Finite Group Databasebeta

← #119978

Subgroups — #119978

Order 512.

776 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21303C211yesmaximal, characteristic
2#20734C211yesmaximal, characteristic
3C2×C4×#103C211yesmaximal, characteristic
4#10851C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#7897C211yesmaximal, characteristic
7C2×#1278C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C22×#103—21no—
12C2×C4×M16C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1985—22no—
17#1984—22no—
18#1824—21no—
19#1803C412yescomplemented
20#1803C412yescomplemented
21#1787—21no—
22C4×#103—22no—
23C4×#103—22no—
24C4×#103—22no—
25C2×#340—21no—
26C2×#339—21no—
27C2×#339—21no—
28#1728—21no—
29#1728—21no—
30#1303—22no—
31#1279—22no—
32#1278—22no—
33C23×Q8D411yescharacteristic
34C22×M16—21no—
35C22×M16D411yescharacteristic
36C22×M16D411yescharacteristic
37C23×C8—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×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8C2×C412yes—
49C2×C4×Q8D412yes—
50C2×#117—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4D411yescharacteristic
54C22×C42—21no—
55C22×C42—21no—
56C22×C42C2311yescharacteristic
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8C2×C411yescharacteristic
67C2×C4⋊C8C2×C411yescharacteristic
68C2×C4⋊C8D412yes—
69C2×#103—28no—
70C2×#103—24no—
71C2×#103—22no—
72C2×#103—22no—
73C2×C22⋊C8—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16—21no—
78C2×#97—21no—
79C2×C4×C8—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8D412yes—
87#384C2×C412yes—
88#382—21no—
89#380—21no—
90#380—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4D412yes—
97C2×#95—21no—
98#340—24no—
99#340—22no—
100#340—22no—
101#339—42no—
102#339—42no—
103#336—24no—
104#336—24no—
105C22×Q8—21no—
106C22×Q8—24no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—42no—
112C22×Q8C22⋊C412yes—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—41no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4#4111yescharacteristic
119C2×M16—21no—
120C2×M16—21no—
121C2×M16—21no—
122C2×M16—21no—
123C2×M16—21no—
124C2×M16—21no—
125C2×M16—21no—
126C2×M16—21no—
127C2×M16—21no—
128C2×M16—21no—
129C2×M16—41no—
130C2×M16—41no—
131C2×M16—41no—
132C2×M16—41no—
133C2×M16—41no—
134C2×M16—41no—
135C2×M16SD1612yes—
136C2×M16Q1612yes—
137C22×C8—24no—
138C22×C8—22no—
139C22×C8—21no—
140C22×C8—21no—
141C22×C8—21no—
142C22×C8—21no—
143C22×C8—22no—
144C22×C8—42no—
145C22×C8—41no—
146C22×C8—41no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—41no—
156C4×Q8—41no—
157C4×Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163#117—41no—
164#117—41no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4C22⋊C412yes—
186C2×C22⋊C4—41no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—41no—
191C2×C42—41no—
192C2×C42—41no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42—41no—
197C2×C42—41no—
198C2×C42—41no—
199C2×C42—41no—
200C2×C42C22×C411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204C2×C42C2×D411yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208C2×C42#4111yescharacteristic
209C2×C42#4111yescharacteristic
210C2×C42#4111yescharacteristic
211C2×C42#4111yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220#103—216no—
221#103—44no—
222#103—44no—
223C22⋊C8—41no—
224C22⋊C8—41no—
225#97—41no—
226#97—41no—
227C4×C8—22no—
228C4×C8—22no—
229C4×C8—41no—
230C4×C8—41no—
231C4×C8—41no—
232C4×C8—41no—
233C4×C8—41no—
234C4×C8—41no—
235#95—22no—
236#95—41no—
237#95—41no—
238#95—41no—
239C24#12111yescharacteristic
240C2×Q8—22no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8—44no—
248C2×Q8—44no—
249C2×Q8—44no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8#10414yes—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—82no—
269C22×C4—82no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4C2×C22⋊C411yescharacteristic
273C22×C4C4×D411yescharacteristic
274C22×C4C4×D411yescharacteristic
275C22×C4#12011yescharacteristic
276C22×C4#12011yescharacteristic
277C22×C4#12111yescharacteristic
278C22×C4#12111yescharacteristic
279C22×C4#12111yescharacteristic
280C22×C4#12311yescharacteristic
281C22×C4#12311yescharacteristic
282C22×C4#12311yescharacteristic
283C22×C4#12311yescharacteristic
284C22×C4#12311yescharacteristic
285C22×C4#12311yescharacteristic
286C22×C4#12411yescharacteristic
287C22×C4#12411yescharacteristic
288C22×C4#12611yescharacteristic
289C22×C4#12611yescharacteristic
290C22×C4C2×SD1611yescharacteristic
291C22×C4C2×Q1611yescharacteristic
292C22×C4#13511yescharacteristic
293C22×C4#13511yescharacteristic
294C22×C4AGL(1,ℤ/8)11yescharacteristic
295C22×C4#13711yescharacteristic
296C22×C4#13711yescharacteristic
297C22×C4#13711yescharacteristic
298M16—22no—
299M16—22no—
300M16—22no—
301M16—22no—
302M16—41no—
303M16—41no—
304M16—41no—
305M16—41no—
306M16—81no—
307M16—81no—
308M16—81no—
309M16—81no—
310C2×C8—24no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—44no—
314C2×C8—44no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—44no—
332C4⋊C4—42no—
333C4⋊C4—44no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C22⋊C4—81no—
345C22⋊C4—81no—
346C42—42no—
347C42—42no—
348C42—42no—
349C42—42no—
350C42—42no—
351C42—42no—
352C42—81no—
353C42—81no—
354C42—81no—
355C42—81no—
356C42#11711yescharacteristic
357C42#11711yescharacteristic
358C42C4×D411yescharacteristic
359C42C4×D411yescharacteristic
360C42#12111yescharacteristic
361C42#12111yescharacteristic
362C42#12111yescharacteristic
363C42#12111yescharacteristic
364C42#12311yescharacteristic
365C42#12311yescharacteristic
366C42#12311yescharacteristic
367C42#12311yescharacteristic
368C42#12411yescharacteristic
369C42#12411yescharacteristic
370C42#12611yescharacteristic
371C42#12611yescharacteristic
372C23—22no—
373C23—22no—
374C23#38611yescharacteristic
375C23#39411yescharacteristic
376C23#39711yescharacteristic
377C23#46011yescharacteristic
378C23#46211yescharacteristic
379C23#46411yescharacteristic
380C23#46411yescharacteristic
381Q8—24no—
382Q8—24no—
383Q8—44no—
384Q8—44no—
385Q8—42no—
386Q8—42no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—24no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4#38111yescharacteristic
418C2×C4#38611yescharacteristic
419C2×C4#38811yescharacteristic
420C2×C4#38811yescharacteristic
421C2×C4#38811yescharacteristic
422C2×C4#38811yescharacteristic
423C2×C4#39411yescharacteristic
424C2×C4#39411yescharacteristic
425C2×C4#39411yescharacteristic
426C2×C4#39711yescharacteristic
427C2×C4#39711yescharacteristic
428C2×C4#39711yescharacteristic
429C2×C4C2×#10412yes—
430C2×C4#42112yes—
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#46111yescharacteristic
440C2×C4#46211yescharacteristic
441C2×C4#46311yescharacteristic
442C2×C4#46411yescharacteristic
443C2×C4#46511yescharacteristic
444C2×C4#46711yescharacteristic
445C2×C4#46811yescharacteristic
446C2×C4#47011yescharacteristic
447C2×C4#48311yescharacteristic
448C2×C4#48411yescharacteristic
449C2×C4#48511yescharacteristic
450C2×C4#48511yescharacteristic
451C2×C4#48711yescharacteristic
452C2×C4#48811yescharacteristic
453C2×C4#48911yescharacteristic
454C2×C4#49111yescharacteristic
455C8—44no—
456C8—42no—
457C8—42no—
458C8—81no—
459C8—81no—
460C8—82no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22#144011yescharacteristic
470C22#187112yes—
471C22#187811yescharacteristic
472C22#188011yescharacteristic
473C22#188112yes—
474C22#205511yescharacteristic
475C22#205611yescharacteristic
476C22#207211yescharacteristic
477C22#207411yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—44no—
485C4—84no—
486C4—82no—
487C4—162no—
488C4#182612yes—
489C4#189611yescharacteristic
490C4#189711yescharacteristic
491C4#192711yescharacteristic
492C4#192811yescharacteristic
493C4#193311yescharacteristic
494C4#193511yescharacteristic
495C4#203511yescharacteristic
496C4#203611yescharacteristic
497C4#204211yescharacteristic
498C4#204311yescharacteristic
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2#899012yes—
504C2#899212yes—
505C2#1119011yescharacteristic
506C2#1119411yescharacteristic
507C2#1120111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
19. #1803C4semidirect
20. #1803C4semidirect

Maximal subgroups

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

subgroupindex
#213032
#207342
C2×C4×#1032
#108512
C2×#13032
#78972
C2×#12782