Finite Group Databasebeta

← #120728

Subgroups — #120728

Order 512.

695 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21940C211yesmaximal, characteristic
2#10854C211yesmaximal, characteristic
3#10846C211yesmaximal, characteristic
4#8023C211yesmaximal, characteristic
5C2×#1289C211yesmaximal, characteristic
6C2×#1289C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C22×C22⋊C8C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C2×#380C2211yescharacteristic
11C2×#380C2211yescharacteristic
12C2×#380C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×C4×C22⋊C4C2211yescharacteristic
15#1852—22no—
16#1852—22no—
17#1808—22no—
18C2×#342—21no—
19C2×#342—21no—
20C2×#342—21no—
21C2×#342—21no—
22#1294C414yescomplemented
23#1289—22no—
24#1289—22no—
25#1282—22no—
26C24×C4C2311yescharacteristic
27C23×C8—21no—
28C23×C8Q812yes—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C22⋊C4—21no—
34C22×C22⋊C4—21no—
35C22×C22⋊C4—21no—
36C22×C22⋊C4—21no—
37C22×C22⋊C4D411yescharacteristic
38C22×C22⋊C4D411yescharacteristic
39C22×C42—21no—
40C2×#107—24no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8C2×C412yes—
51C2×C22⋊C8D412yes—
52C2×C22⋊C8Q812yes—
53#380—21no—
54#380—21no—
55#380—21no—
56#380—21no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65#380—21no—
66#380C2×C412yes—
67#380D412yes—
68#380D412yes—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95C2×C412yes—
78#342—42no—
79#342—42no—
80#342—42no—
81#342—42no—
82#340—24no—
83C25C2×D411yescharacteristic
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—22no—
87C23×C4—41no—
88C23×C4—41no—
89C23×C4—41no—
90C23×C4—82no—
91C23×C4C22×C411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C23×C4C2×Q811yescharacteristic
96C23×C4C2×Q811yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C23×C4#4111yescharacteristic
102C23×C4#4111yescharacteristic
103C23×C4#4111yescharacteristic
104C23×C4#4111yescharacteristic
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—82no—
112C22×C8—82no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4—82no—
123C2×C4⋊C4—82no—
124C2×C4⋊C4—82no—
125C2×C22⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C22⋊C4—21no—
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4—22no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—41no—
141C2×C22⋊C4—41no—
142C2×C22⋊C4—41no—
143C2×C22⋊C4—41no—
144C2×C22⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—41no—
159C2×C22⋊C4D812yes—
160C2×C22⋊C4Q1612yes—
161C2×C42—41no—
162C2×C42—41no—
163C2×C42—82no—
164#107—84no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—41no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C22⋊C8—41no—
172C22⋊C8C4⋊C414yes—
173#95—22no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—41no—
179#95—41no—
180#95—41no—
181#95—41no—
182#95—41no—
183C24—81no—
184C24—81no—
185C24C4×D411yescharacteristic
186C24#12111yescharacteristic
187C24#12111yescharacteristic
188C24#12111yescharacteristic
189C24#12311yescharacteristic
190C24#12311yescharacteristic
191C24C4⋊Q811yescharacteristic
192C24C2×D811yescharacteristic
193C24C2×Q1611yescharacteristic
194C24#13511yescharacteristic
195C24#13511yescharacteristic
196C24AGL(1,ℤ/8)11yescharacteristic
197C24AGL(1,ℤ/8)11yescharacteristic
198C24#13711yescharacteristic
199C24#13711yescharacteristic
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—81no—
220C22×C4—81no—
221C22×C4—81no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—81no—
227C22×C4—81no—
228C22×C4—81no—
229C22×C4—81no—
230C22×C4—82no—
231C22×C4—82no—
232C22×C4—82no—
233C22×C4—82no—
234C22×C4—82no—
235C22×C4—82no—
236C22×C4—81no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—82no—
243C22×C4—82no—
244C22×C4C2×C4⋊C411yescharacteristic
245C22×C4#11711yescharacteristic
246C22×C4#11711yescharacteristic
247C22×C4C4×D411yescharacteristic
248C22×C4C4×D411yescharacteristic
249C22×C4C4×Q811yescharacteristic
250C22×C4#12011yescharacteristic
251C22×C4C22⋊Q811yescharacteristic
252C22×C4C22⋊Q811yescharacteristic
253C22×C4C22⋊Q811yescharacteristic
254C22×C4C22⋊Q811yescharacteristic
255C22×C4C22⋊Q811yescharacteristic
256C22×C4#12311yescharacteristic
257C22×C4#12311yescharacteristic
258C22×C4#12311yescharacteristic
259C22×C4#12411yescharacteristic
260C22×C4#12411yescharacteristic
261C22×C4#12411yescharacteristic
262C22×C4#12411yescharacteristic
263C22×C4#12511yescharacteristic
264C22×C4#12511yescharacteristic
265C22×C4#12511yescharacteristic
266C22×C4#12511yescharacteristic
267C22×C4#12511yescharacteristic
268C22×C4#12611yescharacteristic
269C22×C4#12611yescharacteristic
270C22×C4#12611yescharacteristic
271C22×C4#12611yescharacteristic
272C2×C8—24no—
273C2×C8—44no—
274C2×C8—42no—
275C2×C8—82no—
276C2×C8—82no—
277C2×C8—82no—
278C2×C8—82no—
279C2×C8—82no—
280C4⋊C4—44no—
281C4⋊C4—44no—
282C4⋊C4—82no—
283C4⋊C4—82no—
284C4⋊C4—82no—
285C4⋊C4—82no—
286C4⋊C4—82no—
287C4⋊C4—82no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C42—82no—
313C42—82no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23#38811yescharacteristic
337C23#38811yescharacteristic
338C23#38911yescharacteristic
339C23#39411yescharacteristic
340C23#39711yescharacteristic
341C23#39811yescharacteristic
342C23#39811yescharacteristic
343C23C4×D811yescharacteristic
344C23C4×Q1611yescharacteristic
345C23#44011yescharacteristic
346C23#44011yescharacteristic
347C23#45911yescharacteristic
348C23#45911yescharacteristic
349C23#46211yescharacteristic
350C23#46211yescharacteristic
351C23#46311yescharacteristic
352C23#46311yescharacteristic
353C23#46411yescharacteristic
354C23#46411yescharacteristic
355C23#46611yescharacteristic
356C23#46711yescharacteristic
357C23#46911yescharacteristic
358C23#47011yescharacteristic
359C23#48011yescharacteristic
360C23#48011yescharacteristic
361C23#48211yescharacteristic
362C23#48211yescharacteristic
363C23#48411yescharacteristic
364C23#48411yescharacteristic
365C23#48511yescharacteristic
366C23#48511yescharacteristic
367C23#49911yescharacteristic
368C23#50011yescharacteristic
369C23#50111yescharacteristic
370C23#50111yescharacteristic
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—162no—
422C2×C4—162no—
423C2×C4—162no—
424C2×C4—162no—
425C2×C4—162no—
426C2×C4—162no—
427C2×C4—162no—
428C2×C4—162no—
429C2×C4#38211yescharacteristic
430C2×C4#38511yescharacteristic
431C2×C4#38711yescharacteristic
432C2×C4#38711yescharacteristic
433C2×C4#39311yescharacteristic
434C2×C4#40011yescharacteristic
435C2×C4#40011yescharacteristic
436C2×C4#40011yescharacteristic
437C8—44no—
438C8—82no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22#144211yescharacteristic
482C22#192511yescharacteristic
483C22#192511yescharacteristic
484C22#192811yescharacteristic
485C22#192811yescharacteristic
486C22#194211yescharacteristic
487C22#194411yescharacteristic
488C22#205411yescharacteristic
489C22#205611yescharacteristic
490C22#207511yescharacteristic
491C22#207611yescharacteristic
492C22#208311yescharacteristic
493C22#208311yescharacteristic
494C22#208511yescharacteristic
495C22#208511yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—82no—
504C4—82no—
505C4—162no—
506C4—162no—
507C4—162no—
508C4—162no—
509C4#203212yes—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2#1125611yescharacteristic
525C2#1127711yescharacteristic
526C2#1127911yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
22. #1294C4semidirect

Maximal subgroups

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

subgroupindex
#219402
#108542
#108462
#80232
C2×#12892
C2×#12822