Finite Group Databasebeta

← #117864

Subgroups — #117864

Order 512.

582 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21894C211yesmaximal, characteristic
2C2×#1838C211yesmaximal, characteristic
3C2×#1559C211yesmaximal, characteristic
4C2×#1531C211yesmaximal, characteristic
5C2×#1307C211yesmaximal, characteristic
6#8042C211yesmaximal, characteristic
7#8034C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×#97C2211yescharacteristic
14#2285C2211yescharacteristic
15#1988—21no—
16#1981—21no—
17#1894—22no—
18#1838—22no—
19#1838—22no—
20#1803—22no—
21C2×#341—22no—
22#1559—22no—
23#1559—22no—
24C2×#333—21no—
25C2×#332—21no—
26#1531—22no—
27#1531C414yescomplemented
28C2×#330—22no—
29#1307—22no—
30#1296—22no—
31#1295—22no—
32C22×M16—21no—
33C22×M16D412yes—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533C2×C412yes—
42#533Q812yes—
43C2×C4⋊Q8D411yescharacteristic
44C2×C4⋊Q8D411yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×#117—21no—
51C2×#117—21no—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432C2×C412yes—
60#432D412yes—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423D412yes—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×#103—24no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97—21no—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97C2×C412yes—
84C2×#97D412yes—
85C2×#97D412yes—
86#384D412yes—
87#382—21no—
88#380—21no—
89#380—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92#341—28no—
93#340—24no—
94#333—24no—
95#332—24no—
96#330—28no—
97C22×Q8—21no—
98C22×Q8—21no—
99C23×C4C2×D411yescharacteristic
100C23×C4#4111yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—41no—
106C2×M16—44no—
107C2×M16—44no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—42no—
113C22×C8—42no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8C4⋊C412yes—
124C4⋊Q8C4⋊C412yes—
125#125—22no—
126#125—22no—
127#125—41no—
128#125—41no—
129C22⋊Q8—22no—
130C22⋊Q8—22no—
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—41no—
134C22⋊Q8—41no—
135C22⋊Q8—41no—
136C22⋊Q8—41no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145#117—22no—
146#117—22no—
147#117—41no—
148#117—41no—
149#117—82no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C42—41no—
162C2×C42—41no—
163C2×C42C22×C411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×Q811yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
174C2×C42#4111yescharacteristic
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187#103—84no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192#97—22no—
193#97—22no—
194#97—22no—
195#97—22no—
196#97—22no—
197#97—41no—
198#97—41no—
199#97C22⋊C414yes—
200#95—41no—
201#95—41no—
202C24#12411yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—81no—
210C2×Q8—81no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—42no—
219C22×C4#11711yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4#12011yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12111yescharacteristic
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
237M16—44no—
238M16—44no—
239M16—82no—
240M16—82no—
241C2×C8—24no—
242C2×C8—44no—
243C2×C8—44no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—44no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—82no—
254C2×C8—82no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—82no—
274C42—42no—
275C42—42no—
276C42—82no—
277C42C2×C22⋊C411yescharacteristic
278C42C2×C4⋊C411yescharacteristic
279C42C4×D411yescharacteristic
280C42C4×D411yescharacteristic
281C42#12011yescharacteristic
282C42#12111yescharacteristic
283C42#12111yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42#12311yescharacteristic
290C42#12311yescharacteristic
291C42#12611yescharacteristic
292C42#12711yescharacteristic
293C23—21no—
294C23—21no—
295C23—22no—
296C23—22no—
297C23#38811yescharacteristic
298C23#39311yescharacteristic
299C23#39411yescharacteristic
300Q8—44no—
301Q8—82no—
302Q8—82no—
303Q8—81no—
304Q8—81no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4#38011yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38511yescharacteristic
337C2×C4#38611yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#39011yescharacteristic
340C2×C4#39211yescharacteristic
341C2×C4#39411yescharacteristic
342C2×C4#39611yescharacteristic
343C2×C4#39611yescharacteristic
344C2×C4#39711yescharacteristic
345C2×C4#39911yescharacteristic
346C2×C4#45412yes—
347C2×C4#45512yes—
348C8—44no—
349C8—82no—
350C8—82no—
351C8—82no—
352C8—82no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22#143911yescharacteristic
362C22#204012yes—
363C22#204811yescharacteristic
364C22#204912yes—
365C22#204911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—82no—
378C4—162no—
379C4#186012yes—
380C4#200311yescharacteristic
381C4#200411yescharacteristic
382C2—41no—
383C2—41no—
384C2#1052712yes—
385C2#1052912yes—
386C2#1107911yescharacteristic
387C2#1112011yescharacteristic
388C2#1114311yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
27. #1531C4semidirect

Maximal subgroups

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

subgroupindex
#218942
C2×#18382
C2×#15592
C2×#15312
C2×#13072
#80422
#80342