Finite Group Databasebeta

← #118972

Subgroups — #118972

Order 512.

611 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1986C211yesmaximal, characteristic
2#17708C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C4⋊#338C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1986—22no—
16#1986—22no—
17C2×#339—21no—
18C2×#339—21no—
19C2×#338—21no—
20C2×#338—21no—
21#1550—22no—
22#1550—22no—
23#1549—21no—
24#1549—21no—
25#1548—21no—
26#1548—21no—
27#1542—22no—
28#1542C414yescomplemented
29#1303—22no—
30#1283—22no—
31#1279—22no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16D411yescharacteristic
35C22×M16D411yescharacteristic
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533D412yes—
44C2×C4⋊Q8D411yescharacteristic
45C2×C4⋊Q8D411yescharacteristic
46C2×#125—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8—21no—
49C2×C4×Q8—21no—
50C2×C4×Q8—21no—
51C2×#117—21no—
52C22×C4⋊C4—21no—
53C22×C42—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#431C2×C412yes—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8C2×C412yes—
75C2×C4⋊C8D412yes—
76C2×C4⋊C8D412yes—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C2×#97—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4D412yes—
91C2×#95—21no—
92#339—24no—
93#339—24no—
94#338—42no—
95#338—42no—
96#333—24no—
97#333—24no—
98#332—24no—
99#332—24no—
100C22×Q8—21no—
101C22×Q8—21no—
102C23×C4—41no—
103C23×C4C2×D411yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—21no—
107C2×M16—21no—
108C2×M16—21no—
109C2×M16—21no—
110C2×M16—21no—
111C2×M16—21no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16—21no—
115C2×M16—21no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16SD1612yes—
129C2×M16Q1612yes—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—41no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140C4⋊Q8—21no—
141C4⋊Q8—21no—
142C4⋊Q8C22⋊C412yes—
143C4⋊Q8C22⋊C412yes—
144#125—22no—
145#125—22no—
146#125—41no—
147#125—41no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C22⋊Q8—41no—
153C22⋊Q8—41no—
154C22⋊Q8—41no—
155C22⋊Q8—41no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163C4×Q8—41no—
164#117—22no—
165#117—22no—
166#117—41no—
167#117—41no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C22⋊C4—41no—
178C2×C42—22no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
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—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209C22⋊C8—22no—
210C22⋊C8—41no—
211C22⋊C8—41no—
212C22⋊C8—41no—
213#97—41no—
214#97—41no—
215C4×C8—22no—
216C4×C8—41no—
217C4×C8—41no—
218C4×C8—41no—
219C4×C8—41no—
220C4×C8—41no—
221#95—22no—
222#95—41no—
223C24#12411yescharacteristic
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—82no—
229C2×Q8—82no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4—42no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—81no—
236C22×C4—82no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4#11711yescharacteristic
240C22×C4C4×D411yescharacteristic
241C22×C4C4×D411yescharacteristic
242C22×C4#12011yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4#12111yescharacteristic
246C22×C4#12111yescharacteristic
247C22×C4#12111yescharacteristic
248C22×C4#12311yescharacteristic
249C22×C4#12311yescharacteristic
250C22×C4#12311yescharacteristic
251C22×C4#12311yescharacteristic
252C22×C4#12311yescharacteristic
253C22×C4#12311yescharacteristic
254C22×C4#12611yescharacteristic
255C22×C4#12611yescharacteristic
256C22×C4#12611yescharacteristic
257C22×C4C2×SD1611yescharacteristic
258C22×C4C2×Q1611yescharacteristic
259C22×C4#13511yescharacteristic
260C22×C4#13511yescharacteristic
261C22×C4AGL(1,ℤ/8)11yescharacteristic
262C22×C4#13711yescharacteristic
263C22×C4#13711yescharacteristic
264C22×C4#13711yescharacteristic
265M16—22no—
266M16—22no—
267M16—22no—
268M16—22no—
269M16—41no—
270M16—41no—
271M16—41no—
272M16—41no—
273M16—81no—
274M16—81no—
275M16—81no—
276M16—81no—
277M16—81no—
278M16—81no—
279M16—81no—
280M16—81no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—82no—
296C2×C8—82no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C42—42no—
315C42—42no—
316C42—42no—
317C42—42no—
318C42—81no—
319C42—81no—
320C42C2×C22⋊C411yescharacteristic
321C42#11711yescharacteristic
322C42C4×D411yescharacteristic
323C42C4×D411yescharacteristic
324C42#12011yescharacteristic
325C42#12111yescharacteristic
326C42#12111yescharacteristic
327C42#12111yescharacteristic
328C42#12311yescharacteristic
329C42#12311yescharacteristic
330C42#12311yescharacteristic
331C42#12311yescharacteristic
332C42#12411yescharacteristic
333C42#12411yescharacteristic
334C42#12411yescharacteristic
335C42#12611yescharacteristic
336C23—41no—
337C23—41no—
338C23#38811yescharacteristic
339C23#39411yescharacteristic
340C23#39711yescharacteristic
341C23#48711yescharacteristic
342C23#48811yescharacteristic
343C23#48911yescharacteristic
344C23#49111yescharacteristic
345Q8—82no—
346Q8—82no—
347Q8—82no—
348Q8—82no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—84no—
368C2×C4—84no—
369C2×C4—82no—
370C2×C4#38111yescharacteristic
371C2×C4#38611yescharacteristic
372C2×C4#38611yescharacteristic
373C2×C4#38811yescharacteristic
374C2×C4#38811yescharacteristic
375C2×C4#38811yescharacteristic
376C2×C4#39411yescharacteristic
377C2×C4#39411yescharacteristic
378C2×C4#39411yescharacteristic
379C2×C4#39711yescharacteristic
380C2×C4#39711yescharacteristic
381C2×C4#39711yescharacteristic
382C2×C4C4×SD1611yescharacteristic
383C2×C4C4×Q1611yescharacteristic
384C2×C4#44011yescharacteristic
385C2×C4#44111yescharacteristic
386C2×C4#44811yescharacteristic
387C2×C4#44911yescharacteristic
388C2×C4#45111yescharacteristic
389C2×C4#45211yescharacteristic
390C2×C4#46011yescharacteristic
391C2×C4#46111yescharacteristic
392C2×C4#46211yescharacteristic
393C2×C4#46211yescharacteristic
394C2×C4#46311yescharacteristic
395C2×C4#46411yescharacteristic
396C2×C4#46411yescharacteristic
397C2×C4#46411yescharacteristic
398C2×C4#46511yescharacteristic
399C2×C4#46711yescharacteristic
400C2×C4#46811yescharacteristic
401C2×C4#47011yescharacteristic
402C2×C4#48311yescharacteristic
403C2×C4#48411yescharacteristic
404C2×C4#48511yescharacteristic
405C2×C4#48511yescharacteristic
406C8—42no—
407C8—42no—
408C8—82no—
409C8—82no—
410C8—82no—
411C8—82no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22#144011yescharacteristic
423C22#193311yescharacteristic
424C22#193511yescharacteristic
425C22#204211yescharacteristic
426C22#204311yescharacteristic
427C22#207211yescharacteristic
428C22#207411yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—84no—
437C4—82no—
438C4—82no—
439C4#187811yescharacteristic
440C4#188011yescharacteristic
441C4#192711yescharacteristic
442C4#192811yescharacteristic
443C4#203511yescharacteristic
444C4#203611yescharacteristic
445C4#205012yes—
446C4#205511yescharacteristic
447C4#205611yescharacteristic
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2#1115111yescharacteristic
455C2#1117911yescharacteristic
456C2#1119011yescharacteristic
subgroupG/H
centerC2×C4#388
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1440
prime radicalC24#124
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
28. #1542C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19862
#177082
C4⋊#3382
C2×#13032
#79322
#79012