Finite Group Databasebeta

← #134454

Subgroups — #134454

Order 512.

502 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 106 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#14318C211yesmaximal, characteristic
2C2×#1353C212yesmaximal
3#10847C211yesmaximal, characteristic
4#8558C211yesmaximal, characteristic
5#7251C212yesmaximal
6C2×#423—21no—
7C2×#400C2211yescharacteristic
8C2×#389C411yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1797—21no—
11C2×#343—21no—
12C2×#343C2212yes—
13C2×#324C2212yes—
14#1445C411yescharacteristic
15#1444—21no—
16#1444C411yescharacteristic
17#1442—21no—
18#1441C2211yescharacteristic
19#1436—21no—
20#1434—21no—
21#1434C411yescharacteristic
22#1353—24no—
23#1280—21no—
24C22×M16—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4D411yescharacteristic
30C22×C4⋊C4C2311yescharacteristic
31C22×C42C2×C411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42D411yescharacteristic
34#423—24no—
35#423—42no—
36C2×C4⋊C8—41no—
37C2×C4⋊C8—41no—
38C2×C4⋊C8—41no—
39C2×C22⋊C8—22no—
40#400—21no—
41#400—21no—
42#400D412yes—
43#400Q812yes—
44#389—41no—
45#389—41no—
46C4×C4⋊C4—41no—
47C4×C4⋊C4—41no—
48C2×#95—21no—
49C2×#95—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×#95C2×C411yescharacteristic
59C2×#95C2×C411yescharacteristic
60C2×#95C2×C411yescharacteristic
61C2×#95D411yescharacteristic
62#343—22no—
63#343—22no—
64#343—42no—
65#336—41no—
66#324—22no—
67#324—22no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4C2×D411yescharacteristic
79C2×M16—24no—
80C2×M16—42no—
81C2×M16—42no—
82C2×M16—42no—
83C2×M16—42no—
84C2×M16—42no—
85C22×C8—42no—
86C22×C8—42no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—81no—
100C2×C4⋊C4—81no—
101C2×C4⋊C4—81no—
102C2×C4⋊C4—81no—
103C2×C4⋊C4—81no—
104C2×C4⋊C4C4⋊C412yes—
105C2×C4⋊C4C2×D411yescharacteristic
106C2×C4⋊C4C2×Q811yescharacteristic
107C2×C4⋊C4#4111yescharacteristic
108C2×C4⋊C4#4111yescharacteristic
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—22no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—81no—
117C2×C42—81no—
118C2×C42SD1612yes—
119C2×C42Q1612yes—
120C4⋊C8—44no—
121C4⋊C8—44no—
122C4⋊C8—82no—
123C22⋊C8—42no—
124C22⋊C8—42no—
125#95—21no—
126#95—22no—
127#95—22no—
128#95—22no—
129#95—22no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95—41no—
134#95—41no—
135#95—42no—
136#95—41no—
137#95—41no—
138#95—81no—
139#95—81no—
140#95—81no—
141#95—81no—
142#95—81no—
143#95C4⋊C412yes—
144C24C2×C22⋊C411yescharacteristic
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
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—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4#9911yescharacteristic
202C22×C4#9911yescharacteristic
203C22×C4#10312yes—
204C22×C4#10312yes—
205C22×C4#10412yes—
206C22×C4C2×C4⋊C411yescharacteristic
207C22×C4#11711yescharacteristic
208C22×C4#12111yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4C22⋊Q811yescharacteristic
211C22×C4C22⋊Q811yescharacteristic
212C22×C4C2×SD1611yescharacteristic
213C22×C4C2×Q1611yescharacteristic
214C22×C4AGL(1,ℤ/8)11yescharacteristic
215C22×C4#13711yescharacteristic
216M16—44no—
217M16—44no—
218M16—82no—
219M16—82no—
220C2×C8—44no—
221C2×C8—82no—
222C2×C8—82no—
223C2×C8—82no—
224C2×C8—82no—
225C2×C8—82no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—82no—
235C4⋊C4—84no—
236C4⋊C4—84no—
237C42—22no—
238C42—22no—
239C42—22no—
240C42—22no—
241C42—42no—
242C42—81no—
243C42—81no—
244C42—81no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23#38011yescharacteristic
250C23C2×#9911yescharacteristic
251C23#41011yescharacteristic
252C23C2×#10311yescharacteristic
253C23#41711yescharacteristic
254C23C2×#10411yescharacteristic
255C23#42111yescharacteristic
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
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—22no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
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—41no—
303C2×C4—41no—
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#32812yes—
332C2×C4#32812yes—
333C2×C4#46011yescharacteristic
334C2×C4#46211yescharacteristic
335C2×C4#47511yescharacteristic
336C2×C4#47711yescharacteristic
337C8—84no—
338C8—162no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22C2×#32811yescharacteristic
352C22#150911yescharacteristic
353C22#151311yescharacteristic
354C22#151811yescharacteristic
355C22#179911yescharacteristic
356C22#180311yescharacteristic
357C22#180611yescharacteristic
358C22#212111yescharacteristic
359C22#212311yescharacteristic
360C22#213311yescharacteristic
361C22#213411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—22no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—82no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—161no—
378C4—161no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2#857211yescharacteristic
384C2#1172211yescharacteristic
385C2#1172311yescharacteristic
386C2#1183211yescharacteristic
387C2#1183511yescharacteristic
388C2#1279611yescharacteristic
389C2#1280311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#143182
C2×#13532
#108472
#85582
#72512