Finite Group Databasebeta

← #119227

Subgroups — #119227

Order 512.

640 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21860C211yesmaximal, characteristic
2#21301C211yesmaximal, characteristic
3C2×#1518C211yesmaximal, characteristic
4#10843C211yesmaximal, characteristic
5#8043C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7C2×#1275C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×#97C2211yescharacteristic
13C2×#384C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1990C412yescomplemented
16#1985—22no—
17#1985—22no—
18#1956C412yescomplemented
19#1872—22no—
20#1803—22no—
21C2×#340—21no—
22C2×#340—21no—
23#1729—21no—
24#1729—21no—
25#1518—22no—
26#1518—22no—
27C2×#328—22no—
28#1296—22no—
29#1286—22no—
30#1275—22no—
31C22×M16—21no—
32C23×C8D411yescharacteristic
33C23×C8D411yescharacteristic
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42C2×C4⋊Q8C2×C411yescharacteristic
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×#125—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8D412yes—
47C2×C4×Q8—21no—
48C2×C4×Q8D412yes—
49C2×#117—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C42C2311yescharacteristic
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431D412yes—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8D412yes—
71C2×#103—24no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×C4×C8—21no—
81C2×C4×C8C2×C412yes—
82#384—21no—
83#384—21no—
84#384—21no—
85#384C2×C412yes—
86#382—21no—
87#382—21no—
88#382—21no—
89#382D412yes—
90C2×#95—21no—
91C2×#95—21no—
92#340—24no—
93#340—42no—
94#340—42no—
95#336—24no—
96#336—24no—
97#328—28no—
98C22×Q8—21no—
99C22×Q8C22⋊C412yes—
100C23×C4—41no—
101C23×C4—41no—
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4#4111yescharacteristic
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—41no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—21no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—41no—
126C22×C8SD1612yes—
127C22×C8Q1612yes—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136#125—41no—
137#125—41no—
138#125—41no—
139#125—41no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C22⋊Q8—22no—
144C22⋊Q8—41no—
145C22⋊Q8—41no—
146C22⋊Q8—41no—
147C22⋊Q8—41no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156#117—41no—
157#117—41no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4C22⋊C412yes—
184C2×C22⋊C4—22no—
185C2×C42—22no—
186C2×C42C22×C411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206#103—84no—
207C22⋊C8—22no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211#97—41no—
212#97—41no—
213#97—41no—
214#97—41no—
215C4×C8—22no—
216C4×C8—22no—
217C4×C8—22no—
218C4×C8—41no—
219#95—22no—
220#95—22no—
221#95—41no—
222#95—41no—
223C24#12111yescharacteristic
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—81no—
231C2×Q8—81no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—82no—
241C22×C4—82no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4C2×C22⋊C411yescharacteristic
251C22×C4C4×D411yescharacteristic
252C22×C4C4×D411yescharacteristic
253C22×C4#12011yescharacteristic
254C22×C4#12011yescharacteristic
255C22×C4#12111yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4#12111yescharacteristic
258C22×C4#12311yescharacteristic
259C22×C4#12311yescharacteristic
260C22×C4#12311yescharacteristic
261C22×C4#12311yescharacteristic
262C22×C4#12311yescharacteristic
263C22×C4#12311yescharacteristic
264C22×C4#12411yescharacteristic
265C22×C4#12411yescharacteristic
266C22×C4#12611yescharacteristic
267C22×C4#12611yescharacteristic
268C22×C4C2×SD1611yescharacteristic
269C22×C4C2×Q1611yescharacteristic
270C22×C4#13511yescharacteristic
271C22×C4#13511yescharacteristic
272C22×C4AGL(1,ℤ/8)11yescharacteristic
273C22×C4#13711yescharacteristic
274C22×C4#13711yescharacteristic
275C22×C4#13711yescharacteristic
276M16—81no—
277M16—81no—
278M16—81no—
279M16—81no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—81no—
302C2×C8—81no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—44no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—82no—
321C4⋊C4—82no—
322C4⋊C4—82no—
323C4⋊C4—81no—
324C4⋊C4—81no—
325C4⋊C4—81no—
326C4⋊C4—81no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C42—42no—
330C42—42no—
331C42#11711yescharacteristic
332C42#11711yescharacteristic
333C42C4×D411yescharacteristic
334C42C4×D411yescharacteristic
335C42#12111yescharacteristic
336C42#12111yescharacteristic
337C42#12111yescharacteristic
338C42#12111yescharacteristic
339C42#12311yescharacteristic
340C42#12311yescharacteristic
341C42#12311yescharacteristic
342C42#12311yescharacteristic
343C42#12411yescharacteristic
344C42#12411yescharacteristic
345C42#12611yescharacteristic
346C42#12611yescharacteristic
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23#38611yescharacteristic
352C23#39411yescharacteristic
353C23#39711yescharacteristic
354C23#46011yescharacteristic
355C23#46211yescharacteristic
356C23#46411yescharacteristic
357C23#46411yescharacteristic
358Q8—44no—
359Q8—82no—
360Q8—82no—
361Q8—82no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—161no—
391C2×C4—161no—
392C2×C4—161no—
393C2×C4—161no—
394C2×C4—162no—
395C2×C4—162no—
396C2×C4#38111yescharacteristic
397C2×C4#38611yescharacteristic
398C2×C4#38811yescharacteristic
399C2×C4#38811yescharacteristic
400C2×C4#38811yescharacteristic
401C2×C4#38811yescharacteristic
402C2×C4#39411yescharacteristic
403C2×C4#39411yescharacteristic
404C2×C4#39411yescharacteristic
405C2×C4#39711yescharacteristic
406C2×C4#39711yescharacteristic
407C2×C4#39711yescharacteristic
408C2×C4C4×SD1611yescharacteristic
409C2×C4C4×Q1611yescharacteristic
410C2×C4#44011yescharacteristic
411C2×C4#44111yescharacteristic
412C2×C4#44811yescharacteristic
413C2×C4#44911yescharacteristic
414C2×C4#45111yescharacteristic
415C2×C4#45211yescharacteristic
416C2×C4#46111yescharacteristic
417C2×C4#46211yescharacteristic
418C2×C4#46311yescharacteristic
419C2×C4#46411yescharacteristic
420C2×C4#46511yescharacteristic
421C2×C4#46711yescharacteristic
422C2×C4#46811yescharacteristic
423C2×C4#47011yescharacteristic
424C2×C4#48311yescharacteristic
425C2×C4#48411yescharacteristic
426C2×C4#48511yescharacteristic
427C2×C4#48511yescharacteristic
428C2×C4#48711yescharacteristic
429C2×C4#48811yescharacteristic
430C2×C4#48911yescharacteristic
431C2×C4#49111yescharacteristic
432C8—42no—
433C8—42no—
434C8—82no—
435C8—82no—
436C8—82no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22#144011yescharacteristic
450C22#187811yescharacteristic
451C22#188011yescharacteristic
452C22#190211yescharacteristic
453C22#190311yescharacteristic
454C22#190911yescharacteristic
455C22#191011yescharacteristic
456C22#205511yescharacteristic
457C22#205611yescharacteristic
458C22#207211yescharacteristic
459C22#207411yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—82no—
469C4—82no—
470C4—162no—
471C4—162no—
472C4#192711yescharacteristic
473C4#192811yescharacteristic
474C4#193311yescharacteristic
475C4#193511yescharacteristic
476C4#203511yescharacteristic
477C4#203611yescharacteristic
478C4#204211yescharacteristic
479C4#204311yescharacteristic
480C2—21no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2#928811yescharacteristic
485C2#929011yescharacteristic
486C2#929211yescharacteristic
487C2#929411yescharacteristic
488C2#1115411yescharacteristic
489C2#1118511yescharacteristic
490C2#1119011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
15. #1990C4semidirect
18. #1956C4semidirect

Maximal subgroups

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

subgroupindex
#218602
#213012
C2×#15182
#108432
#80432
C2×#12862
C2×#12752