Finite Group Databasebeta

← #117014

Subgroups — #117014

Order 512.

612 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1991C211yesmaximal, characteristic
2C2×#1568C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4C2×#1470C211yesmaximal, characteristic
5#8033C211yesmaximal, characteristic
6#7914C211yesmaximal, characteristic
7#7848C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1991—21no—
16#1991—21no—
17#1991—21no—
18#1991—21no—
19C2×#340C411yescharacteristic
20C2×#340C411yescharacteristic
21C2×#340C411yescharacteristic
22C2×#340C411yescharacteristic
23#1568—22no—
24#1568—22no—
25C2×#335—21no—
26C2×#334—21no—
27#1528—22no—
28#1528—22no—
29C2×#330—22no—
30#1470—22no—
31#1470—22no—
32C2×#324—22no—
33#1295—22no—
34#1280—22no—
35#1273—21no—
36#1273—21no—
37C22×M16—21no—
38C23×C8C2×C411yescharacteristic
39C23×C8C2×C411yescharacteristic
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125—21no—
46C2×#125—21no—
47C2×#125—21no—
48C2×#125—21no—
49C2×#125—21no—
50C2×#125D412yes—
51C2×#125Q812yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C42C2311yescharacteristic
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432D412yes—
66#432D412yes—
67#431—21no—
68#431—21no—
69#431—21no—
70#431—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8D412yes—
77C4×M16—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16—21no—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97D412yes—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8D411yescharacteristic
91C2×C4×C8D411yescharacteristic
92C2×C4×C8D411yescharacteristic
93C2×C4×C8D411yescharacteristic
94#382—21no—
95#382—21no—
96#382—21no—
97#382—21no—
98C2×#95—21no—
99C2×#95—21no—
100#340—21no—
101#340—21no—
102#340—21no—
103#340—21no—
104#340—21no—
105#340—21no—
106#340—21no—
107#340—21no—
108#335—24no—
109#334—24no—
110#330—28no—
111#324—28no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4C22×C411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4#4111yescharacteristic
119C2×M16—24no—
120C2×M16—42no—
121C2×M16—41no—
122C2×M16—41no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—41no—
132C22×C8—41no—
133C22×C8—41no—
134C22×C8—41no—
135C22×C8C22⋊C411yescharacteristic
136C22×C8C22⋊C411yescharacteristic
137C22×C8C22⋊C411yescharacteristic
138C22×C8C22⋊C411yescharacteristic
139#125—22no—
140#125—22no—
141#125—22no—
142#125—22no—
143#125—22no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—41no—
148#125—41no—
149#125—41no—
150#125—41no—
151#125—41no—
152#125—41no—
153#125—41no—
154#125—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
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—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—41no—
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⋊C4—41no—
185C2×C4⋊C4C4⋊C412yes—
186C2×C4⋊C4C4⋊C412yes—
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×Q811yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42#4111yescharacteristic
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211#97—22no—
212#97—22no—
213#97—22no—
214#97—22no—
215#97—41no—
216#97—41no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8—41no—
226C4×C8—41no—
227C4×C8—41no—
228C4×C8—41no—
229#95—41no—
230#95—41no—
231#95—41no—
232#95—41no—
233C24C4×D411yescharacteristic
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4C2×C22⋊C411yescharacteristic
261C22×C4C2×C4⋊C411yescharacteristic
262C22×C4#11711yescharacteristic
263C22×C4C4×D411yescharacteristic
264C22×C4C4×D411yescharacteristic
265C22×C4C4×D411yescharacteristic
266C22×C4#12011yescharacteristic
267C22×C4#12111yescharacteristic
268C22×C4#12111yescharacteristic
269C22×C4#12111yescharacteristic
270C22×C4C22⋊Q811yescharacteristic
271C22×C4C22⋊Q811yescharacteristic
272C22×C4#12311yescharacteristic
273C22×C4#12311yescharacteristic
274C22×C4#12411yescharacteristic
275C22×C4#12411yescharacteristic
276C22×C4#12611yescharacteristic
277C22×C4#12711yescharacteristic
278M16—44no—
279M16—44no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—24no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—81no—
303C2×C8—81no—
304C2×C8—81no—
305C2×C8—81no—
306C2×C8#10112yes—
307C2×C8#10112yes—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C42#12011yescharacteristic
331C42#12011yescharacteristic
332C42#12111yescharacteristic
333C42#12111yescharacteristic
334C42#12111yescharacteristic
335C42#12111yescharacteristic
336C42#12111yescharacteristic
337C42C22⋊Q811yescharacteristic
338C42C22⋊Q811yescharacteristic
339C42C22⋊Q811yescharacteristic
340C42C22⋊Q811yescharacteristic
341C42#12311yescharacteristic
342C42#12311yescharacteristic
343C42#12311yescharacteristic
344C42#12411yescharacteristic
345C42#12611yescharacteristic
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23#38511yescharacteristic
351C23#38811yescharacteristic
352C23#39011yescharacteristic
353C23#44312yes—
354C23#44412yes—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—162no—
398C2×C4—162no—
399C2×C4#38011yescharacteristic
400C2×C4#38511yescharacteristic
401C2×C4#38611yescharacteristic
402C2×C4#38811yescharacteristic
403C2×C4#39211yescharacteristic
404C2×C4#39311yescharacteristic
405C2×C4#39411yescharacteristic
406C2×C4#39411yescharacteristic
407C2×C4#39611yescharacteristic
408C2×C4#39611yescharacteristic
409C2×C4#39711yescharacteristic
410C2×C4#39911yescharacteristic
411C2×C4C2×#10111yescharacteristic
412C2×C4C2×#10111yescharacteristic
413C2×C4#41311yescharacteristic
414C2×C4#41311yescharacteristic
415C8—22no—
416C8—22no—
417C8—44no—
418C8—41no—
419C8—41no—
420C8—82no—
421C8—82no—
422C8—82no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—21no—
430C22—21no—
431C22#143911yescharacteristic
432C22#186612yes—
433C22#192912yes—
434C22#196611yescharacteristic
435C22#196711yescharacteristic
436C22#197411yescharacteristic
437C22#197511yescharacteristic
438C22#197611yescharacteristic
439C22#197611yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—82no—
451C4—82no—
452C4—161no—
453C4—161no—
454C4#180111yescharacteristic
455C4#180111yescharacteristic
456C4#190111yescharacteristic
457C4#190111yescharacteristic
458C2—22no—
459C2—22no—
460C2#978811yescharacteristic
461C2#978911yescharacteristic
462C2#979011yescharacteristic
463C2#979211yescharacteristic
464C2#1104511yescharacteristic
465C2#1112511yescharacteristic
466C2#1112611yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19912
C2×#15682
C2×#15282
C2×#14702
#80332
#79142
#78482