Finite Group Databasebeta

← #99099

Subgroups — #99099

Order 512.

680 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13755C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4#7025C212yesmaximal
5#7025C212yesmaximal
6C2×C4×C4⋊C4C411yescharacteristic
7C2×C4×C4⋊C4C411yescharacteristic
8C2×#376—21no—
9C2×C43C2211yescharacteristic
10C2×#336—21no—
11C2×#336—21no—
12C2×#336—21no—
13C2×#336—21no—
14C2×#336C2212yes—
15C2×#336C2212yes—
16C4⋊#95C411yescharacteristic
17C4⋊#95C411yescharacteristic
18C4⋊#95C2211yescharacteristic
19C4⋊#95C2211yescharacteristic
20#1434—21no—
21#1434—21no—
22C4×#95—21no—
23C23×C8—22no—
24C23×C8—22no—
25C22×C4⋊C4C2×C411yescharacteristic
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C42—21no—
30C22×C42—21no—
31C22×C42C2×C411yescharacteristic
32C22×C42C2×C411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38C4×C4⋊C4—22no—
39C4×C4⋊C4—22no—
40C4×C4⋊C4—22no—
41C4×C4⋊C4C814yescomplemented
42#376—42no—
43#376—42no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C43—22no—
55C43—22no—
56#336—24no—
57#336—24no—
58#336—22no—
59#336—22no—
60#336—22no—
61#336—22no—
62#336—42no—
63#336—42no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22×C411yescharacteristic
73C23×C4C2×D411yescharacteristic
74C23×C4C2×D411yescharacteristic
75C22×C8—24no—
76C22×C8—24no—
77C22×C8—42no—
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—
88C22×C8—42no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4C2×C812yes—
102C2×C4⋊C4C2×C812yes—
103C2×C4⋊C4M1612yes—
104C2×C4⋊C4M1612yes—
105C2×C42—21no—
106C2×C42—21no—
107C2×C42—22no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—22no—
111C2×C42—24no—
112C2×C42—24no—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—22no—
118C2×C42—22no—
119C2×C42—22no—
120C2×C42—22no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42—42no—
130C2×C42—42no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42C2×C812yes—
134C2×C42M1612yes—
135C2×C42D812yes—
136C2×C42SD1612yes—
137C2×C42#4112yes—
138C2×C42#4112yes—
139#95—24no—
140#95—24no—
141#95—42no—
142#95—42no—
143#95—42no—
144#95—42no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—42no—
150#95—41no—
151#95—41no—
152C24C2×C22⋊C411yescharacteristic
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—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
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×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C22⋊C812yes—
216C22×C4C22⋊C812yes—
217C22×C4#10212yes—
218C22×C4#10212yes—
219C22×C4#10412yes—
220C22×C4#10412yes—
221C22×C4#11711yescharacteristic
222C22×C4#11711yescharacteristic
223C22×C4#12312yes—
224C22×C4#12312yes—
225C22×C4C22×C811yescharacteristic
226C22×C4C2×M1611yescharacteristic
227C22×C4C2×M1611yescharacteristic
228C22×C4C2×M1611yescharacteristic
229C22×C4C2×D811yescharacteristic
230C22×C4C2×SD1611yescharacteristic
231C22×C4#13512yes—
232C22×C4AGL(1,ℤ/8)11yescharacteristic
233C22×C4#13712yes—
234C22×C4#13711yescharacteristic
235C2×C8—44no—
236C2×C8—44no—
237C2×C8—44no—
238C2×C8—44no—
239C2×C8—44no—
240C2×C8—44no—
241C2×C8—82no—
242C2×C8—82no—
243C2×C8—82no—
244C2×C8—82no—
245C2×C8—82no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—82no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—24no—
262C42—24no—
263C42—42no—
264C42—42no—
265C42—44no—
266C42—44no—
267C42—42no—
268C42—42no—
269C42—48no—
270C42—48no—
271C42—42no—
272C42—42no—
273C23#38111yescharacteristic
274C23C2×C22⋊C811yescharacteristic
275C23#40711yescharacteristic
276C23#41011yescharacteristic
277C23#41011yescharacteristic
278C23#41311yescharacteristic
279C23#41311yescharacteristic
280C23C2×#10211yescharacteristic
281C23#41611yescharacteristic
282C23#41711yescharacteristic
283C23#41911yescharacteristic
284C23C2×#10411yescharacteristic
285C23C2×#10411yescharacteristic
286C23#42111yescharacteristic
287C23#42111yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
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—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4D4⋊C814yes—
372C2×C4#43111yescharacteristic
373C2×C4#43111yescharacteristic
374C2×C4#43211yescharacteristic
375C2×C4#43211yescharacteristic
376C2×C4#48012yes—
377C2×C4#48212yes—
378C2×C4#48312yes—
379C2×C4#48512yes—
380C8—84no—
381C8—84no—
382C22#145811yescharacteristic
383C22#145811yescharacteristic
384C22#146411yescharacteristic
385C22#146411yescharacteristic
386C22C2×D4⋊C811yescharacteristic
387C22#147611yescharacteristic
388C22#147711yescharacteristic
389C22#147911yescharacteristic
390C22#148611yescharacteristic
391C22#148811yescharacteristic
392C22#148911yescharacteristic
393C22#149111yescharacteristic
394C22#150011yescharacteristic
395C22#150211yescharacteristic
396C22#150611yescharacteristic
397C22#150911yescharacteristic
398C22#151211yescharacteristic
399C22#151511yescharacteristic
400C22#151711yescharacteristic
401C22#152111yescharacteristic
402C22#152411yescharacteristic
403C22#152911yescharacteristic
404C22#153211yescharacteristic
405C22#153511yescharacteristic
406C22#154011yescharacteristic
407C22#154711yescharacteristic
408C22#155411yescharacteristic
409C22#155911yescharacteristic
410C22#181711yescharacteristic
411C22#182011yescharacteristic
412C22#182211yescharacteristic
413C22#182311yescharacteristic
414C22#182511yescharacteristic
415C22#182611yescharacteristic
416C22#182611yescharacteristic
417C4—24no—
418C4—22no—
419C4—22no—
420C4—22no—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—82no—
430C4—82no—
431C4—82no—
432C4—82no—
433C2#756011yescharacteristic
434C2#757411yescharacteristic
435C2#758111yescharacteristic
436C2#759611yescharacteristic
437C2#761111yescharacteristic
438C2#761411yescharacteristic
439C2#763011yescharacteristic
440C2#764211yescharacteristic
441C2#869911yescharacteristic
442C2#870611yescharacteristic
443C2#870811yescharacteristic
444C2#871411yescharacteristic
445C2#871611yescharacteristic
446C2#872011yescharacteristic
447C2#872611yescharacteristic
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
41. C4×C4⋊C4C8semidirect

Maximal subgroups

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

subgroupindex
#137552
#107952
#70252