Finite Group Databasebeta

← #105997

Subgroups — #105997

Order 512.

930 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2924C211yesmaximal, characteristic
2C2×#1826C211yesmaximal, characteristic
3#20699C211yesmaximal, characteristic
4#8057C211yesmaximal, characteristic
5#8051C211yesmaximal, characteristic
6#7927C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C22×#117C2211yescharacteristic
9#2924—22no—
10#2924—22no—
11#2924—22no—
12#2924—22no—
13C2×#433—22no—
14C2×#432—21no—
15C2×#431—21no—
16C2×#424C412yescomplemented
17C2×#407C2211yescharacteristic
18C2×#407C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C2×#405C412yescomplemented
22#2280C2211yescharacteristic
23C2×C4×C22⋊C4C2211yescharacteristic
24#1826—22no—
25#1826C412yescomplemented
26#1826C412yescomplemented
27#1825—22no—
28#1824C412yescomplemented
29#1823C412yescomplemented
30#1735—22no—
31C2×#339—22no—
32#1298—22no—
33#1297—22no—
34#1282—22no—
35#1282—21no—
36#1282—21no—
37C24×C4C2311yescharacteristic
38C22×M16—21no—
39C22×M16C2×C412yes—
40C23×C8—21no—
41C23×C8C2×C412yes—
42C2×#117—21no—
43C2×#117—21no—
44C2×#117—21no—
45C2×#117—21no—
46C2×#117—21no—
47C2×#117—21no—
48C2×#117—21no—
49C2×#117C2×C411yescharacteristic
50C2×#117C2×C411yescharacteristic
51C2×#117C2×C411yescharacteristic
52C2×#117C2×C411yescharacteristic
53C2×#117D412yes—
54C2×#117D412yes—
55C2×#117D412yes—
56C2×#117Q812yes—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C42—21no—
62C22×C42—21no—
63#433—28no—
64#433—28no—
65#432—24no—
66#432—24no—
67#431—24no—
68#431—24no—
69#424—24no—
70#424—24no—
71C2×C4⋊C8—22no—
72C2×C4⋊C8—22no—
73#407—21no—
74#407—21no—
75#407—21no—
76#407—21no—
77#407—21no—
78#407C2×C412yes—
79#407D412yes—
80#407D412yes—
81C2×C22⋊C8—21no—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C2×C22⋊C8—21no—
85C2×C22⋊C8—21no—
86C2×C22⋊C8—21no—
87C2×C22⋊C8—21no—
88C2×C22⋊C8—21no—
89C2×C22⋊C8—21no—
90C2×C22⋊C8—21no—
91C2×C22⋊C8—21no—
92C2×C22⋊C8—21no—
93C2×C22⋊C8—21no—
94C2×C22⋊C8C2×C412yes—
95C2×C22⋊C8D411yescharacteristic
96C2×C22⋊C8D411yescharacteristic
97C2×C22⋊C8D412yes—
98#405—24no—
99#405—24no—
100C2×#97—22no—
101C2×C4×C8—22no—
102#381—21no—
103#380—21no—
104#380C2×C412yes—
105#379—21no—
106C4×C22⋊C4—21no—
107C4×C22⋊C4—21no—
108C4×C22⋊C4—21no—
109C4×C22⋊C4—21no—
110C4×C22⋊C4—21no—
111C4×C22⋊C4C2×C412yes—
112C2×#95—21no—
113#340—24no—
114#340—24no—
115#339—24no—
116#339—24no—
117C25#4111yescharacteristic
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—44no—
121C23×C4—41no—
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2×Q811yescharacteristic
133C23×C4#4111yescharacteristic
134C23×C4#4111yescharacteristic
135C23×C4#4111yescharacteristic
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—44no—
139C2×M16—41no—
140C2×M16—44no—
141C2×M16C22⋊C414yes—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—44no—
147C22×C8—44no—
148C22×C8—41no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8C22⋊C412yes—
152C22×C8C22⋊C412yes—
153#117—21no—
154#117—21no—
155#117—21no—
156#117—21no—
157#117—21no—
158#117—21no—
159#117—21no—
160#117—21no—
161#117—22no—
162#117—22no—
163#117—22no—
164#117—22no—
165#117—22no—
166#117—22no—
167#117—22no—
168#117—22no—
169#117—44no—
170#117C22⋊C412yes—
171#117C22⋊C412yes—
172#117C22⋊C412yes—
173#117C22⋊C412yes—
174#117C4⋊C412yes—
175#117C4⋊C412yes—
176#117C4⋊C412yes—
177#117C4⋊C412yes—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C4211yescharacteristic
186C2×C4⋊C4C4211yescharacteristic
187C2×C4⋊C4C4211yescharacteristic
188C2×C4⋊C4C4211yescharacteristic
189C2×C4⋊C4C22⋊C412yes—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C4⋊C412yes—
192C2×C4⋊C4C4⋊C412yes—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—41no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—21no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—44no—
218C2×C42—41no—
219C2×C42—41no—
220C4⋊C8—28no—
221C4⋊C8—28no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—22no—
230C22⋊C8—22no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—41no—
237C22⋊C8—41no—
238C22⋊C8—41no—
239C22⋊C8—41no—
240#97—28no—
241C4×C8—28no—
242#95—22no—
243#95—22no—
244#95—41no—
245#95—41no—
246C24—22no—
247C24—22no—
248C24—42no—
249C24—81no—
250C24#11711yescharacteristic
251C24C4×D411yescharacteristic
252C24C4×D411yescharacteristic
253C24#12111yescharacteristic
254C24C22⋊Q811yescharacteristic
255C24#12311yescharacteristic
256C24#12311yescharacteristic
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C2×C4211yescharacteristic
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C2×C22⋊C411yescharacteristic
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C2×C4⋊C411yescharacteristic
294C22×C4C2×C4⋊C411yescharacteristic
295C22×C4C2×C4⋊C411yescharacteristic
296C22×C4#11711yescharacteristic
297C22×C4C4×D411yescharacteristic
298C22×C4C4×D411yescharacteristic
299C22×C4C4×D411yescharacteristic
300C22×C4C4×D411yescharacteristic
301C22×C4C4×D411yescharacteristic
302C22×C4C4×D411yescharacteristic
303C22×C4#12011yescharacteristic
304C22×C4#12011yescharacteristic
305C22×C4#12011yescharacteristic
306C22×C4#12011yescharacteristic
307C22×C4#12111yescharacteristic
308C22×C4#12111yescharacteristic
309C22×C4#12111yescharacteristic
310C22×C4C22⋊Q811yescharacteristic
311C22×C4C22⋊Q811yescharacteristic
312C22×C4C22⋊Q811yescharacteristic
313C22×C4#12311yescharacteristic
314C22×C4#12311yescharacteristic
315M16—44no—
316M16—44no—
317M16—44no—
318M16—82no—
319C2×C8—22no—
320C2×C8—24no—
321C2×C8—22no—
322C2×C8—44no—
323C2×C8—44no—
324C2×C8—44no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—44no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—82no—
331C2×C8—82no—
332C2×C8—82no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—44no—
342C4⋊C4#9512yes—
343C4⋊C4#9512yes—
344C4⋊C4#9512yes—
345C4⋊C4#9512yes—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—24no—
355C22⋊C4—44no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42—22no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—22no—
369C42—44no—
370C42—82no—
371C42—82no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—21no—
378C23—21no—
379C23—22no—
380C23—22no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—84no—
395C23—84no—
396C23C4×C22⋊C411yescharacteristic
397C23#38011yescharacteristic
398C23#38111yescharacteristic
399C23#38511yescharacteristic
400C23#38511yescharacteristic
401C23#38611yescharacteristic
402C23#38611yescharacteristic
403C23#44312yes—
404C23#44412yes—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—44no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—88no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4C2×#9511yescharacteristic
454C2×C4C4×C22⋊C411yescharacteristic
455C2×C4#37911yescharacteristic
456C2×C4#38011yescharacteristic
457C2×C4#38511yescharacteristic
458C2×C4#38511yescharacteristic
459C2×C4#38611yescharacteristic
460C2×C4#38611yescharacteristic
461C2×C4#41014yes—
462C8—42no—
463C8—42no—
464C8—44no—
465C8—82no—
466C8—82no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22—82no—
491C22—82no—
492C22—81no—
493C22—81no—
494C22C22⋊#9511yescharacteristic
495C22#176411yescharacteristic
496C22#176511yescharacteristic
497C22#182012yes—
498C22#186612yes—
499C22#187612yes—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—84no—
511C4—162no—
512C4#174012yes—
513C4#178212yes—
514C2—22no—
515C2—22no—
516C2—22no—
517C2—21no—
518C2—21no—
519C2—41no—
520C2—41no—
521C2—41no—
522C2#1072611yescharacteristic
523C2#1077811yescharacteristic
524C2#1079111yescharacteristic
subgroupG/H
centerC2×C4#379
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC22C22⋊#95
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
16. C2×#424C4semidirect
21. C2×#405C4semidirect
25. #1826C4semidirect
26. #1826C4semidirect
28. #1824C4semidirect
29. #1823C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29242
C2×#18262
#206992
#80572
#80512
#79272
C2×#12822