Finite Group Databasebeta

← #415140

Subgroups — #415140

Order 512.

1074 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1989C211yesmaximal, characteristic
2C2×#1989C211yesmaximal, characteristic
3C2×#1947C211yesmaximal, characteristic
4C2×#1843C211yesmaximal, characteristic
5#14283C211yesmaximal, characteristic
6#13783C211yesmaximal, characteristic
7#11232C212yesmaximal
8#11232C212yesmaximal
9#11228C212yesmaximal
10#11227C212yesmaximal
11#10849C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C22×#107C2212yes—
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×C4⋊C8C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C2×#389C2212yes—
19C2×#384C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×#376C2211yescharacteristic
23#1989—24no—
24#1989—24no—
25#1947—24no—
26#1843—24no—
27C2×#340C2211yescharacteristic
28C2×#340C2212yes—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36#1441—21no—
37#1441—21no—
38#1441—22no—
39#1436—22no—
40C4⋊#95—21no—
41C4⋊#95C2212yes—
42C4⋊#95C2212yes—
43C4⋊#95C2212yes—
44#1434—21no—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C23×C8C2312yes—
48C2×#125—22no—
49C2×#125—22no—
50C2×#125—22no—
51C2×#125—22no—
52C2×#125—22no—
53C2×#125Q814yes—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42—21no—
67C22×C42C2312yes—
68C22×C42C2311yescharacteristic
69C2×#107—24no—
70C2×#107—42no—
71C2×#107—42no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—24no—
75C2×C4⋊C8—24no—
76C2×C4⋊C8—22no—
77C2×C4⋊C8—22no—
78C2×C4⋊C8—24no—
79C2×C4⋊C8—24no—
80C2×C4⋊C8—22no—
81C2×C4⋊C8—42no—
82C2×C4⋊C8—42no—
83C2×C4⋊C8D414yes—
84#389—24no—
85#389Q818yes—
86#384—22no—
87#384—22no—
88C4×C4⋊C4—22no—
89C4×C4⋊C4—22no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4D414yes—
92#376—22no—
93#376—22no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95D411yescharacteristic
104C2×#95D411yescharacteristic
105C2×#95D412yes—
106#340—24no—
107#340—24no—
108#340—24no—
109#340—22no—
110#340—22no—
111#340—22no—
112#340—22no—
113#340—42no—
114#340—42no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—21no—
120C23×C4—22no—
121C23×C4C2×D412yes—
122C23×C4C2×D412yes—
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2411yescharacteristic
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—21no—
133C22×C8—21no—
134C22×C8—21no—
135C22×C8—21no—
136C22×C8—21no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8C2×D414yes—
143#125—28no—
144#125—28no—
145#125—44no—
146#125—44no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—28no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—81no—
186C2×C4⋊C4—81no—
187C2×C4⋊C4C2×D412yes—
188C2×C4⋊C4C2×D412yes—
189C2×C4⋊C4C2×Q812yes—
190C2×C4⋊C4C2×Q812yes—
191C2×C4⋊C4C2×Q814yes—
192C2×C4⋊C4C2×Q814yes—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—24no—
198C2×C42—42no—
199C2×C42—82no—
200C2×C42—81no—
201C2×C42—81no—
202C2×C42C2×D412yes—
203C2×C42C2×D412yes—
204C2×C42C2×Q814yes—
205C2×C42C2×Q812yes—
206C2×C42#4114yes—
207C2×C42#4112yes—
208C2×C42#4112yes—
209C2×C42#4112yes—
210#107—48no—
211C4⋊C8—28no—
212C4⋊C8—48no—
213C4⋊C8—48no—
214C4⋊C8—44no—
215#95—24no—
216#95—22no—
217#95—22no—
218#95—24no—
219#95—28no—
220#95—42no—
221#95—82no—
222#95—82no—
223#95—82no—
224#95—82no—
225#95—82no—
226#95—82no—
227C24C22×D411yescharacteristic
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4#12112yes—
283C22×C4#12112yes—
284C22×C4#12112yes—
285C22×C4#12112yes—
286C22×C4C22⋊Q814yes—
287C22×C4C22⋊Q814yes—
288C22×C4C22⋊Q812yes—
289C22×C4C22⋊Q812yes—
290C22×C4C22×D411yescharacteristic
291C22×C4C22×D411yescharacteristic
292C22×C4C22×Q811yescharacteristic
293C22×C4C22×Q812yes—
294C22×C4C2×#4111yescharacteristic
295C22×C4C2×#4111yescharacteristic
296C22×C4C2×#4111yescharacteristic
297C22×C4C2×#4112yes—
298C22×C4H(5,𝔽2)12yes—
299C22×C42−1+412yes—
300C2×C8—24no—
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—48no—
335C4⋊C4—48no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—88no—
341C4⋊C4—84no—
342C4⋊C4—84no—
343C4⋊C4C4⋊Q814yes—
344C42—24no—
345C42—24no—
346C42—24no—
347C42—24no—
348C42—84no—
349C42—84no—
350C42#12114yes—
351C42C22⋊Q814yes—
352C42C22⋊Q814yes—
353C42#12614yes—
354C23C2×#12111yescharacteristic
355C23C2×#12111yescharacteristic
356C23C2×C22⋊Q812yes—
357C23C2×C22⋊Q811yescharacteristic
358C23#53712yes—
359C23#57612yes—
360C23#57611yescharacteristic
361C23#57711yescharacteristic
362C23#57711yescharacteristic
363C23#57812yes—
364C23#57811yescharacteristic
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#39614yes—
426C2×C4#39614yes—
427C2×C4C2×#12111yescharacteristic
428C2×C4C2×C22⋊Q811yescharacteristic
429C2×C4C2×C22⋊Q811yescharacteristic
430C2×C4C2×#12611yescharacteristic
431C2×C4C2×C4⋊Q811yescharacteristic
432C2×C4#53211yescharacteristic
433C2×C4#53312yes—
434C2×C4#53511yescharacteristic
435C2×C4#53611yescharacteristic
436C2×C4#54212yes—
437C2×C4#54612yes—
438C2×C4D4×Q812yes—
439C2×C4#55212yes—
440C2×C4#55412yes—
441C2×C4#55712yes—
442C2×C4#55712yes—
443C2×C4Q8212yes—
444C2×C4#55912yes—
445C8—44no—
446C8—81no—
447C8—81no—
448C22C2×#39611yescharacteristic
449C22#241712yes—
450C22#258212yes—
451C22#262011yescharacteristic
452C22#285711yescharacteristic
453C22#304111yescharacteristic
454C22#304411yescharacteristic
455C22#304511yescharacteristic
456C22#304611yescharacteristic
457C22#306112yes—
458C22#306211yescharacteristic
459C22#306311yescharacteristic
460C22#308112yes—
461C22#308212yes—
462C22#308312yes—
463C22#308312yes—
464C22#308312yes—
465C22#308311yescharacteristic
466C22#308411yescharacteristic
467C22#325712yes—
468C22#325812yes—
469C22#325912yes—
470C22#326112yes—
471C4—24no—
472C4—24no—
473C4—44no—
474C4—44no—
475C4—44no—
476C4—84no—
477C4—82no—
478C4—82no—
479C4—82no—
480C4—162no—
481C4#245112yes—
482C4#251112yes—
483C4#254411yescharacteristic
484C4#254611yescharacteristic
485C4#256511yescharacteristic
486C4#256711yescharacteristic
487C2#1518411yescharacteristic
488C2#2361111yescharacteristic
489C2#2361611yescharacteristic
490C2#2484812yes—
491C2#2485012yes—
492C2#2929212yes—
493C2#2929412yes—
494C2#2983411yescharacteristic
495C2#2983711yescharacteristic
496C2#3320311yescharacteristic
497C2#3320611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19892
C2×#19472
C2×#18432
#142832
#137832
#112322
#112282
#112272
#108492