Finite Group Databasebeta

← #119681

Subgroups — #119681

Order 512.

778 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20740C211yesmaximal, characteristic
2C2×#1491C211yesmaximal, characteristic
3#13786C211yesmaximal, characteristic
4#10851C211yesmaximal, characteristic
5C2×#1300C211yesmaximal, characteristic
6#8022C211yesmaximal, characteristic
7C2×#1285C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12C2×#391—21no—
13#2285C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15C2×#376C2211yescharacteristic
16#1823—21no—
17#1803C412yescomplemented
18#1803C412yescomplemented
19#1787—21no—
20#1763—22no—
21C2×#339—22no—
22#1491—22no—
23#1491—22no—
24C2×Q8⋊C8—22no—
25#1436—22no—
26C4⋊#95—21no—
27#1434—21no—
28#1434—21no—
29#1300—22no—
30#1294—21no—
31#1294—21no—
32#1285—22no—
33C23×Q8D411yescharacteristic
34C22×M16—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×Q8—21no—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×#117—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4D411yescharacteristic
51C22×C42—21no—
52C22×C42—21no—
53C22×C42D412yes—
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432D412yes—
63C2×C4⋊C8—21no—
64C2×C4⋊C8C2×C412yes—
65C2×#103—22no—
66C2×#103—22no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C4×M16—21no—
70C4×M16—21no—
71C4×M16—21no—
72C4×M16D412yes—
73C2×#97—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×C4×C8—21no—
77#391—28no—
78#384C2×C411yescharacteristic
79#384C2×C411yescharacteristic
80#382—21no—
81#380—21no—
82#380—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89#376—21no—
90#376—21no—
91#376—21no—
92#376—21no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95D411yescharacteristic
100C2×#95D411yescharacteristic
101#340—22no—
102#340—22no—
103#339—44no—
104Q8⋊C8—28no—
105C22×Q8—24no—
106C22×Q8—21no—
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—22no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C2×M16—22no—
122C2×M16—22no—
123C2×M16—22no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C22×C8—22no—
128C22×C8—41no—
129C22×C8—41no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146#117—42no—
147#117—42no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4C22⋊C412yes—
170C2×C22⋊C4—41no—
171C2×C42—24no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—22no—
176C2×C42—42no—
177C2×C42—41no—
178C2×C42—41no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42—42no—
184C2×C42—42no—
185C2×C42—41no—
186C2×C42C22×C411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—41no—
202#103—44no—
203#103—44no—
204C22⋊C8—22no—
205C22⋊C8—41no—
206C22⋊C8—41no—
207C22⋊C8—41no—
208#97—22no—
209#97—22no—
210#97—41no—
211#97—41no—
212#97—41no—
213#97—41no—
214C4×C8—22no—
215C4×C8—41no—
216#95—28no—
217#95—28no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—41no—
223#95—41no—
224#95—41no—
225#95—41no—
226#95—41no—
227#95—41no—
228#95—82no—
229#95—82no—
230C24#12011yescharacteristic
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—44no—
238C2×Q8—44no—
239C2×Q8—44no—
240C2×Q8—44no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8#10414yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C4×D411yescharacteristic
290C22×C4C4×D411yescharacteristic
291C22×C4#12111yescharacteristic
292C22×C4#12111yescharacteristic
293C22×C4#12111yescharacteristic
294C22×C4#12111yescharacteristic
295C22×C4#12111yescharacteristic
296C22×C4#12111yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12311yescharacteristic
300C22×C4#12311yescharacteristic
301C22×C4#12311yescharacteristic
302C22×C4#12311yescharacteristic
303C22×C4#12311yescharacteristic
304C22×C4#12411yescharacteristic
305C22×C4#12411yescharacteristic
306M16—24no—
307M16—42no—
308M16—42no—
309M16—42no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—81no—
318C2×C8—81no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—44no—
322C4⋊C4—44no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—81no—
334C4⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C42—44no—
338C42—44no—
339C42—44no—
340C42—42no—
341C42—42no—
342C42—42no—
343C42—42no—
344C42—82no—
345C42—82no—
346C42#11711yescharacteristic
347C42#11711yescharacteristic
348C42C4×D411yescharacteristic
349C42C4×D411yescharacteristic
350C42#12011yescharacteristic
351C42#12311yescharacteristic
352C42#12311yescharacteristic
353C42#12311yescharacteristic
354C42#12311yescharacteristic
355C42#12311yescharacteristic
356C42#12411yescharacteristic
357C42#12411yescharacteristic
358C42#12611yescharacteristic
359C42#12611yescharacteristic
360C42#12611yescharacteristic
361C42#12611yescharacteristic
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23#38611yescharacteristic
367C23#39411yescharacteristic
368C23#39411yescharacteristic
369C23#45311yescharacteristic
370C23#45411yescharacteristic
371C23#45511yescharacteristic
372C23#45611yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—44no—
376Q8—44no—
377Q8—42no—
378Q8—42no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
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—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—81no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4#38111yescharacteristic
445C2×C4#38611yescharacteristic
446C2×C4#38811yescharacteristic
447C2×C4#38811yescharacteristic
448C2×C4#38811yescharacteristic
449C2×C4#38811yescharacteristic
450C2×C4#39411yescharacteristic
451C2×C4#39411yescharacteristic
452C2×C4#39711yescharacteristic
453C2×C4#39711yescharacteristic
454C2×C4#39711yescharacteristic
455C2×C4#39711yescharacteristic
456C2×C4C2×#10412yes—
457C2×C4#42112yes—
458C8—44no—
459C8—82no—
460C8—82no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22#144011yescharacteristic
474C22#188211yescharacteristic
475C22#188311yescharacteristic
476C22#189611yescharacteristic
477C22#189711yescharacteristic
478C22#190511yescharacteristic
479C22#190511yescharacteristic
480C22#203711yescharacteristic
481C22#203811yescharacteristic
482C22#203911yescharacteristic
483C22#204011yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—44no—
495C4—84no—
496C4—82no—
497C4—82no—
498C4—82no—
499C4—161no—
500C4—161no—
501C4#182612yes—
502C4#187112yes—
503C2—21no—
504C2—21no—
505C2—21no—
506C2—21no—
507C2#932411yescharacteristic
508C2#932611yescharacteristic
509C2#932811yescharacteristic
510C2#933011yescharacteristic
511C2#1118411yescharacteristic
512C2#1119511yescharacteristic
513C2#1120111yescharacteristic
subgroupG/H
center, socleC23#386
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
17. #1803C4semidirect
18. #1803C4semidirect

Maximal subgroups

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

subgroupindex
#207402
C2×#14912
#137862
#108512
C2×#13002
#80222
C2×#12852