Finite Group Databasebeta

← #224558

Subgroups — #224558

Order 512.

812 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#34951C211yesmaximal, characteristic
2#22821C211yesmaximal, characteristic
3C4×#446C211yesmaximal, characteristic
4#9673C211yesmaximal, characteristic
5#9673C212yesmaximal
6#9647C212yesmaximal
7#9637C211yesmaximal, characteristic
8#8570C212yesmaximal
9#8564C211yesmaximal, characteristic
10#8180C212yesmaximal
11C4×Q8⋊C8C211yesmaximal, characteristic
12C2×#446—21no—
13#2585—22no—
14#2582C411yescharacteristic
15#2568C411yescharacteristic
16#2552C411yescharacteristic
17#2546C411yescharacteristic
18#2511C412yes—
19#2509—21no—
20#2453—21no—
21#2446C412yes—
22#2402—22no—
23C4×C4⋊Q8C2211yescharacteristic
24C4×C4⋊Q8C2212yes—
25C4×#125—21no—
26#2295—21no—
27#2295C2212yes—
28C42×Q8C2211yescharacteristic
29C42×Q8C2211yescharacteristic
30#1984—21no—
31#1916—22no—
32#1842C2211yescharacteristic
33#1831C2212yes—
34#1771—22no—
35#1770—21no—
36C8×C4⋊C4—21no—
37C4×C4⋊C8C2211yescharacteristic
38C4×C4⋊C8C2212yes—
39C4×C4⋊C8C2211yescharacteristic
40C4×C4⋊C8C2212yes—
41C4×#97C2212yes—
42C42×C8C2211yescharacteristic
43C2×Q8⋊C8C2212yes—
44C2×Q8⋊C8C2211yescharacteristic
45C2×Q8⋊C8C2211yescharacteristic
46C2×Q8⋊C8C2212yes—
47C2×Q8⋊C8C2212yes—
48C2×Q8⋊C8C2212yes—
49C2×Q8⋊C8C2212yes—
50#1279C2212yes—
51#1279C2211yescharacteristic
52#1279C2211yescharacteristic
53C2×C4⋊Q8C2×C411yescharacteristic
54C2×C4⋊Q8C2×C412yes—
55C2×#125—21no—
56C2×C4×Q8C2×C411yescharacteristic
57C2×C4×Q8C2×C411yescharacteristic
58C2×C4×Q8C2×C411yescharacteristic
59C2×C4×Q8D411yescharacteristic
60C2×C4×Q8D411yescharacteristic
61C2×C4×Q8C2311yescharacteristic
62C2×C4×Q8C2312yes—
63#446—28no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—22no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8C2311yescharacteristic
69C2×C4⋊C8C2312yes—
70C2×C4⋊C8C2311yescharacteristic
71C2×#97—22no—
72C2×#97—22no—
73C2×C4×C8—21no—
74C2×C4×C8—21no—
75C2×C4×C8—21no—
76C2×C4×C8—22no—
77C2×C4×C8C2311yescharacteristic
78C2×C4×C8C2312yes—
79C2×C4×C8C2311yescharacteristic
80#400—22no—
81#400—22no—
82#400—22no—
83#400—22no—
84#398—22no—
85#398—22no—
86#398—22no—
87#398—22no—
88#391—21no—
89#391—21no—
90#391C2×C412yes—
91#391C2×C412yes—
92#391C2×C412yes—
93#391C2×C412yes—
94#391C2×C412yes—
95#389—21no—
96#389—21no—
97#389—21no—
98#389—21no—
99#389—21no—
100#389—22no—
101#389—22no—
102#389—21no—
103#389C2×C412yes—
104#389C2×C412yes—
105#387—22no—
106#387—22no—
107#387—22no—
108#387—22no—
109#387—22no—
110#387—22no—
111#384C2×C411yescharacteristic
112#384C2×C412yes—
113#382—21no—
114C4×C4⋊C4—22no—
115C4×C4⋊C4—21no—
116C4×C4⋊C4—22no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4—22no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4—21no—
122C4×C4⋊C4C2×C411yescharacteristic
123C4×C4⋊C4C2×C411yescharacteristic
124C4×C4⋊C4C2×C412yes—
125C4×C4⋊C4C2×C411yescharacteristic
126C4×C4⋊C4D411yescharacteristic
127C4×C4⋊C4D412yes—
128C4×C4⋊C4D412yes—
129C4×C4⋊C4D411yescharacteristic
130C4×C4⋊C4C2311yescharacteristic
131#376—22no—
132C43—21no—
133C43C2312yes—
134C43C2311yescharacteristic
135#336—22no—
136#336—22no—
137#336—21no—
138#336—22no—
139#336—22no—
140#336—21no—
141Q8⋊C8—22no—
142Q8⋊C8—24no—
143Q8⋊C8—24no—
144Q8⋊C8—22no—
145Q8⋊C8—42no—
146Q8⋊C8—42no—
147Q8⋊C8—42no—
148C22×Q8C22⋊C411yescharacteristic
149C22×Q8C22×C412yes—
150C22×Q8C22×C411yescharacteristic
151C22×C8—21no—
152C22×C8—21no—
153C22×C8—22no—
154C22×C8—21no—
155C22×C8—21no—
156C22×C8—22no—
157C4⋊Q8—24no—
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—42no—
161#125—44no—
162C4×Q8—24no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×Q8—21no—
171C4×Q8—22no—
172C4×Q8—21no—
173C4×Q8—22no—
174C4×Q8—21no—
175C4×Q8—22no—
176C4×Q8—21no—
177C4×Q8—22no—
178C4×Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C22⋊C411yescharacteristic
194C2×C4⋊C4C22⋊C412yes—
195C2×C4⋊C4C22⋊C412yes—
196C2×C4⋊C4C22⋊C411yescharacteristic
197C2×C4⋊C4C22⋊C412yes—
198C2×C4⋊C4C22⋊C411yescharacteristic
199C2×C4⋊C4C22×C411yescharacteristic
200C2×C4⋊C4C22×C411yescharacteristic
201C2×C4⋊C4C22×C411yescharacteristic
202C2×C4⋊C4C22×C412yes—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—22no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22×C411yescharacteristic
211C2×C42C22×C412yes—
212C2×C42C22×C412yes—
213C2×C42C22×C411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D412yes—
216C2×C42C2×D412yes—
217C2×C42C2×D412yes—
218C2×C42C2×D411yescharacteristic
219C2×C42C2×D411yescharacteristic
220C2×C42C2×D412yes—
221C2×C42C2×D411yescharacteristic
222C2×C42C2411yescharacteristic
223C4⋊C8—24no—
224C4⋊C8—28no—
225C4⋊C8—21no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8—22no—
229C4⋊C8—21no—
230C4⋊C8—42no—
231C4⋊C8—81no—
232C4⋊C8#4112yes—
233#97—28no—
234#97—44no—
235C4×C8—24no—
236C4×C8—21no—
237C4×C8—22no—
238C4×C8—21no—
239C4×C8—22no—
240C4×C8—21no—
241C4×C8—42no—
242C4×C8—42no—
243C4×C8—82no—
244C4×C8#4112yes—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—22no—
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—21no—
260#95C22⋊C412yes—
261#95C22⋊C412yes—
262#95C22⋊C412yes—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8#13112yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4C2×C22⋊C412yes—
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C412yes—
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C23×C411yescharacteristic
293C22×C4C22×D411yescharacteristic
294C22×C4C22×D411yescharacteristic
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—24no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—42no—
303C2×C8—41no—
304C2×C8—42no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—42no—
309C2×C8—41no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—41no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C4⋊C4—41no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—44no—
337C4⋊C4—44no—
338C4⋊C4—42no—
339C4⋊C4—81no—
340C4⋊C4—82no—
341C4⋊C4—82no—
342C4⋊C4#10414yes—
343C42—21no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—21no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—21no—
353C42—22no—
354C42—21no—
355C42—22no—
356C42—24no—
357C42—41no—
358C42—42no—
359C42—42no—
360C42—41no—
361C42—42no—
362C42—41no—
363C42—42no—
364C42—41no—
365C42—41no—
366C42—42no—
367C42—42no—
368C42—81no—
369C42#13112yes—
370C42#13112yes—
371C42#13712yes—
372C42#13712yes—
373C42C2×#4111yescharacteristic
374C42C2×#4111yescharacteristic
375C42H(5,𝔽2)11yescharacteristic
376C422−1+411yescharacteristic
377C23C22×C22⋊C411yescharacteristic
378Q8—22no—
379Q8—22no—
380Q8—41no—
381Q8—41no—
382Q8—44no—
383Q8—42no—
384Q8—42no—
385Q8—42no—
386Q8—42no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4#40812yes—
426C2×C4#40812yes—
427C2×C4#41912yes—
428C2×C4#41912yes—
429C2×C4C2×#10414yes—
430C2×C4C2×#10412yes—
431C2×C4C4×#4111yescharacteristic
432C2×C4#52011yescharacteristic
433C2×C4#54811yescharacteristic
434C2×C4#54811yescharacteristic
435C2×C4#55011yescharacteristic
436C2×C4#55011yescharacteristic
437C2×C4C2×#13111yescharacteristic
438C2×C4C2×#13111yescharacteristic
439C2×C4C2×#13111yescharacteristic
440C2×C4#56811yescharacteristic
441C2×C4C2×#13711yescharacteristic
442C2×C4C2×#13711yescharacteristic
443C2×C4#57711yescharacteristic
444C2×C4#57811yescharacteristic
445C8—24no—
446C8—42no—
447C8—44no—
448C8—42no—
449C8—81no—
450C8—82no—
451C22#234111yescharacteristic
452C22C2×#40811yescharacteristic
453C22#288011yescharacteristic
454C22C2×#41911yescharacteristic
455C22#289811yescharacteristic
456C22C22×#10411yescharacteristic
457C22#290111yescharacteristic
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—24no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—41no—
468C4—82no—
469C4—81no—
470C4—82no—
471C4—81no—
472C4—81no—
473C4#148514yes—
474C4#296611yescharacteristic
475C4#296911yescharacteristic
476C4#299311yescharacteristic
477C4#299411yescharacteristic
478C4#337211yescharacteristic
479C4#337411yescharacteristic
480C4#339811yescharacteristic
481C4#340011yescharacteristic
482C2C2×#148511yescharacteristic
483C2#1746911yescharacteristic
484C2#1751411yescharacteristic
485C2#1751911yescharacteristic
486C2#2253111yescharacteristic
487C2#2254711yescharacteristic
488C2#2255011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socle, prime radicalC23C22×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×Q8 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#349512
#228212
C4×#4462
#96732
#96472
#96372
#85702
#85642
#81802
C4×Q8⋊C82