Finite Group Databasebeta

← #190439

Subgroups — #190439

Order 512.

865 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34187C211yesmaximal, characteristic
2C2×#1467C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#8737C214yesmaximal
5#8735C214yesmaximal
6#7928C212yesmaximal
7#7926C212yesmaximal
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2212yes—
10C2×#431C2212yes—
11#2356—21no—
12#2356—21no—
13#2356—21no—
14#2356—21no—
15#2355—21no—
16#2355—21no—
17#2355—21no—
18#2355—21no—
19#2313C412yes—
20#2313C2212yes—
21#2310C412yes—
22#2285C411yescharacteristic
23#2285C411yescharacteristic
24#2283C411yescharacteristic
25#2283C411yescharacteristic
26#2283C2211yescharacteristic
27#2283C2211yescharacteristic
28#2274C2212yes—
29#1467—21no—
30#1467—21no—
31#1467—21no—
32#1467—21no—
33#1461—21no—
34#1461—21no—
35#1461—21no—
36#1461—21no—
37C2×#324C2212yes—
38C2×#324C2212yes—
39C2×#324C2212yes—
40C2×#324C2212yes—
41#1282C2218yes—
42#1282C2218yes—
43C23×Q8C2×C411yescharacteristic
44C2×C4×Q8—22no—
45C2×C4×Q8—22no—
46C2×C4×Q8—22no—
47C2×C4×Q8—22no—
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8D411yescharacteristic
51C2×C4×Q8D411yescharacteristic
52C2×C4×Q8D411yescharacteristic
53C2×C4×Q8D411yescharacteristic
54C2×C4×Q8D411yescharacteristic
55C2×C4×Q8D411yescharacteristic
56C2×#117C2×C412yes—
57C2×#117C2×C412yes—
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C42C2×C411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42C2311yescharacteristic
64#432—22no—
65#432—22no—
66#432—22no—
67#432—22no—
68#431—22no—
69#431—22no—
70#431—22no—
71#431—22no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—22no—
74C2×C22⋊C8C2314yes—
75C2×C22⋊C8C2314yes—
76C2×#97—22no—
77C2×C4×C8—22no—
78#391—22no—
79#391—22no—
80#391—22no—
81#391—22no—
82#387—22no—
83#387—22no—
84#387—22no—
85#387—22no—
86#387—22no—
87#387—22no—
88#387—22no—
89#387—22no—
90#384—21no—
91#384—21no—
92#383—21no—
93#383—21no—
94#383—21no—
95#383—21no—
96#382—21no—
97#382—21no—
98#382—21no—
99#382—21no—
100#382—21no—
101#382—21no—
102#381C2×C412yes—
103#381C2×C412yes—
104#381C2×C412yes—
105#381C2×C412yes—
106#380C2×C412yes—
107#380C2×C412yes—
108#380C2×C411yescharacteristic
109#380C2×C411yescharacteristic
110#380C2×C411yescharacteristic
111#380C2×C411yescharacteristic
112C4×C4⋊C4—22no—
113C4×C4⋊C4—22no—
114C4×C4⋊C4—22no—
115C4×C4⋊C4—22no—
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4—21no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4—21no—
122C4×C4⋊C4—21no—
123C4×C4⋊C4—21no—
124C4×C22⋊C4C2×C412yes—
125C4×C22⋊C4C2×C412yes—
126C4×C22⋊C4C2312yes—
127C4×C22⋊C4C2312yes—
128#376—21no—
129#376—21no—
130#376—21no—
131#376—21no—
132#324—22no—
133#324—22no—
134#324—22no—
135#324—22no—
136#324—22no—
137#324—22no—
138#324—22no—
139#324—22no—
140C22×Q8—22no—
141C22×Q8—22no—
142C22×Q8—24no—
143C22×Q8—42no—
144C22×Q8C22⋊C411yescharacteristic
145C22×Q8C22⋊C411yescharacteristic
146C22×Q8C22⋊C411yescharacteristic
147C22×Q8C22⋊C411yescharacteristic
148C23×C4C22×C411yescharacteristic
149C23×C4C22×C411yescharacteristic
150C23×C4C22×C411yescharacteristic
151C23×C4C22×C411yescharacteristic
152C23×C4C22×C411yescharacteristic
153C23×C4C22×C411yescharacteristic
154C23×C4C2411yescharacteristic
155C22×C8—24no—
156C22×C8—24no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×Q8—22no—
172C4×Q8—22no—
173#117—28no—
174#117—44no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4C22⋊C411yescharacteristic
190C2×C4⋊C4C22⋊C411yescharacteristic
191C2×C4⋊C4C22⋊C411yescharacteristic
192C2×C4⋊C4C22⋊C411yescharacteristic
193C2×C4⋊C4C2×D411yescharacteristic
194C2×C4⋊C4C2×D411yescharacteristic
195C2×C4⋊C4C2×D411yescharacteristic
196C2×C4⋊C4C2×D411yescharacteristic
197C2×C4⋊C4C2×D411yescharacteristic
198C2×C4⋊C4C2×D411yescharacteristic
199C2×C4⋊C4C2×D411yescharacteristic
200C2×C4⋊C4C2×D411yescharacteristic
201C2×C22⋊C4C22×C412yes—
202C2×C22⋊C4C22×C412yes—
203C2×C22⋊C4C22×C412yes—
204C2×C22⋊C4C22×C412yes—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C22⋊C411yescharacteristic
220C2×C42C22⋊C411yescharacteristic
221C2×C42C22⋊C411yescharacteristic
222C2×C42C22⋊C411yescharacteristic
223C2×C42C22⋊C411yescharacteristic
224C2×C42C22⋊C411yescharacteristic
225C2×C42C22⋊C411yescharacteristic
226C2×C42C22⋊C411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42#4112yes—
232C2×C42#4112yes—
233C2×C42#4112yes—
234C2×C42#4112yes—
235C4⋊C8—42no—
236C4⋊C8—42no—
237C4⋊C8—42no—
238C4⋊C8—42no—
239C22⋊C8—24no—
240C22⋊C8—24no—
241C22⋊C8—24no—
242C22⋊C8—24no—
243#97—42no—
244#97—42no—
245C4×C8—42no—
246C4×C8—42no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—22no—
252#95—22no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—22no—
265C24C23×C411yescharacteristic
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—48no—
279C2×Q8—48no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—42no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—81no—
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C411yescharacteristic
305C22×C4C2×C22⋊C411yescharacteristic
306C22×C4C2×C22⋊C411yescharacteristic
307C22×C4C2×C22⋊C411yescharacteristic
308C22×C4C2×C22⋊C411yescharacteristic
309C22×C4C2×C22⋊C411yescharacteristic
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C2×C22⋊C411yescharacteristic
312C22×C4C2×C22⋊C411yescharacteristic
313C22×C4#11711yescharacteristic
314C22×C4#11711yescharacteristic
315C22×C4#11712yes—
316C22×C4#11712yes—
317C22×C4#11711yescharacteristic
318C22×C4#11711yescharacteristic
319C22×C4#13114yes—
320C22×C4C22×D411yescharacteristic
321C22×C4C22×D411yescharacteristic
322C22×C4C2×#4112yes—
323C22×C4C2×#4112yes—
324C2×C8—44no—
325C2×C8—44no—
326C2×C8—84no—
327C2×C8—84no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—44no—
345C4⋊C4—44no—
346C4⋊C4—82no—
347C4⋊C4—82no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C42—21no—
353C42—21no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42—21no—
366C42—21no—
367C42—21no—
368C42—44no—
369C42—44no—
370C42—82no—
371C42—82no—
372C42—82no—
373C42—82no—
374C42#12312yes—
375C42#12312yes—
376C42#12312yes—
377C42#12312yes—
378C42#12312yes—
379C42#12312yes—
380C42#12312yes—
381C42#12312yes—
382C23—41no—
383C23—41no—
384C23C22×C22⋊C411yescharacteristic
385C23C2×#11711yescharacteristic
386C23C2×#11711yescharacteristic
387C23C2×#13112yes—
388C23#56812yes—
389Q8—44no—
390Q8—44no—
391Q8—44no—
392Q8—44no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4#38111yescharacteristic
448C2×C4#38111yescharacteristic
449C2×C4#38111yescharacteristic
450C2×C4#38112yes—
451C2×C4#38112yes—
452C2×C4#38111yescharacteristic
453C2×C4#40812yes—
454C2×C4#40812yes—
455C2×C4C2×#12312yes—
456C2×C4C2×#12312yes—
457C8—84no—
458C8—84no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22C2×#38111yescharacteristic
468C22C2×#40811yescharacteristic
469C22#287911yescharacteristic
470C22#292412yes—
471C22#292412yes—
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—82no—
489C4—82no—
490C4—82no—
491C4#183012yes—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—22no—
496C2#2068511yescharacteristic
497C2#2071011yescharacteristic
498C2C2×#183011yescharacteristic
subgroupG/H
center, socleC22C2×#381
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#341872
C2×#14672
C2×#14612
#87372
#87352
#79282
#79262