Finite Group Databasebeta

← #99884

Subgroups — #99884

Order 512.

533 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22599C211yesmaximal, characteristic
2C2×#1927C211yesmaximal, characteristic
3#9878C211yesmaximal, characteristic
4#8706C211yesmaximal, characteristic
5#7575C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C2×#431—21no—
9C22×#106C411yescharacteristic
10C22×#103C411yescharacteristic
11C22×#103C411yescharacteristic
12C2×#391C2211yescharacteristic
13C2×C4×C4⋊C4C2211yescharacteristic
14#1939—21no—
15#1927—21no—
16#1927—21no—
17#1927—21no—
18#1927—21no—
19#1916—22no—
20#1817—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23C8×C4⋊C4—21no—
24C4×C22⋊C8C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#340C411yescharacteristic
27C2×#336C2211yescharacteristic
28#1280—21no—
29#1280—21no—
30#1279—21no—
31#1279—21no—
32#1272—22no—
33C23×Q8C2×C411yescharacteristic
34C23×C8C2×C411yescharacteristic
35C23×C8C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41#431—42no—
42#431—42no—
43C2×#106—21no—
44C2×#106—21no—
45C2×#106—42no—
46C2×C4⋊C8—22no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—22no—
52C2×#103—21no—
53C2×#103—21no—
54C2×#103—42no—
55C2×#103C814yescomplemented
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8D411yescharacteristic
60C2×C22⋊C8D411yescharacteristic
61C2×C4×C8—22no—
62C2×C4×C8—21no—
63C2×C4×C8—21no—
64#391—21no—
65#391—21no—
66#391—21no—
67#391—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4D411yescharacteristic
71C4×C4⋊C4D411yescharacteristic
72C4×C4⋊C4D411yescharacteristic
73C4×C4⋊C4D411yescharacteristic
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77#340—21no—
78#340—21no—
79#336—22no—
80#336—22no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336D412yes—
87C22×Q8—21no—
88C22×Q8—21no—
89C22×Q8—21no—
90C22×Q8—21no—
91C22×Q8—21no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8—41no—
95C22×Q8—41no—
96C22×Q8C2×C812yes—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4—21no—
100C23×C4—21no—
101C23×C4C22×C411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4#4111yescharacteristic
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—21no—
107C22×C8—21no—
108C22×C8—21no—
109C22×C8—22no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8C2×C812yes—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C4⋊C4C22⋊C411yescharacteristic
131C2×C4⋊C4C22⋊C411yescharacteristic
132C2×C4⋊C4C22⋊C411yescharacteristic
133C2×C4⋊C4C2×C812yes—
134C2×C4⋊C4M1612yes—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149#106—42no—
150#106—42no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—44no—
156#103—24no—
157#103—24no—
158#103—42no—
159#103—42no—
160C22⋊C8—21no—
161C22⋊C8—22no—
162C22⋊C8—21no—
163C22⋊C8—21no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169C22⋊C8SD1612yes—
170C4×C8—41no—
171C4×C8—41no—
172C4×C8—41no—
173C4×C8—41no—
174C4×C8—44no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—21no—
179#95—41no—
180#95—41no—
181#95—41no—
182#95—41no—
183C24C4×D411yescharacteristic
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—81no—
197C2×Q8—81no—
198C2×Q8—81no—
199C2×Q8—81no—
200C2×Q8—81no—
201C2×Q8—81no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—81no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4—81no—
236C22×C4C2×C22⋊C411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4#12011yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4C22×C811yescharacteristic
243C22×C4C2×M1611yescharacteristic
244C22×C4#13111yescharacteristic
245C22×C4#13111yescharacteristic
246C22×C4C2×SD1611yescharacteristic
247C22×C4#13511yescharacteristic
248C22×C4AGL(1,ℤ/8)11yescharacteristic
249C22×C4#13711yescharacteristic
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—42no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—42no—
267C2×C8—41no—
268C2×C8—81no—
269C2×C8—81no—
270C2×C8—81no—
271C2×C8—81no—
272C2×C8—81no—
273C2×C8—81no—
274C2×C8—81no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4C22⋊C812yes—
287C4⋊C4C22⋊C812yes—
288C4⋊C4#10012yes—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—41no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C42—41no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23#38611yescharacteristic
308C23C8×D411yescharacteristic
309C23#43511yescharacteristic
310C23C4×SD1611yescharacteristic
311C23#44011yescharacteristic
312C23#44311yescharacteristic
313C23#44411yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—82no—
317Q8—82no—
318Q8—81no—
319Q8—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—161no—
373C2×C4—161no—
374C2×C4C2×C22⋊C811yescharacteristic
375C2×C4#40811yescharacteristic
376C2×C4#41011yescharacteristic
377C2×C4#41011yescharacteristic
378C2×C4C2×#10011yescharacteristic
379C2×C4#41311yescharacteristic
380C2×C4C8×D411yescharacteristic
381C2×C4#43511yescharacteristic
382C2×C4#45011yescharacteristic
383C2×C4#45211yescharacteristic
384C2×C4#46111yescharacteristic
385C2×C4#46311yescharacteristic
386C8—42no—
387C8—42no—
388C8—82no—
389C8—81no—
390C8—82no—
391C8—81no—
392C8—161no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22C8×SD1611yescharacteristic
406C22SD16⋊C811yescharacteristic
407C22#158211yescharacteristic
408C22#158511yescharacteristic
409C22#186911yescharacteristic
410C22#187611yescharacteristic
411C22#187711yescharacteristic
412C22#189911yescharacteristic
413C22#190011yescharacteristic
414C22#190211yescharacteristic
415C22#190511yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—41no—
424C4—42no—
425C4—42no—
426C4—42no—
427C4—81no—
428C4—82no—
429C4—161no—
430C4#145811yescharacteristic
431C4#146011yescharacteristic
432C4#146911yescharacteristic
433C4#147311yescharacteristic
434C2—21no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2#894511yescharacteristic
439C2#908011yescharacteristic
440C2#908811yescharacteristic
441C2#924011yescharacteristic
442C2#924411yescharacteristic
443C2#924711yescharacteristic
444C2#925611yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
55. C2×#103C8semidirect

Maximal subgroups

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

subgroupindex
#225992
C2×#19272
#98782
#87062
#75752
#70202
#70162