21no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4D411yescharacteristic
35C22×C4⋊C4D411yescharacteristic
36C22×C42—21no—
37C22×C42C2311yescharacteristic
38C2×#107—22no—
39C2×#106—22no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97C2×C412yes—
46#391—21no—
47#389—21no—
48#389—21no—
49#384C2×C411yescharacteristic
50#382—21no—
51#382—21no—
52#382C2×C412yes—
53#382D412yes—
54#380—21no—
55#380—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95D411yescharacteristic
69C2×#95D411yescharacteristic
70C2×#95D411yescharacteristic
71C2×#95D411yescharacteristic
72#340—22no—
73#340—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77#328—42no—
78#328—42no—
79C22×Q8—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C22×C8—22no—
90C22×C8—41no—
91C22×C8—41no—
92C4⋊Q8—42no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C22⋊Q8—41no—
96C22⋊Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—81no—
107C2×C4⋊C4—81no—
108C2×C4⋊C4—81no—
109C2×C4⋊C4—81no—
110C2×C4⋊C4C22⋊C412yes—
111C2×C4⋊C4C22⋊C412yes—
112C2×C22⋊C4—41no—
113C2×C42—42no—
114C2×C42—42no—
115C2×C42—81no—
116C2×C42—81no—
117C2×C42C22×C411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42#4111yescharacteristic
120C2×C42#4111yescharacteristic
121#107—82no—
122#106—82no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—22no—
127C22⋊C8—41no—
128C22⋊C8—41no—
129#97—42no—
130#97—42no—
131#97—42no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95—22no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—42no—
141#95—42no—
142#95—42no—
143#95—42no—
144#95—42no—
145#95—42no—
146#95—41no—
147#95—41no—
148#95—81no—
149#95—81no—
150#95—81no—
151#95—81no—
152C24#12011yescharacteristic
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—81no—
156C2×Q8—81no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
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—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×C4C2×C22⋊C411yescharacteristic
214C22×C4C4×D411yescharacteristic
215C22×C4C4×D411yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12311yescharacteristic
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4—84no—
241C22⋊C4—81no—
242C22⋊C4—81no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—84no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23#38611yescharacteristic
253C23#45311yescharacteristic
254C23#45411yescharacteristic
255C23#45511yescharacteristic
256C23#45611yescharacteristic
257C23#45611yescharacteristic
258C23#45611yescharacteristic
259Q8—161no—
260Q8—161no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
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—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
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#41012yes—
333C8—44no—
334C8—82no—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22#166011yescharacteristic
349C22#166111yescharacteristic
350C22#166311yescharacteristic
351C22#166411yescharacteristic
352C22#188211yescharacteristic
353C22#188311yescharacteristic
354C22#188611yescharacteristic
355C22#189911yescharacteristic
356C22#190611yescharacteristic
357C22#190611yescharacteristic
358C22#191111yescharacteristic
359C4—22no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4—82no—
367C4—82no—
368C4—82no—
369C4—161no—
370C4—161no—
371C4—161no—
372C4—161no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2—21no—
377C2#900011yescharacteristic
378C2#936211yescharacteristic
379C2#936711yescharacteristic
380C2#937911yescharacteristic
381C2#938111yescharacteristic
382C2#944011yescharacteristic
383C2#946111yescharacteristic
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
11. #1993C4semidirect
14. #1847C4semidirect

Maximal subgroups

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

subgroupindex
#279562
#144772
#98882
#96832
#87192
#70362