Finite Group Databasebeta

← #116078

Subgroups — #116078

Order 512.

671 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21332C211yesmaximal, characteristic
2#20793C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4C2×#1481C211yesmaximal, characteristic
5#8095C211yesmaximal, characteristic
6#7924C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#424—22no—
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1996—22no—
17#1996C414yes—
18#1843—22no—
19#1842—22no—
20#1740—22no—
21#1493—22no—
22#1487—22no—
23#1481—22no—
24#1481—22no—
25#1481—22no—
26C2×Q8⋊C8—22no—
27#1303—22no—
28#1282—22no—
29#1279—22no—
30C22×M16—21no—
31C23×C8—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40C2×C4⋊Q8Q811yescharacteristic
41C2×C4⋊Q8Q811yescharacteristic
42C2×#125—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8C2×C412yes—
45C2×C4×Q8—21no—
46C2×C4×Q8D412yes—
47C2×#117—21no—
48C2×#117—21no—
49C2×#117D412yes—
50C22×C42C2311yescharacteristic
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#424—44no—
60#424—44no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—28no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8D412yes—
75C2×C4⋊C8D412yes—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C4×C8—21no—
79C2×C4×C8D412yes—
80#384—21no—
81#382—21no—
82#380—21no—
83#380C2×C412yes—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C22⋊C4C2×C412yes—
89C4×C22⋊C4D412yes—
90#376—21no—
91C43—21no—
92#342—28no—
93Q8⋊C8—28no—
94Q8⋊C8—28no—
95C22×Q8—21no—
96C22×Q8C4⋊C412yes—
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—42no—
103C2×M16—42no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—42no—
111C22×C8—42no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120#125—41no—
121#125—41no—
122#125—41no—
123#125—41no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C22⋊Q8—41no—
129C22⋊Q8—41no—
130C22⋊Q8—41no—
131C22⋊Q8—41no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—41no—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140#117—22no—
141#117—22no—
142#117—41no—
143#117—41no—
144#117—41no—
145#117—41no—
146#117—42no—
147#117—42no—
148#117SD1614yes—
149#117Q1614yes—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4C4⋊C412yes—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4C22⋊C414yes—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—41no—
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×Q811yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C2×C42#4111yescharacteristic
179C2×C42#4111yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—416no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C22⋊C8—22no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C4×C8—22no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—41no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95—41no—
205C24C2×C22⋊C411yescharacteristic
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—44no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—82no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—81no—
218C22×C4C2×C4⋊C411yescharacteristic
219C22×C4#11711yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12411yescharacteristic
235C22×C4#12711yescharacteristic
236C22×C4C2×SD1612yes—
237C22×C4C2×Q1612yes—
238C22×C4AGL(1,ℤ/8)12yes—
239C22×C4#13712yes—
240M16—82no—
241M16—81no—
242M16—81no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—44no—
248C2×C8—44no—
249C2×C8—82no—
250C2×C8—82no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—82no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—44no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C22⋊C4—24no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—44no—
275C22⋊C4#10318yes—
276C42—24no—
277C42—24no—
278C42—44no—
279C42—42no—
280C42—42no—
281C42—82no—
282C42—81no—
283C42—81no—
284C42#12011yescharacteristic
285C42#12011yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12311yescharacteristic
295C42#12311yescharacteristic
296C42#12411yescharacteristic
297C42#12411yescharacteristic
298C42#12611yescharacteristic
299C42#12611yescharacteristic
300C23—41no—
301C23—41no—
302C23#38011yescharacteristic
303C23#38611yescharacteristic
304C23#39011yescharacteristic
305C23C2×#10312yes—
306C23#41712yes—
307Q8—44no—
308Q8—44no—
309Q8—82no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—28no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4#38511yescharacteristic
334C2×C4#38511yescharacteristic
335C2×C4#38811yescharacteristic
336C2×C4#38811yescharacteristic
337C2×C4#39211yescharacteristic
338C2×C4#39311yescharacteristic
339C2×C4#39411yescharacteristic
340C2×C4#39411yescharacteristic
341C2×C4#39611yescharacteristic
342C2×C4#39611yescharacteristic
343C2×C4#39711yescharacteristic
344C2×C4#39911yescharacteristic
345C2×C4#45012yes—
346C2×C4#45112yes—
347C2×C4#46012yes—
348C2×C4#46212yes—
349C2×C4#47512yes—
350C2×C4#47712yes—
351C2×C4#48312yes—
352C2×C4#48412yes—
353C2×C4#48712yes—
354C2×C4#48912yes—
355C2×C4#49211yescharacteristic
356C2×C4#49411yescharacteristic
357C2×C4#49611yescharacteristic
358C2×C4#49711yescharacteristic
359C8—82no—
360C8—82no—
361C8—82no—
362C8—82no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22#143911yescharacteristic
372C22#180312yes—
373C22#187212yes—
374C22#195611yescharacteristic
375C22#195911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—48no—
384C4—82no—
385C4—82no—
386C4—162no—
387C4#186812yes—
388C4#201411yescharacteristic
389C4#201611yescharacteristic
390C4#202412yes—
391C4#207212yes—
392C4#209511yescharacteristic
393C4#209611yescharacteristic
394C2—22no—
395C2—21no—
396C2—22no—
397C2—21no—
398C2#1105011yescharacteristic
399C2#1108811yescharacteristic
400C2#1109411yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#213322
#207932
#174862
C2×#14812
#80952
#79242
#78932