Finite Group Databasebeta

← #102923

Subgroups — #102923

Order 512.

651 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
1C2×#2084C211yesmaximal, characteristic
2C2×#2072C211yesmaximal, characteristic
3#17079C211yesmaximal, characteristic
4#11373C211yesmaximal, characteristic
5C2×#1272C211yesmaximal, characteristic
6C2×#1271C211yesmaximal, characteristic
7#7025C211yesmaximal, characteristic
8C22×#106—21no—
9C22×#103—21no—
10C2×#391C2211yescharacteristic
11C2×#389C2211yescharacteristic
12C2×#384C2211yescharacteristic
13#2084—22no—
14#2084—22no—
15#2072—22no—
16#2072—22no—
17C2×#340—21no—
18C2×#340—21no—
19C2×#340—22no—
20C2×#336C2211yescharacteristic
21C2×#336C2211yescharacteristic
22C2×#336C2211yescharacteristic
23#1446—21no—
24#1445—21no—
25#1442—21no—
26#1442—21no—
27#1441—22no—
28C4⋊#95C2211yescharacteristic
29#1272—22no—
30#1271—22no—
31C23×Q8D411yescharacteristic
32C23×C8—21no—
33C23×C8—21no—
34C23×C8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D412yes—
41C22×C4⋊C4D411yescharacteristic
42C22×C4⋊C4D411yescharacteristic
43C22×C42C2311yescharacteristic
44C2×#106—24no—
45C2×#106—42no—
46C2×#106—42no—
47C2×#103—24no—
48C2×#103—42no—
49C2×#103—42no—
50#391—21no—
51#391—21no—
52#391—21no—
53#391—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384D412yes—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71#340—24no—
72#340—24no—
73#340—44no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336D412yes—
79#336D412yes—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—42no—
86C22×Q8—42no—
87C22×Q8SD1612yes—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4—22no—
93C23×C4—41no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C22×C8—24no—
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—42no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—42no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—42no—
111C22×C8—41no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4SD1612yes—
148C2×C42—42no—
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42#4111yescharacteristic
153#106—48no—
154#103—48no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165#95—82no—
166#95—82no—
167#95—82no—
168#95—82no—
169C24#12011yescharacteristic
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—44no—
173C2×Q8—44no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—82no—
179C2×Q8—82no—
180C2×Q8—81no—
181C2×Q8—81no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—81no—
221C22×C4—81no—
222C22×C4—81no—
223C22×C4#12011yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12711yescharacteristic
229C22×C4C2×SD1611yescharacteristic
230C22×C4C2×SD1611yescharacteristic
231C22×C4#13511yescharacteristic
232C22×C4#13511yescharacteristic
233C22×C4#13512yes—
234C22×C4AGL(1,ℤ/8)11yescharacteristic
235C22×C4AGL(1,ℤ/8)11yescharacteristic
236C22×C4#13711yescharacteristic
237C22×C4#13711yescharacteristic
238C22×C4#13712yes—
239C2×C8—24no—
240C2×C8—44no—
241C2×C8—44no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—44no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—82no—
250C2×C8—82no—
251C2×C8—82no—
252C2×C8—81no—
253C2×C8—81no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—44no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—82no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C23#39211yescharacteristic
282C23#44811yescharacteristic
283C23#44811yescharacteristic
284C23#44911yescharacteristic
285C23#44911yescharacteristic
286C23#45212yes—
287C23#45311yescharacteristic
288C23#45411yescharacteristic
289C23#45512yes—
290C23#45612yes—
291C23#45812yes—
292Q8—44no—
293Q8—82no—
294Q8—82no—
295Q8—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—161no—
351C2×C4—161no—
352C2×C4—161no—
353C2×C4—161no—
354C2×C4#45011yescharacteristic
355C2×C4#45011yescharacteristic
356C2×C4#45211yescharacteristic
357C2×C4#45211yescharacteristic
358C2×C4#46412yes—
359C2×C4#46511yescharacteristic
360C2×C4#46511yescharacteristic
361C2×C4#46811yescharacteristic
362C2×C4#46811yescharacteristic
363C2×C4#49511yescharacteristic
364C2×C4#49711yescharacteristic
365C8—44no—
366C8—82no—
367C8—82no—
368C22#160812yes—
369C22#160912yes—
370C22#161112yes—
371C22#161212yes—
372C22#161512yes—
373C22#161812yes—
374C22#162011yescharacteristic
375C22#162311yescharacteristic
376C22#162611yescharacteristic
377C22#162611yescharacteristic
378C22#164312yes—
379C22#164612yes—
380C22#165212yes—
381C22#165312yes—
382C22#166112yes—
383C22#166412yes—
384C22#200011yescharacteristic
385C22#200011yescharacteristic
386C22#200411yescharacteristic
387C22#200511yescharacteristic
388C22#200611yescharacteristic
389C22#201511yescharacteristic
390C22#202211yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—161no—
405C4—162no—
406C4—161no—
407C4—162no—
408C2#781312yes—
409C2#781412yes—
410C2#781812yes—
411C2#782012yes—
412C2#992611yescharacteristic
413C2#992711yescharacteristic
414C2#996911yescharacteristic
415C2#1006411yescharacteristic
416C2#1006911yescharacteristic
417C2#1008611yescharacteristic
418C2#1023011yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutator, Frattini, cosocleC22×C42C23
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ 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
C2×#20842
C2×#20722
#170792
#113732
C2×#12722
C2×#12712
#70252