Finite Group Databasebeta

← #507776

Subgroups — #507776

Order 512.

650 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#466C211yesmaximal, characteristic, complemented
2C4×#466C211yesmaximal, characteristic, complemented
3#13494C211yesmaximal, characteristic, complemented
4#13381C211yesmaximal, characteristic, complemented
5#13380C211yesmaximal, characteristic, complemented
6#13304C211yesmaximal, characteristic
7#13131C211yesmaximal, characteristic, complemented
8#13130C211yesmaximal, characteristic, complemented
9#13112C211yesmaximal, characteristic, complemented
10#13111C211yesmaximal, characteristic, complemented
11#13012C211yesmaximal, characteristic, complemented
12#13012C211yesmaximal, characteristic, complemented
13#12937C211yesmaximal, characteristic, complemented
14#12937C211yesmaximal, characteristic, complemented
15#12844C211yesmaximal, characteristic, complemented
16C22×D16C2211yescharacteristic
17C2×#466C2211yescharacteristic
18C2×#466C2211yescharacteristic
19C2×C4×D8C2211yescharacteristic
20C2×C4×D8C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22C4×#121—21no—
23C4×#121—21no—
24C2×#367C2211yescharacteristic
25C2×#367C2211yescharacteristic
26C2×#366C2211yescharacteristic
27C2×#357C2211yescharacteristic
28C2×#357C2211yescharacteristic
29C2×#357C2211yescharacteristic
30C2×#357C2211yescharacteristic
31C2×#357C2211yescharacteristic
32C2×#357C2211yescharacteristic
33C2×C22⋊C16C2211yescharacteristic
34C2×C22⋊C16C2211yescharacteristic
35#1970C2211yescharacteristic
36#1970C2211yescharacteristic
37#1942C2211yescharacteristic
38#1942C2211yescharacteristic
39#1934—21no—
40#1934—21no—
41#1893—21no—
42#1893—21no—
43#1808C2211yescharacteristic
44#1808C2211yescharacteristic
45C4×#107C2211yescharacteristic
46C4×#107C2211yescharacteristic
47C4×#102—21no—
48C4×#102—21no—
49#1380C2211yescharacteristic
50#1380C2211yescharacteristic
51#1380C2211yescharacteristic
52#1380C2211yescharacteristic
53#1380C2211yescharacteristic
54#1380C2211yescharacteristic
55#1374C2211yescharacteristic
56#1374C2211yescharacteristic
57#1374C2211yescharacteristic
58#1374C2211yescharacteristic
59C22×D8C2311yescharacteristic
60C22×D8C2311yescharacteristic
61C23×C8D411yescharacteristic
62C23×C8C2311yescharacteristic
63C2×#121—21no—
64C2×#121—21no—
65C2×C4×D4—21no—
66C2×C4×D4—21no—
67C2×C4×D4—41no—
68C2×C4×D4—41no—
69C22×C42D411yescharacteristic
70C2×D16—22no—
71C2×D16—22no—
72C2×D16—41no—
73C22×C16C2311yescharacteristic
74C22×C16C2311yescharacteristic
75C22×C16C2311yescharacteristic
76C22×C16C2311yescharacteristic
77#466—22no—
78#466—22no—
79#466—22no—
80#466—22no—
81C4×D8—41no—
82C4×D8—41no—
83C4×D8—41no—
84C4×D8—41no—
85C2×#107C2311yescharacteristic
86C2×#107C2311yescharacteristic
87C2×#107C2311yescharacteristic
88C2×#107C2311yescharacteristic
89C2×#107C2311yescharacteristic
90C2×#107C2311yescharacteristic
91C2×#102—21no—
92C2×#102—21no—
93C2×#102—21no—
94C2×#102—21no—
95C2×#102—21no—
96C2×#102—21no—
97C2×C4×C8—41no—
98C2×C4×C8—41no—
99C2×C4×C8D411yescharacteristic
100C2×C4×C8D411yescharacteristic
101C2×C4×C8C2311yescharacteristic
102C2×C4×C8C2311yescharacteristic
103#390—21no—
104#390—21no—
105#389—21no—
106#389—21no—
107#388—41no—
108#388—41no—
109#386—41no—
110#386—41no—
111#380—21no—
112#380—21no—
113C4×C4⋊C4—21no—
114C4×C4⋊C4—21no—
115C4×C22⋊C4—41no—
116C4×C22⋊C4—41no—
117#367—22no—
118#367—41no—
119#366—22no—
120#357—22no—
121#357—22no—
122#357—22no—
123#357—22no—
124#357—41no—
125#357—41no—
126C22⋊C16—41no—
127C22⋊C16—41no—
128#340—21no—
129#340—21no—
130#340—21no—
131#340—21no—
132#340—21no—
133#340—21no—
134C22×D4—21no—
135C22×D4—21no—
136C22×D4—41no—
137C22×D4—41no—
138C23×C4—41no—
139C23×C4—41no—
140C23×C4D811yescharacteristic
141C23×C4D811yescharacteristic
142C23×C4C2×D411yescharacteristic
143C2×D8—21no—
144C2×D8—21no—
145C2×D8—21no—
146C2×D8—21no—
147C2×D8—21no—
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—21no—
151C2×D8—21no—
152C2×D8—21no—
153C2×D8#4112yes—
154C2×D8#4112yes—
155C22×C8—21no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—21no—
161C22×C8—41no—
162C22×C8—41no—
163C22×C8—41no—
164C22×C8C2×D411yescharacteristic
165C22×C8C2×D411yescharacteristic
166C22×C8C2×D411yescharacteristic
167C22×C8C2411yescharacteristic
168#121—24no—
169#121—24no—
170#121—42no—
171#121—42no—
172C4×D4—42no—
173C4×D4—42no—
174C4×D4—42no—
175C4×D4—42no—
176C4×D4—84no—
177C4×D4—84no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C42—41no—
197C2×C42—41no—
198C2×C42—41no—
199C2×C42—41no—
200C2×C42D811yescharacteristic
201C2×C42D811yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204D16—44no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—21no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217#107—21no—
218#107—21no—
219#107—21no—
220#107—21no—
221#107—21no—
222#107—21no—
223#107—21no—
224#107—21no—
225#107—21no—
226#107—21no—
227#107#4112yes—
228#107#4112yes—
229#102—24no—
230#102—24no—
231#102—42no—
232#102—42no—
233#102—42no—
234#102—42no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—41no—
240C4×C8—41no—
241#95—41no—
242#95—41no—
243#95—41no—
244#95—41no—
245#95—41no—
246#95—41no—
247C24—41no—
248C24—41no—
249C24C2×D811yescharacteristic
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—82no—
265C2×D4—82no—
266C2×D4—82no—
267C2×D4—82no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—82no—
287C22×C4—82no—
288C22×C4—82no—
289C22×C4—82no—
290C22×C4—82no—
291C22×C4—82no—
292C22×C4C2×D811yescharacteristic
293C22×C4C2×D811yescharacteristic
294C22×C4C2×D811yescharacteristic
295C22×C4C2×D811yescharacteristic
296C22×C4C2×D811yescharacteristic
297C22×C4C22×D411yescharacteristic
298D8—22no—
299D8—22no—
300D8—22no—
301D8—22no—
302D8—41no—
303D8—41no—
304D8—41no—
305D8—41no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—44no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8C2×#4111yescharacteristic
321C2×C8C2×#4111yescharacteristic
322C2×C8C2×#4111yescharacteristic
323C2×C8C2×#4111yescharacteristic
324C2×C8H(5,𝔽2)11yescharacteristic
325C2×C8H(5,𝔽2)11yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—82no—
339C4⋊C4—82no—
340C22⋊C4—44no—
341C22⋊C4—44no—
342C22⋊C4—82no—
343C22⋊C4—82no—
344C22⋊C4—82no—
345C22⋊C4—82no—
346C22⋊C4—82no—
347C22⋊C4—82no—
348C22⋊C4—82no—
349C22⋊C4—82no—
350C42—21no—
351C42—21no—
352C42—21no—
353C42—21no—
354C42—41no—
355C42—41no—
356C42—82no—
357C42—82no—
358C16—41no—
359C16—41no—
360C16—41no—
361C16—41no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—42no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23#50912yes—
383C23C22×D811yescharacteristic
384D4—42no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—88no—
389D4—88no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4—81no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—164no—
432C2×C4—164no—
433C2×C4#50812yes—
434C2×C4#50912yes—
435C2×C4#52511yescharacteristic
436C2×C4#52511yescharacteristic
437C2×C4#53411yescharacteristic
438C2×C4#57511yescharacteristic
439C2×C4#57511yescharacteristic
440C2×C4#57511yescharacteristic
441C8—41no—
442C8—41no—
443C8—41no—
444C8#55111yescharacteristic
445C8#55311yescharacteristic
446C8#55311yescharacteristic
447C8#55911yescharacteristic
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—82no—
456C22—82no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—161no—
462C22—161no—
463C22—161no—
464C22—161no—
465C22—161no—
466C22—161no—
467C22—161no—
468C22—161no—
469C22#310011yescharacteristic
470C22#310011yescharacteristic
471C22#318611yescharacteristic
472C22C2×#50811yescharacteristic
473C22C2×#50911yescharacteristic
474C22C2×#50911yescharacteristic
475C22#341411yescharacteristic
476C4—22no—
477C4—22no—
478C4—41no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—82no—
483C4—161no—
484C4—161no—
485C4—161no—
486C4—161no—
487C4#260011yescharacteristic
488C4#311111yescharacteristic
489C4#311111yescharacteristic
490C4#319711yescharacteristic
491C2—42no—
492C2—162no—
493C2—162no—
494C2#2940811yescharacteristic
495C2#3366211yescharacteristic
496C2#3366611yescharacteristic
497C2#3366911yescharacteristic
498C2#3367411yescharacteristic
499C2#3375411yescharacteristic
500C2#3376011yescharacteristic
subgroupG/H
center, socleC23C22×D8
commutator, Frattini, cosocleC22×C8C24
prime radical#13304C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×C8 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×#466C2semidirect
2. C4×#466C2semidirect
3. #13494C2semidirect
4. #13381C2semidirect
5. #13380C2semidirect
7. #13131C2semidirect
8. #13130C2semidirect
9. #13112C2semidirect
10. #13111C2semidirect
11. #13012C2semidirect
12. #13012C2semidirect
13. #12937C2semidirect
14. #12937C2semidirect
15. #12844C2semidirect

Maximal subgroups

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

subgroupindex
C4×#4662
#134942
#133812
#133802
#133042
#131312
#131302
#131122
#131112
#130122
#129372
#128442