Finite Group Databasebeta

← #121483

Subgroups — #121483

Order 512.

632 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21982C211yesmaximal, characteristic
2#21964C211yesmaximal, characteristic
3#20800C211yesmaximal, characteristic
4#10857C211yesmaximal, characteristic
5C2×#1299C211yesmaximal, characteristic
6#8028C211yesmaximal, characteristic
7#7896C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#428—22no—
10C2×#423C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2285C2211yescharacteristic
14#2285C2211yescharacteristic
15C2×#384C2211yescharacteristic
16#1948—21no—
17#1948—21no—
18#1947—22no—
19#1947—21no—
20#1947—21no—
21#1852—22no—
22#1847—22no—
23#1845—21no—
24#1845—21no—
25#1844—21no—
26#1834—21no—
27#1809—22no—
28C2×#343—22no—
29#1299C414yescomplemented
30#1295—22no—
31#1279—22no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16D412yes—
35C2×#117—21no—
36C2×#117—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4D412yes—
40C22×C42C2311yescharacteristic
41#431—21no—
42#431—21no—
43#431C2×C412yes—
44#431Q812yes—
45#428—48no—
46C2×#107—24no—
47C2×#107—22no—
48C2×#107—24no—
49C2×#106—24no—
50C2×#106—22no—
51#423—21no—
52#423—21no—
53#423C2×C412yes—
54#423Q812yes—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8D412yes—
58C2×C22⋊C8—21no—
59C4×M16—21no—
60C4×M16—21no—
61C4×M16—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16C2×C412yes—
65C4×M16Q812yes—
66C4×M16Q812yes—
67C2×#97—21no—
68C2×#97D412yes—
69C2×C4×C8—21no—
70C2×C4×C8—21no—
71C2×C4×C8—21no—
72#384—21no—
73#384—21no—
74#384—21no—
75#384—21no—
76#384D411yescharacteristic
77#384D411yescharacteristic
78#384D411yescharacteristic
79#384D411yescharacteristic
80#382—21no—
81#382—21no—
82#380—21no—
83#380—21no—
84#380—21no—
85#380—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90#343—44no—
91#340—22no—
92#340—22no—
93#340—24no—
94C23×C4—22no—
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C2×M16—24no—
99C2×M16—24no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16C4⋊C414yes—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—41no—
116#117—44no—
117#117—82no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
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—44no—
133C2×C4⋊C4—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—82no—
140C2×C22⋊C4—41no—
141C2×C22⋊C4—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42C22×C411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×Q811yescharacteristic
150C2×C42C2×Q811yescharacteristic
151C2×C42C2×Q811yescharacteristic
152C2×C42C2×Q811yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156#107—48no—
157#107—82no—
158#107—84no—
159#106—48no—
160#106—82no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8C4⋊C414yes—
167C22⋊C8—22no—
168C22⋊C8—22no—
169#97—22no—
170#97—22no—
171#97—41no—
172#97C4⋊C414yes—
173C4×C8—22no—
174C4×C8—22no—
175C4×C8—22no—
176C4×C8—22no—
177C4×C8—22no—
178C4×C8—41no—
179#95—41no—
180#95—41no—
181#95—41no—
182#95—41no—
183C24#12111yescharacteristic
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4—44no—
198C22×C4—82no—
199C22×C4—82no—
200C22×C4C2×C4⋊C411yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4C4×Q811yescharacteristic
203C22×C4#12011yescharacteristic
204C22×C4#12011yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12111yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4C22⋊Q811yescharacteristic
210C22×C4C22⋊Q811yescharacteristic
211C22×C4#12311yescharacteristic
212C22×C4#12511yescharacteristic
213C22×C4#12511yescharacteristic
214C22×C4#12511yescharacteristic
215C22×C4#12711yescharacteristic
216C22×C4C4⋊Q811yescharacteristic
217C22×C4C4⋊Q811yescharacteristic
218M16—28no—
219M16—28no—
220M16—24no—
221M16—42no—
222M16—42no—
223M16—42no—
224M16—44no—
225M16—82no—
226C2×C8—24no—
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—44no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—82no—
257C4⋊C4—82no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—82no—
261C22⋊C4—82no—
262C22⋊C4—82no—
263C42—82no—
264C42—82no—
265C42C2×C4⋊C411yescharacteristic
266C42C2×C4⋊C411yescharacteristic
267C42C4×D411yescharacteristic
268C42C4×D411yescharacteristic
269C42C22⋊Q811yescharacteristic
270C42C22⋊Q811yescharacteristic
271C42C22⋊Q811yescharacteristic
272C42C22⋊Q811yescharacteristic
273C42C22⋊Q811yescharacteristic
274C42C22⋊Q811yescharacteristic
275C42#12311yescharacteristic
276C42#12311yescharacteristic
277C42C4⋊Q811yescharacteristic
278C42C4⋊Q811yescharacteristic
279C42C4⋊Q811yescharacteristic
280C42C4⋊Q811yescharacteristic
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23#38911yescharacteristic
288C23#39211yescharacteristic
289C23#39811yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—164no—
328C2×C4#38411yescharacteristic
329C2×C4#38511yescharacteristic
330C2×C4#38511yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38911yescharacteristic
333C2×C4#38911yescharacteristic
334C2×C4#39511yescharacteristic
335C2×C4#39511yescharacteristic
336C2×C4#39511yescharacteristic
337C2×C4#39811yescharacteristic
338C2×C4#39811yescharacteristic
339C2×C4#39911yescharacteristic
340C2×C4#45311yescharacteristic
341C2×C4#45312yes—
342C2×C4#45411yescharacteristic
343C2×C4#45511yescharacteristic
344C2×C4#45611yescharacteristic
345C2×C4#45612yes—
346C2×C4#47212yes—
347C2×C4#47312yes—
348C8—28no—
349C8—44no—
350C8—44no—
351C8—44no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22#144411yescharacteristic
363C22#200211yescharacteristic
364C22#200511yescharacteristic
365C22#200611yescharacteristic
366C22#200711yescharacteristic
367C22#201811yescharacteristic
368C22#202011yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—161no—
376C4—161no—
377C4—162no—
378C4—161no—
379C4—161no—
380C4#185611yescharacteristic
381C4#185711yescharacteristic
382C4#185912yes—
383C4#195212yes—
384C4#206012yes—
385C4#206011yescharacteristic
386C4#206111yescharacteristic
387C4#208912yes—
388C2—41no—
389C2—41no—
390C2#1010411yescharacteristic
391C2#1010711yescharacteristic
392C2#1011711yescharacteristic
393C2#1011811yescharacteristic
394C2#1133111yescharacteristic
395C2#1134011yescharacteristic
396C2#1134211yescharacteristic
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
29. #1299C4semidirect

Maximal subgroups

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

subgroupindex
#219822
#219642
#208002
#108572
C2×#12992
#80282
#78962