Finite Group Databasebeta

← #115922

Subgroups — #115922

Order 512.

672 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21951C211yesmaximal, characteristic
2#21312C211yesmaximal, characteristic
3C2×#1518C211yesmaximal, characteristic
4C2×#1481C211yesmaximal, characteristic
5#10850C211yesmaximal, characteristic
6C2×#1301C211yesmaximal, characteristic
7C2×#1286C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1989—22no—
16#1988C412yescomplemented
17#1987C412yescomplemented
18#1939—22no—
19#1939—22no—
20#1797—22no—
21#1736—21no—
22#1736—21no—
23C2×#340—21no—
24C2×#340—21no—
25#1518—22no—
26#1518—22no—
27C2×#328—22no—
28#1481—22no—
29#1481—22no—
30C2×Q8⋊C8—22no—
31#1301—22no—
32#1286—22no—
33C22×M16—21no—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533D412yes—
42#533Q812yes—
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×C4⋊Q8C2×C411yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×#117—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C42—21no—
55C22×C42C2311yescharacteristic
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—24no—
77C2×C4⋊C8C2×C412yes—
78C2×C4⋊C8D412yes—
79C2×C22⋊C8—21no—
80C2×C22⋊C8D412yes—
81C2×C4×C8—21no—
82C2×C4×C8D412yes—
83#382—21no—
84#382—21no—
85#382—21no—
86#382D412yes—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4C2×C412yes—
90C4×C4⋊C4D412yes—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—42no—
99#340—42no—
100#336—24no—
101#328—28no—
102Q8⋊C8—28no—
103C22×Q8—21no—
104C22×Q8—21no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4—41no—
108C23×C4C2×D411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4#4111yescharacteristic
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—41no—
126C22×C8—41no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8C4⋊C412yes—
134C4⋊Q8C4⋊C412yes—
135#125—22no—
136#125—22no—
137#125—41no—
138#125—41no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C22⋊Q8—41no—
146C22⋊Q8—41no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155#117—22no—
156#117—22no—
157#117—41no—
158#117—41no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C22⋊C412yes—
180C2×C4⋊C4C22⋊C412yes—
181C2×C4⋊C4SD1612yes—
182C2×C4⋊C4Q1612yes—
183C2×C22⋊C4—41no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—41no—
187C2×C42—82no—
188C2×C42C22×C411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×Q811yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42#4111yescharacteristic
199C2×C42#4111yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211C4⋊C8—41no—
212C4⋊C8—84no—
213C22⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—41no—
216C22⋊C8—41no—
217C4×C8—22no—
218C4×C8—22no—
219C4×C8—41no—
220C4×C8—41no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95—41no—
226#95—41no—
227C24#12111yescharacteristic
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—81no—
235C2×Q8—81no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4C2×C22⋊C411yescharacteristic
260C22×C4C4×D411yescharacteristic
261C22×C4C4×D411yescharacteristic
262C22×C4#12011yescharacteristic
263C22×C4#12011yescharacteristic
264C22×C4#12111yescharacteristic
265C22×C4#12111yescharacteristic
266C22×C4#12111yescharacteristic
267C22×C4#12111yescharacteristic
268C22×C4#12111yescharacteristic
269C22×C4C22⋊Q811yescharacteristic
270C22×C4C22⋊Q811yescharacteristic
271C22×C4C22⋊Q811yescharacteristic
272C22×C4#12311yescharacteristic
273C22×C4#12311yescharacteristic
274C22×C4#12311yescharacteristic
275C22×C4#12411yescharacteristic
276C22×C4#12611yescharacteristic
277C22×C4C2×SD1611yescharacteristic
278C22×C4C2×Q1611yescharacteristic
279C22×C4#13511yescharacteristic
280C22×C4#13511yescharacteristic
281C22×C4AGL(1,ℤ/8)11yescharacteristic
282C22×C4#13711yescharacteristic
283C22×C4#13711yescharacteristic
284C22×C4#13711yescharacteristic
285M16—81no—
286M16—81no—
287M16—81no—
288M16—81no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—81no—
302C2×C8—81no—
303C2×C8—81no—
304C2×C8—81no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—81no—
327C4⋊C4—81no—
328C4⋊C4#10314yes—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C42—44no—
332C42—42no—
333C42—42no—
334C42—82no—
335C42C2×C4⋊C411yescharacteristic
336C42#11711yescharacteristic
337C42C4×D411yescharacteristic
338C42C4×D411yescharacteristic
339C42#12011yescharacteristic
340C42#12111yescharacteristic
341C42#12111yescharacteristic
342C42C22⋊Q811yescharacteristic
343C42C22⋊Q811yescharacteristic
344C42C22⋊Q811yescharacteristic
345C42#12311yescharacteristic
346C42#12311yescharacteristic
347C42#12411yescharacteristic
348C42#12411yescharacteristic
349C42#12611yescharacteristic
350C42#12711yescharacteristic
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23#38611yescharacteristic
356C23#39411yescharacteristic
357C23#39611yescharacteristic
358C23#46511yescharacteristic
359C23#46711yescharacteristic
360C23#46811yescharacteristic
361C23#47011yescharacteristic
362Q8—44no—
363Q8—82no—
364Q8—82no—
365Q8—82no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—161no—
402C2×C4—161no—
403C2×C4—161no—
404C2×C4—161no—
405C2×C4#38011yescharacteristic
406C2×C4#38511yescharacteristic
407C2×C4#38511yescharacteristic
408C2×C4#38811yescharacteristic
409C2×C4#38811yescharacteristic
410C2×C4#39011yescharacteristic
411C2×C4#39211yescharacteristic
412C2×C4#39311yescharacteristic
413C2×C4#39411yescharacteristic
414C2×C4#39611yescharacteristic
415C2×C4#39711yescharacteristic
416C2×C4#39911yescharacteristic
417C2×C4C2×#10311yescharacteristic
418C2×C4#41611yescharacteristic
419C2×C4#41711yescharacteristic
420C2×C4#41911yescharacteristic
421C2×C4#46011yescharacteristic
422C2×C4#46111yescharacteristic
423C2×C4#46111yescharacteristic
424C2×C4#46211yescharacteristic
425C2×C4#46211yescharacteristic
426C2×C4#46211yescharacteristic
427C2×C4#46311yescharacteristic
428C2×C4#46311yescharacteristic
429C2×C4#46411yescharacteristic
430C2×C4#46411yescharacteristic
431C2×C4#46411yescharacteristic
432C2×C4#46411yescharacteristic
433C2×C4#46511yescharacteristic
434C2×C4#46711yescharacteristic
435C2×C4#46811yescharacteristic
436C2×C4#47011yescharacteristic
437C2×C4#47511yescharacteristic
438C2×C4#47711yescharacteristic
439C2×C4#47911yescharacteristic
440C2×C4#47911yescharacteristic
441C8—82no—
442C8—82no—
443C8—82no—
444C8—82no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22#143911yescharacteristic
458C22#188111yescharacteristic
459C22#188111yescharacteristic
460C22#189211yescharacteristic
461C22#189411yescharacteristic
462C22#190411yescharacteristic
463C22#190511yescharacteristic
464C22#205511yescharacteristic
465C22#205611yescharacteristic
466C22#206611yescharacteristic
467C22#206811yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—44no—
477C4—82no—
478C4—82no—
479C4—82no—
480C4—162no—
481C4#180311yescharacteristic
482C4#180511yescharacteristic
483C4#198111yescharacteristic
484C4#198311yescharacteristic
485C4#205511yescharacteristic
486C4#205611yescharacteristic
487C4#206611yescharacteristic
488C4#206811yescharacteristic
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2#930311yescharacteristic
494C2#930411yescharacteristic
495C2#930711yescharacteristic
496C2#930811yescharacteristic
497C2#1105711yescharacteristic
498C2#1106511yescharacteristic
499C2#1107711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
16. #1988C4semidirect
17. #1987C4semidirect

Maximal subgroups

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

subgroupindex
#219512
#213122
C2×#15182
C2×#14812
#108502
C2×#13012
C2×#12862