Finite Group Databasebeta

← #616396

Subgroups — #616396

Order 512.

2798 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2862C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic
3C2×#2546C211yesmaximal, characteristic
4C2×C42×Q8C211yesmaximal, characteristic
5#15237C214yesmaximal
6#15085C218yesmaximal
7#14703C214yesmaximal
8#14155C211yesmaximal, characteristic
9#14155C211yesmaximal, characteristic
10#14024C214yesmaximal
11#14003C214yesmaximal
12C4×#382C211yesmaximal, characteristic
13C22×C4⋊Q8C2211yescharacteristic
14C22×C4⋊Q8C2211yescharacteristic
15C22×C4⋊Q8C2212yes—
16C22×C4×Q8C2212yes—
17C22×C4×Q8C2211yescharacteristic
18#2862—28no—
19#2568—28no—
20#2546—28no—
21C2×#400C2214yes—
22C2×#398C2214yes—
23C2×#391C2212yes—
24C2×#391C2212yes—
25C2×#391C2214yes—
26C2×#391C2214yes—
27C2×#391C2214yes—
28C2×#391C2214yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#389C2214yes—
32C2×#382C2214yes—
33C2×#382C2212yes—
34C2×#382C2212yes—
35C42×Q8—28no—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2212yes—
40C2×C4×C4⋊C4C2212yes—
41C2×C4×C4⋊C4C2214yes—
42C2×C43C2212yes—
43C2×C43C2211yescharacteristic
44#1445C2214yes—
45#1445C2214yes—
46#1443C22116yes—
47#1441C22116yes—
48#1436C22116yes—
49C4⋊#95C2214yes—
50C4⋊#95C2214yes—
51C4⋊#95C2212yes—
52#1434C22116yes—
53#1434C2214yes—
54C4×#95C2214yes—
55C23×Q8C2312yes—
56C23×Q8C2312yes—
57C23×Q8C2311yescharacteristic
58C2×C4⋊Q8—28no—
59C2×C4⋊Q8—216no—
60C2×C4⋊Q8—24no—
61C2×C4⋊Q8—24no—
62C2×C4⋊Q8—24no—
63C2×C4⋊Q8—24no—
64C2×C4⋊Q8—24no—
65C2×C4⋊Q8—24no—
66C2×C4×Q8—28no—
67C2×C4×Q8—28no—
68C2×C4×Q8—28no—
69C2×C4×Q8—24no—
70C2×C4×Q8—24no—
71C2×C4×Q8D418yes—
72C22×C4⋊C4C2312yes—
73C22×C4⋊C4C2318yes—
74C22×C4⋊C4C2312yes—
75C22×C4⋊C4C2314yes—
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2312yes—
83C22×C42C2314yes—
84C22×C42C2312yes—
85C22×C42C2312yes—
86C22×C42C2314yes—
87C22×C42C2312yes—
88C22×C42C2312yes—
89C22×C42C2312yes—
90C22×C42C2312yes—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94#400—216no—
95#398—216no—
96#391—28no—
97#391—28no—
98#391—216no—
99#391—216no—
100#391—216no—
101#391—216no—
102#391—28no—
103#391—28no—
104#389—216no—
105#382—28no—
106#382—28no—
107#382—216no—
108C4×C4⋊C4—24no—
109C4×C4⋊C4—216no—
110C4×C4⋊C4—28no—
111C4×C4⋊C4—28no—
112C4×C4⋊C4—24no—
113C4×C4⋊C4—24no—
114C2×#95C2312yes—
115C2×#95C2318yes—
116C2×#95C2312yes—
117C2×#95C2318yes—
118C2×#95C2318yes—
119C2×#95C2318yes—
120C2×#95C2318yes—
121C2×#95C2318yes—
122C2×#95C23116yes—
123C2×#95C23116yes—
124C2×#95C2318yes—
125C2×#95C2314yes—
126C2×#95C2312yes—
127C43—28no—
128C43D418yes—
129C22×Q8—22no—
130C22×Q8—24no—
131C22×Q8—24no—
132C22×Q8—24no—
133C22×Q8—24no—
134C22×Q8—22no—
135C22×Q8—24no—
136C22×Q8—24no—
137C22×Q8—24no—
138C22×Q8—28no—
139C22×Q8—28no—
140C22×Q8—28no—
141C22×Q8—28no—
142C22×Q8C2×D414yes—
143C22×Q8#4118yes—
144C23×C4C2414yes—
145C23×C4C2414yes—
146C23×C4C2414yes—
147C23×C4C2412yes—
148C23×C4C2412yes—
149C23×C4C2414yes—
150C23×C4C2414yes—
151C23×C4C2411yescharacteristic
152C23×C4C2412yes—
153C23×C4C2412yes—
154C23×C4C2411yescharacteristic
155C23×C4C2411yescharacteristic
156C4⋊Q8—432no—
157C4⋊Q8—416no—
158C4⋊Q8—416no—
159C4×Q8—264no—
160C4×Q8—232no—
161C2×C4⋊C4—28no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—28no—
167C2×C4⋊C4—28no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—216no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—232no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4C2×D414yes—
190C2×C4⋊C4C2×D418yes—
191C2×C4⋊C4#4118yes—
192C2×C4⋊C4#4118yes—
193C2×C42—28no—
194C2×C42—24no—
195C2×C42—28no—
196C2×C42—28no—
197C2×C42—24no—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—24no—
201C2×C42—24no—
202C2×C42—28no—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42—28no—
206C2×C42—24no—
207C2×C42—28no—
208C2×C42—28no—
209C2×C42—28no—
210C2×C42—216no—
211C2×C42C2×D418yes—
212C2×C42C2×D418yes—
213C2×C42C2×D414yes—
214C2×C42C2×D418yes—
215C2×C42C2×D414yes—
216C2×C42C2×D414yes—
217C2×C42C2×D414yes—
218C2×C42#4114yes—
219#95—28no—
220#95—24no—
221#95—24no—
222#95—24no—
223#95—216no—
224#95—216no—
225#95—216no—
226#95—216no—
227#95—216no—
228#95—216no—
229#95—232no—
230#95—232no—
231#95—216no—
232C24C2511yescharacteristic
233C2×Q8—28no—
234C2×Q8—216no—
235C2×Q8—216no—
236C2×Q8—28no—
237C2×Q8—48no—
238C2×Q8—48no—
239C2×Q8—416no—
240C2×Q8—48no—
241C2×Q8—416no—
242C2×Q8—48no—
243C2×Q8—48no—
244C2×Q8—48no—
245C2×Q8—416no—
246C2×Q8—416no—
247C2×Q8#124116yes—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—28no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—28no—
265C22×C4—28no—
266C22×C4—24no—
267C22×C4—28no—
268C22×C4—28no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—28no—
278C22×C4—28no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—28no—
282C22×C4—28no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4C22×D414yes—
286C22×C4C22×D414yes—
287C22×C4C22×D412yes—
288C22×C4C22×D412yes—
289C22×C4C22×D414yes—
290C22×C4C22×D414yes—
291C22×C4C22×D412yes—
292C22×C4C22×D412yes—
293C22×C4C22×D412yes—
294C22×C4C22×D412yes—
295C22×C4C2×#4118yes—
296C22×C4C2×#4118yes—
297C22×C4C2×#4112yes—
298C22×C4C2×#4118yes—
299C22×C4C2×#4112yes—
300C22×C4C2×#4112yes—
301C22×C4C2×#4114yes—
302C22×C4C2×#4114yes—
303C22×C4C2×#4114yes—
304C22×C42−1+418yes—
305C22×C42−1+414yes—
306C4⋊C4—232no—
307C4⋊C4—216no—
308C4⋊C4—28no—
309C4⋊C4—216no—
310C4⋊C4—216no—
311C4⋊C4—48no—
312C4⋊C4—48no—
313C4⋊C4—48no—
314C4⋊C4—48no—
315C4⋊C4—432no—
316C4⋊C4—48no—
317C42—232no—
318C42—216no—
319C42—216no—
320C42—28no—
321C42—28no—
322C42—216no—
323C42—48no—
324C42—48no—
325C42—48no—
326C42—416no—
327C42#121116yes—
328C23C23×D411yescharacteristic
329C23C23×D411yescharacteristic
330C23C22×#4111yescharacteristic
331C23C22×#4112yes—
332C23C22×#4112yes—
333C23C22×#4112yes—
334C23C2×2−1+412yes—
335C23C2×2−1+414yes—
336Q8—232no—
337Q8—816no—
338Q8—816no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—28no—
349C2×C4—28no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—28no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—28no—
356C2×C4—216no—
357C2×C4—216no—
358C2×C4—28no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—48no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—48no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—48no—
372C2×C4—44no—
373C2×C4—48no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—48no—
380C2×C4—48no—
381C2×C4—48no—
382C2×C4—44no—
383C2×C4—48no—
384C2×C4C2×#12114yes—
385C2×C4C2×#12114yes—
386C2×C4C2×#12114yes—
387C2×C4#52518yes—
388C2×C4C2×#12418yes—
389C2×C4C2×#12414yes—
390C2×C4#52918yes—
391C2×C4#53214yes—
392C2×C4#53214yes—
393C2×C4#53618yes—
394C2×C4#53614yes—
395C2×C4#54818yes—
396C2×C4#55618yes—
397C22C22×#12111yescharacteristic
398C22C2×#52512yes—
399C22C22×#12411yescharacteristic
400C22C2×#52912yes—
401C22C2×#53211yescharacteristic
402C22C2×#53211yescharacteristic
403C22C2×#53611yescharacteristic
404C22C2×#53612yes—
405C22C2×#54812yes—
406C22C2×#55612yes—
407C22#348214yes—
408C22#348214yes—
409C22#349912yes—
410C22#350912yes—
411C22#352314yes—
412C22#352314yes—
413C4—28no—
414C4—28no—
415C4—24no—
416C4—48no—
417C4—44no—
418C4—48no—
419C4—44no—
420C4—84no—
421C4—84no—
422C4—84no—
423C4#254518yes—
424C4#285018yes—
425C2C2×#254511yescharacteristic
426C2#3497912yes—
427C2#3524812yes—
428C2#3531611yescharacteristic
429C2#3631314yes—
430C2#3644612yes—
431C2#3650812yes—
432C2C2×#285011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#28622
C2×#25682
C2×#25462
C2×C42×Q82
#152372
#150852
#147032
#141552
#140242
#140032
C4×#3822