Finite Group Databasebeta

← #117582

Subgroups — #117582

Order 512.

633 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21329C211yesmaximal, characteristic
2#21169C211yesmaximal, characteristic
3C2×#1542C211yesmaximal, characteristic
4#17575C211yesmaximal, characteristic
5#8095C211yesmaximal, characteristic
6#7924C211yesmaximal, characteristic
7#7877C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#427—21no—
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1995—22no—
17#1994—22no—
18#1949—22no—
19#1948—21no—
20#1947—21no—
21#1735—21no—
22#1733—21no—
23#1733—21no—
24#1542—21no—
25#1542—21no—
26#1542—22no—
27C2×#333C412yescomplemented
28C2×#332C412yescomplemented
29#1520—22no—
30#1518—22no—
31#1503—22no—
32#1303—22no—
33#1282—22no—
34#1277—22no—
35C22×M16—21no—
36C23×C8—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533D412yes—
44#533Q812yes—
45C2×C4⋊Q8C2×C411yescharacteristic
46C2×C4⋊Q8C2×C411yescharacteristic
47C2×#125—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C4×Q8—21no—
51C2×C4×Q8—21no—
52C2×#117—21no—
53C2×#117—21no—
54C2×#117D411yescharacteristic
55C2×#117D411yescharacteristic
56C22×C42C2311yescharacteristic
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#427—42no—
66#427—42no—
67C2×#107—22no—
68C2×#106—22no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423D412yes—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8C2×C412yes—
80C2×C4⋊C8C2×C412yes—
81C2×C4⋊C8D411yescharacteristic
82C2×C4⋊C8D411yescharacteristic
83C2×C4⋊C8D412yes—
84C2×C22⋊C8—21no—
85C2×C22⋊C8D412yes—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88#384—21no—
89#382D412yes—
90#380—21no—
91#380—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C22⋊C4—21no—
97C4×C22⋊C4—21no—
98#376—21no—
99C43—21no—
100#340—22no—
101#340—22no—
102#339—24no—
103#339—24no—
104#333—22no—
105#333—22no—
106#332—22no—
107#332—22no—
108#328—28no—
109C22×Q8—21no—
110C22×Q8—21no—
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C23×C4#4111yescharacteristic
114C2×M16—22no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C22×C8—22no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8C4⋊C412yes—
138C4⋊Q8C4⋊C412yes—
139#125—22no—
140#125—22no—
141#125—41no—
142#125—41no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C22⋊Q8—41no—
148C22⋊Q8—41no—
149C22⋊Q8—41no—
150C22⋊Q8—41no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—41no—
156C4×Q8—41no—
157C4×Q8—41no—
158C4×Q8—41no—
159#117—21no—
160#117—21no—
161#117—21no—
162#117—21no—
163#117—22no—
164#117—22no—
165#117—21no—
166#117—21no—
167#117—41no—
168#117—41no—
169#117—41no—
170#117—41no—
171#117—41no—
172#117—41no—
173#117SD1612yes—
174#117Q1612yes—
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—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—41no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42C22×C411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×Q811yescharacteristic
203C2×C42#4111yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208#107—44no—
209#106—44no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—22no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220C4⋊C8—41no—
221C4⋊C8—41no—
222C4⋊C8C22⋊C412yes—
223C4⋊C8C22⋊C412yes—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227C22⋊C8—41no—
228C4×C8—41no—
229C4×C8—41no—
230C4×C8—41no—
231C4×C8—41no—
232#95—22no—
233#95—22no—
234#95—41no—
235#95—41no—
236C24#12111yescharacteristic
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—82no—
242C2×Q8—82no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4#11711yescharacteristic
251C22×C4C4×D411yescharacteristic
252C22×C4C4×D411yescharacteristic
253C22×C4#12011yescharacteristic
254C22×C4#12011yescharacteristic
255C22×C4#12011yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4#12111yescharacteristic
258C22×C4#12111yescharacteristic
259C22×C4#12111yescharacteristic
260C22×C4C22⋊Q811yescharacteristic
261C22×C4C22⋊Q811yescharacteristic
262C22×C4C22⋊Q811yescharacteristic
263C22×C4#12311yescharacteristic
264C22×C4#12411yescharacteristic
265C22×C4#12611yescharacteristic
266C22×C4#12611yescharacteristic
267C22×C4#12711yescharacteristic
268C22×C4C2×SD1611yescharacteristic
269C22×C4C2×Q1611yescharacteristic
270C22×C4#13511yescharacteristic
271C22×C4#13511yescharacteristic
272C22×C4AGL(1,ℤ/8)11yescharacteristic
273C22×C4#13711yescharacteristic
274C22×C4#13711yescharacteristic
275C22×C4#13711yescharacteristic
276M16—42no—
277M16—42no—
278M16—81no—
279M16—81no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—44no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—81no—
295C2×C8—81no—
296C2×C8—82no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—82no—
316C4⋊C4—82no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C42—22no—
326C42—22no—
327C42—42no—
328C42—42no—
329C42—41no—
330C42—41no—
331C42—82no—
332C42—82no—
333C42—81no—
334C42—81no—
335C42C2×C22⋊C411yescharacteristic
336C42C2×C4⋊C411yescharacteristic
337C42C4×D411yescharacteristic
338C42C4×D411yescharacteristic
339C42#12111yescharacteristic
340C42#12111yescharacteristic
341C42#12111yescharacteristic
342C42C22⋊Q811yescharacteristic
343C42C22⋊Q811yescharacteristic
344C42C22⋊Q811yescharacteristic
345C42#12311yescharacteristic
346C42#12311yescharacteristic
347C42#12311yescharacteristic
348C42#12311yescharacteristic
349C42#12411yescharacteristic
350C42#12411yescharacteristic
351C23—41no—
352C23—41no—
353C23#38811yescharacteristic
354C23#39211yescharacteristic
355C23#39611yescharacteristic
356C23#46511yescharacteristic
357C23#46711yescharacteristic
358C23#46811yescharacteristic
359C23#47011yescharacteristic
360Q8—82no—
361Q8—82no—
362Q8—82no—
363Q8—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4#38011yescharacteristic
390C2×C4#38511yescharacteristic
391C2×C4#38511yescharacteristic
392C2×C4#38611yescharacteristic
393C2×C4#38811yescharacteristic
394C2×C4#39011yescharacteristic
395C2×C4#39311yescharacteristic
396C2×C4#39411yescharacteristic
397C2×C4#39411yescharacteristic
398C2×C4#39611yescharacteristic
399C2×C4#39711yescharacteristic
400C2×C4#39911yescharacteristic
401C2×C4C4×SD1611yescharacteristic
402C2×C4C4×Q1611yescharacteristic
403C2×C4#44011yescharacteristic
404C2×C4#44111yescharacteristic
405C2×C4#44811yescharacteristic
406C2×C4#44911yescharacteristic
407C2×C4#45011yescharacteristic
408C2×C4#45111yescharacteristic
409C2×C4#45111yescharacteristic
410C2×C4#45211yescharacteristic
411C2×C4#45211yescharacteristic
412C2×C4#45211yescharacteristic
413C2×C4#46111yescharacteristic
414C2×C4#46211yescharacteristic
415C2×C4#46311yescharacteristic
416C2×C4#46411yescharacteristic
417C2×C4#47511yescharacteristic
418C2×C4#47711yescharacteristic
419C2×C4#47911yescharacteristic
420C2×C4#47911yescharacteristic
421C2×C4#48711yescharacteristic
422C2×C4#48811yescharacteristic
423C2×C4#48911yescharacteristic
424C2×C4#49111yescharacteristic
425C8—42no—
426C8—42no—
427C8—82no—
428C8—82no—
429C8—82no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22#143911yescharacteristic
441C22#193311yescharacteristic
442C22#193511yescharacteristic
443C22#200011yescharacteristic
444C22#200111yescharacteristic
445C22#206611yescharacteristic
446C22#206811yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—82no—
455C4—82no—
456C4—82no—
457C4—82no—
458C4—162no—
459C4#186311yescharacteristic
460C4#186511yescharacteristic
461C4#187711yescharacteristic
462C4#187811yescharacteristic
463C4#197612yes—
464C4#202411yescharacteristic
465C4#202611yescharacteristic
466C4#204211yescharacteristic
467C4#204311yescharacteristic
468C2—21no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—21no—
474C2#1106711yescharacteristic
475C2#1112611yescharacteristic
476C2#1114111yescharacteristic
subgroupG/H
centerC2×C4#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
27. C2×#333C4semidirect
28. C2×#332C4semidirect

Maximal subgroups

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

subgroupindex
#213292
#211692
C2×#15422
#175752
#80952
#79242
#78772