Finite Group Databasebeta

← #121450

Subgroups — #121450

Order 512.

662 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21365C211yesmaximal, characteristic
2#20801C211yesmaximal, characteristic
3#14298C211yesmaximal, characteristic
4#8030C211yesmaximal, characteristic
5#8018C211yesmaximal, characteristic
6C2×#1288C211yesmaximal, characteristic
7#7904C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#428—21no—
11C2×#428—21no—
12C2×C4×M16C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#383C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1948—21no—
18#1947—21no—
19#1853—21no—
20#1852—21no—
21#1847—21no—
22#1847—21no—
23#1846—22no—
24#1776—22no—
25#1444—21no—
26#1444—21no—
27#1442—21no—
28#1442—21no—
29#1436—22no—
30#1295—22no—
31#1294—22no—
32#1288C414yescomplemented
33#1279—22no—
34C22×M16—21no—
35C2×#117—21no—
36C22×C4⋊C4—22no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C42—21no—
42C22×C42C2311yescharacteristic
43#432—21no—
44#432—21no—
45#432—21no—
46#432—21no—
47#432—21no—
48#432C2×C412yes—
49#432Q812yes—
50#432Q812yes—
51#428—44no—
52#428—44no—
53C2×#107—22no—
54C2×#107—22no—
55C2×#107—22no—
56C2×#106—22no—
57C2×#106—22no—
58C2×#106—22no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×C22⋊C8—21no—
63C4×M16—21no—
64C4×M16—21no—
65C4×M16C2×C412yes—
66C4×M16Q812yes—
67C2×#97—21no—
68C2×#97—21no—
69C2×#97D412yes—
70C2×C4×C8D412yes—
71#384D411yescharacteristic
72#384D411yescharacteristic
73#383—21no—
74#383—21no—
75#383C2×C412yes—
76#383Q812yes—
77#382—21no—
78#382—21no—
79#382—21no—
80#382—21no—
81#382—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—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95D412yes—
99#340—22no—
100#340—22no—
101C23×C4—21no—
102C23×C4—22no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C2×M16—24no—
110C2×M16—24no—
111C2×M16—22no—
112C2×M16—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—41no—
116#117—42no—
117#117—42no—
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—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—44no—
137C2×C4⋊C4—82no—
138C2×C4⋊C4—82no—
139C2×C22⋊C4—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—82no—
144C2×C42C22×C411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×Q811yescharacteristic
149C2×C42C2×Q811yescharacteristic
150C2×C42C2×Q811yescharacteristic
151C2×C42C2×Q811yescharacteristic
152C2×C42#4111yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156#107—44no—
157#107—44no—
158#107—44no—
159#106—44no—
160#106—44no—
161#106—44no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—41no—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—41no—
170#97—22no—
171#97—22no—
172#97—22no—
173#97—22no—
174#97—41no—
175#97C4⋊C414yescomplemented
176C4×C8—22no—
177C4×C8C4⋊C414yescomplemented
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—44no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—82no—
193#95—82no—
194#95C4⋊C414yes—
195C24#12011yescharacteristic
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—24no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C2×C4⋊C411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4#12011yescharacteristic
234C22×C4#12011yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4C22⋊Q811yescharacteristic
242C22×C4C22⋊Q811yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12711yescharacteristic
245C22×C4C4⋊Q811yescharacteristic
246C22×C4C4⋊Q811yescharacteristic
247C22×C4C4⋊Q811yescharacteristic
248M16—28no—
249M16—28no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—81no—
258C2×C8—81no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—88no—
280C22⋊C4—82no—
281C42—82no—
282C42—82no—
283C42—82no—
284C42C2×C4⋊C411yescharacteristic
285C42C2×C4⋊C411yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12511yescharacteristic
295C42#12511yescharacteristic
296C42#12511yescharacteristic
297C42C4⋊Q811yescharacteristic
298C42C4⋊Q811yescharacteristic
299C42C4⋊Q811yescharacteristic
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#38511yescharacteristic
305C23#39211yescharacteristic
306C23#39511yescharacteristic
307C23#45312yes—
308C23#45612yes—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—84no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4#38411yescharacteristic
366C2×C4#38511yescharacteristic
367C2×C4#38511yescharacteristic
368C2×C4#38911yescharacteristic
369C2×C4#38911yescharacteristic
370C2×C4#38911yescharacteristic
371C2×C4#39511yescharacteristic
372C2×C4#39511yescharacteristic
373C2×C4#39811yescharacteristic
374C2×C4#39811yescharacteristic
375C2×C4#39811yescharacteristic
376C2×C4#39911yescharacteristic
377C8—28no—
378C8—44no—
379C8—82no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22#144411yescharacteristic
389C22#185912yes—
390C22#200211yescharacteristic
391C22#200511yescharacteristic
392C22#200811yescharacteristic
393C22#200911yescharacteristic
394C22#201011yescharacteristic
395C22#201011yescharacteristic
396C22#206012yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—84no—
410C4—82no—
411C4—82no—
412C4—161no—
413C4—161no—
414C4—161no—
415C4—161no—
416C2—22no—
417C2—22no—
418C2#1001811yescharacteristic
419C2#1002011yescharacteristic
420C2#1002311yescharacteristic
421C2#1002511yescharacteristic
422C2#1133311yescharacteristic
423C2#1133511yescharacteristic
424C2#1134011yescharacteristic
subgroupG/H
center, socleC23#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
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
32. #1288C4semidirect
175. #97C4⋊C4semidirect
177. C4×C8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
#213652
#208012
#142982
#80302
#80182
C2×#12882
#79042