Finite Group Databasebeta

← #923689

Subgroups — #923689

Order 512.

2234 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2453C212yesmaximal
2C2×#2446C212yesmaximal
3#17113C214yesmaximal
4#16349C214yesmaximal
5#16329C214yesmaximal
6#15974C214yesmaximal
7#15218C211yesmaximal, characteristic
8#15194C212yesmaximal
9#15192C212yesmaximal
10#15180C211yesmaximal, characteristic
11#14261C212yesmaximal
12#14017C212yesmaximal
13#13856C211yesmaximal, characteristic
14C22×C4⋊Q8C2211yescharacteristic
15C22×#125C2211yescharacteristic
16C22×C4×Q8C2212yes—
17#2453—216no—
18#2446—216no—
19C2×#400C2214yes—
20C2×#400C2214yes—
21C2×#398C2214yes—
22C2×#398C2214yes—
23C2×#391C2212yes—
24C2×#391C2212yes—
25C2×#391C2212yes—
26C2×#391C2212yes—
27C2×#391C2212yes—
28C2×#389C2212yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2214yes—
32C2×#387C2214yes—
33C2×#387C2214yes—
34C2×#387C2214yes—
35C2×C4×C4⋊C4C2212yes—
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×#376C2211yescharacteristic
40#1445C2214yes—
41#1445C2214yes—
42#1444C2212yes—
43#1444C2212yes—
44#1444C2212yes—
45#1444C2212yes—
46#1444C2214yes—
47#1444C2214yes—
48#1444C2214yes—
49#1443C2214yes—
50#1443C2214yes—
51#1443C2214yes—
52#1443C2214yes—
53#1442C2214yes—
54#1442C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1441C2214yes—
59#1441C2214yes—
60#1441C2214yes—
61#1441C2214yes—
62#1436C2214yes—
63#1436C2214yes—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C23×Q8C2312yes—
70C2×C4⋊Q8—28no—
71C2×C4⋊Q8—42no—
72C2×#125—28no—
73C2×#125—42no—
74C2×C4×Q8—28no—
75C2×C4×Q8—28no—
76C2×C4×Q8—44no—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2314yes—
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2314yes—
83C22×C4⋊C4C2314yes—
84C22×C4⋊C4C2314yes—
85C22×C4⋊C4C2314yes—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2312yes—
88C22×C4⋊C4C2312yes—
89C22×C4⋊C4C2314yes—
90C22×C4⋊C4C2312yes—
91C22×C4⋊C4C2312yes—
92C22×C42C2312yes—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2314yes—
96C22×C42C2312yes—
97C22×C42C2311yescharacteristic
98#400—216no—
99#400—216no—
100#398—216no—
101#398—216no—
102#391—28no—
103#391—28no—
104#391—28no—
105#391—28no—
106#391D4116yes—
107#389—28no—
108#389—28no—
109#389—28no—
110#389—216no—
111#387—216no—
112#387—216no—
113#387—216no—
114C4×C4⋊C4—28no—
115C4×C4⋊C4—28no—
116C4×C4⋊C4—42no—
117C4×C4⋊C4—42no—
118#376—24no—
119C2×#95C2314yes—
120C2×#95C2314yes—
121C2×#95C2314yes—
122C2×#95C2314yes—
123C2×#95C2312yes—
124C2×#95C2312yes—
125C2×#95C2314yes—
126C2×#95C2314yes—
127C2×#95C2314yes—
128C2×#95C2314yes—
129C2×#95C2314yes—
130C2×#95C2314yes—
131C2×#95C2314yes—
132C2×#95C2312yes—
133C2×#95C2311yescharacteristic
134C2×#95C2312yes—
135C2×#95C2311yescharacteristic
136C2×#95C2312yes—
137C2×#95C2314yes—
138C2×#95C2314yes—
139C2×#95C2314yes—
140C2×#95C2314yes—
141C2×#95C2314yes—
142C2×#95C2314yes—
143C2×#95C2314yes—
144C2×#95C2314yes—
145C2×#95C2311yescharacteristic
146C2×#95C2312yes—
147C2×#95C2311yescharacteristic
148C2×#95C2314yes—
149C2×#95C2314yes—
150C22×Q8—24no—
151C22×Q8—24no—
152C22×Q8—24no—
153C22×Q8—24no—
154C22×Q8—24no—
155C22×Q8—24no—
156C22×Q8C2×D418yes—
157C23×C4C2412yes—
158C23×C4C2412yes—
159C23×C4C2414yes—
160C23×C4C2414yes—
161C23×C4C2414yes—
162C23×C4C2412yes—
163C23×C4C2414yes—
164C23×C4C2412yes—
165C23×C4C2411yescharacteristic
166C23×C4C2411yescharacteristic
167C23×C4C2412yes—
168C23×C4C2412yes—
169C23×C4C2411yescharacteristic
170C4⋊Q8—416no—
171#125—416no—
172C4×Q8—432no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—28no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—28no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—28no—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—28no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—28no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4—44no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—44no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4—44no—
215C2×C4⋊C4—42no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4C2×D418yes—
218C2×C42—24no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—24no—
222C2×C42—24no—
223C2×C42—24no—
224C2×C42—28no—
225C2×C42—28no—
226C2×C42—24no—
227C2×C42—24no—
228C2×C42—24no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42—44no—
232C2×C42C2×D418yes—
233C2×C42#4114yes—
234#95—24no—
235#95—24no—
236#95—24no—
237#95—24no—
238#95—28no—
239#95—28no—
240#95—28no—
241#95—28no—
242#95—28no—
243#95—28no—
244#95—28no—
245#95—28no—
246#95—28no—
247#95—22no—
248#95—24no—
249#95—22no—
250#95—28no—
251#95—28no—
252#95—44no—
253#95—44no—
254#95—44no—
255#95—44no—
256#95—44no—
257#95—44no—
258#95—44no—
259#95—44no—
260#95—41no—
261#95—42no—
262#95—41no—
263#95C2×D4116yes—
264#95C2×D4116yes—
265C24C2511yescharacteristic
266C2×Q8—216no—
267C2×Q8—216no—
268C2×Q8—216no—
269C2×Q8—48no—
270C2×Q8—48no—
271C2×Q8—48no—
272C2×Q8—48no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4C22×D414yes—
346C22×C4C22×D418yes—
347C22×C4C22×D414yes—
348C22×C4C22×D418yes—
349C22×C4C22×D414yes—
350C22×C4C2×#4112yes—
351C22×C4C2×#4112yes—
352C22×C4C2×#4112yes—
353C22×C4H(5,𝔽2)12yes—
354C22×C42−1+414yes—
355C22×C42−1+414yes—
356C22×C42−1+412yes—
357C22×C42−1+414yes—
358C4⋊C4—216no—
359C4⋊C4—216no—
360C4⋊C4—48no—
361C4⋊C4—48no—
362C4⋊C4—416no—
363C4⋊C4—416no—
364C4⋊C4—416no—
365C4⋊C4—416no—
366C4⋊C4—416no—
367C4⋊C4—416no—
368C4⋊C4—48no—
369C4⋊C4—48no—
370C4⋊C4—48no—
371C4⋊C4—48no—
372C4⋊C4—48no—
373C42—28no—
374C42—216no—
375C42—416no—
376C42—48no—
377C42—44no—
378C42—44no—
379C23C23×D412yes—
380C23C22×#4111yescharacteristic
381C23C2×H(5,𝔽2)11yescharacteristic
382C23C2×2−1+411yescharacteristic
383C23C2×2−1+412yes—
384C23C2×2−1+412yes—
385C23C2×2−1+412yes—
386C23#58512yes—
387C23#58512yes—
388Q8—432no—
389C2×C4—28no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—28no—
394C2×C4—28no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—28no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4#53618yes—
470C2×C4#53914yes—
471C2×C4D4214yes—
472C2×C4#54718yes—
473C2×C4#56314yes—
474C22C2×#53612yes—
475C22C2×#53911yescharacteristic
476C22#346112yes—
477C22C2×D4211yescharacteristic
478C22C2×#54712yes—
479C22#348612yes—
480C22#348712yes—
481C22#348912yes—
482C22#348912yes—
483C22#350911yescharacteristic
484C22#351211yescharacteristic
485C22C2×#56311yescharacteristic
486C22#354112yes—
487C22#354112yes—
488C22#355512yes—
489C22#355512yes—
490C22#355512yes—
491C22#355611yescharacteristic
492C22#355612yes—
493C22#355711yescharacteristic
494C22#355712yes—
495C4—42no—
496C4—48no—
497C4—42no—
498C4—44no—
499C4—44no—
500C4—48no—
501C4—44no—
502C4—44no—
503C4—84no—
504C4—84no—
505C4—82no—
506C4—82no—
507C4#268018yes—
508C2#3739411yescharacteristic
509C2#3752211yescharacteristic
510C2#3779312yes—
511C2#3779912yes—
512C2#4281112yes—
513C2#4288412yes—
514C2#4526712yes—
515C2C2×#268011yescharacteristic
516C2#5314312yes—
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×#24532
C2×#24462
#171132
#163492
#163292
#159742
#152182
#151942
#151922
#151802
#142612
#140172
#138562