Finite Group Databasebeta

← #116850

Subgroups — #116850

Order 512.

645 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21332C211yesmaximal, characteristic
2#21169C211yesmaximal, characteristic
3#17575C211yesmaximal, characteristic
4C2×#1481C211yesmaximal, characteristic
5#8039C211yesmaximal, characteristic
6#7981C211yesmaximal, characteristic
7#7854C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#427—21no—
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14#2285C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1996—22no—
17#1996—22no—
18#1949—22no—
19#1948—21no—
20#1947—21no—
21#1740—21no—
22#1740—21no—
23#1735—21no—
24#1520—22no—
25#1518—22no—
26#1503—22no—
27#1481—22no—
28#1481—21no—
29#1481—21no—
30C2×Q8⋊C8C414yescomplemented
31#1296—22no—
32#1289—22no—
33#1274—22no—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43C2×C4⋊Q8Q811yescharacteristic
44C2×C4⋊Q8Q811yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8D412yes—
48C2×C4×Q8—21no—
49C2×C4×Q8C2×C412yes—
50C2×#117—21no—
51C2×#117—21no—
52C2×#117—21no—
53C2×#117D411yescharacteristic
54C2×#117D411yescharacteristic
55C22×C42C2311yescharacteristic
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431D412yes—
64#427—42no—
65#427—42no—
66C2×#107—22no—
67C2×#106—22no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8C2×C412yes—
74C2×C4⋊C8D412yes—
75C2×C4⋊C8D411yescharacteristic
76C2×C4⋊C8D411yescharacteristic
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C2×C4×C8—21no—
80C2×C4×C8C2×C412yes—
81#384—21no—
82#384—21no—
83#382—21no—
84#382D412yes—
85#380—21no—
86#380—21no—
87#380—21no—
88#380D412yes—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4—21no—
95C4×C22⋊C4—21no—
96C4×C22⋊C4—21no—
97#376—21no—
98C43—21no—
99#342—24no—
100#342—24no—
101#340—22no—
102#340—22no—
103#328—28no—
104Q8⋊C8—24no—
105Q8⋊C8—24no—
106C22×Q8—21no—
107C22×Q8C4⋊C412yes—
108C23×C4C2×D411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C22×C8—22no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129#125—41no—
130#125—41no—
131#125—41no—
132#125—41no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—41no—
138C22⋊Q8—41no—
139C22⋊Q8—41no—
140C22⋊Q8—41no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149#117—21no—
150#117—21no—
151#117—21no—
152#117—21no—
153#117—21no—
154#117—21no—
155#117—41no—
156#117—41no—
157#117—41no—
158#117—41no—
159#117—41no—
160#117—41no—
161#117—41no—
162#117—41no—
163#117—41no—
164#117—41no—
165#117—41no—
166#117—41no—
167#117SD1612yes—
168#117Q1612yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4C4⋊C412yes—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—41no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—41no—
192C2×C42—41no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42C22×C411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×Q811yescharacteristic
201C2×C42#4111yescharacteristic
202C2×C42#4111yescharacteristic
203C2×C42#4111yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207#107—44no—
208#106—44no—
209C4⋊C8—22no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—41no—
215C4⋊C8—41no—
216C4⋊C8—41no—
217C4⋊C8C22⋊C412yes—
218C4⋊C8C22⋊C412yes—
219C22⋊C8—22no—
220C22⋊C8—41no—
221C22⋊C8—41no—
222C22⋊C8—41no—
223C4×C8—22no—
224C4×C8—22no—
225C4×C8—22no—
226C4×C8—41no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—41no—
231#95—41no—
232#95—41no—
233C24#12011yescharacteristic
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—82no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—81no—
248C22×C4C2×C4⋊C411yescharacteristic
249C22×C4C4×D411yescharacteristic
250C22×C4C4×D411yescharacteristic
251C22×C4#12011yescharacteristic
252C22×C4#12011yescharacteristic
253C22×C4#12111yescharacteristic
254C22×C4#12111yescharacteristic
255C22×C4#12111yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4#12111yescharacteristic
258C22×C4#12111yescharacteristic
259C22×C4C22⋊Q811yescharacteristic
260C22×C4C22⋊Q811yescharacteristic
261C22×C4#12311yescharacteristic
262C22×C4#12311yescharacteristic
263C22×C4#12311yescharacteristic
264C22×C4#12411yescharacteristic
265C22×C4#12711yescharacteristic
266C22×C4C2×SD1611yescharacteristic
267C22×C4C2×Q1611yescharacteristic
268C22×C4#13511yescharacteristic
269C22×C4#13511yescharacteristic
270C22×C4AGL(1,ℤ/8)11yescharacteristic
271C22×C4#13711yescharacteristic
272C22×C4#13711yescharacteristic
273C22×C4#13711yescharacteristic
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—82no—
287C2×C8—82no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—82no—
307C4⋊C4—82no—
308C4⋊C4—82no—
309C4⋊C4—82no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—81no—
321C22⋊C4—81no—
322C42—22no—
323C42—22no—
324C42—42no—
325C42—42no—
326C42—41no—
327C42—41no—
328C42—82no—
329C42—82no—
330C42—81no—
331C42—81no—
332C42—81no—
333C42—81no—
334C42C2×C22⋊C411yescharacteristic
335C42#11711yescharacteristic
336C42C4×D411yescharacteristic
337C42C4×D411yescharacteristic
338C42#12111yescharacteristic
339C42#12111yescharacteristic
340C42C22⋊Q811yescharacteristic
341C42C22⋊Q811yescharacteristic
342C42C22⋊Q811yescharacteristic
343C42C22⋊Q811yescharacteristic
344C42#12311yescharacteristic
345C42#12311yescharacteristic
346C42#12411yescharacteristic
347C42#12411yescharacteristic
348C42#12611yescharacteristic
349C42#12611yescharacteristic
350C23—41no—
351C23—41no—
352C23#38511yescharacteristic
353C23#39211yescharacteristic
354C23#39411yescharacteristic
355C23#44811yescharacteristic
356C23#44911yescharacteristic
357C23#45111yescharacteristic
358C23#45211yescharacteristic
359Q8—44no—
360Q8—82no—
361Q8—82no—
362Q8—82no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
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—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4#38011yescharacteristic
392C2×C4#38511yescharacteristic
393C2×C4#38611yescharacteristic
394C2×C4#38811yescharacteristic
395C2×C4#38811yescharacteristic
396C2×C4#39011yescharacteristic
397C2×C4#39311yescharacteristic
398C2×C4#39411yescharacteristic
399C2×C4#39611yescharacteristic
400C2×C4#39611yescharacteristic
401C2×C4#39711yescharacteristic
402C2×C4#39911yescharacteristic
403C2×C4C4×SD1611yescharacteristic
404C2×C4C4×Q1611yescharacteristic
405C2×C4#44011yescharacteristic
406C2×C4#44111yescharacteristic
407C2×C4#45011yescharacteristic
408C2×C4#45111yescharacteristic
409C2×C4#45211yescharacteristic
410C2×C4#45211yescharacteristic
411C2×C4#46111yescharacteristic
412C2×C4#46211yescharacteristic
413C2×C4#46311yescharacteristic
414C2×C4#46411yescharacteristic
415C2×C4#46511yescharacteristic
416C2×C4#46711yescharacteristic
417C2×C4#46811yescharacteristic
418C2×C4#47011yescharacteristic
419C2×C4#47511yescharacteristic
420C2×C4#47711yescharacteristic
421C2×C4#47911yescharacteristic
422C2×C4#47911yescharacteristic
423C2×C4#48711yescharacteristic
424C2×C4#48811yescharacteristic
425C2×C4#48911yescharacteristic
426C2×C4#49111yescharacteristic
427C8—42no—
428C8—42no—
429C8—82no—
430C8—82no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22#143911yescharacteristic
442C22#186311yescharacteristic
443C22#186511yescharacteristic
444C22#200011yescharacteristic
445C22#200111yescharacteristic
446C22#204211yescharacteristic
447C22#204311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—82no—
456C4—82no—
457C4—82no—
458C4—82no—
459C4—162no—
460C4—162no—
461C4#181212yes—
462C4#187711yescharacteristic
463C4#187811yescharacteristic
464C4#193311yescharacteristic
465C4#193511yescharacteristic
466C4#202411yescharacteristic
467C4#202611yescharacteristic
468C4#206611yescharacteristic
469C4#206811yescharacteristic
470C2—21no—
471C2—21no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#1106711yescharacteristic
477C2#1109811yescharacteristic
478C2#1111511yescharacteristic
subgroupG/H
centerC2×C4#388
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#120
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
30. C2×Q8⋊C8C4semidirect

Maximal subgroups

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

subgroupindex
#213322
#211692
#175752
C2×#14812
#80392
#79812
#78542