Finite Group Databasebeta

← #119818

Subgroups — #119818

Order 512.

648 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21312C211yesmaximal, characteristic
2C2×#1550C211yesmaximal, characteristic
3C2×#1493C211yesmaximal, characteristic
4#10847C211yesmaximal, characteristic
5C2×#1292C211yesmaximal, characteristic
6C2×#1279C211yesmaximal, characteristic
7#7874C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#423C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1989—22no—
16#1988—21no—
17#1987—21no—
18C2×#343—21no—
19C2×#343—21no—
20#1736—21no—
21#1736—21no—
22#1550—22no—
23#1550C414yescomplemented
24C2×#333—21no—
25C2×#332—21no—
26#1493—22no—
27#1493—22no—
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30#1292—22no—
31#1279—21no—
32#1279—21no—
33#1277—22no—
34C22×M16—21no—
35C22×M16—21no—
36C22×M16—21no—
37C23×C8—21no—
38C23×C8—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533C2×C412yes—
46#533D412yes—
47C2×C4⋊Q8D411yescharacteristic
48C2×C4⋊Q8D411yescharacteristic
49C2×#125—21no—
50C2×C22⋊Q8—21no—
51C2×C22⋊Q8—21no—
52C2×C4×Q8—21no—
53C2×C4×Q8—21no—
54C2×#117—21no—
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C42—21no—
58C22×C42C2311yescharacteristic
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423C2×C412yes—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
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⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8C2×C412yes—
82C2×C4⋊C8D412yes—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8D411yescharacteristic
89C2×C4×C8D411yescharacteristic
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C2×#95—21no—
95#343—42no—
96#343—42no—
97#340—22no—
98#340—22no—
99#340—22no—
100#340—22no—
101#333—24no—
102#332—24no—
103Q8⋊C8—24no—
104Q8⋊C8—24no—
105C22×Q8—21no—
106C22×Q8—21no—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4C2×D411yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—41no—
129C2×M16—41no—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—42no—
135C22×C8—42no—
136C22×C8—41no—
137C22×C8—41no—
138C22×C8—41no—
139C22×C8—41no—
140C22×C8—41no—
141C22×C8—41no—
142C22×C8—81no—
143C22×C8—81no—
144C4⋊Q8—21no—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147C4⋊Q8—21no—
148C4⋊Q8—21no—
149C4⋊Q8—21no—
150C4⋊Q8C22⋊C412yes—
151C4⋊Q8C22⋊C412yes—
152#125—22no—
153#125—22no—
154#125—41no—
155#125—41no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158C22⋊Q8—22no—
159C22⋊Q8—22no—
160C22⋊Q8—41no—
161C22⋊Q8—41no—
162C22⋊Q8—41no—
163C22⋊Q8—41no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—41no—
169C4×Q8—41no—
170C4×Q8—41no—
171C4×Q8—41no—
172#117—22no—
173#117—22no—
174#117—41no—
175#117—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
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—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4SD1612yes—
193C2×C4⋊C4Q1612yes—
194C2×C22⋊C4—41no—
195C2×C42—41no—
196C2×C42—41no—
197C2×C42—41no—
198C2×C42—81no—
199C2×C42—81no—
200C2×C42C22×C411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204C2×C42C2×D411yescharacteristic
205C2×C42C2×D411yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208C2×C42#4111yescharacteristic
209C2×C42#4111yescharacteristic
210C2×C42#4111yescharacteristic
211C2×C42#4111yescharacteristic
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C4⋊C8—41no—
221C4⋊C8—41no—
222C4⋊C8—41no—
223C4⋊C8—41no—
224C4⋊C8—41no—
225C4⋊C8—41no—
226C4⋊C8—41no—
227C4⋊C8—41no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—41no—
233C4×C8—41no—
234#95—41no—
235#95—41no—
236C24#12311yescharacteristic
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—81no—
246C2×Q8—81no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4#11711yescharacteristic
266C22×C4C4×D411yescharacteristic
267C22×C4C4×D411yescharacteristic
268C22×C4#12011yescharacteristic
269C22×C4#12111yescharacteristic
270C22×C4#12111yescharacteristic
271C22×C4#12111yescharacteristic
272C22×C4#12111yescharacteristic
273C22×C4#12111yescharacteristic
274C22×C4#12311yescharacteristic
275C22×C4#12311yescharacteristic
276C22×C4#12311yescharacteristic
277C22×C4#12411yescharacteristic
278C22×C4#12411yescharacteristic
279C22×C4#12411yescharacteristic
280C22×C4#12611yescharacteristic
281C22×C4#12611yescharacteristic
282C22×C4#12611yescharacteristic
283C22×C4C2×SD1611yescharacteristic
284C22×C4C2×Q1611yescharacteristic
285C22×C4#13511yescharacteristic
286C22×C4#13511yescharacteristic
287C22×C4AGL(1,ℤ/8)11yescharacteristic
288C22×C4#13711yescharacteristic
289C22×C4#13711yescharacteristic
290C22×C4#13711yescharacteristic
291M16—42no—
292M16—42no—
293M16—42no—
294M16—42no—
295M16—81no—
296M16—81no—
297M16—81no—
298M16—81no—
299M16—81no—
300M16—81no—
301M16—81no—
302M16—81no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—44no—
308C2×C8—44no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—82no—
318C2×C8—81no—
319C2×C8—81no—
320C2×C8—81no—
321C2×C8—81no—
322C2×C8—81no—
323C2×C8—81no—
324C2×C8—82no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C42—42no—
348C42—42no—
349C42—82no—
350C42—81no—
351C42—81no—
352C42C2×C22⋊C411yescharacteristic
353C42#11711yescharacteristic
354C42C4×D411yescharacteristic
355C42C4×D411yescharacteristic
356C42#12011yescharacteristic
357C42#12111yescharacteristic
358C42#12111yescharacteristic
359C42#12111yescharacteristic
360C42#12311yescharacteristic
361C42#12311yescharacteristic
362C42#12311yescharacteristic
363C42#12311yescharacteristic
364C42#12311yescharacteristic
365C42#12311yescharacteristic
366C42#12411yescharacteristic
367C42#12611yescharacteristic
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23#38811yescharacteristic
373C23#39411yescharacteristic
374C23#39711yescharacteristic
375C23#48311yescharacteristic
376C23#48411yescharacteristic
377C23#48511yescharacteristic
378C23#48511yescharacteristic
379Q8—42no—
380Q8—42no—
381Q8—82no—
382Q8—82no—
383Q8—81no—
384Q8—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4#38111yescharacteristic
420C2×C4#38611yescharacteristic
421C2×C4#38611yescharacteristic
422C2×C4#38811yescharacteristic
423C2×C4#38811yescharacteristic
424C2×C4#38811yescharacteristic
425C2×C4#39411yescharacteristic
426C2×C4#39411yescharacteristic
427C2×C4#39411yescharacteristic
428C2×C4#39711yescharacteristic
429C2×C4#39711yescharacteristic
430C2×C4#39711yescharacteristic
431C2×C4C4×SD1611yescharacteristic
432C2×C4C4×Q1611yescharacteristic
433C2×C4#44011yescharacteristic
434C2×C4#44111yescharacteristic
435C2×C4#44811yescharacteristic
436C2×C4#44911yescharacteristic
437C2×C4#45111yescharacteristic
438C2×C4#45211yescharacteristic
439C2×C4#46011yescharacteristic
440C2×C4#46111yescharacteristic
441C2×C4#46211yescharacteristic
442C2×C4#46211yescharacteristic
443C2×C4#46311yescharacteristic
444C2×C4#46411yescharacteristic
445C2×C4#46411yescharacteristic
446C2×C4#46411yescharacteristic
447C2×C4#46511yescharacteristic
448C2×C4#46711yescharacteristic
449C2×C4#46811yescharacteristic
450C2×C4#47011yescharacteristic
451C2×C4#47111yescharacteristic
452C2×C4#47111yescharacteristic
453C2×C4#47211yescharacteristic
454C2×C4#47311yescharacteristic
455C2×C4#48711yescharacteristic
456C2×C4#48811yescharacteristic
457C2×C4#48911yescharacteristic
458C2×C4#49111yescharacteristic
459C8—42no—
460C8—42no—
461C8—82no—
462C8—82no—
463C8—82no—
464C8—82no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#144011yescharacteristic
478C22#192711yescharacteristic
479C22#192811yescharacteristic
480C22#203511yescharacteristic
481C22#203611yescharacteristic
482C22#205011yescharacteristic
483C22#205011yescharacteristic
484C22#205111yescharacteristic
485C22#205211yescharacteristic
486C22#207211yescharacteristic
487C22#207411yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—82no—
495C4—82no—
496C4—82no—
497C4—82no—
498C4#187811yescharacteristic
499C4#188011yescharacteristic
500C4#190711yescharacteristic
501C4#190811yescharacteristic
502C4#193311yescharacteristic
503C4#193511yescharacteristic
504C4#204211yescharacteristic
505C4#204311yescharacteristic
506C4#205511yescharacteristic
507C4#205611yescharacteristic
508C4#207811yescharacteristic
509C4#207911yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2#1046011yescharacteristic
515C2#1046111yescharacteristic
516C2#1046211yescharacteristic
517C2#1046311yescharacteristic
518C2#1115111yescharacteristic
519C2#1119011yescharacteristic
520C2#1119211yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
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
23. #1550C4semidirect

Maximal subgroups

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

subgroupindex
#213122
C2×#15502
C2×#14932
#108472
C2×#12922
C2×#12792
#78742