Finite Group Databasebeta

← #116574

Subgroups — #116574

Order 512.

673 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
1C2×#1986C211yesmaximal, characteristic
2#20806C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#17486C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#430—22no—
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1986—22no—
17#1986C414yes—
18#1849—22no—
19#1848—22no—
20C2×#339—22no—
21#1493—22no—
22#1493—22no—
23#1487—22no—
24#1487—22no—
25#1481—22no—
26#1481—22no—
27#1303—22no—
28#1283—22no—
29#1279—22no—
30C22×M16—21no—
31C22×M16—21no—
32C22×M16D412yes—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533C2×C412yes—
40#533D412yes—
41C2×C4⋊Q8Q811yescharacteristic
42C2×C4⋊Q8Q811yescharacteristic
43C2×#125—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×#117—21no—
49C22×C4⋊C4—21no—
50C22×C42—21no—
51C22×C42C2311yescharacteristic
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431D412yes—
60#430—44no—
61#430—44no—
62C2×#108—28no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423D412yes—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16C2×C412yes—
82C4×M16D412yes—
83C2×#97—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8D412yes—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4C2×C412yes—
91C2×#95—21no—
92#339—28no—
93Q8⋊C8—28no—
94Q8⋊C8—28no—
95C22×Q8—21no—
96C22×Q8—21no—
97C23×C4—41no—
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—42no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16C22⋊C414yes—
113C2×M16SD1614yes—
114C2×M16Q1614yes—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8C4⋊C412yes—
127C4⋊Q8C4⋊C412yes—
128#125—22no—
129#125—22no—
130#125—41no—
131#125—41no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—41no—
137C22⋊Q8—41no—
138C22⋊Q8—41no—
139C22⋊Q8—41no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148#117—22no—
149#117—22no—
150#117—41no—
151#117—41no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C42—22no—
163C2×C42—41no—
164C2×C42—42no—
165C2×C42—42no—
166C2×C42—41no—
167C2×C42C22×C411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×Q811yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C2×C42#4111yescharacteristic
179#108—416no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196#97—22no—
197#97—22no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—22no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—41no—
204#95—22no—
205#95—41no—
206C24#12411yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—82no—
212C2×Q8—82no—
213C22×C4—42no—
214C22×C4—44no—
215C22×C4—42no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—81no—
219C22×C4—82no—
220C22×C4—82no—
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12311yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12411yescharacteristic
235C22×C4#12411yescharacteristic
236C22×C4#12611yescharacteristic
237C22×C4#12611yescharacteristic
238C22×C4#12711yescharacteristic
239C22×C4C2×SD1612yes—
240C22×C4C2×Q1612yes—
241C22×C4AGL(1,ℤ/8)12yes—
242C22×C4#13712yes—
243M16—24no—
244M16—24no—
245M16—24no—
246M16—44no—
247M16—44no—
248M16—82no—
249M16—81no—
250M16—81no—
251M16#10318yes—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—82no—
260C2×C8—82no—
261C2×C8—81no—
262C2×C8—81no—
263C2×C8—82no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C42—42no—
282C42—42no—
283C42—44no—
284C42—81no—
285C42—81no—
286C42C2×C4⋊C411yescharacteristic
287C42#11711yescharacteristic
288C42C4×D411yescharacteristic
289C42C4×D411yescharacteristic
290C42#12011yescharacteristic
291C42#12011yescharacteristic
292C42#12111yescharacteristic
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42C22⋊Q811yescharacteristic
298C42C22⋊Q811yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42#12311yescharacteristic
301C42#12311yescharacteristic
302C23—41no—
303C23—41no—
304C23#39011yescharacteristic
305C23#39311yescharacteristic
306C23#39711yescharacteristic
307C23#48712yes—
308C23#48912yes—
309Q8—44no—
310Q8—44no—
311Q8—82no—
312Q8—82no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
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—41no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—88no—
332C2×C4—82no—
333C2×C4#38011yescharacteristic
334C2×C4#38511yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38611yescharacteristic
337C2×C4#38811yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#39211yescharacteristic
340C2×C4#39411yescharacteristic
341C2×C4#39411yescharacteristic
342C2×C4#39611yescharacteristic
343C2×C4#39611yescharacteristic
344C2×C4#39911yescharacteristic
345C2×C4C2×#10312yes—
346C2×C4#41712yes—
347C2×C4#45012yes—
348C2×C4#45112yes—
349C2×C4#46012yes—
350C2×C4#46212yes—
351C2×C4#47512yes—
352C2×C4#47712yes—
353C2×C4#48312yes—
354C2×C4#48412yes—
355C2×C4#49211yescharacteristic
356C2×C4#49411yescharacteristic
357C2×C4#49611yescharacteristic
358C2×C4#49711yescharacteristic
359C8—28no—
360C8—82no—
361C8—82no—
362C8—82no—
363C8—82no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—42no—
371C22—42no—
372C22#143911yescharacteristic
373C22#195611yescharacteristic
374C22#195911yescharacteristic
375C22#202412yes—
376C22#207212yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—84no—
385C4—82no—
386C4—82no—
387C4#180312yes—
388C4#186112yes—
389C4#187212yes—
390C4#201411yescharacteristic
391C4#201611yescharacteristic
392C4#209511yescharacteristic
393C4#209611yescharacteristic
394C2—21no—
395C2—22no—
396C2—21no—
397C2—22no—
398C2#1105011yescharacteristic
399C2#1111411yescharacteristic
400C2#1111811yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#124
LCSG ▷ C2×C42 ▷ 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
C2×#19862
#208062
#174862
C2×#13032
#79322
#79012