Finite Group Databasebeta

← #119900

Subgroups — #119900

Order 512.

630 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21322C211yesmaximal, characteristic
2C2×#1550C211yesmaximal, characteristic
3C2×#1481C211yesmaximal, characteristic
4#10853C211yesmaximal, characteristic
5#8043C211yesmaximal, characteristic
6C2×#1296C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×#384C2211yescharacteristic
15#1992—22no—
16#1990—21no—
17#1990—21no—
18C2×#341—21no—
19C2×#341—21no—
20#1736—21no—
21#1736—21no—
22#1550—22no—
23#1550C414yescomplemented
24C2×#333—21no—
25C2×#332—21no—
26#1481—22no—
27#1481—22no—
28C2×Q8⋊C8—22no—
29#1296—22no—
30#1296—22no—
31#1283—22no—
32C22×M16—21no—
33C22×M16D411yescharacteristic
34C22×M16D411yescharacteristic
35C23×C8—21no—
36C23×C8—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533C2×C412yes—
44#533D412yes—
45C2×C4⋊Q8D411yescharacteristic
46C2×C4⋊Q8D411yescharacteristic
47C2×#125—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C4×Q8—21no—
51C2×C4×Q8—21no—
52C2×#117—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C42C2311yescharacteristic
57#431—21no—
58#431—21no—
59#431—21no—
60#431D412yes—
61#423—21no—
62#423—21no—
63#423—21no—
64#423C2×C412yes—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—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—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8C2×C412yes—
79C2×C4⋊C8D412yes—
80C2×C22⋊C8—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16—21no—
85C2×#97—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384D412yes—
92#341—42no—
93#341—42no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#333—24no—
99#332—24no—
100Q8⋊C8—28no—
101C22×Q8—21no—
102C22×Q8—21no—
103C23×C4—41no—
104C23×C4C2×D411yescharacteristic
105C23×C4#4111yescharacteristic
106C23×C4#4111yescharacteristic
107C2×M16—21no—
108C2×M16—21no—
109C2×M16—21no—
110C2×M16—21no—
111C2×M16—21no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16—21no—
115C2×M16—21no—
116C2×M16—21no—
117C2×M16—22no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16SD1612yes—
124C2×M16Q1612yes—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8—41no—
132C22×C8—41no—
133C22×C8—41no—
134C22×C8—41no—
135C22×C8—41no—
136C22×C8—41no—
137C22×C8—41no—
138C22×C8—41no—
139C22×C8—81no—
140C22×C8—81no—
141C4⋊Q8—21no—
142C4⋊Q8—21no—
143C4⋊Q8—21no—
144C4⋊Q8—21no—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147C4⋊Q8C22⋊C412yes—
148C4⋊Q8C22⋊C412yes—
149#125—22no—
150#125—22no—
151#125—41no—
152#125—41no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—41no—
158C22⋊Q8—41no—
159C22⋊Q8—41no—
160C22⋊Q8—41no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—41no—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169#117—22no—
170#117—22no—
171#117—41no—
172#117—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4—81no—
191C2×C4⋊C4—81no—
192C2×C22⋊C4—41no—
193C2×C42—41no—
194C2×C42C22×C411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42#4111yescharacteristic
201C2×C42#4111yescharacteristic
202C2×C42#4111yescharacteristic
203C2×C42#4111yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—22no—
209C4⋊C8—22no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—41no—
214C4⋊C8—41no—
215C4⋊C8—41no—
216C4⋊C8—41no—
217C4⋊C8—41no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222#97—41no—
223#97—41no—
224C4×C8—22no—
225C4×C8—41no—
226C4×C8—41no—
227C4×C8—41no—
228C24#12411yescharacteristic
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—81no—
238C2×Q8—81no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—82no—
249C22×C4—82no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4#11711yescharacteristic
253C22×C4C4×D411yescharacteristic
254C22×C4C4×D411yescharacteristic
255C22×C4#12011yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4#12111yescharacteristic
258C22×C4#12111yescharacteristic
259C22×C4#12111yescharacteristic
260C22×C4#12111yescharacteristic
261C22×C4#12311yescharacteristic
262C22×C4#12311yescharacteristic
263C22×C4#12311yescharacteristic
264C22×C4#12311yescharacteristic
265C22×C4#12311yescharacteristic
266C22×C4#12311yescharacteristic
267C22×C4#12611yescharacteristic
268C22×C4#12611yescharacteristic
269C22×C4#12611yescharacteristic
270C22×C4C2×SD1611yescharacteristic
271C22×C4C2×Q1611yescharacteristic
272C22×C4#13511yescharacteristic
273C22×C4#13511yescharacteristic
274C22×C4AGL(1,ℤ/8)11yescharacteristic
275C22×C4#13711yescharacteristic
276C22×C4#13711yescharacteristic
277C22×C4#13711yescharacteristic
278M16—22no—
279M16—22no—
280M16—22no—
281M16—22no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—42no—
287M16—42no—
288M16—81no—
289M16—81no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—81no—
303C2×C8—81no—
304C2×C8—82no—
305C2×C8—81no—
306C2×C8—81no—
307C2×C8—81no—
308C2×C8—81no—
309C2×C8—81no—
310C2×C8—81no—
311C2×C8—81no—
312C2×C8—81no—
313C2×C8—82no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—82no—
329C4⋊C4—82no—
330C4⋊C4—82no—
331C4⋊C4—81no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—81no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C42—42no—
338C42—42no—
339C42C2×C22⋊C411yescharacteristic
340C42#11711yescharacteristic
341C42C4×D411yescharacteristic
342C42C4×D411yescharacteristic
343C42#12011yescharacteristic
344C42#12111yescharacteristic
345C42#12111yescharacteristic
346C42#12111yescharacteristic
347C42#12311yescharacteristic
348C42#12311yescharacteristic
349C42#12311yescharacteristic
350C42#12311yescharacteristic
351C42#12411yescharacteristic
352C42#12411yescharacteristic
353C42#12411yescharacteristic
354C42#12611yescharacteristic
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23#38811yescharacteristic
360C23#39411yescharacteristic
361C23#39711yescharacteristic
362C23#48711yescharacteristic
363C23#48811yescharacteristic
364C23#48911yescharacteristic
365C23#49111yescharacteristic
366Q8—42no—
367Q8—42no—
368Q8—82no—
369Q8—82no—
370Q8—81no—
371Q8—81no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—162no—
400C2×C4—162no—
401C2×C4#38111yescharacteristic
402C2×C4#38611yescharacteristic
403C2×C4#38611yescharacteristic
404C2×C4#38811yescharacteristic
405C2×C4#38811yescharacteristic
406C2×C4#38811yescharacteristic
407C2×C4#39411yescharacteristic
408C2×C4#39411yescharacteristic
409C2×C4#39411yescharacteristic
410C2×C4#39711yescharacteristic
411C2×C4#39711yescharacteristic
412C2×C4#39711yescharacteristic
413C2×C4C4×SD1611yescharacteristic
414C2×C4C4×Q1611yescharacteristic
415C2×C4#44011yescharacteristic
416C2×C4#44111yescharacteristic
417C2×C4#44811yescharacteristic
418C2×C4#44911yescharacteristic
419C2×C4#45111yescharacteristic
420C2×C4#45211yescharacteristic
421C2×C4#46011yescharacteristic
422C2×C4#46111yescharacteristic
423C2×C4#46211yescharacteristic
424C2×C4#46211yescharacteristic
425C2×C4#46311yescharacteristic
426C2×C4#46411yescharacteristic
427C2×C4#46411yescharacteristic
428C2×C4#46411yescharacteristic
429C2×C4#46511yescharacteristic
430C2×C4#46711yescharacteristic
431C2×C4#46811yescharacteristic
432C2×C4#47011yescharacteristic
433C2×C4#47111yescharacteristic
434C2×C4#47111yescharacteristic
435C2×C4#47211yescharacteristic
436C2×C4#47311yescharacteristic
437C2×C4#48311yescharacteristic
438C2×C4#48411yescharacteristic
439C2×C4#48511yescharacteristic
440C2×C4#48511yescharacteristic
441C8—42no—
442C8—42no—
443C8—82no—
444C8—82no—
445C8—82no—
446C8—82no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22#144011yescharacteristic
460C22#193311yescharacteristic
461C22#193511yescharacteristic
462C22#204211yescharacteristic
463C22#204311yescharacteristic
464C22#204811yescharacteristic
465C22#204911yescharacteristic
466C22#205111yescharacteristic
467C22#205211yescharacteristic
468C22#207211yescharacteristic
469C22#207411yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—82no—
477C4—82no—
478C4—162no—
479C4#187811yescharacteristic
480C4#188011yescharacteristic
481C4#190711yescharacteristic
482C4#190811yescharacteristic
483C4#192711yescharacteristic
484C4#192811yescharacteristic
485C4#203511yescharacteristic
486C4#203611yescharacteristic
487C4#205511yescharacteristic
488C4#205611yescharacteristic
489C4#207811yescharacteristic
490C4#207911yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2#1055311yescharacteristic
496C2#1055411yescharacteristic
497C2#1055511yescharacteristic
498C2#1055611yescharacteristic
499C2#1115211yescharacteristic
500C2#1119011yescharacteristic
501C2#1119211yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
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
#213222
C2×#15502
C2×#14812
#108532
#80432
C2×#12962
C2×#12832