Finite Group Databasebeta

← #118068

Subgroups — #118068

Order 512.

732 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21838C211yesmaximal, characteristic
2#21365C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4#14160C211yesmaximal, characteristic
5#10851C211yesmaximal, characteristic
6C2×#1285C211yesmaximal, characteristic
7#7904C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12#2285C2211yescharacteristic
13C2×C4×C4⋊C4C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1992—21no—
16#1992—21no—
17#1989—22no—
18#1948—21no—
19#1947—21no—
20#1853—21no—
21#1852—21no—
22#1824—21no—
23#1823—21no—
24#1776—22no—
25C2×#339—22no—
26#1528—22no—
27#1528C414yescomplemented
28C2×#330—22no—
29#1441—21no—
30#1441—21no—
31#1436—22no—
32C4⋊#95—21no—
33C4⋊#95—21no—
34#1285—22no—
35#1279—22no—
36C22×M16—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125—21no—
46C2×#125—21no—
47C2×#125C2×C412yes—
48C2×#125Q812yes—
49C2×#117—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C42—21no—
58C22×C42D412yes—
59C22×C42C2311yescharacteristic
60#432—21no—
61#432—21no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432—21no—
66#432C2×C412yes—
67#432D412yes—
68C2×#107—22no—
69C2×#106—22no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8D412yes—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16C2×C412yes—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97D412yes—
81C2×C4×C8—21no—
82#384D411yescharacteristic
83#384D411yescharacteristic
84#382—21no—
85#380—21no—
86#380—21no—
87C4×C4⋊C4—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—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—22no—
102C2×#95—22no—
103#340—22no—
104#340—22no—
105#340—22no—
106#340—22no—
107#340—22no—
108#340—22no—
109#339—44no—
110#330—28no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C2×M16—22no—
120C2×M16—22no—
121C2×M16—22no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—41no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132#125—22no—
133#125—22no—
134#125—22no—
135#125—22no—
136#125—41no—
137#125—41no—
138#125—41no—
139#125—41no—
140#125—41no—
141#125—41no—
142#125—41no—
143#125—41no—
144#117—42no—
145#117—42no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4C4⋊C412yes—
185C2×C4⋊C4C4⋊C412yes—
186C2×C22⋊C4—41no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—42no—
190C2×C42—42no—
191C2×C42—42no—
192C2×C42—42no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42C22×C411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×Q811yescharacteristic
202C2×C42#4111yescharacteristic
203C2×C42#4111yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208#107—44no—
209#106—44no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217C22⋊C8—41no—
218#97—22no—
219#97—22no—
220#97—41no—
221#97—41no—
222#97—41no—
223#97C22⋊C414yes—
224C4×C8—22no—
225C4×C8—41no—
226#95—44no—
227#95—44no—
228#95—41no—
229#95—41no—
230#95—41no—
231#95—41no—
232#95—41no—
233#95—41no—
234#95—82no—
235#95—82no—
236C24#12011yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×C4⋊C411yescharacteristic
281C22×C4C4×D411yescharacteristic
282C22×C4C4×D411yescharacteristic
283C22×C4#12011yescharacteristic
284C22×C4#12011yescharacteristic
285C22×C4#12111yescharacteristic
286C22×C4#12111yescharacteristic
287C22×C4#12111yescharacteristic
288C22×C4#12111yescharacteristic
289C22×C4#12111yescharacteristic
290C22×C4#12111yescharacteristic
291C22×C4C22⋊Q811yescharacteristic
292C22×C4C22⋊Q811yescharacteristic
293C22×C4#12311yescharacteristic
294C22×C4#12311yescharacteristic
295C22×C4#12311yescharacteristic
296C22×C4#12411yescharacteristic
297C22×C4#12711yescharacteristic
298M16—24no—
299M16—42no—
300M16—42no—
301M16—42no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—42no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—44no—
324C4⋊C4—44no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C22⋊C4—81no—
344C22⋊C4—81no—
345C42—44no—
346C42—82no—
347C42—82no—
348C42—82no—
349C42—82no—
350C42C2×C22⋊C411yescharacteristic
351C42#11711yescharacteristic
352C42C4×D411yescharacteristic
353C42C4×D411yescharacteristic
354C42#12111yescharacteristic
355C42#12111yescharacteristic
356C42C22⋊Q811yescharacteristic
357C42C22⋊Q811yescharacteristic
358C42C22⋊Q811yescharacteristic
359C42C22⋊Q811yescharacteristic
360C42#12311yescharacteristic
361C42#12311yescharacteristic
362C42#12411yescharacteristic
363C42#12411yescharacteristic
364C42#12611yescharacteristic
365C42#12611yescharacteristic
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23#38511yescharacteristic
371C23#39211yescharacteristic
372C23#39411yescharacteristic
373C23#45311yescharacteristic
374C23#45411yescharacteristic
375C23#45511yescharacteristic
376C23#45611yescharacteristic
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—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—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—82no—
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#38011yescharacteristic
443C2×C4#38511yescharacteristic
444C2×C4#38611yescharacteristic
445C2×C4#38811yescharacteristic
446C2×C4#38811yescharacteristic
447C2×C4#39011yescharacteristic
448C2×C4#39311yescharacteristic
449C2×C4#39411yescharacteristic
450C2×C4#39611yescharacteristic
451C2×C4#39611yescharacteristic
452C2×C4#39711yescharacteristic
453C2×C4#39911yescharacteristic
454C2×C4#45412yes—
455C2×C4#45612yes—
456C8—44no—
457C8—44no—
458C8—82no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22#143911yescharacteristic
472C22#185911yescharacteristic
473C22#186011yescharacteristic
474C22#200311yescharacteristic
475C22#200511yescharacteristic
476C22#200611yescharacteristic
477C22#200711yescharacteristic
478C22#201011yescharacteristic
479C22#201011yescharacteristic
480C22#203711yescharacteristic
481C22#203811yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—84no—
493C4—82no—
494C4—82no—
495C4—82no—
496C4—82no—
497C4—161no—
498C4—161no—
499C4#185712yes—
500C4#203812yes—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2#1000511yescharacteristic
506C2#1000711yescharacteristic
507C2#1000911yescharacteristic
508C2#1001111yescharacteristic
509C2#1108311yescharacteristic
510C2#1111311yescharacteristic
511C2#1113611yescharacteristic
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
27. #1528C4semidirect

Maximal subgroups

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

subgroupindex
#218382
#213652
C2×#15282
#141602
#108512
C2×#12852
#79042