Finite Group Databasebeta

← #119927

Subgroups — #119927

Order 512.

589 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21311C211yesmaximal, characteristic
2#17708C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#10856C211yesmaximal, characteristic
5C2×#1301C211yesmaximal, characteristic
6#7877C211yesmaximal, characteristic
7#7866C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1989—22no—
16#1988—21no—
17#1987—21no—
18C2×#344—21no—
19C2×#344—21no—
20#1735—21no—
21#1735—21no—
22#1550C414yescomplemented
23#1549—21no—
24#1548—21no—
25#1542—22no—
26#1493—22no—
27#1487—22no—
28#1481—22no—
29#1301—22no—
30#1277—22no—
31#1276—22no—
32C22×M16—21no—
33C22×M16—21no—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533C2×C412yes—
42#533D412yes—
43C2×C4⋊Q8D411yescharacteristic
44C2×C4⋊Q8D411yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×#117—21no—
51C2×#117D411yescharacteristic
52C2×#117D411yescharacteristic
53C22×C42C2311yescharacteristic
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431D412yes—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423C2×C412yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8C2×C412yes—
80C2×C4⋊C8D412yes—
81C2×C4⋊C8D412yes—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C22⋊C4—21no—
89C4×C22⋊C4—21no—
90#376—21no—
91C43—21no—
92#344—42no—
93#344—42no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#333—24no—
99#332—24no—
100Q8⋊C8—28no—
101C22×Q8—21no—
102C22×Q8—21no—
103C23×C4C2×D411yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—22no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8C22⋊C412yes—
136C4⋊Q8C22⋊C412yes—
137#125—22no—
138#125—22no—
139#125—41no—
140#125—41no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145C22⋊Q8—41no—
146C22⋊Q8—41no—
147C22⋊Q8—41no—
148C22⋊Q8—41no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157#117—21no—
158#117—21no—
159#117—21no—
160#117—21no—
161#117—22no—
162#117—22no—
163#117—21no—
164#117—21no—
165#117—41no—
166#117—41no—
167#117SD1612yes—
168#117Q1612yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—41no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—41no—
183C2×C42—41no—
184C2×C42—41no—
185C2×C42C22×C411yescharacteristic
186C2×C42C2×D411yescharacteristic
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
197C4⋊C8—22no—
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211C4⋊C8—41no—
212C4⋊C8—41no—
213C22⋊C8—22no—
214C22⋊C8—41no—
215C22⋊C8—41no—
216C22⋊C8—41no—
217C4×C8—22no—
218C4×C8—41no—
219C4×C8—41no—
220C4×C8—41no—
221#95—41no—
222#95—41no—
223C24#12311yescharacteristic
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—82no—
229C2×Q8—82no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—81no—
236C22×C4#11711yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4#12011yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12111yescharacteristic
242C22×C4#12111yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4#12311yescharacteristic
246C22×C4#12311yescharacteristic
247C22×C4#12311yescharacteristic
248C22×C4#12411yescharacteristic
249C22×C4#12411yescharacteristic
250C22×C4#12411yescharacteristic
251C22×C4#12611yescharacteristic
252C22×C4#12611yescharacteristic
253C22×C4#12611yescharacteristic
254C22×C4C2×SD1611yescharacteristic
255C22×C4C2×Q1611yescharacteristic
256C22×C4#13511yescharacteristic
257C22×C4#13511yescharacteristic
258C22×C4AGL(1,ℤ/8)11yescharacteristic
259C22×C4#13711yescharacteristic
260C22×C4#13711yescharacteristic
261C22×C4#13711yescharacteristic
262M16—42no—
263M16—42no—
264M16—81no—
265M16—81no—
266M16—81no—
267M16—81no—
268M16—81no—
269M16—81no—
270C2×C8—44no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—82no—
281C2×C8—81no—
282C2×C8—81no—
283C2×C8—81no—
284C2×C8—81no—
285C2×C8—81no—
286C2×C8—81no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—22no—
310C42—22no—
311C42—42no—
312C42—42no—
313C42—41no—
314C42—41no—
315C42—82no—
316C42—82no—
317C42C2×C22⋊C411yescharacteristic
318C42#11711yescharacteristic
319C42C4×D411yescharacteristic
320C42C4×D411yescharacteristic
321C42#12011yescharacteristic
322C42#12111yescharacteristic
323C42#12111yescharacteristic
324C42#12111yescharacteristic
325C42#12311yescharacteristic
326C42#12311yescharacteristic
327C42#12311yescharacteristic
328C42#12311yescharacteristic
329C42#12311yescharacteristic
330C42#12311yescharacteristic
331C42#12411yescharacteristic
332C42#12611yescharacteristic
333C23—41no—
334C23—41no—
335C23#38811yescharacteristic
336C23#39411yescharacteristic
337C23#39711yescharacteristic
338C23#48311yescharacteristic
339C23#48411yescharacteristic
340C23#48511yescharacteristic
341C23#48511yescharacteristic
342Q8—44no—
343Q8—82no—
344Q8—82no—
345Q8—82no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4#38111yescharacteristic
369C2×C4#38611yescharacteristic
370C2×C4#38611yescharacteristic
371C2×C4#38811yescharacteristic
372C2×C4#38811yescharacteristic
373C2×C4#38811yescharacteristic
374C2×C4#39411yescharacteristic
375C2×C4#39411yescharacteristic
376C2×C4#39411yescharacteristic
377C2×C4#39711yescharacteristic
378C2×C4#39711yescharacteristic
379C2×C4#39711yescharacteristic
380C2×C4C4×SD1611yescharacteristic
381C2×C4C4×Q1611yescharacteristic
382C2×C4#44011yescharacteristic
383C2×C4#44111yescharacteristic
384C2×C4#44811yescharacteristic
385C2×C4#44911yescharacteristic
386C2×C4#45111yescharacteristic
387C2×C4#45211yescharacteristic
388C2×C4#46011yescharacteristic
389C2×C4#46111yescharacteristic
390C2×C4#46211yescharacteristic
391C2×C4#46211yescharacteristic
392C2×C4#46311yescharacteristic
393C2×C4#46411yescharacteristic
394C2×C4#46411yescharacteristic
395C2×C4#46411yescharacteristic
396C2×C4#46511yescharacteristic
397C2×C4#46711yescharacteristic
398C2×C4#46811yescharacteristic
399C2×C4#47011yescharacteristic
400C2×C4#48711yescharacteristic
401C2×C4#48811yescharacteristic
402C2×C4#48911yescharacteristic
403C2×C4#49111yescharacteristic
404C8—82no—
405C8—82no—
406C8—82no—
407C8—82no—
408C8—82no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22#144011yescharacteristic
420C22#192711yescharacteristic
421C22#192811yescharacteristic
422C22#203511yescharacteristic
423C22#203611yescharacteristic
424C22#207211yescharacteristic
425C22#207411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—82no—
434C4—82no—
435C4—82no—
436C4—82no—
437C4#187811yescharacteristic
438C4#188011yescharacteristic
439C4#188112yes—
440C4#193311yescharacteristic
441C4#193511yescharacteristic
442C4#204211yescharacteristic
443C4#204311yescharacteristic
444C4#205511yescharacteristic
445C4#205611yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2#1115311yescharacteristic
453C2#1119011yescharacteristic
454C2#1119411yescharacteristic
subgroupG/H
centerC2×C4#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1440
prime radicalC24#123
LCSG ▷ C2×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
22. #1550C4semidirect

Maximal subgroups

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

subgroupindex
#213112
#177082
#174862
#108562
C2×#13012
#78772
#78662