Finite Group Databasebeta

← #113692

Subgroups — #113692

Order 512.

926 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35281C211yesmaximal, characteristic
2#17708C211yesmaximal, characteristic
3C2×#1548C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5#17486C211yesmaximal, characteristic
6#10856C211yesmaximal, characteristic
7#7924C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C22×C4⋊Q8C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14#2868—21no—
15#2862—21no—
16#2660—22no—
17#2567—22no—
18#2546—22no—
19#2502—22no—
20#2434C414yes—
21#2317—22no—
22C4×#117C2211yescharacteristic
23C2×#344—22no—
24#1550—22no—
25#1549—21no—
26#1548—22no—
27#1548—22no—
28#1548—22no—
29#1548—22no—
30#1548—21no—
31#1542—22no—
32C2×#333—22no—
33C2×#333—22no—
34#1493—22no—
35#1487—22no—
36#1481—22no—
37#1282—22no—
38C23×Q8C2×C412yes—
39C22×M16—21no—
40C22×M16—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49C2×C4⋊Q8—24no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8D412yes—
61C2×C4⋊Q8D411yescharacteristic
62C2×C4⋊Q8D412yes—
63C2×C4⋊Q8D411yescharacteristic
64C2×#125—21no—
65C2×C22⋊Q8—21no—
66C2×C22⋊Q8C2×C412yes—
67C2×C4×Q8—21no—
68C2×C4×Q8D412yes—
69C2×#117—21no—
70C2×#117D412yes—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C42C2311yescharacteristic
74#431—21no—
75#431—21no—
76#431—21no—
77#431—21no—
78#431—21no—
79#431—21no—
80#431—21no—
81#431D412yes—
82#423—21no—
83#423—21no—
84#423—21no—
85#423—21no—
86#423—21no—
87#423—21no—
88#423—21no—
89#423D412yes—
90C2×C4⋊C8—21no—
91C2×C4⋊C8—21no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—21no—
94C2×C4⋊C8D412yes—
95C2×C4⋊C8D412yes—
96C2×C22⋊C8—21no—
97C2×C22⋊C8—21no—
98C2×C4×C8—21no—
99C2×C4×C8—21no—
100#398—28no—
101#395—28no—
102#391—24no—
103#391—24no—
104#389—28no—
105#385—28no—
106#384—24no—
107#384—24no—
108#382—24no—
109C4×C4⋊C4—21no—
110C4×C4⋊C4—21no—
111C4×C22⋊C4C2×C412yes—
112C4×C22⋊C4D412yes—
113#376—21no—
114C43—21no—
115#344—44no—
116#333—28no—
117#333—28no—
118#333—24no—
119#332—24no—
120Q8⋊C8—28no—
121C22×Q8—22no—
122C22×Q8—21no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—84no—
128C22×Q8C22⋊C412yes—
129C22×Q8C22⋊C414yes—
130C23×C4—22no—
131C23×C4C22×C411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C23×C4C2×D411yescharacteristic
134C2×M16—22no—
135C2×M16—41no—
136C2×M16—41no—
137C2×M16—41no—
138C2×M16—42no—
139C2×M16—42no—
140C2×M16—42no—
141C2×M16—42no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—41no—
145C22×C8—41no—
146C4⋊Q8—21no—
147C4⋊Q8—22no—
148C4⋊Q8—22no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151C4⋊Q8—21no—
152C4⋊Q8—22no—
153C4⋊Q8—22no—
154C4⋊Q8—22no—
155C4⋊Q8—22no—
156C4⋊Q8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—21no—
162C4⋊Q8—41no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4⋊Q8—41no—
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168C4⋊Q8—41no—
169C4⋊Q8—41no—
170C4⋊Q8—88no—
171#125—41no—
172#125—41no—
173#125—41no—
174#125—41no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—41no—
180C22⋊Q8—41no—
181C22⋊Q8—41no—
182C22⋊Q8—41no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8—22no—
187C4×Q8—41no—
188C4×Q8—41no—
189C4×Q8—41no—
190C4×Q8—41no—
191#117—22no—
192#117—22no—
193#117—41no—
194#117—41no—
195#117—41no—
196#117—41no—
197#117SD1614yes—
198#117Q1614yes—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—216no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C22⋊C412yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4C22⋊C414yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C2×D411yescharacteristic
226C2×C42C2×D411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42C2×D411yescharacteristic
233C2×C42#4111yescharacteristic
234C2×C42#4111yescharacteristic
235C2×C42#4111yescharacteristic
236C2×C42#4111yescharacteristic
237C4⋊C8—22no—
238C4⋊C8—22no—
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8—41no—
245C4⋊C8—41no—
246C4⋊C8—41no—
247C4⋊C8—41no—
248C4⋊C8—41no—
249C22⋊C8—22no—
250C22⋊C8—41no—
251C22⋊C8—41no—
252C22⋊C8—41no—
253C4×C8—22no—
254C4×C8—41no—
255C4×C8—41no—
256C4×C8—41no—
257#95—216no—
258#95—22no—
259#95—22no—
260C24C2×C22⋊C411yescharacteristic
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—24no—
264C2×Q8—24no—
265C2×Q8—44no—
266C2×Q8—48no—
267C2×Q8—44no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—84no—
273C2×Q8—84no—
274C2×Q8—84no—
275C2×Q8—84no—
276C2×Q8—84no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—84no—
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C4×D411yescharacteristic
289C22×C4C4×D411yescharacteristic
290C22×C4C4×D411yescharacteristic
291C22×C4C4×D411yescharacteristic
292C22×C4#12011yescharacteristic
293C22×C4#12011yescharacteristic
294C22×C4#12011yescharacteristic
295C22×C4#12011yescharacteristic
296C22×C4#12111yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12411yescharacteristic
301C22×C4#12411yescharacteristic
302C22×C4#12711yescharacteristic
303C22×C4#12711yescharacteristic
304C22×C4C2×SD1612yes—
305C22×C4C2×Q1612yes—
306C22×C4#13712yes—
307C22×C4#13712yes—
308M16—44no—
309M16—82no—
310M16—82no—
311M16—81no—
312M16—81no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—44no—
318C2×C8—82no—
319C2×C8—81no—
320C2×C8—81no—
321C2×C8—82no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—816no—
345C22⋊C4—24no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4#10318yes—
349C42—24no—
350C42—24no—
351C42—44no—
352C42—44no—
353C42—42no—
354C42—42no—
355C42#12011yescharacteristic
356C42#12011yescharacteristic
357C42#12011yescharacteristic
358C42#12011yescharacteristic
359C42#12111yescharacteristic
360C42#12111yescharacteristic
361C42#12111yescharacteristic
362C42#12111yescharacteristic
363C42#12111yescharacteristic
364C42#12111yescharacteristic
365C42#12111yescharacteristic
366C42#12111yescharacteristic
367C42#12311yescharacteristic
368C42#12311yescharacteristic
369C42#12311yescharacteristic
370C42#12311yescharacteristic
371C23—41no—
372C23—41no—
373C23#37911yescharacteristic
374C23#39011yescharacteristic
375C23#39011yescharacteristic
376C23C2×#10312yes—
377C23#41912yes—
378Q8—44no—
379Q8—82no—
380Q8—84no—
381Q8—84no—
382Q8—82no—
383Q8—84no—
384Q8—84no—
385Q8—82no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—28no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—48no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4#38611yescharacteristic
410C2×C4#38611yescharacteristic
411C2×C4#38611yescharacteristic
412C2×C4#38611yescharacteristic
413C2×C4#39211yescharacteristic
414C2×C4#39211yescharacteristic
415C2×C4#39211yescharacteristic
416C2×C4#39211yescharacteristic
417C2×C4#39411yescharacteristic
418C2×C4#39411yescharacteristic
419C2×C4#39411yescharacteristic
420C2×C4#39411yescharacteristic
421C2×C4#44812yes—
422C2×C4#44812yes—
423C2×C4#45112yes—
424C2×C4#45112yes—
425C2×C4#46112yes—
426C2×C4#46112yes—
427C2×C4#46212yes—
428C2×C4#46212yes—
429C2×C4#48712yes—
430C2×C4#49112yes—
431C2×C4#49211yescharacteristic
432C2×C4#49411yescharacteristic
433C2×C4#49711yescharacteristic
434C2×C4#49711yescharacteristic
435C8—82no—
436C8—82no—
437C8—82no—
438C8—82no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—42no—
446C22—42no—
447C22#143811yescharacteristic
448C22#178712yes—
449C22#195611yescharacteristic
450C22#196011yescharacteristic
451C22#198112yes—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—48no—
459C4—84no—
460C4—82no—
461C4—82no—
462C4#191412yes—
463C4#200912yes—
464C4#201311yescharacteristic
465C4#201311yescharacteristic
466C4#201611yescharacteristic
467C4#201611yescharacteristic
468C4#204312yes—
469C4#204312yes—
470C2—22no—
471C2—21no—
472C2—21no—
473C2—22no—
474C2#1097311yescharacteristic
475C2#1100511yescharacteristic
476C2#1101011yescharacteristic
subgroupG/H
center, socleC22#1438
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#352812
#177082
C2×#15482
#174862
#108562
#79242