Finite Group Databasebeta

← #141973

Subgroups — #141973

Order 512.

600 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 94 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#14040C211yesmaximal, characteristic
2#8557C211yesmaximal, characteristic
3#8152C211yesmaximal, characteristic
4#7187C212yesmaximal
5#7187C212yesmaximal
6C2×#385C411yescharacteristic
7C2×C4×C22⋊C4C2211yescharacteristic
8C22×#95C411yescharacteristic
9#1797—21no—
10#1749—21no—
11C2×#323C2212yes—
12C2×#323C2212yes—
13#1445—21no—
14#1443—21no—
15#1436—21no—
16#1434—21no—
17C22⋊#95C411yescharacteristic
18C22⋊#95C411yescharacteristic
19C22⋊#95C2211yescharacteristic
20C22⋊#95C2211yescharacteristic
21#1280—21no—
22#1280—21no—
23C24×C4C2×C411yescharacteristic
24C24×C4C2×C411yescharacteristic
25C24×C4C2×C411yescharacteristic
26C22×C4⋊C4—21no—
27C22×C22⋊C4C2×C411yescharacteristic
28C22×C22⋊C4C2×C411yescharacteristic
29C22×C22⋊C4C2×C411yescharacteristic
30C22×C22⋊C4C2311yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C2×C4⋊C8—41no—
34C2×C22⋊C8—22no—
35C2×C22⋊C8—22no—
36C2×#97—41no—
37#385—22no—
38#385—22no—
39C4×C22⋊C4—41no—
40C4×C22⋊C4—41no—
41C2×#95—21no—
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—
52C2×#95—41no—
53C2×#95—41no—
54C2×#95D411yescharacteristic
55C2×#95D411yescharacteristic
56#336—41no—
57#336—41no—
58#323—22no—
59#323—24no—
60#323Q814yes—
61C25C22×C411yescharacteristic
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—22no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—22no—
71C23×C4—41no—
72C23×C4—42no—
73C23×C4—42no—
74C23×C4—41no—
75C23×C4—41no—
76C23×C4—41no—
77C23×C4—41no—
78C23×C4—81no—
79C23×C4—81no—
80C23×C4—81no—
81C23×C4—81no—
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4M1612yes—
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C22×C8—42no—
90C22×C8—42no—
91C2×C4⋊C4—24no—
92C2×C4⋊C4—81no—
93C2×C4⋊C4—81no—
94C2×C22⋊C4—21no—
95C2×C22⋊C4—21no—
96C2×C22⋊C4—21no—
97C2×C22⋊C4—22no—
98C2×C22⋊C4—41no—
99C2×C22⋊C4—41no—
100C2×C22⋊C4—41no—
101C2×C22⋊C4—41no—
102C2×C22⋊C4—41no—
103C2×C22⋊C4—41no—
104C2×C22⋊C4—41no—
105C2×C22⋊C4—41no—
106C2×C22⋊C4M1612yes—
107C2×C22⋊C4C2×Q812yes—
108C2×C22⋊C4#4112yes—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—42no—
114C2×C42—81no—
115C4⋊C8—82no—
116C22⋊C8—24no—
117C22⋊C8—42no—
118C22⋊C8—42no—
119C22⋊C8—42no—
120#97—82no—
121#95—24no—
122#95—41no—
123#95—41no—
124#95—42no—
125#95—42no—
126#95—42no—
127#95—42no—
128#95—41no—
129#95—41no—
130#95—81no—
131#95—81no—
132#95—81no—
133#95—81no—
134#95—81no—
135C24—21no—
136C24—21no—
137C24—21no—
138C24—21no—
139C24—41no—
140C24—41no—
141C24—41no—
142C24—41no—
143C24C2×C22⋊C411yescharacteristic
144C24C4×Q812yes—
145C24C2×M1611yescharacteristic
146C24C2×M1611yescharacteristic
147C24#13112yes—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
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—41no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
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—42no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—82no—
214C22×C4—82no—
215C22×C4—84no—
216C22×C4—84no—
217C22×C4—84no—
218C22×C4—84no—
219C22×C4—84no—
220C22×C4—82no—
221C22×C4—82no—
222C22×C4—82no—
223C22×C4—82no—
224C22×C4#9911yescharacteristic
225C22×C4#9911yescharacteristic
226C22×C4C22⋊Q812yes—
227C22×C4#12411yescharacteristic
228C22×C4C4⋊Q811yescharacteristic
229C2×C8—44no—
230C2×C8—82no—
231C2×C8—82no—
232C2×C8—82no—
233C2×C8—82no—
234C2×C8—82no—
235C4⋊C4—84no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—82no—
243C42—42no—
244C42—42no—
245C42—81no—
246C42—81no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—41no—
260C23—41no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—41no—
266C23—41no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#39111yescharacteristic
278C23#40711yescharacteristic
279C23#40811yescharacteristic
280C23C2×#9911yescharacteristic
281C23#41011yescharacteristic
282C23#41311yescharacteristic
283C23#41311yescharacteristic
284C23#44612yes—
285C23#44612yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—84no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—84no—
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—84no—
336C2×C4—84no—
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—84no—
346C2×C4—84no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4#35212yes—
355C8—84no—
356C8—162no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—44no—
376C22—44no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22#146411yescharacteristic
386C22#146511yescharacteristic
387C22#146811yescharacteristic
388C22#147311yescharacteristic
389C22#198511yescharacteristic
390C22#199611yescharacteristic
391C22#199811yescharacteristic
392C22C2×#35211yescharacteristic
393C22#212011yescharacteristic
394C22#212111yescharacteristic
395C22#212211yescharacteristic
396C4—22no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—42no—
401C4—82no—
402C4—81no—
403C4—81no—
404C4—82no—
405C4—82no—
406C4—81no—
407C4—161no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2—42no—
413C2—42no—
414C2#988111yescharacteristic
415C2#1152611yescharacteristic
416C2#1152711yescharacteristic
417C2#1154211yescharacteristic
418C2#1154711yescharacteristic
419C2#1329411yescharacteristic
420C2#1329511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutator, prime radicalC25C22×C4
Frattini, cosocleC22×C22⋊C4C23
LCSG ▷ C25 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#140402
#85572
#81522
#71872