Finite Group Databasebeta

← #119709

Subgroups — #119709

Order 512.

844 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20734C211yesmaximal, characteristic
2C2×#1487C211yesmaximal, characteristic
3C4×#391C211yesmaximal, characteristic
4#10839C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#8014C211yesmaximal, characteristic
7C2×#1276C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#391—21no—
13#2285C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15C2×C43C2211yescharacteristic
16#1824—21no—
17#1803C412yescomplemented
18#1803C412yescomplemented
19#1787—21no—
20C4×#103—22no—
21C2×#339—21no—
22C2×#339—21no—
23#1487—22no—
24#1487—22no—
25C2×Q8⋊C8—22no—
26#1436—22no—
27C4⋊#95—21no—
28C4×#95—21no—
29C4×#95—21no—
30#1303—22no—
31#1294—22no—
32#1276—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×C42—21no—
54C22×C42—21no—
55C22×C42D411yescharacteristic
56C22×C42D411yescharacteristic
57C22×C42C2311yescharacteristic
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431D412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423D412yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8C2×C412yes—
74C2×#103—22no—
75C2×#103—22no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C4×C8—21no—
79C2×C4×C8—21no—
80#391—28no—
81#384C2×C411yescharacteristic
82#384C2×C411yescharacteristic
83#382—21no—
84#380—21no—
85#380—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95D412yes—
97C43—21no—
98C43—21no—
99C43—21no—
100C43—21no—
101#340—22no—
102#340—22no—
103#339—42no—
104#339—42no—
105Q8⋊C8—28no—
106C22×Q8—24no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—42no—
113C22×Q8C22⋊C412yes—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C2×M16—22no—
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C22×C8—22no—
129C22×C8—41no—
130C22×C8—41no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—41no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147#117—41no—
148#117—41no—
149#117—41no—
150#117—41no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4C22⋊C412yes—
173C2×C22⋊C4—41no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—24no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—21no—
186C2×C42—21no—
187C2×C42—42no—
188C2×C42—42no—
189C2×C42—42no—
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×C42—41no—
201C2×C42—41no—
202C2×C42—41no—
203C2×C42—41no—
204C2×C42—41no—
205C2×C42SD1612yes—
206C2×C42Q1612yes—
207C2×C42C22×C411yescharacteristic
208C2×C42C2×D411yescharacteristic
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42#4111yescharacteristic
212C2×C42#4111yescharacteristic
213C2×C42#4111yescharacteristic
214C2×C42#4111yescharacteristic
215C2×C42#4111yescharacteristic
216C2×C42#4111yescharacteristic
217C2×C42#4111yescharacteristic
218C2×C42#4111yescharacteristic
219C4⋊C8—22no—
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—41no—
225C4⋊C8—41no—
226C4⋊C8—41no—
227#103—44no—
228#103—44no—
229C22⋊C8—22no—
230C22⋊C8—41no—
231C22⋊C8—41no—
232C22⋊C8—41no—
233C4×C8—22no—
234C4×C8—41no—
235C4×C8—41no—
236C4×C8—41no—
237#95—28no—
238#95—28no—
239#95—22no—
240#95—22no—
241#95—44no—
242#95—44no—
243#95—41no—
244#95—41no—
245C24#12011yescharacteristic
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—44no—
253C2×Q8—44no—
254C2×Q8—44no—
255C2×Q8—44no—
256C2×Q8—42no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8#10414yes—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
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—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C4×D411yescharacteristic
299C22×C4C4×D411yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12111yescharacteristic
302C22×C4#12111yescharacteristic
303C22×C4#12111yescharacteristic
304C22×C4#12111yescharacteristic
305C22×C4#12111yescharacteristic
306C22×C4#12111yescharacteristic
307C22×C4#12111yescharacteristic
308C22×C4#12311yescharacteristic
309C22×C4#12311yescharacteristic
310C22×C4#12311yescharacteristic
311C22×C4#12311yescharacteristic
312C22×C4#12311yescharacteristic
313C22×C4#12411yescharacteristic
314C22×C4#12411yescharacteristic
315C22×C4C2×SD1611yescharacteristic
316C22×C4C2×Q1611yescharacteristic
317C22×C4#13511yescharacteristic
318C22×C4#13511yescharacteristic
319C22×C4AGL(1,ℤ/8)11yescharacteristic
320C22×C4#13711yescharacteristic
321C22×C4#13711yescharacteristic
322C22×C4#13711yescharacteristic
323M16—42no—
324M16—42no—
325M16—81no—
326M16—81no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—81no—
333C2×C8—81no—
334C2×C8—81no—
335C2×C8—81no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—44no—
339C4⋊C4—44no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—81no—
353C4⋊C4—81no—
354C22⋊C4—81no—
355C22⋊C4—81no—
356C42—22no—
357C42—22no—
358C42—22no—
359C42—22no—
360C42—44no—
361C42—44no—
362C42—44no—
363C42—44no—
364C42—42no—
365C42—42no—
366C42—42no—
367C42—42no—
368C42—41no—
369C42—41no—
370C42—41no—
371C42—41no—
372C42—81no—
373C42—81no—
374C42—81no—
375C42—81no—
376C42—81no—
377C42—81no—
378C42#11711yescharacteristic
379C42#11711yescharacteristic
380C42C4×D411yescharacteristic
381C42C4×D411yescharacteristic
382C42#12011yescharacteristic
383C42#12311yescharacteristic
384C42#12311yescharacteristic
385C42#12311yescharacteristic
386C42#12311yescharacteristic
387C42#12311yescharacteristic
388C42#12411yescharacteristic
389C42#12411yescharacteristic
390C42#12611yescharacteristic
391C42#12611yescharacteristic
392C42#12611yescharacteristic
393C42#12611yescharacteristic
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23#38611yescharacteristic
399C23#39411yescharacteristic
400C23#39411yescharacteristic
401C23#44811yescharacteristic
402C23#44911yescharacteristic
403C23#45111yescharacteristic
404C23#45211yescharacteristic
405Q8—24no—
406Q8—24no—
407Q8—44no—
408Q8—44no—
409Q8—42no—
410Q8—42no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4#38111yescharacteristic
463C2×C4#38611yescharacteristic
464C2×C4#38811yescharacteristic
465C2×C4#38811yescharacteristic
466C2×C4#38811yescharacteristic
467C2×C4#38811yescharacteristic
468C2×C4#39411yescharacteristic
469C2×C4#39411yescharacteristic
470C2×C4#39711yescharacteristic
471C2×C4#39711yescharacteristic
472C2×C4#39711yescharacteristic
473C2×C4#39711yescharacteristic
474C2×C4C2×#10412yes—
475C2×C4#42112yes—
476C2×C4C4×SD1611yescharacteristic
477C2×C4C4×Q1611yescharacteristic
478C2×C4#44011yescharacteristic
479C2×C4#44111yescharacteristic
480C2×C4#46011yescharacteristic
481C2×C4#46111yescharacteristic
482C2×C4#46211yescharacteristic
483C2×C4#46211yescharacteristic
484C2×C4#46311yescharacteristic
485C2×C4#46411yescharacteristic
486C2×C4#46411yescharacteristic
487C2×C4#46411yescharacteristic
488C2×C4#46511yescharacteristic
489C2×C4#46711yescharacteristic
490C2×C4#46811yescharacteristic
491C2×C4#47011yescharacteristic
492C2×C4#48311yescharacteristic
493C2×C4#48411yescharacteristic
494C2×C4#48511yescharacteristic
495C2×C4#48511yescharacteristic
496C2×C4#48711yescharacteristic
497C2×C4#48811yescharacteristic
498C2×C4#48911yescharacteristic
499C2×C4#49111yescharacteristic
500C8—82no—
501C8—82no—
502C8—82no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22#144011yescharacteristic
516C22#187811yescharacteristic
517C22#188011yescharacteristic
518C22#189611yescharacteristic
519C22#189711yescharacteristic
520C22#190611yescharacteristic
521C22#190611yescharacteristic
522C22#203511yescharacteristic
523C22#203611yescharacteristic
524C22#204211yescharacteristic
525C22#204311yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—44no—
533C4—44no—
534C4—44no—
535C4—84no—
536C4—82no—
537C4—161no—
538C4—161no—
539C4#182612yes—
540C4#187112yes—
541C4#192711yescharacteristic
542C4#192811yescharacteristic
543C4#193311yescharacteristic
544C4#193511yescharacteristic
545C4#205511yescharacteristic
546C4#205611yescharacteristic
547C4#207211yescharacteristic
548C4#207411yescharacteristic
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2#923211yescharacteristic
554C2#923411yescharacteristic
555C2#923611yescharacteristic
556C2#923811yescharacteristic
557C2#1119011yescharacteristic
558C2#1119311yescharacteristic
559C2#1120111yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24#120
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
17. #1803C4semidirect
18. #1803C4semidirect

Maximal subgroups

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

subgroupindex
#207342
C2×#14872
C4×#3912
#108392
C2×#13032
#80142
C2×#12762