Finite Group Databasebeta

← #106578

Subgroups — #106578

Order 512.

881 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#60124C211yesmaximal, characteristic
2#20377C211yesmaximal, characteristic
3#17357C211yesmaximal, characteristic
4#8064C212yesmaximal, complemented
5#7992C212yesmaximal, complemented
6C22×#117C2211yescharacteristic
7#2924—24no—
8#2924—24no—
9#2921—21no—
10#2921C412yes—
11#2920—21no—
12#2920C2212yes—
13#2920C2212yes—
14#2905C412yes—
15C2×#407—21no—
16C2×#407—21no—
17#2873—21no—
18C2×C4×M16C2211yescharacteristic
19C2×C4×M16C2211yescharacteristic
20#1750—21no—
21#1750—21no—
22#1750C412yes—
23#1750C412yes—
24#1728—21no—
25#1464—21no—
26#1464—21no—
27#1463C412yes—
28#1462C412yes—
29#1458—21no—
30#1458—21no—
31#1299—24no—
32#1291—24no—
33C24×C4D411yescharacteristic
34C22×M16—22no—
35C22×M16—21no—
36C22×M16—21no—
37C2×#117—22no—
38C2×#117—22no—
39C2×#117—22no—
40C2×#117—22no—
41C2×#117C2×C411yescharacteristic
42C2×#117C2×C411yescharacteristic
43C2×#117C2×C411yescharacteristic
44C2×#117C2×C411yescharacteristic
45C2×#117D411yescharacteristic
46C2×#117D411yescharacteristic
47C2×#117D411yescharacteristic
48C2×#117D411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4Q811yescharacteristic
51C22×C22⋊C4C2×C411yescharacteristic
52C22×C22⋊C4Q811yescharacteristic
53C22×C42D411yescharacteristic
54C22×C42C2311yescharacteristic
55#433—28no—
56#433—28no—
57#432—22no—
58#432—22no—
59#432—22no—
60#432—22no—
61#432—22no—
62#432D414yes—
63#431—22no—
64#431—22no—
65#431—22no—
66#431—22no—
67#431—22no—
68#431D414yes—
69#424—28no—
70#423—22no—
71#423—22no—
72#423C2×C414yes—
73#407—28no—
74#407—22no—
75#407—22no—
76#407—22no—
77#407—22no—
78#407C2×C414yes—
79C2×C22⋊C8—22no—
80C2×C22⋊C8—22no—
81C2×C22⋊C8—22no—
82C2×C22⋊C8—22no—
83#405—28no—
84C4×M16—22no—
85C4×M16—22no—
86C4×M16—22no—
87C4×M16—22no—
88C4×M16—22no—
89C4×M16—22no—
90C4×M16—22no—
91C2×#97—21no—
92C2×#97C2×C412yes—
93C2×C4×C8—21no—
94C2×C4×C8C2×C412yes—
95#336—22no—
96#336—22no—
97#324—22no—
98#324—22no—
99#323—22no—
100#323—22no—
101C25C4⋊C411yescharacteristic
102C23×C4—24no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4—42no—
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22⋊C411yescharacteristic
111C23×C4C22⋊C411yescharacteristic
112C23×C4C4⋊C411yescharacteristic
113C23×C4C4⋊C411yescharacteristic
114C23×C4C4⋊C411yescharacteristic
115C23×C4C22×C411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2×Q811yescharacteristic
118C2×M16—24no—
119C2×M16—24no—
120C2×M16—24no—
121C2×M16—24no—
122C2×M16—24no—
123C2×M16—42no—
124C2×M16—42no—
125C2×M16—44no—
126C2×M16—44no—
127C2×M16—41no—
128C2×M16—41no—
129C2×M16—41no—
130C2×M16—41no—
131C22×C8—24no—
132C22×C8—22no—
133C22×C8—22no—
134#117—22no—
135#117—22no—
136#117—22no—
137#117—22no—
138#117—22no—
139#117—22no—
140#117—22no—
141#117—22no—
142#117—22no—
143#117—22no—
144#117—22no—
145#117—22no—
146#117—22no—
147#117—22no—
148#117—22no—
149#117—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4C4211yescharacteristic
155C2×C4⋊C4C4211yescharacteristic
156C2×C4⋊C4C22⋊C411yescharacteristic
157C2×C4⋊C4C22⋊C411yescharacteristic
158C2×C4⋊C4C4⋊C411yescharacteristic
159C2×C4⋊C4C4⋊C411yescharacteristic
160C2×C4⋊C4C4⋊C411yescharacteristic
161C2×C4⋊C4C4⋊C411yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4—22no—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4C4211yescharacteristic
167C2×C22⋊C4C4211yescharacteristic
168C2×C22⋊C4C22⋊C411yescharacteristic
169C2×C22⋊C4C22⋊C411yescharacteristic
170C2×C22⋊C4C4⋊C411yescharacteristic
171C2×C22⋊C4C4⋊C411yescharacteristic
172C2×C22⋊C4C4⋊C411yescharacteristic
173C2×C22⋊C4C4⋊C411yescharacteristic
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42C22⋊C411yescharacteristic
179C2×C42C22⋊C411yescharacteristic
180C2×C42C22⋊C411yescharacteristic
181C2×C42C22⋊C411yescharacteristic
182C2×C42C22×C411yescharacteristic
183C2×C42C22×C411yescharacteristic
184C2×C42C2×D412yes—
185C2×C42C2×D412yes—
186C2×C42C2×D411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42#4112yes—
189C2×C42#4112yes—
190C4⋊C8—24no—
191C4⋊C8—24no—
192C4⋊C8—24no—
193C4⋊C8—42no—
194C4⋊C8—42no—
195C4⋊C8C22⋊C418yes—
196C22⋊C8—28no—
197C22⋊C8—28no—
198C22⋊C8—24no—
199C22⋊C8—24no—
200C22⋊C8—24no—
201C22⋊C8—24no—
202C22⋊C8—24no—
203C22⋊C8—24no—
204#97—24no—
205#97—24no—
206#97—24no—
207#97—42no—
208#97—42no—
209C4×C8—24no—
210C4×C8—24no—
211C4×C8—24no—
212C4×C8—42no—
213C4×C8—42no—
214C24—21no—
215C24—21no—
216C24—22no—
217C24—41no—
218C24—81no—
219C24—81no—
220C24#9511yescharacteristic
221C24#9511yescharacteristic
222C24C2×C4⋊C411yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4#9511yescharacteristic
257C22×C4#9511yescharacteristic
258C22×C4#9511yescharacteristic
259C22×C4#9511yescharacteristic
260C22×C4#9511yescharacteristic
261C22×C4#9511yescharacteristic
262C22×C4#10414yes—
263C22×C4C2×C4211yescharacteristic
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C2×C22⋊C411yescharacteristic
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C4⋊C411yescharacteristic
268C22×C4C2×C4⋊C411yescharacteristic
269C22×C4C4×D412yes—
270C22×C4C4×D412yes—
271C22×C4#12011yescharacteristic
272C22×C4#12011yescharacteristic
273C22×C4C22⋊Q812yes—
274C22×C4C22⋊Q812yes—
275C22×C4#12311yescharacteristic
276C22×C4#12311yescharacteristic
277M16—44no—
278M16—44no—
279M16—44no—
280M16—44no—
281M16—48no—
282M16—44no—
283M16—44no—
284M16—84no—
285C2×C8—24no—
286C2×C8—24no—
287C2×C8—28no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—48no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—44no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42C2×C22⋊C412yes—
319C42#11712yes—
320C42C4×D412yes—
321C42C4×D412yes—
322C42#12012yes—
323C42#12112yes—
324C42#12112yes—
325C42#12312yes—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—42no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—81no—
345C23—84no—
346C23—84no—
347C23#33912yes—
348C23C2×#9511yescharacteristic
349C23#38511yescharacteristic
350C23#38511yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4#33912yes—
393C2×C4C4×C22⋊C412yes—
394C2×C4#37911yescharacteristic
395C2×C4#38012yes—
396C2×C4#38111yescharacteristic
397C2×C4#38512yes—
398C2×C4#38611yescharacteristic
399C2×C4#38611yescharacteristic
400C2×C4#38612yes—
401C2×C4C2×#10412yes—
402C2×C4#42112yes—
403C8—44no—
404C8—44no—
405C8—48no—
406C8—84no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—22no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—42no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—84no—
429C22C22⋊#9511yescharacteristic
430C22C2×#33911yescharacteristic
431C22#173311yescharacteristic
432C4—22no—
433C4—22no—
434C4—21no—
435C4—21no—
436C4—22no—
437C4—22no—
438C4—22no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4#178912yes—
445C4#182612yes—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—41no—
450C2—42no—
451C2—81no—
452C2#1073311yescharacteristic
453C2#1074411yescharacteristic
454C2#1075711yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC25C4⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #8064C2semidirect
5. #7992C2semidirect

Maximal subgroups

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

subgroupindex
#601242
#203772
#173572
#80642
#79922