Finite Group Databasebeta

← #101121

Subgroups — #101121

Order 512.

540 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 98 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#21912C211yesmaximal, characteristic
2#15106C211yesmaximal, characteristic
3#10802C211yesmaximal, characteristic
4#7610C212yesmaximal
5#7037C212yesmaximal
6C2×#398—21no—
7C2×#389C2211yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9#1916—24no—
10#1817C2212yes—
11#1797—21no—
12C4×C22⋊C8—21no—
13C2×#343—21no—
14C2×#343—21no—
15#1728C2212yes—
16#1445C411yescharacteristic
17#1445C411yescharacteristic
18#1444C411yescharacteristic
19#1444C411yescharacteristic
20#1441—21no—
21#1436—21no—
22#1436—21no—
23#1434C2211yescharacteristic
24#1271—24no—
25C22×M16—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4D411yescharacteristic
32C22×C4⋊C4D411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42C2311yescharacteristic
36C2×C4⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×C4×C8—22no—
39#398—42no—
40#398—42no—
41#389—22no—
42#389—22no—
43C4×C4⋊C4—22no—
44C4×C4⋊C4—22no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95C2×C411yescharacteristic
55C2×#95C2×C411yescharacteristic
56C2×#95C2×C411yescharacteristic
57C2×#95C2×C411yescharacteristic
58#343—24no—
59#343—42no—
60#336—22no—
61#336—22no—
62#336—22no—
63#336—22no—
64#336—22no—
65#336D414yes—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22×C411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C2×M16—24no—
78C2×M16—42no—
79C2×M16—42no—
80C2×M16—42no—
81C2×M16—42no—
82C2×M16—42no—
83C22×C8—24no—
84C22×C8—42no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—81no—
104C2×C4⋊C4—81no—
105C2×C4⋊C4D812yes—
106C2×C4⋊C4SD1612yes—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—41no—
112C2×C42—41no—
113C2×C42—81no—
114C2×C42—81no—
115C2×C42C2×D412yes—
116C2×C42#4112yes—
117C4⋊C8—82no—
118C22⋊C8—42no—
119C22⋊C8—42no—
120C4×C8—82no—
121#95—24no—
122#95—22no—
123#95—22no—
124#95—41no—
125#95—41no—
126#95—42no—
127#95—42no—
128#95—42no—
129#95—42no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95—41no—
134#95—81no—
135#95—81no—
136C24C2×C22⋊C411yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
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#10212yes—
195C22×C4#10212yes—
196C22×C4#10412yes—
197C22×C4C4×D412yes—
198C22×C4#12011yescharacteristic
199C22×C4#12112yes—
200C22×C4#12311yescharacteristic
201C22×C4C2×D811yescharacteristic
202C22×C4C2×SD1611yescharacteristic
203C22×C4#13512yes—
204M16—44no—
205M16—44no—
206M16—82no—
207M16—82no—
208C2×C8—44no—
209C2×C8—44no—
210C2×C8—44no—
211C2×C8—44no—
212C2×C8—82no—
213C2×C8—82no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C4⋊C4—82no—
220C4⋊C4—84no—
221C4⋊C4—84no—
222C4⋊C4—82no—
223C4⋊C4—82no—
224C42—42no—
225C42—42no—
226C42—42no—
227C42—42no—
228C42—81no—
229C42—81no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23#38611yescharacteristic
235C23#41011yescharacteristic
236C23#41011yescharacteristic
237C23C2×#10211yescharacteristic
238C23#41611yescharacteristic
239C23C2×#10411yescharacteristic
240C23#42111yescharacteristic
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
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#45612yes—
310C2×C4#46512yes—
311C2×C4#46612yes—
312C8—84no—
313C8—84no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22#150011yescharacteristic
327C22#150211yescharacteristic
328C22#151711yescharacteristic
329C22#152111yescharacteristic
330C22#187111yescharacteristic
331C22#188611yescharacteristic
332C22#189111yescharacteristic
333C22#189311yescharacteristic
334C22#189911yescharacteristic
335C22#191111yescharacteristic
336C22#191511yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—42no—
344C4—41no—
345C4—82no—
346C4—82no—
347C4—82no—
348C4—81no—
349C4—161no—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2#903011yescharacteristic
355C2#911411yescharacteristic
356C2#918911yescharacteristic
357C2#939411yescharacteristic
358C2#946111yescharacteristic
359C2#948511yescharacteristic
360C2#951411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#219122
#151062
#108022
#76102
#70372