Finite Group Databasebeta

← #101973

Subgroups — #101973

Order 512.

828 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#14708C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic, complemented
3#10795C211yesmaximal, characteristic, complemented
4C2×#1272C212yesmaximal, complemented
5C2×#1270C212yesmaximal
6C22×#124C411yescharacteristic
7C2×#391C411yescharacteristic
8C2×#391C2211yescharacteristic
9C2×#390C411yescharacteristic
10C2×#390C2211yescharacteristic
11C2×#382C411yescharacteristic
12C2×C43C2211yescharacteristic
13C2×#336—21no—
14C2×#336—21no—
15C2×#336—21no—
16C2×#336—21no—
17C2×#336C2212yes—
18C2×#336C2212yes—
19#1437—21no—
20#1437—21no—
21#1437—21no—
22#1437—21no—
23#1272—24no—
24#1270—24no—
25C23×Q8C2×C411yescharacteristic
26C23×D4C2×C411yescharacteristic
27C23×C8—22no—
28C23×C8—22no—
29C2×#124—22no—
30C2×#124—22no—
31C2×#124—42no—
32C2×#124—42no—
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C22⋊C4—21no—
36C22×C22⋊C4—21no—
37C22×C22⋊C4—21no—
38C22×C22⋊C4—21no—
39C22×C22⋊C4—21no—
40C22×C22⋊C4—21no—
41C22×C42C2×C411yescharacteristic
42C22×C42C2×C411yescharacteristic
43C22×C42D411yescharacteristic
44C22×C42D411yescharacteristic
45C22×C42D411yescharacteristic
46C22×C42D411yescharacteristic
47C22×C42C2311yescharacteristic
48#391—22no—
49#391—22no—
50#391—42no—
51#390—22no—
52#390—22no—
53#390—42no—
54#382—42no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C43—42no—
62#336—24no—
63#336—22no—
64#336—22no—
65#336—22no—
66#336—42no—
67#336—42no—
68#336—42no—
69#336D414yes—
70C25—21no—
71C22×Q8—21no—
72C22×Q8—22no—
73C22×Q8—22no—
74C22×Q8—41no—
75C22×Q8—41no—
76C22×Q8—41no—
77C22×Q8—41no—
78C22×Q8M1612yes—
79C22×D4—22no—
80C22×D4—21no—
81C22×D4—22no—
82C22×D4—41no—
83C22×D4—41no—
84C22×D4—41no—
85C22×D4—41no—
86C22×D4M1612yes—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C22⋊C411yescharacteristic
91C23×C4C22⋊C411yescharacteristic
92C23×C4C22⋊C411yescharacteristic
93C23×C4C22⋊C411yescharacteristic
94C23×C4C22×C411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C22×C8—24no—
98C22×C8—24no—
99C22×C8—42no—
100C22×C8—42no—
101C22×C8—42no—
102C22×C8—42no—
103C22×C8—42no—
104C22×C8—42no—
105C22×C8—42no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—42no—
109C22×C8—42no—
110C22×C8—42no—
111#124—48no—
112#124—48no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C22⋊C4—24no—
120C2×C22⋊C4—24no—
121C2×C22⋊C4—42no—
122C2×C22⋊C4—42no—
123C2×C22⋊C4—42no—
124C2×C22⋊C4—42no—
125C2×C22⋊C4—42no—
126C2×C22⋊C4—42no—
127C2×C22⋊C4—42no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—42no—
130C2×C22⋊C4—42no—
131C2×C22⋊C4—42no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—42no—
135C2×C22⋊C4—42no—
136C2×C22⋊C4—42no—
137C2×C22⋊C4—41no—
138C2×C22⋊C4—41no—
139C2×C42—22no—
140C2×C42—22no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42—41no—
157C2×C42—41no—
158C2×C42—41no—
159C2×C42—41no—
160C2×C42—41no—
161C2×C42C2×D412yes—
162C2×C42#4112yes—
163#95—42no—
164#95—42no—
165#95—42no—
166#95—42no—
167#95—42no—
168#95—41no—
169#95—41no—
170C24—22no—
171C24—41no—
172C24—41no—
173C24—41no—
174C24—41no—
175C24—41no—
176C24—41no—
177C24—41no—
178C24—41no—
179C24—41no—
180C24—41no—
181C24—41no—
182C24—41no—
183C24—41no—
184C24—41no—
185C24C2×C22⋊C411yescharacteristic
186C2×Q8—24no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—82no—
193C2×Q8—82no—
194C2×Q8—82no—
195C2×Q8—82no—
196C2×D4—24no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—82no—
203C2×D4—82no—
204C2×D4—82no—
205C2×D4—82no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4#9912yes—
264C22×C4#10012yes—
265C22×C4#10012yes—
266C22×C4#10412yes—
267C22×C4C4×D412yes—
268C22×C4#12112yes—
269C22×C4#12411yescharacteristic
270C22×C4#12711yescharacteristic
271C22×C4C2×M1611yescharacteristic
272C22×C4C2×M1611yescharacteristic
273C22×C4#13112yes—
274C22×C4#13512yes—
275C22×C4#13512yes—
276C22×C4#13512yes—
277C22×C4AGL(1,ℤ/8)11yescharacteristic
278C22×C4#13711yescharacteristic
279C2×C8—44no—
280C2×C8—44no—
281C2×C8—44no—
282C2×C8—44no—
283C2×C8—44no—
284C2×C8—44no—
285C2×C8—82no—
286C2×C8—82no—
287C2×C8—82no—
288C2×C8—82no—
289C2×C8—82no—
290C2×C8—82no—
291C2×C8—82no—
292C2×C8—82no—
293C4⋊C4—82no—
294C4⋊C4—82no—
295C22⋊C4—48no—
296C22⋊C4—48no—
297C22⋊C4—84no—
298C22⋊C4—84no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C22⋊C4—82no—
302C22⋊C4—82no—
303C42—24no—
304C42—24no—
305C42—42no—
306C42—42no—
307C42—44no—
308C42—44no—
309C42—44no—
310C42—44no—
311C42—42no—
312C42—42no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23—81no—
348C23#39011yescharacteristic
349C23#40711yescharacteristic
350C23#40811yescharacteristic
351C23C2×#9911yescharacteristic
352C23#41011yescharacteristic
353C23C2×#10011yescharacteristic
354C23C2×#10011yescharacteristic
355C23#41611yescharacteristic
356C23#41611yescharacteristic
357C23#41611yescharacteristic
358C23#41711yescharacteristic
359C23C2×#10411yescharacteristic
360C23#42111yescharacteristic
361C23#42111yescharacteristic
362C23#42111yescharacteristic
363Q8—84no—
364Q8—84no—
365D4—84no—
366D4—84no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
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—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4#43512yes—
441C2×C4#43512yes—
442C2×C4#46312yes—
443C2×C4#46412yes—
444C2×C4#48812yes—
445C2×C4#49512yes—
446C8—84no—
447C8—84no—
448C22—82no—
449C22—82no—
450C22—82no—
451C22—82no—
452C22—82no—
453C22—82no—
454C22—82no—
455C22—161no—
456C22—161no—
457C22—161no—
458C22—161no—
459C22—161no—
460C22—161no—
461C22—161no—
462C22—161no—
463C22#146211yescharacteristic
464C22#146611yescharacteristic
465C22#146911yescharacteristic
466C22#147111yescharacteristic
467C22#148211yescharacteristic
468C22#148211yescharacteristic
469C22#148811yescharacteristic
470C22#148811yescharacteristic
471C22#148811yescharacteristic
472C22#148911yescharacteristic
473C22#149411yescharacteristic
474C22#149511yescharacteristic
475C22#150011yescharacteristic
476C22#150111yescharacteristic
477C22#151211yescharacteristic
478C22#151311yescharacteristic
479C22#151611yescharacteristic
480C22#151611yescharacteristic
481C22#152111yescharacteristic
482C22#152111yescharacteristic
483C22#152711yescharacteristic
484C22#153011yescharacteristic
485C22#153311yescharacteristic
486C22#153611yescharacteristic
487C22#154311yescharacteristic
488C22#154311yescharacteristic
489C22#155111yescharacteristic
490C22#155111yescharacteristic
491C22#195511yescharacteristic
492C22#195811yescharacteristic
493C22#196311yescharacteristic
494C22#196411yescharacteristic
495C22#196511yescharacteristic
496C22#198011yescharacteristic
497C22#198311yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—82no—
509C4—161no—
510C4—161no—
511C2—162no—
512C2#761211yescharacteristic
513C2#761811yescharacteristic
514C2#764511yescharacteristic
515C2#764911yescharacteristic
516C2#765611yescharacteristic
517C2#767011yescharacteristic
518C2#771611yescharacteristic
519C2#773011yescharacteristic
520C2#964511yescharacteristic
521C2#965311yescharacteristic
522C2#967611yescharacteristic
523C2#968111yescharacteristic
524C2#968911yescharacteristic
525C2#969911yescharacteristic
526C2#971611yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC23×D4C2×C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #10795C2semidirect
3. #10795C2semidirect
4. C2×#1272C2semidirect

Maximal subgroups

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

subgroupindex
#147082
#107952
C2×#12722
C2×#12702