Finite Group Databasebeta

← #470698

Subgroups — #470698

Order 512.

852 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14709C211yesmaximal, characteristic
2#14689C211yesmaximal, characteristic
3#11385C211yesmaximal, characteristic
4#11385C211yesmaximal, characteristic
5#11372C212yesmaximal
6#11358C212yesmaximal
7#11316C212yesmaximal
8#11315C212yesmaximal
9#11268C211yesmaximal, characteristic
10#11268C211yesmaximal, characteristic
11#10795C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×#382C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C43C2211yescharacteristic
17C2×#340C2212yes—
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#336C2211yescharacteristic
26C2×#336C2211yescharacteristic
27C2×#336C2212yes—
28C2×#336C2212yes—
29#1436—22no—
30#1436—22no—
31C4⋊#95C2211yescharacteristic
32C4⋊#95C2211yescharacteristic
33C4⋊#95C2211yescharacteristic
34C4⋊#95C2212yes—
35C4⋊#95C2211yescharacteristic
36C4⋊#95C2212yes—
37#1434—22no—
38#1434—22no—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C2×#125—24no—
42C2×#125—22no—
43C2×#125—22no—
44C2×#125—42no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4C2311yescharacteristic
47C22×C4⋊C4C2311yescharacteristic
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C42D412yes—
53C22×C42D412yes—
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57#382—24no—
58#382—24no—
59#382—42no—
60C2×#95—22no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—22no—
73C43—22no—
74C43—22no—
75#340—24no—
76#340—24no—
77#340—42no—
78#340—42no—
79#340—42no—
80#340—42no—
81#340—42no—
82#340—42no—
83#336—22no—
84#336—22no—
85#336—24no—
86#336—42no—
87C23×C4—22no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4—22no—
93C23×C4C2×D412yes—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D412yes—
97C23×C4C2411yescharacteristic
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112#125—48no—
113#125—48no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—28no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4#4114yes—
145C2×C42—22no—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—24no—
151C2×C42—24no—
152C2×C42—24no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—42no—
160C2×C42—42no—
161C2×C42—42no—
162C2×C42#4112yes—
163C2×C42#4112yes—
164C2×C42#4114yes—
165#95—44no—
166#95—44no—
167#95—44no—
168#95—44no—
169#95—44no—
170#95—44no—
171#95—44no—
172#95—42no—
173#95—42no—
174#95—42no—
175#95—42no—
176#95—44no—
177#95—44no—
178C24C22×D411yescharacteristic
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—24no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—42no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4#12314yes—
234C22×C4#12412yes—
235C22×C4#12412yes—
236C22×C4#13514yes—
237C22×C4C2×#4112yes—
238C22×C4C2×#4111yescharacteristic
239C22×C4C2×#4111yescharacteristic
240C22×C4C2×#4112yes—
241C22×C4H(5,𝔽2)12yes—
242C22×C4H(5,𝔽2)11yescharacteristic
243C22×C42−1+411yescharacteristic
244C22×C42−1+411yescharacteristic
245C22×C42−1+412yes—
246C22×C42−1+411yescharacteristic
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—416no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C42—24no—
279C42—24no—
280C42—24no—
281C42—24no—
282C42—48no—
283C42—48no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C23C2×#12311yescharacteristic
289C23#52511yescharacteristic
290C23C2×#12411yescharacteristic
291C23#53511yescharacteristic
292C23#53611yescharacteristic
293C23#53611yescharacteristic
294C23#53711yescharacteristic
295C23C2×#13512yes—
296C23#57512yes—
297C23#57512yes—
298C23#57512yes—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4#54112yes—
358C2×C4#54112yes—
359C2×C4#54111yescharacteristic
360C2×C4#54111yescharacteristic
361C2×C4#54211yescharacteristic
362C2×C4#54211yescharacteristic
363C2×C4#54212yes—
364C2×C4#54212yes—
365C2×C4#55112yes—
366C2×C4#55112yes—
367C2×C4#55212yes—
368C2×C4#55212yes—
369C2×C4#55612yes—
370C2×C4#55912yes—
371C2×C4#56212yes—
372C2×C4#56312yes—
373C8—82no—
374C8—82no—
375C22#248211yescharacteristic
376C22#250311yescharacteristic
377C22#259211yescharacteristic
378C22#262511yescharacteristic
379C22#263411yescharacteristic
380C22#264011yescharacteristic
381C22#282011yescharacteristic
382C22#309112yes—
383C22#309312yes—
384C22#310212yes—
385C22#311112yes—
386C22#313111yescharacteristic
387C22#313511yescharacteristic
388C22#314211yescharacteristic
389C22#314211yescharacteristic
390C22#321212yes—
391C22#321912yes—
392C22#323212yes—
393C22#323312yes—
394C22#324012yes—
395C22#324012yes—
396C22#325012yes—
397C22#325612yes—
398C4—42no—
399C4—42no—
400C4—44no—
401C4—44no—
402C4—84no—
403C4—161no—
404C4—162no—
405C4—161no—
406C4—161no—
407C4—161no—
408C4#275412yes—
409C4#275412yes—
410C4#276212yes—
411C4#276212yes—
412C2#1669511yescharacteristic
413C2#2759012yes—
414C2#2796311yescharacteristic
415C2#2796711yescharacteristic
416C2#2935111yescharacteristic
417C2#2935311yescharacteristic
418C2#2994012yes—
419C2#3009712yes—
420C2#3020711yescharacteristic
421C2#3021711yescharacteristic
422C2#3282212yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#147092
#146892
#113852
#113722
#113582
#113162
#113152
#112682
#107952