Finite Group Databasebeta

← #102415

Subgroups — #102415

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14699C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4#7025C212yesmaximal
5#7025C212yesmaximal
6C2×#389C411yescharacteristic
7C2×#389C411yescharacteristic
8C2×#387—21no—
9C2×C43C2211yescharacteristic
10C2×#336—21no—
11C2×#336—21no—
12C2×#336—21no—
13C2×#336—21no—
14C2×#336C2212yes—
15C2×#336C2212yes—
16#1436—21no—
17#1436—21no—
18C4⋊#95C411yescharacteristic
19C4⋊#95C411yescharacteristic
20C4⋊#95C2211yescharacteristic
21C4⋊#95C2211yescharacteristic
22#1434—21no—
23C23×C8—22no—
24C23×C8—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C42C2×C411yescharacteristic
32C22×C42C2×C411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38#389—22no—
39#389—22no—
40#389—42no—
41#387—44no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C43—42no—
53#336—24no—
54#336—22no—
55#336—24no—
56#336—42no—
57#336—42no—
58#336—42no—
59#336Q814yes—
60C23×C4—21no—
61C23×C4—21no—
62C23×C4—21no—
63C23×C4—21no—
64C23×C4C22⋊C411yescharacteristic
65C23×C4C22⋊C411yescharacteristic
66C23×C4C22⋊C411yescharacteristic
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22×C411yescharacteristic
69C23×C4C2×D411yescharacteristic
70C23×C4C2×D411yescharacteristic
71C22×C8—24no—
72C22×C8—24no—
73C22×C8—42no—
74C22×C8—42no—
75C22×C8—42no—
76C22×C8—42no—
77C22×C8—42no—
78C22×C8—42no—
79C22×C8—42no—
80C22×C8—42no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8—42no—
84C22×C8—42no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—42no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4M1612yes—
104C2×C4⋊C4M1612yes—
105C2×C42—22no—
106C2×C42—22no—
107C2×C42—22no—
108C2×C42—22no—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—22no—
112C2×C42—22no—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—41no—
116C2×C42—41no—
117C2×C42—41no—
118C2×C42—41no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42—41no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42SD1612yes—
126C2×C42Q1612yes—
127C2×C42C2×Q812yes—
128C2×C42#4112yes—
129#95—24no—
130#95—42no—
131#95—42no—
132#95—42no—
133#95—42no—
134#95—42no—
135#95—42no—
136#95—42no—
137#95—42no—
138#95—42no—
139C24C2×C22⋊C411yescharacteristic
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—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—22no—
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#9912yes—
205C22×C4#10312yes—
206C22×C4#10312yes—
207C22×C4#10412yes—
208C22×C4C4×Q812yes—
209C22×C4C22⋊Q812yes—
210C22×C4#12411yescharacteristic
211C22×C4C4⋊Q811yescharacteristic
212C22×C4C2×M1611yescharacteristic
213C22×C4C2×M1611yescharacteristic
214C22×C4#13112yes—
215C22×C4C2×SD1611yescharacteristic
216C22×C4C2×Q1611yescharacteristic
217C22×C4#13512yes—
218C22×C4#13512yes—
219C22×C4AGL(1,ℤ/8)12yes—
220C2×C8—44no—
221C2×C8—44no—
222C2×C8—44no—
223C2×C8—44no—
224C2×C8—44no—
225C2×C8—44no—
226C2×C8—82no—
227C2×C8—82no—
228C2×C8—82no—
229C2×C8—82no—
230C2×C8—82no—
231C2×C8—82no—
232C2×C8—82no—
233C2×C8—82no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—48no—
239C4⋊C4—82no—
240C4⋊C4—82no—
241C4⋊C4—84no—
242C42—42no—
243C42—42no—
244C42—42no—
245C42—42no—
246C42—44no—
247C42—44no—
248C42—44no—
249C42—44no—
250C42—42no—
251C42—42no—
252C23#39111yescharacteristic
253C23#40711yescharacteristic
254C23#40811yescharacteristic
255C23C2×#9911yescharacteristic
256C23#41011yescharacteristic
257C23#41311yescharacteristic
258C23#41311yescharacteristic
259C23C2×#10311yescharacteristic
260C23#41611yescharacteristic
261C23#41611yescharacteristic
262C23#41811yescharacteristic
263C23C2×#10411yescharacteristic
264C23#42111yescharacteristic
265C23#42111yescharacteristic
266C23#42111yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
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—81no—
346C2×C4—81no—
347C2×C4#44612yes—
348C2×C4#44612yes—
349C2×C4#47612yes—
350C2×C4#47712yes—
351C2×C4#48812yes—
352C2×C4#49912yes—
353C8—84no—
354C8—84no—
355C22#146411yescharacteristic
356C22#146511yescharacteristic
357C22#146811yescharacteristic
358C22#147311yescharacteristic
359C22#148211yescharacteristic
360C22#148211yescharacteristic
361C22#148711yescharacteristic
362C22#148811yescharacteristic
363C22#148811yescharacteristic
364C22#149011yescharacteristic
365C22#149311yescharacteristic
366C22#149611yescharacteristic
367C22#150011yescharacteristic
368C22#150111yescharacteristic
369C22#151011yescharacteristic
370C22#151411yescharacteristic
371C22#151611yescharacteristic
372C22#151811yescharacteristic
373C22#152011yescharacteristic
374C22#152111yescharacteristic
375C22#152911yescharacteristic
376C22#153211yescharacteristic
377C22#153511yescharacteristic
378C22#153511yescharacteristic
379C22#154211yescharacteristic
380C22#154211yescharacteristic
381C22#155311yescharacteristic
382C22#155311yescharacteristic
383C22#198511yescharacteristic
384C22#198611yescharacteristic
385C22#198711yescharacteristic
386C22#199111yescharacteristic
387C22#199511yescharacteristic
388C22#199611yescharacteristic
389C22#199811yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—42no—
397C4—42no—
398C4—42no—
399C4—42no—
400C4—82no—
401C4—82no—
402C4—161no—
403C4—161no—
404C2#760811yescharacteristic
405C2#762011yescharacteristic
406C2#764411yescharacteristic
407C2#764811yescharacteristic
408C2#766111yescharacteristic
409C2#766911yescharacteristic
410C2#771811yescharacteristic
411C2#772611yescharacteristic
412C2#986811yescharacteristic
413C2#987511yescharacteristic
414C2#988111yescharacteristic
415C2#988611yescharacteristic
416C2#989311yescharacteristic
417C2#989711yescharacteristic
418C2#991111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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
#146992
#107952
#70252