Finite Group Databasebeta

← #106913

Subgroups — #106913

Order 512.

949 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34128C211yesmaximal, characteristic
2C4×#419C211yesmaximal, characteristic
3#17449C211yesmaximal, characteristic
4#8074C211yesmaximal, characteristic
5#8068C211yesmaximal, characteristic
6#8048C211yesmaximal, characteristic
7#7940C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#419—21no—
12C2×C4×M16C2211yescharacteristic
13#2356—22no—
14#2356C412yescomplemented
15#2351C412yescomplemented
16#2344—22no—
17#2344—21no—
18Q8×C22⋊C4—21no—
19#2295—22no—
20#2295—21no—
21#2283—21no—
22#2283C2211yescharacteristic
23C42×Q8—21no—
24C4×#117—21no—
25C4×#117C2211yescharacteristic
26C4×#117C2211yescharacteristic
27#1763C414yescomplemented
28C4×#103—22no—
29#1736—21no—
30#1491—22no—
31#1487C414yescomplemented
32#1479—21no—
33#1479—21no—
34#1300—22no—
35#1300—22no—
36#1297—21no—
37#1297—21no—
38#1284—22no—
39C23×Q8D411yescharacteristic
40C22×M16—21no—
41C2×C4×Q8—22no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8C2×C411yescharacteristic
49C2×C4×Q8C2×C411yescharacteristic
50C2×C4×Q8C2×C412yes—
51C2×C4×Q8C2×C412yes—
52C2×C4×Q8D411yescharacteristic
53C2×C4×Q8D411yescharacteristic
54C2×C4×Q8D412yes—
55C2×C4×Q8Q812yes—
56C2×#117—22no—
57C2×#117—21no—
58C2×#117—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4D411yescharacteristic
61C22×C42—21no—
62C22×C42C2311yescharacteristic
63#432—21no—
64#432—21no—
65#432—21no—
66#432—21no—
67#431—21no—
68#431—21no—
69#431—21no—
70#431C2×C412yes—
71#423—21no—
72#423C2×C412yes—
73#419—28no—
74C2×#103—24no—
75#407—21no—
76#407—21no—
77C4×M16—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C2×#97C2×C412yes—
84C2×C4×C8—21no—
85#391—24no—
86#391—22no—
87#389—22no—
88#389—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#383—21no—
93#383—22no—
94#382—22no—
95#382C2×C412yes—
96#381—22no—
97#381D412yes—
98#380—22no—
99#380—21no—
100C4×C4⋊C4—24no—
101C4×C4⋊C4—22no—
102C4×C4⋊C4—22no—
103C4×C4⋊C4—22no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—22no—
107C4×C4⋊C4—21no—
108C4×C4⋊C4C2×C412yes—
109C4×C4⋊C4C2×C412yes—
110C4×C22⋊C4—22no—
111C4×C22⋊C4—21no—
112C4×C22⋊C4—21no—
113C4×C22⋊C4—21no—
114C4×C22⋊C4—21no—
115C4×C22⋊C4D411yescharacteristic
116C4×C22⋊C4D411yescharacteristic
117#376—22no—
118#376—22no—
119#376—21no—
120#376D412yes—
121#376D412yes—
122C43—22no—
123C43—21no—
124C43—21no—
125#340—24no—
126Q8⋊C8—24no—
127Q8⋊C8—24no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—24no—
132C22×Q8—42no—
133C22×Q8C22⋊C411yescharacteristic
134C22×Q8C22⋊C412yes—
135C22×Q8C22⋊C411yescharacteristic
136C22×Q8C4⋊C412yes—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C2×M16—24no—
143C2×M16—22no—
144C2×M16—42no—
145C2×M16—41no—
146C2×M16—41no—
147C2×M16—41no—
148C22×C8—22no—
149C4×Q8—21no—
150C4×Q8—21no—
151C4×Q8—21no—
152C4×Q8—21no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—21no—
162C4×Q8—21no—
163C4×Q8—21no—
164C4×Q8—21no—
165C4×Q8—44no—
166C4×Q8—44no—
167C4×Q8C4212yes—
168C4×Q8C4212yes—
169C4×Q8C22⋊C412yes—
170C4×Q8C22⋊C412yes—
171C4×Q8C4⋊C412yes—
172C4×Q8C4⋊C412yes—
173C4×Q8C4⋊C412yes—
174C4×Q8C4⋊C412yes—
175#117—24no—
176#117—44no—
177#117—48no—
178#117—42no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4C22⋊C412yes—
196C2×C4⋊C4C22⋊C411yescharacteristic
197C2×C4⋊C4C22⋊C411yescharacteristic
198C2×C4⋊C4C4⋊C412yes—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—41no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—24no—
212C2×C42—24no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—41no—
220C2×C42—41no—
221C2×C42C22×C411yescharacteristic
222C2×C42C22×C411yescharacteristic
223C2×C42C22×C411yescharacteristic
224C2×C42C2×D411yescharacteristic
225C2×C42C2×D411yescharacteristic
226C2×C42C2×D411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×Q811yescharacteristic
229C2×C42#4111yescharacteristic
230C2×C42#4111yescharacteristic
231C2×C42#4111yescharacteristic
232C2×C42#4111yescharacteristic
233C4⋊C8—22no—
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—41no—
237#103—216no—
238C22⋊C8—22no—
239C22⋊C8—41no—
240C22⋊C8—41no—
241C22⋊C8—41no—
242#97—22no—
243#97—22no—
244#97—41no—
245#97—41no—
246C4×C8—22no—
247C4×C8—41no—
248C4×C8—41no—
249C4×C8—41no—
250#95—24no—
251#95—24no—
252#95—24no—
253#95—24no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—41no—
260#95C22⋊C412yes—
261#95C22⋊C412yes—
262#95C22⋊C414yes—
263C24#12011yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—24no—
270C2×Q8—24no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—44no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—44no—
277C2×Q8—44no—
278C2×Q8#9512yes—
279C2×Q8#9512yes—
280C2×Q8#10414yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—42no—
299C22×C4C2×C22⋊C411yescharacteristic
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C4⋊C411yescharacteristic
304C22×C4C4×D411yescharacteristic
305C22×C4C4×D411yescharacteristic
306C22×C4C4×D411yescharacteristic
307C22×C4C4×D411yescharacteristic
308C22×C4#12011yescharacteristic
309C22×C4#12011yescharacteristic
310C22×C4#12011yescharacteristic
311C22×C4#12111yescharacteristic
312C22×C4#12111yescharacteristic
313C22×C4C22⋊Q811yescharacteristic
314C22×C4C22⋊Q811yescharacteristic
315C22×C4#12311yescharacteristic
316C22×C4#12311yescharacteristic
317M16—44no—
318M16—44no—
319M16—82no—
320M16—82no—
321C2×C8—24no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—42no—
340C4⋊C4—44no—
341C4⋊C4—48no—
342C4⋊C4—48no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4#9512yes—
346C4⋊C4#9512yes—
347C22⋊C4—24no—
348C22⋊C4—44no—
349C22⋊C4—42no—
350C22⋊C4—44no—
351C42—22no—
352C42—22no—
353C42—22no—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—22no—
359C42—42no—
360C42—42no—
361C42—44no—
362C42—44no—
363C42—48no—
364C42—48no—
365C42—44no—
366C42—42no—
367C42—42no—
368C42—82no—
369C42—82no—
370C42C2×C4211yescharacteristic
371C42C2×C22⋊C411yescharacteristic
372C42C2×C4⋊C411yescharacteristic
373C42C2×C4⋊C411yescharacteristic
374C42#11711yescharacteristic
375C42#11711yescharacteristic
376C42C4×D411yescharacteristic
377C42C4×D411yescharacteristic
378C42C4×D411yescharacteristic
379C42C4×D411yescharacteristic
380C42#12111yescharacteristic
381C42#12111yescharacteristic
382C42C22⋊Q811yescharacteristic
383C42C22⋊Q811yescharacteristic
384C42#12311yescharacteristic
385C42#12311yescharacteristic
386C23—22no—
387C23—22no—
388C23—41no—
389C23#37911yescharacteristic
390C23#38511yescharacteristic
391C23#38611yescharacteristic
392Q8—24no—
393Q8—22no—
394Q8—22no—
395Q8—22no—
396Q8—44no—
397Q8—44no—
398Q8—42no—
399Q8#33914yes—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4C2×#9511yescharacteristic
444C2×C4C4×C22⋊C411yescharacteristic
445C2×C4C4×C22⋊C411yescharacteristic
446C2×C4#38011yescharacteristic
447C2×C4#38011yescharacteristic
448C2×C4#38111yescharacteristic
449C2×C4#38511yescharacteristic
450C2×C4#38511yescharacteristic
451C2×C4#38511yescharacteristic
452C2×C4#38611yescharacteristic
453C2×C4#38611yescharacteristic
454C2×C4#38611yescharacteristic
455C2×C4C2×#10412yes—
456C2×C4#42112yes—
457C8—44no—
458C8—82no—
459C8—82no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—44no—
468C22C22⋊#9511yescharacteristic
469C22#178912yes—
470C22#190612yes—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—24no—
481C4—44no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—84no—
486C4—82no—
487C4—84no—
488C4C2×#33911yescharacteristic
489C4#173311yescharacteristic
490C4#182612yes—
491C4#190512yes—
492C2—22no—
493C2—22no—
494C2—41no—
495C2#1073311yescharacteristic
496C2#1077211yescharacteristic
497C2#1078611yescharacteristic
subgroupG/H
centerC2×C4#386
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
socleC22C22⋊#95
prime radicalC24#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
14. #2356C4semidirect
15. #2351C4semidirect
27. #1763C4semidirect
31. #1487C4semidirect

Maximal subgroups

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

subgroupindex
#341282
C4×#4192
#174492
#80742
#80682
#80482
#79402