Finite Group Databasebeta

← #416459

Subgroups — #416459

Order 512.

794 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21170C211yesmaximal, characteristic
2C2×#1947C211yesmaximal, characteristic
3#21145C211yesmaximal, characteristic
4#20764C211yesmaximal, characteristic
5#11365C212yesmaximal
6#11290C212yesmaximal
7#11239C212yesmaximal
8#11216C212yesmaximal
9#10857C211yesmaximal, characteristic
10#10853C211yesmaximal, characteristic
11C4×#343C211yesmaximal, characteristic
12C2×#428C2212yes—
13C22×#107C2212yes—
14C2×#424C2212yes—
15C2×#423C2211yescharacteristic
16C22×C4⋊C8C2211yescharacteristic
17C2×C4×M16C2211yescharacteristic
18C2×C4×M16C2211yescharacteristic
19#2285C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22#1949—22no—
23#1948—21no—
24#1947—22no—
25#1947—22no—
26#1947—21no—
27#1940—22no—
28#1939—22no—
29#1836—22no—
30#1834—21no—
31#1834—21no—
32C2×#343C2211yescharacteristic
33C2×#343C2212yes—
34C2×#343C2211yescharacteristic
35C2×#343C2211yescharacteristic
36C2×#343C2211yescharacteristic
37C2×#343C2212yes—
38C2×#341C2212yes—
39C2×#341C2212yes—
40#1736C2212yes—
41#1736C2212yes—
42#1736C2212yes—
43C2×#340C2212yes—
44#1729C2212yes—
45C22×M16C2311yescharacteristic
46C22×M16C2311yescharacteristic
47C22×M16C2312yes—
48C22×M16C2311yescharacteristic
49C22×M16C2311yescharacteristic
50C23×C8C2312yes—
51C2×#117C2312yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42—21no—
58C22×C42C2311yescharacteristic
59#428—24no—
60#428—42no—
61C2×#107—24no—
62C2×#107—22no—
63C2×#107—24no—
64C2×#107—42no—
65C2×#106—22no—
66#424—24no—
67#424—42no—
68#423—22no—
69#423Q814yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—24no—
75C2×C4⋊C8D412yes—
76C2×C4⋊C8D412yes—
77C4×M16—22no—
78C4×M16—22no—
79C4×M16—22no—
80C4×M16Q814yes—
81C2×#97—21no—
82C2×#97—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85#384—21no—
86#384—21no—
87#384—21no—
88#384—21no—
89#384D411yescharacteristic
90#384D411yescharacteristic
91#382D412yes—
92#380—21no—
93#380—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—21no—
99C4×C4⋊C4—21no—
100C2×#95—21no—
101#343—22no—
102#343—22no—
103#343—24no—
104#343—22no—
105#343—22no—
106#343—42no—
107#341—42no—
108#341—42no—
109#340—24no—
110#340—22no—
111#340—22no—
112#340—22no—
113#340—22no—
114#340—22no—
115#340—22no—
116#336—24no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4#4111yescharacteristic
121C23×C4#4111yescharacteristic
122C23×C4C2411yescharacteristic
123C2×M16—21no—
124C2×M16—21no—
125C2×M16—22no—
126C2×M16—21no—
127C2×M16—21no—
128C2×M16—21no—
129C2×M16—21no—
130C2×M16—21no—
131C2×M16—21no—
132C2×M16—21no—
133C2×M16—21no—
134C2×M16—22no—
135C2×M16—21no—
136C2×M16—21no—
137C2×M16—21no—
138C2×M16—21no—
139C2×M16—22no—
140C2×M16—21no—
141C2×M16—21no—
142C2×M16—22no—
143C2×M16—22no—
144C2×M16—21no—
145C2×M16—21no—
146C2×M16—21no—
147C2×M16—21no—
148C2×M16C2×Q812yes—
149C2×M16C2×Q812yes—
150C2×M16C2×Q814yes—
151C2×M16#4112yes—
152C2×M16#4112yes—
153C22×C8—21no—
154C22×C8—21no—
155C22×C8—21no—
156C22×C8—22no—
157C22×C8—21no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8C2×D414yes—
165#117—22no—
166#117—22no—
167#117—22no—
168#117—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—82no—
194C2×C4⋊C4—82no—
195C2×C4⋊C4C2×D412yes—
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4#4112yes—
198C2×C4⋊C4#4112yes—
199C2×C22⋊C4—22no—
200C2×C42—22no—
201C2×C42—41no—
202C2×C42—41no—
203C2×C42—82no—
204C2×C42C2×D411yescharacteristic
205C2×C42C2×D411yescharacteristic
206C2×C42C2×D411yescharacteristic
207C2×C42C2×D411yescharacteristic
208C2×C42C2×Q812yes—
209C2×C42C2×Q812yes—
210C2×C42#4112yes—
211C2×C42#4112yes—
212#107—44no—
213#107—48no—
214#106—44no—
215C4⋊C8—24no—
216C4⋊C8—24no—
217C4⋊C8—24no—
218C4⋊C8—24no—
219C4⋊C8—48no—
220#97—24no—
221#97—42no—
222C4×C8—24no—
223C4×C8—42no—
224#95—22no—
225#95—22no—
226#95—41no—
227#95—41no—
228C24C2×#4111yescharacteristic
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—82no—
249C22×C4—82no—
250C22×C4#12111yescharacteristic
251C22×C4#12111yescharacteristic
252C22×C4#12111yescharacteristic
253C22×C4#12111yescharacteristic
254C22×C4#12512yes—
255C22×C4#12512yes—
256C22×C4#12512yes—
257C22×C4#12512yes—
258C22×C4C22×D411yescharacteristic
259C22×C4C22×D411yescharacteristic
260C22×C4C22×Q811yescharacteristic
261C22×C4C22×Q811yescharacteristic
262C22×C4C2×#4111yescharacteristic
263C22×C4C2×#4111yescharacteristic
264C22×C4C2×#4111yescharacteristic
265C22×C4C2×#4111yescharacteristic
266C22×C4C2×#4111yescharacteristic
267C22×C4C2×#4111yescharacteristic
268C22×C4H(5,𝔽2)11yescharacteristic
269C22×C4H(5,𝔽2)11yescharacteristic
270C22×C42−1+411yescharacteristic
271C22×C42−1+411yescharacteristic
272M16—22no—
273M16—22no—
274M16—22no—
275M16—22no—
276M16—22no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—24no—
281M16—24no—
282M16—42no—
283M16—41no—
284M16—42no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—22no—
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—82no—
335C4⋊C4—82no—
336C4⋊C4—82no—
337C4⋊C4—82no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C42—42no—
341C42—42no—
342C42—82no—
343C42—82no—
344C42C22⋊Q812yes—
345C42C22⋊Q812yes—
346C42C22⋊Q812yes—
347C42C22⋊Q812yes—
348C42#12312yes—
349C42#12312yes—
350C42C4⋊Q812yes—
351C42C4⋊Q812yes—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23C2×#12111yescharacteristic
357C23C2×#12511yescharacteristic
358C23C2×#12511yescharacteristic
359C23#52911yescharacteristic
360C23#52911yescharacteristic
361C23#54211yescharacteristic
362C23#54211yescharacteristic
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—162no—
393C2×C4—162no—
394C2×C4#39812yes—
395C2×C4#39812yes—
396C2×C4#39812yes—
397C2×C4#39812yes—
398C2×C4#47212yes—
399C2×C4#47312yes—
400C2×C4C2×C22⋊Q811yescharacteristic
401C2×C4C2×C22⋊Q811yescharacteristic
402C2×C4C2×#12311yescharacteristic
403C2×C4#52911yescharacteristic
404C2×C4#52911yescharacteristic
405C2×C4C2×C4⋊Q811yescharacteristic
406C2×C4#53311yescharacteristic
407C2×C4#53311yescharacteristic
408C2×C4#54011yescharacteristic
409C2×C4#54111yescharacteristic
410C2×C4#54411yescharacteristic
411C2×C4#54411yescharacteristic
412C2×C4#54611yescharacteristic
413C2×C4#54611yescharacteristic
414C2×C4#54611yescharacteristic
415C2×C4#54711yescharacteristic
416C2×C4#54811yescharacteristic
417C2×C4#54811yescharacteristic
418C2×C4#54811yescharacteristic
419C2×C4#55011yescharacteristic
420C2×C4#55211yescharacteristic
421C2×C4#55311yescharacteristic
422C2×C4#55411yescharacteristic
423C2×C4#55411yescharacteristic
424C2×C4#55511yescharacteristic
425C2×C4#55611yescharacteristic
426C2×C4#55711yescharacteristic
427C2×C4#55711yescharacteristic
428C8—44no—
429C8—42no—
430C8—42no—
431C8—42no—
432C8—42no—
433C8—44no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22C2×#39811yescharacteristic
447C22#242611yescharacteristic
448C22#242711yescharacteristic
449C22#250811yescharacteristic
450C22#250911yescharacteristic
451C22#264711yescharacteristic
452C22#286411yescharacteristic
453C22C2×#47211yescharacteristic
454C22C2×#47311yescharacteristic
455C22#306811yescharacteristic
456C22#306911yescharacteristic
457C4—22no—
458C4—22no—
459C4—22no—
460C4—82no—
461C4—82no—
462C4—82no—
463C4—82no—
464C4—162no—
465C4#208914yes—
466C4#242011yescharacteristic
467C4#242111yescharacteristic
468C4#243911yescharacteristic
469C4#244111yescharacteristic
470C4#245311yescharacteristic
471C4#245411yescharacteristic
472C4#255011yescharacteristic
473C4#255011yescharacteristic
474C2—21no—
475C2—21no—
476C2—21no—
477C2—21no—
478C2#1522511yescharacteristic
479C2C2×#208911yescharacteristic
480C2#2367511yescharacteristic
481C2#2531211yescharacteristic
482C2#2531411yescharacteristic
483C2#2535811yescharacteristic
484C2#2536011yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC23×C4C24
prime radicalC24C2×#41
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ 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
#211702
C2×#19472
#211452
#207642
#113652
#112902
#112392
#112162
#108572
#108532
C4×#3432