Finite Group Databasebeta

← #362987

Subgroups — #362987

Order 512.

1062 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2370C211yesmaximal, characteristic
2#21023C212yesmaximal
3#11383C212yesmaximal
4#11204C212yesmaximal
5#10913C212yesmaximal
6#10847C211yesmaximal, characteristic
7#10802C211yesmaximal, characteristic
8#10802C211yesmaximal, characteristic
9#10802C211yesmaximal, characteristic
10#10802C211yesmaximal, characteristic
11C4×#343C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C2×#423C2212yes—
14C2×C4×M16C2212yes—
15#2370—22no—
16#2370—22no—
17#2370—22no—
18#2370—22no—
19C2×#389C412yes—
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#387C412yes—
23C2×#387C412yes—
24C2×C4×C4⋊C4C412yes—
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29#1917—22no—
30#1917—22no—
31#1916—22no—
32#1916—22no—
33C2×#343C2211yescharacteristic
34C2×#343C2211yescharacteristic
35C2×#343C2211yescharacteristic
36C2×#343C2212yes—
37C2×#343C2212yes—
38C2×#343C2212yes—
39C2×#343C2212yes—
40C2×#343C2212yes—
41C2×#343C2212yes—
42C2×#343C2211yescharacteristic
43#1728C2212yes—
44#1728C2212yes—
45#1728C2212yes—
46#1728C2212yes—
47C22×M16C2312yes—
48C22×M16C2312yes—
49C22×M16C2312yes—
50C22×M16C2312yes—
51C2×#125—24no—
52C2×#125—22no—
53C2×#125—22no—
54C2×#125—22no—
55C2×#125—22no—
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C412yes—
59C22×C4⋊C4C2×C412yes—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C42C2×C412yes—
67C22×C42C2×C412yes—
68C22×C42C2×C412yes—
69C22×C42C2311yescharacteristic
70C22×C42C2311yescharacteristic
71C22×C42C2311yescharacteristic
72#423—24no—
73#423—42no—
74C2×C4⋊C8—22no—
75C2×C4⋊C8—22no—
76C4×M16—24no—
77C4×M16—42no—
78C2×#97—22no—
79C2×C4×C8—22no—
80#389—24no—
81#389—24no—
82#389—22no—
83#389—22no—
84#389—22no—
85#389—22no—
86#387—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—22no—
94C4×C4⋊C4—22no—
95C4×C4⋊C4—22no—
96C4×C4⋊C4—22no—
97C4×C4⋊C4—22no—
98C4×C4⋊C4—22no—
99C4×C4⋊C4—22no—
100C4×C4⋊C4D412yes—
101C4×C4⋊C4D412yes—
102C4×C4⋊C4D412yes—
103C4×C4⋊C4D412yes—
104C2×#95C2×C412yes—
105C2×#95C2×C412yes—
106C2×#95C2×C412yes—
107C2×#95C2×C412yes—
108C2×#95C2×C412yes—
109C2×#95C2×C411yescharacteristic
110C2×#95C2×C411yescharacteristic
111#343—24no—
112#343—24no—
113#343—24no—
114#343—24no—
115#343—24no—
116#343—22no—
117#343—22no—
118#343—22no—
119#343—42no—
120#343Q814yes—
121#336—22no—
122#336—22no—
123#336—22no—
124#336—22no—
125#336—22no—
126#336—22no—
127#336—22no—
128#336—22no—
129C23×C4C22×C411yescharacteristic
130C23×C4C22×C411yescharacteristic
131C23×C4C22×C412yes—
132C23×C4C22×C411yescharacteristic
133C23×C4C22×C411yescharacteristic
134C23×C4C22×C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C22×C412yes—
137C23×C4C22×C412yes—
138C23×C4C22×C412yes—
139C23×C4C2411yescharacteristic
140C2×M16—22no—
141C2×M16—22no—
142C2×M16—22no—
143C2×M16—22no—
144C2×M16—22no—
145C2×M16—22no—
146C2×M16—22no—
147C2×M16—22no—
148C2×M16—22no—
149C2×M16—22no—
150C2×M16—22no—
151C2×M16—22no—
152C2×M16—22no—
153C2×M16—22no—
154C2×M16—22no—
155C2×M16—22no—
156C2×M16—22no—
157C2×M16—22no—
158C2×M16—22no—
159C2×M16—22no—
160C2×M16—22no—
161C2×M16—22no—
162C2×M16C2×Q814yes—
163C2×M16#4114yes—
164C22×C8—22no—
165C22×C8—22no—
166C22×C8—22no—
167C22×C8—22no—
168#125—28no—
169#125—28no—
170#125—28no—
171#125—28no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—82no—
197C2×C4⋊C4C22⋊C412yes—
198C2×C4⋊C4C22⋊C412yes—
199C2×C4⋊C4C22⋊C412yes—
200C2×C4⋊C4C22⋊C412yes—
201C2×C4⋊C4C2×Q812yes—
202C2×C4⋊C4#4114yes—
203C2×C4⋊C4#4112yes—
204C2×C4⋊C4#4112yes—
205C2×C4⋊C4#4112yes—
206C2×C42—22no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—44no—
222C2×C42—82no—
223C2×C42—82no—
224C2×C42C2×D412yes—
225C2×C42C2×D412yes—
226C2×C42C2×D412yes—
227C2×C42C2×D412yes—
228C2×C42C2×D412yes—
229C2×C42C2×D412yes—
230C4⋊C8—44no—
231C4⋊C8—44no—
232#97—44no—
233C4×C8—44no—
234#95—24no—
235#95—24no—
236#95—24no—
237#95—22no—
238#95—22no—
239#95—24no—
240#95C22⋊C411yescharacteristic
241#95C22⋊C411yescharacteristic
242#95C22⋊C411yescharacteristic
243#95C22⋊C411yescharacteristic
244#95C22⋊C412yes—
245#95C22⋊C412yes—
246C24C23×C411yescharacteristic
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C2×C22⋊C412yes—
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C412yes—
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C2×C22⋊C411yescharacteristic
294C22×C4C2×C22⋊C411yescharacteristic
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4#11714yes—
298C22×C4#11714yes—
299C22×C4C4×Q814yes—
300C22×C4C22×D412yes—
301C22×C4C22×Q811yescharacteristic
302C22×C4C2×#4112yes—
303C22×C4C2×#4111yescharacteristic
304C22×C4C2×#4111yescharacteristic
305C22×C4C2×#4111yescharacteristic
306C22×C4C2×#4112yes—
307C22×C4H(5,𝔽2)11yescharacteristic
308C22×C42−1+411yescharacteristic
309C22×C42−1+412yes—
310M16—24no—
311M16—24no—
312M16—24no—
313M16—24no—
314M16—42no—
315M16—42no—
316M16—42no—
317M16—42no—
318M16—42no—
319M16—42no—
320M16—42no—
321M16—42no—
322M16—42no—
323M16—42no—
324M16—42no—
325M16—42no—
326C2×C8—24no—
327C2×C8—24no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—28no—
339C4⋊C4—28no—
340C4⋊C4—216no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—44no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—44no—
355C4⋊C4—84no—
356C42—22no—
357C42—22no—
358C42—22no—
359C42—22no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42—22no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—44no—
369C42—44no—
370C42—82no—
371C42—82no—
372C42—82no—
373C42—82no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23C22×C22⋊C411yescharacteristic
379C23C2×#11711yescharacteristic
380C23C2×#11711yescharacteristic
381C23C2×C4×Q811yescharacteristic
382C23C4×#4111yescharacteristic
383C23#51911yescharacteristic
384C23#52011yescharacteristic
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4#41312yes—
443C2×C4#41312yes—
444C2×C4#52512yes—
445C2×C4#52512yes—
446C2×C4#52912yes—
447C2×C4#53312yes—
448C2×C4#54112yes—
449C2×C4#54212yes—
450C2×C4#54612yes—
451C2×C4#54712yes—
452C2×C4#54812yes—
453C2×C4D4×Q812yes—
454C2×C4#55212yes—
455C2×C4#55411yescharacteristic
456C2×C4#55612yes—
457C2×C4#55611yescharacteristic
458C2×C4#55711yescharacteristic
459C2×C4#55911yescharacteristic
460C8—44no—
461C8—44no—
462C8—82no—
463C8—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22#228011yescharacteristic
477C22#229511yescharacteristic
478C22#232011yescharacteristic
479C22#233911yescharacteristic
480C22Q8×C22⋊C411yescharacteristic
481C22#235511yescharacteristic
482C22#235611yescharacteristic
483C22C2×#41311yescharacteristic
484C22C2×#41311yescharacteristic
485C22#288811yescharacteristic
486C22#288911yescharacteristic
487C4—22no—
488C4—22no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—42no—
493C4—44no—
494C4—42no—
495C4—44no—
496C4—41no—
497C4—41no—
498C4—44no—
499C4—82no—
500C4#245812yes—
501C4#246212yes—
502C4#246512yes—
503C4#246912yes—
504C2—21no—
505C2—21no—
506C2—21no—
507C2—21no—
508C2#1392711yescharacteristic
509C2#2072811yescharacteristic
510C2#2073111yescharacteristic
511C2#2248011yescharacteristic
512C2#2248211yescharacteristic
513C2#2251511yescharacteristic
514C2#2251711yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ 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×#23702
#210232
#113832
#112042
#109132
#108472
#108022
C4×#3432