Finite Group Databasebeta

← #121498

Subgroups — #121498

Order 512.

538 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21988C211yesmaximal, characteristic
2#21365C211yesmaximal, characteristic
3#21359C211yesmaximal, characteristic
4#8031C211yesmaximal, characteristic
5C2×#1287C211yesmaximal, characteristic
6#7912C211yesmaximal, characteristic
7#7900C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12#2285C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1948—21no—
16#1948—21no—
17#1948—21no—
18#1948—21no—
19#1947—21no—
20#1947—21no—
21#1854—22no—
22#1853—21no—
23#1853—21no—
24#1853—21no—
25#1852—21no—
26#1847—21no—
27#1836—21no—
28#1776—22no—
29C4×#106—22no—
30#1295—22no—
31#1287C414yescomplemented
32#1280—22no—
33#1279—22no—
34C2×#117—21no—
35C2×#117—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C42—21no—
39C22×C42C2311yescharacteristic
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432—21no—
46#432—21no—
47#432C2×C412yes—
48#432C2×C412yes—
49#432Q812yes—
50#432Q812yes—
51#432Q812yes—
52#431—21no—
53#431—21no—
54#431C2×C412yes—
55#431Q812yes—
56C2×#107—22no—
57C2×#107—22no—
58C2×#106—22no—
59C2×#106—22no—
60C2×#106—22no—
61C2×#106—22no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C2×C22⋊C8D412yes—
70C2×#97—21no—
71C2×#97—21no—
72C2×#97D412yes—
73C2×C4×C8D412yes—
74#384D411yescharacteristic
75#384D411yescharacteristic
76#384D411yescharacteristic
77#384D411yescharacteristic
78#382—21no—
79#382—21no—
80#380—21no—
81#380—21no—
82#380—21no—
83#380—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C2×#95—21no—
93#340—22no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—22no—
99C23×C4—21no—
100C23×C4—21no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4#4111yescharacteristic
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108#117—82no—
109#117—82no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C22⋊C4—41no—
129C2×C22⋊C4—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—82no—
135C2×C42C22×C411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×Q811yescharacteristic
141C2×C42C2×Q811yescharacteristic
142C2×C42C2×Q811yescharacteristic
143C2×C42C2×Q811yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146C2×C42#4111yescharacteristic
147#107—44no—
148#107—82no—
149#106—44no—
150#106—44no—
151#106—44no—
152#106—82no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—41no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—22no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—41no—
168C22⋊C8C4⋊C414yes—
169#97—22no—
170#97—22no—
171#97—22no—
172#97—22no—
173#97—41no—
174#97C4⋊C414yes—
175C4×C8—22no—
176C4×C8C4⋊C414yes—
177#95—41no—
178#95—41no—
179#95—41no—
180#95—41no—
181#95—41no—
182#95—41no—
183C24#12111yescharacteristic
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4C2×C4⋊C411yescharacteristic
205C22×C4C4×D411yescharacteristic
206C22×C4C4×Q811yescharacteristic
207C22×C4#12011yescharacteristic
208C22×C4#12011yescharacteristic
209C22×C4#12011yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12511yescharacteristic
217C22×C4#12511yescharacteristic
218C22×C4#12511yescharacteristic
219C22×C4#12711yescharacteristic
220C22×C4C4⋊Q811yescharacteristic
221C22×C4C4⋊Q811yescharacteristic
222C2×C8—24no—
223C2×C8—24no—
224C2×C8—24no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—81no—
233C2×C8—81no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C22⋊C4—82no—
256C22⋊C4—82no—
257C42—82no—
258C42—82no—
259C42—82no—
260C42—82no—
261C42C2×C4⋊C411yescharacteristic
262C42C2×C4⋊C411yescharacteristic
263C42C4×D411yescharacteristic
264C42C4×D411yescharacteristic
265C42C22⋊Q811yescharacteristic
266C42C22⋊Q811yescharacteristic
267C42C22⋊Q811yescharacteristic
268C42C22⋊Q811yescharacteristic
269C42C22⋊Q811yescharacteristic
270C42C22⋊Q811yescharacteristic
271C42#12311yescharacteristic
272C42#12311yescharacteristic
273C42C4⋊Q811yescharacteristic
274C42C4⋊Q811yescharacteristic
275C42C4⋊Q811yescharacteristic
276C42C4⋊Q811yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23#38911yescharacteristic
284C23#39211yescharacteristic
285C23#39811yescharacteristic
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4#38411yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38511yescharacteristic
333C2×C4#38511yescharacteristic
334C2×C4#38911yescharacteristic
335C2×C4#38911yescharacteristic
336C2×C4#39511yescharacteristic
337C2×C4#39511yescharacteristic
338C2×C4#39511yescharacteristic
339C2×C4#39811yescharacteristic
340C2×C4#39811yescharacteristic
341C2×C4#39911yescharacteristic
342C2×C4#47112yes—
343C2×C4#47112yes—
344C8—44no—
345C8—44no—
346C8—44no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22#144411yescharacteristic
359C22#200811yescharacteristic
360C22#200911yescharacteristic
361C22#201011yescharacteristic
362C22#201011yescharacteristic
363C22#201911yescharacteristic
364C22#201911yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—82no—
377C4—161no—
378C4—161no—
379C4—161no—
380C4—161no—
381C4#195112yes—
382C4#209012yes—
383C2—41no—
384C2—41no—
385C2#1003911yescharacteristic
386C2#1004011yescharacteristic
387C2#1004311yescharacteristic
388C2#1004411yescharacteristic
389C2#1133011yescharacteristic
390C2#1133311yescharacteristic
391C2#1133511yescharacteristic
subgroupG/H
center, socleC23#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
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
31. #1287C4semidirect

Maximal subgroups

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

subgroupindex
#219882
#213652
#213592
#80312
C2×#12872
#79122
#79002