Finite Group Databasebeta

← #118006

Subgroups — #118006

Order 512.

798 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21359C211yesmaximal, characteristic
2#20647C211yesmaximal, characteristic
3C2×#1479C211yesmaximal, characteristic
4#13942C211yesmaximal, characteristic
5#8026C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#419—21no—
13C2×#391—21no—
14#2285C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1948—22no—
18#1853—22no—
19#1805—22no—
20#1803—22no—
21C4×#106—22no—
22#1736—21no—
23#1479—22no—
24#1479C414yescomplemented
25C2×Q8⋊C8—22no—
26#1441—22no—
27C4⋊#95—21no—
28#1434—22no—
29#1294—22no—
30#1286—22no—
31#1279—22no—
32C23×Q8D411yescharacteristic
33C22×M16—21no—
34C2×C4×Q8—21no—
35C2×C4×Q8—21no—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8C2×C412yes—
45C2×C4×Q8Q812yes—
46C2×#117—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4D411yescharacteristic
50C22×C4⋊C4D412yes—
51C22×C42—21no—
52C22×C42—21no—
53C22×C42C2311yescharacteristic
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431C2×C412yes—
60#431C2×C412yes—
61#431D412yes—
62C2×#106—24no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8D412yes—
71#419—42no—
72#419—42no—
73C2×#103—24no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C4×C8—21no—
77C2×C4×C8D412yes—
78#391—42no—
79#391—42no—
80#384D412yes—
81#382—21no—
82#382—21no—
83#382—21no—
84#382—21no—
85#382—21no—
86#380—21no—
87#380—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95D412yes—
99#340—24no—
100#340—24no—
101Q8⋊C8—28no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8C4⋊C412yes—
114C22×Q8SD1612yes—
115C22×Q8SD1612yes—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—41no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—41no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148#117—41no—
149#117—41no—
150#117—41no—
151#117—41no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4C4⋊C412yes—
176C2×C22⋊C4—41no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42—41no—
184C2×C42—41no—
185C2×C42—41no—
186C2×C42—41no—
187C2×C42—41no—
188C2×C42—41no—
189C2×C42—41no—
190C2×C42C22×C411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×Q811yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42#4111yescharacteristic
199C2×C42#4111yescharacteristic
200C2×C42#4111yescharacteristic
201C2×C42#4111yescharacteristic
202#106—48no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211#103—48no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—41no—
216C4×C8—22no—
217C4×C8—22no—
218C4×C8—41no—
219C4×C8C22⋊C414yes—
220#95—22no—
221#95—22no—
222#95—48no—
223#95—48no—
224#95—41no—
225#95—41no—
226#95—41no—
227#95—41no—
228#95—41no—
229#95—41no—
230C24#12011yescharacteristic
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8#10614yescomplemented
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—44no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4C2×C4⋊C411yescharacteristic
286C22×C4C4×D411yescharacteristic
287C22×C4C4×D411yescharacteristic
288C22×C4#12011yescharacteristic
289C22×C4#12011yescharacteristic
290C22×C4#12111yescharacteristic
291C22×C4#12111yescharacteristic
292C22×C4#12111yescharacteristic
293C22×C4#12111yescharacteristic
294C22×C4#12111yescharacteristic
295C22×C4#12111yescharacteristic
296C22×C4C22⋊Q811yescharacteristic
297C22×C4C22⋊Q811yescharacteristic
298C22×C4#12311yescharacteristic
299C22×C4#12311yescharacteristic
300C22×C4#12311yescharacteristic
301C22×C4#12411yescharacteristic
302C22×C4#12711yescharacteristic
303C22×C4C2×SD1611yescharacteristic
304C22×C4C2×SD1611yescharacteristic
305C22×C4#13511yescharacteristic
306C22×C4#13511yescharacteristic
307C22×C4AGL(1,ℤ/8)11yescharacteristic
308C22×C4AGL(1,ℤ/8)11yescharacteristic
309C22×C4#13711yescharacteristic
310C22×C4#13711yescharacteristic
311M16—81no—
312M16—81no—
313M16—81no—
314M16—81no—
315C2×C8—24no—
316C2×C8—44no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—82no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—44no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—82no—
338C4⋊C4—81no—
339C4⋊C4—81no—
340C4⋊C4—81no—
341C4⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C42—42no—
345C42—42no—
346C42—42no—
347C42—42no—
348C42—81no—
349C42—81no—
350C42—81no—
351C42—81no—
352C42—81no—
353C42—81no—
354C42C2×C22⋊C411yescharacteristic
355C42#11711yescharacteristic
356C42C4×D411yescharacteristic
357C42C4×D411yescharacteristic
358C42#12111yescharacteristic
359C42#12111yescharacteristic
360C42C22⋊Q811yescharacteristic
361C42C22⋊Q811yescharacteristic
362C42C22⋊Q811yescharacteristic
363C42C22⋊Q811yescharacteristic
364C42#12311yescharacteristic
365C42#12311yescharacteristic
366C42#12411yescharacteristic
367C42#12411yescharacteristic
368C42#12611yescharacteristic
369C42#12611yescharacteristic
370C23—22no—
371C23—22no—
372C23#38511yescharacteristic
373C23#39211yescharacteristic
374C23#39411yescharacteristic
375C23#44811yescharacteristic
376C23#44911yescharacteristic
377C23#45011yescharacteristic
378C23#45211yescharacteristic
379Q8—24no—
380Q8—24no—
381Q8—42no—
382Q8—42no—
383Q8—42no—
384Q8—42no—
385Q8—42no—
386Q8—42no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#38011yescharacteristic
426C2×C4#38511yescharacteristic
427C2×C4#38611yescharacteristic
428C2×C4#38811yescharacteristic
429C2×C4#38811yescharacteristic
430C2×C4#39011yescharacteristic
431C2×C4#39311yescharacteristic
432C2×C4#39411yescharacteristic
433C2×C4#39611yescharacteristic
434C2×C4#39611yescharacteristic
435C2×C4#39711yescharacteristic
436C2×C4#39911yescharacteristic
437C2×C4C2×#10611yescharacteristic
438C2×C4#42711yescharacteristic
439C2×C4#42811yescharacteristic
440C2×C4#42811yescharacteristic
441C2×C4#44811yescharacteristic
442C2×C4#44911yescharacteristic
443C2×C4#45011yescharacteristic
444C2×C4#45211yescharacteristic
445C2×C4#46511yescharacteristic
446C2×C4#46511yescharacteristic
447C2×C4#46511yescharacteristic
448C2×C4#46511yescharacteristic
449C2×C4#46811yescharacteristic
450C2×C4#46811yescharacteristic
451C2×C4#46911yescharacteristic
452C2×C4#47011yescharacteristic
453C2×C4#48111yescharacteristic
454C2×C4#48111yescharacteristic
455C2×C4#48211yescharacteristic
456C2×C4#48211yescharacteristic
457C2×C4#48311yescharacteristic
458C2×C4#48311yescharacteristic
459C2×C4#48511yescharacteristic
460C2×C4#48511yescharacteristic
461C8—44no—
462C8—82no—
463C8—82no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22#143911yescharacteristic
473C22#185311yescharacteristic
474C22#185411yescharacteristic
475C22#200011yescharacteristic
476C22#200011yescharacteristic
477C22#200912yes—
478C22#201012yes—
479C22#203411yescharacteristic
480C22#203511yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—44no—
490C4—84no—
491C4—82no—
492C4—162no—
493C4—162no—
494C4#180711yescharacteristic
495C4#180911yescharacteristic
496C4#185311yescharacteristic
497C4#185411yescharacteristic
498C4#203411yescharacteristic
499C4#203511yescharacteristic
500C4#207711yescharacteristic
501C4#207711yescharacteristic
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2#999912yes—
507C2#1000112yes—
508C2#1108311yescharacteristic
509C2#1109511yescharacteristic
510C2#1113011yescharacteristic
subgroupG/H
center, socleC23#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
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
24. #1479C4semidirect
258. C2×Q8#106semidirect

Maximal subgroups

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

subgroupindex
#213592
#206472
C2×#14792
#139422
#80262
C2×#12862
#79012