Finite Group Databasebeta

← #119694

Subgroups — #119694

Order 512.

696 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20647C211yesmaximal, characteristic
2C2×#1805C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#8039C211yesmaximal, characteristic
5#8026C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7877C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×#419—21no—
14C22×#103—21no—
15#2285C2211yescharacteristic
16C2×#382C2211yescharacteristic
17#1805—22no—
18#1805—22no—
19#1805C414yescomplemented
20#1803—22no—
21#1736—21no—
22C2×#340—21no—
23#1461—22no—
24#1461—22no—
25C2×#324—22no—
26#1296—22no—
27#1294—22no—
28#1286—22no—
29#1277—22no—
30C23×Q8D411yescharacteristic
31C22×M16—21no—
32C23×C8—21no—
33C2×C4×Q8—21no—
34C2×C4×Q8—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×Q8C2×C412yes—
44C2×C4×Q8D412yes—
45C2×#117—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4D411yescharacteristic
49C22×C42—21no—
50C22×C42C2311yescharacteristic
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8C2×C412yes—
72C2×C4⋊C8D412yes—
73#419—42no—
74#419—42no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—42no—
78C2×#103—42no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8D412yes—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83#384D412yes—
84#382—21no—
85#382—21no—
86#382—21no—
87#382—21no—
88#382C2×C412yes—
89#380—21no—
90#380—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C2×#95—21no—
94C2×#95—21no—
95#340—24no—
96#340—24no—
97#324—28no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8C22⋊C412yes—
110C22×Q8D812yes—
111C22×Q8SD1612yes—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—41no—
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4#4111yescharacteristic
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8—41no—
132C22×C8—41no—
133C22×C8—41no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C4×Q8—41no—
150#117—41no—
151#117—41no—
152#117—41no—
153#117—41no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—41no—
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⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4C22⋊C412yes—
175C2×C22⋊C4—41no—
176C2×C42—22no—
177C2×C42—22no—
178C2×C42—41no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42C22×C411yescharacteristic
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42#4111yescharacteristic
189C2×C42#4111yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—22no—
197C4⋊C8—22no—
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—41no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207#103—48no—
208#103—48no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—41no—
213C4×C8—22no—
214C4×C8—41no—
215C4×C8—41no—
216C4×C8—41no—
217#95—22no—
218#95—22no—
219#95—41no—
220#95—41no—
221#95—41no—
222#95—41no—
223C24#12111yescharacteristic
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8#10214yes—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—82no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C4×D411yescharacteristic
273C22×C4C4×D411yescharacteristic
274C22×C4#12011yescharacteristic
275C22×C4#12011yescharacteristic
276C22×C4#12111yescharacteristic
277C22×C4#12111yescharacteristic
278C22×C4#12111yescharacteristic
279C22×C4#12311yescharacteristic
280C22×C4#12311yescharacteristic
281C22×C4#12311yescharacteristic
282C22×C4#12311yescharacteristic
283C22×C4#12311yescharacteristic
284C22×C4#12311yescharacteristic
285C22×C4#12411yescharacteristic
286C22×C4#12411yescharacteristic
287C22×C4#12611yescharacteristic
288C22×C4#12611yescharacteristic
289C22×C4C2×D811yescharacteristic
290C22×C4C2×SD1611yescharacteristic
291C22×C4#13511yescharacteristic
292C22×C4#13511yescharacteristic
293C22×C4AGL(1,ℤ/8)11yescharacteristic
294C22×C4#13711yescharacteristic
295C22×C4#13711yescharacteristic
296C22×C4#13711yescharacteristic
297M16—81no—
298M16—81no—
299M16—81no—
300M16—81no—
301C2×C8—44no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—82no—
311C2×C8—81no—
312C2×C8—81no—
313C2×C8—81no—
314C2×C8—81no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—82no—
328C4⋊C4—82no—
329C4⋊C4—81no—
330C4⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C42—42no—
334C42—42no—
335C42—42no—
336C42—42no—
337C42—81no—
338C42—81no—
339C42#11711yescharacteristic
340C42#11711yescharacteristic
341C42C4×D411yescharacteristic
342C42C4×D411yescharacteristic
343C42#12111yescharacteristic
344C42#12111yescharacteristic
345C42#12111yescharacteristic
346C42#12111yescharacteristic
347C42#12311yescharacteristic
348C42#12311yescharacteristic
349C42#12311yescharacteristic
350C42#12311yescharacteristic
351C42#12411yescharacteristic
352C42#12411yescharacteristic
353C42#12611yescharacteristic
354C42#12611yescharacteristic
355C23—22no—
356C23—22no—
357C23#38611yescharacteristic
358C23#39411yescharacteristic
359C23#39711yescharacteristic
360C23#46511yescharacteristic
361C23#46611yescharacteristic
362C23#46811yescharacteristic
363C23#47011yescharacteristic
364Q8—24no—
365Q8—24no—
366Q8—42no—
367Q8—42no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—42no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—162no—
402C2×C4—162no—
403C2×C4#38111yescharacteristic
404C2×C4#38611yescharacteristic
405C2×C4#38811yescharacteristic
406C2×C4#38811yescharacteristic
407C2×C4#38811yescharacteristic
408C2×C4#38811yescharacteristic
409C2×C4#39411yescharacteristic
410C2×C4#39411yescharacteristic
411C2×C4#39411yescharacteristic
412C2×C4#39711yescharacteristic
413C2×C4#39711yescharacteristic
414C2×C4#39711yescharacteristic
415C2×C4C2×#10211yescharacteristic
416C2×C4#41611yescharacteristic
417C2×C4#41711yescharacteristic
418C2×C4#41911yescharacteristic
419C2×C4#44711yescharacteristic
420C2×C4#44811yescharacteristic
421C2×C4#45211yescharacteristic
422C2×C4#45211yescharacteristic
423C2×C4#46511yescharacteristic
424C2×C4#46611yescharacteristic
425C2×C4#46811yescharacteristic
426C2×C4#47011yescharacteristic
427C2×C4#48011yescharacteristic
428C2×C4#48011yescharacteristic
429C2×C4#48011yescharacteristic
430C2×C4#48111yescharacteristic
431C2×C4#48211yescharacteristic
432C2×C4#48211yescharacteristic
433C2×C4#48311yescharacteristic
434C2×C4#48311yescharacteristic
435C2×C4#48511yescharacteristic
436C2×C4#48511yescharacteristic
437C2×C4#48511yescharacteristic
438C2×C4#48511yescharacteristic
439C8—82no—
440C8—82no—
441C8—82no—
442C8—82no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22#144011yescharacteristic
452C22#189311yescharacteristic
453C22#189411yescharacteristic
454C22#203311yescharacteristic
455C22#203511yescharacteristic
456C22#204912yes—
457C22#205312yes—
458C22#207511yescharacteristic
459C22#207711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—44no—
469C4—82no—
470C4—162no—
471C4—162no—
472C4#182311yescharacteristic
473C4#182511yescharacteristic
474C4#187311yescharacteristic
475C4#187411yescharacteristic
476C4#203311yescharacteristic
477C4#203511yescharacteristic
478C4#207511yescharacteristic
479C4#207711yescharacteristic
480C2—21no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2#1046612yes—
485C2#1047012yes—
486C2#1117611yescharacteristic
487C2#1118811yescharacteristic
488C2#1119911yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
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
19. #1805C4semidirect

Maximal subgroups

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

subgroupindex
#206472
C2×#18052
C2×#14612
#80392
#80262
C2×#12862
#78772