Finite Group Databasebeta

← #102394

Subgroups — #102394

Order 512.

692 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#14699C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3C4×#336C211yesmaximal, characteristic
4#7025C212yesmaximal
5#7025C212yesmaximal
6C22×C4×C8—21no—
7C2×#389C411yescharacteristic
8C2×#389C411yescharacteristic
9C2×#387—21no—
10C2×C43C2211yescharacteristic
11C2×#336—21no—
12C2×#336—21no—
13C2×#336—21no—
14C2×#336C2212yes—
15C2×#336C2212yes—
16#1436—21no—
17#1436—21no—
18C4⋊#95C411yescharacteristic
19C4⋊#95C411yescharacteristic
20C4⋊#95C2211yescharacteristic
21C4⋊#95C2211yescharacteristic
22#1434—21no—
23C23×C8—22no—
24C23×C8—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C42C2×C411yescharacteristic
32C22×C42C2×C411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38C2×C4×C8—24no—
39C2×C4×C8—42no—
40C2×C4×C8—42no—
41#389—22no—
42#389—42no—
43#389C814yescomplemented
44#387—42no—
45#387—42no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C43—42no—
57#336—24no—
58#336—24no—
59#336—22no—
60#336—24no—
61#336—42no—
62#336Q814yes—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22×C411yescharacteristic
72C23×C4C2×D411yescharacteristic
73C23×C4C2×D411yescharacteristic
74C22×C8—24no—
75C22×C8—24no—
76C22×C8—24no—
77C22×C8—24no—
78C22×C8—42no—
79C22×C8—42no—
80C22×C8—42no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8—42no—
84C22×C8—42no—
85C22×C8—42no—
86C22×C8—42no—
87C22×C8—42no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4C2×C812yes—
107C2×C4⋊C4C2×C812yes—
108C2×C42—22no—
109C2×C42—22no—
110C2×C42—22no—
111C2×C42—22no—
112C2×C42—22no—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—22no—
116C2×C42—22no—
117C2×C42—22no—
118C2×C42—41no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42—41no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42C2×C812yes—
127C2×C42M1612yes—
128C2×C42D812yes—
129C2×C42SD1612yes—
130C2×C42C2×Q812yes—
131C2×C42#4112yes—
132C4×C8—48no—
133#95—24no—
134#95—42no—
135#95—42no—
136#95—42no—
137#95—42no—
138#95—42no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—42no—
144#95—42no—
145C24C2×C22⋊C411yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
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—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C22⋊C812yes—
207C22×C4C22⋊C812yes—
208C22×C4#9912yes—
209C22×C4#10212yes—
210C22×C4#10212yes—
211C22×C4#10412yes—
212C22×C4#10412yes—
213C22×C4#10412yes—
214C22×C4C4×Q812yes—
215C22×C4C22⋊Q812yes—
216C22×C4#12411yescharacteristic
217C22×C4C4⋊Q811yescharacteristic
218C22×C4C22×C811yescharacteristic
219C22×C4C2×M1611yescharacteristic
220C22×C4#13112yes—
221C22×C4C2×D811yescharacteristic
222C22×C4C2×SD1611yescharacteristic
223C22×C4#13512yes—
224C22×C4#13512yes—
225C22×C4#13712yes—
226C2×C8—28no—
227C2×C8—44no—
228C2×C8—44no—
229C2×C8—44no—
230C2×C8—44no—
231C2×C8—44no—
232C2×C8—44no—
233C2×C8—44no—
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—82no—
237C2×C8—82no—
238C2×C8—82no—
239C2×C8—82no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—48no—
245C4⋊C4—82no—
246C4⋊C4—82no—
247C4⋊C4—84no—
248C42—24no—
249C42—24no—
250C42—42no—
251C42—42no—
252C42—42no—
253C42—42no—
254C42—44no—
255C42—44no—
256C42—44no—
257C42—44no—
258C23#39111yescharacteristic
259C23C2×C22⋊C811yescharacteristic
260C23#40811yescharacteristic
261C23C2×#9911yescharacteristic
262C23#41011yescharacteristic
263C23#41311yescharacteristic
264C23#41311yescharacteristic
265C23C2×#10211yescharacteristic
266C23#41611yescharacteristic
267C23#41611yescharacteristic
268C23#41911yescharacteristic
269C23C2×#10411yescharacteristic
270C23C2×#10411yescharacteristic
271C23C2×#10411yescharacteristic
272C23#42111yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4D4⋊C814yes—
352C2×C4#32714yes—
353C2×C4C8×Q812yes—
354C2×C4#44612yes—
355C2×C4#47412yes—
356C2×C4#47512yes—
357C2×C4#48812yes—
358C2×C4#49912yes—
359C8—48no—
360C8—84no—
361C22#145811yescharacteristic
362C22#145911yescharacteristic
363C22#146811yescharacteristic
364C22#147311yescharacteristic
365C22C2×D4⋊C811yescharacteristic
366C22#147611yescharacteristic
367C22#147611yescharacteristic
368C22#147911yescharacteristic
369C22#148011yescharacteristic
370C22#148511yescharacteristic
371C22#149411yescharacteristic
372C22#149411yescharacteristic
373C22C2×#32711yescharacteristic
374C22#150011yescharacteristic
375C22#150111yescharacteristic
376C22#150211yescharacteristic
377C22#150611yescharacteristic
378C22#150811yescharacteristic
379C22#151611yescharacteristic
380C22#152111yescharacteristic
381C22#152411yescharacteristic
382C22#152411yescharacteristic
383C22#152911yescharacteristic
384C22#153211yescharacteristic
385C22#154011yescharacteristic
386C22#154011yescharacteristic
387C22#155411yescharacteristic
388C22#155411yescharacteristic
389C22#198411yescharacteristic
390C22#198611yescharacteristic
391C22#198811yescharacteristic
392C22#199111yescharacteristic
393C22#199411yescharacteristic
394C22#199611yescharacteristic
395C22#199811yescharacteristic
396C4—24no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—22no—
403C4—24no—
404C4—42no—
405C4—42no—
406C4—82no—
407C4—82no—
408C4—161no—
409C4—161no—
410C2#756011yescharacteristic
411C2#756511yescharacteristic
412C2#758111yescharacteristic
413C2#758311yescharacteristic
414C2#765411yescharacteristic
415C2#767211yescharacteristic
416C2#767511yescharacteristic
417C2#769311yescharacteristic
418C2#986511yescharacteristic
419C2#987111yescharacteristic
420C2#988011yescharacteristic
421C2#988611yescharacteristic
422C2#989211yescharacteristic
423C2#989911yescharacteristic
424C2#990911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
43. #389C8semidirect

Maximal subgroups

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

subgroupindex
#146992
#107952
C4×#3362
#70252