Finite Group Databasebeta

← #128184

Subgroups — #128184

Order 512.

678 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17357C211yesmaximal, characteristic
2#17357C211yesmaximal, characteristic
3#13939C211yesmaximal, characteristic
4#7324C214yesmaximal
5C22×#117C2211yescharacteristic
6#2920—21no—
7#2920—21no—
8C2×#380C411yescharacteristic
9C2×C4×C22⋊C4C411yescharacteristic
10#1464—21no—
11#1464—21no—
12#1464C412yescomplemented
13#1464C412yescomplemented
14#1463—21no—
15#1463—21no—
16#1462C2212yes—
17#1462C2212yes—
18#1458—21no—
19#1458—21no—
20#1458C412yescomplemented
21#1458C412yescomplemented
22#1440C412yes—
23#1440C2212yes—
24C4⋊#95—21no—
25C4⋊#95—21no—
26#1434—21no—
27#1434—21no—
28C24×C4C2×C411yescharacteristic
29C2×#117—41no—
30C2×#117—41no—
31C2×#117—41no—
32C2×#117—41no—
33C2×#117C2×C411yescharacteristic
34C2×#117C2×C411yescharacteristic
35C2×#117C2×C411yescharacteristic
36C2×#117C2×C411yescharacteristic
37C2×#117D411yescharacteristic
38C2×#117D411yescharacteristic
39C2×#117Q811yescharacteristic
40C2×#117Q811yescharacteristic
41C22×C4⋊C4—21no—
42C22×C4⋊C4D411yescharacteristic
43C22×C4⋊C4D411yescharacteristic
44C22×C22⋊C4C2×C412yes—
45C22×C22⋊C4C2×C411yescharacteristic
46C22×C22⋊C4C2×C412yes—
47C22×C22⋊C4C2311yescharacteristic
48C22×C42—21no—
49C22×C42D411yescharacteristic
50C22×C42D411yescharacteristic
51#432—22no—
52#432—22no—
53#432—41no—
54#432—41no—
55#431—22no—
56#431—22no—
57#431—41no—
58#431—41no—
59#423—41no—
60#423—41no—
61#407—22no—
62#407—22no—
63C4×M16—41no—
64C4×M16—41no—
65#380—41no—
66#380—41no—
67C4×C22⋊C4—41no—
68C4×C22⋊C4—41no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75#324—22no—
76#324—22no—
77#324—22no—
78#324—22no—
79#323—22no—
80#323—22no—
81#323C2×C414yes—
82#323C2×C414yes—
83C25C22×C411yescharacteristic
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4—42no—
91C23×C4—42no—
92C23×C4C4211yescharacteristic
93C23×C4C4211yescharacteristic
94C23×C4C22⋊C411yescharacteristic
95C23×C4C22⋊C411yescharacteristic
96C23×C4C22⋊C411yescharacteristic
97C23×C4C22⋊C411yescharacteristic
98C23×C4C4⋊C411yescharacteristic
99C23×C4C4⋊C411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C2×M16—42no—
103C2×M16—42no—
104#117—41no—
105#117—41no—
106#117—41no—
107#117—41no—
108#117—41no—
109#117—41no—
110#117—41no—
111#117—41no—
112#117—41no—
113#117—41no—
114#117—41no—
115#117—41no—
116#117—41no—
117#117—41no—
118#117—41no—
119#117—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C4⋊C4C22⋊C411yescharacteristic
131C2×C4⋊C4C4⋊C411yescharacteristic
132C2×C4⋊C4C4⋊C411yescharacteristic
133C2×C4⋊C4C4⋊C411yescharacteristic
134C2×C4⋊C4C4⋊C411yescharacteristic
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—42no—
140C2×C22⋊C4—44no—
141C2×C22⋊C4—42no—
142C2×C22⋊C4—82no—
143C2×C22⋊C4C4211yescharacteristic
144C2×C22⋊C4C4211yescharacteristic
145C2×C22⋊C4C4⋊C411yescharacteristic
146C2×C22⋊C4C4⋊C411yescharacteristic
147C2×C22⋊C4C22×C411yescharacteristic
148C2×C22⋊C4C22×C411yescharacteristic
149C2×C22⋊C4C2×D411yescharacteristic
150C2×C22⋊C4C2×Q811yescharacteristic
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—42no—
160C2×C42—42no—
161C2×C42—42no—
162C2×C42C22⋊C411yescharacteristic
163C2×C42C22⋊C411yescharacteristic
164C2×C42C22⋊C411yescharacteristic
165C2×C42C22⋊C411yescharacteristic
166C2×C42C4⋊C411yescharacteristic
167C2×C42C4⋊C411yescharacteristic
168C2×C42C4⋊C411yescharacteristic
169C2×C42C4⋊C411yescharacteristic
170C4⋊C8—42no—
171C4⋊C8—42no—
172C4⋊C8—42no—
173C4⋊C8—42no—
174C22⋊C8—24no—
175C22⋊C8—24no—
176C22⋊C8—42no—
177C22⋊C8—42no—
178#97—42no—
179#97—42no—
180C4×C8—42no—
181C4×C8—42no—
182#95—44no—
183#95—44no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188#95—82no—
189#95—82no—
190C24—21no—
191C24—21no—
192C24—41no—
193C24—41no—
194C24—42no—
195C24—41no—
196C24—41no—
197C24C2×C4211yescharacteristic
198C24C2×C22⋊C411yescharacteristic
199C24C2×C4⋊C411yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4#9511yescharacteristic
255C22×C4#9511yescharacteristic
256C22×C4#9511yescharacteristic
257C22×C4#9511yescharacteristic
258C22×C4#9511yescharacteristic
259C22×C4#9511yescharacteristic
260C22×C4#9511yescharacteristic
261C22×C4#9511yescharacteristic
262C22×C4#9911yescharacteristic
263C22×C4#9911yescharacteristic
264C22×C4#9911yescharacteristic
265C22×C4#9911yescharacteristic
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C411yescharacteristic
268C22×C4C2×C4⋊C411yescharacteristic
269C22×C4C2×C4⋊C411yescharacteristic
270M16—84no—
271M16—82no—
272M16—82no—
273C2×C8—44no—
274C2×C8—44no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—84no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—44no—
293C22⋊C4—44no—
294C22⋊C4—84no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42—21no—
311C42—84no—
312C23—22no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—41no—
333C23—41no—
334C23—82no—
335C23—82no—
336C23—82no—
337C23—82no—
338C23C2×#9511yescharacteristic
339C23C2×#9911yescharacteristic
340C23C2×#9911yescharacteristic
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#34211yescharacteristic
404C2×C4#34211yescharacteristic
405C2×C4#34211yescharacteristic
406C2×C4#34211yescharacteristic
407C2×C4#34412yes—
408C2×C4#34412yes—
409C8—84no—
410C8—84no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—84no—
432C22—82no—
433C22—82no—
434C22C2×#34211yescharacteristic
435C22C2×#34411yescharacteristic
436C22C2×#34411yescharacteristic
437C22#212012yes—
438C22#212211yescharacteristic
439C22#212311yescharacteristic
440C4—22no—
441C4—22no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—41no—
447C4—41no—
448C4—41no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—41no—
454C4—84no—
455C4—162no—
456C2—22no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—81no—
462C2—81no—
463C2#811411yescharacteristic
464C2#1257311yescharacteristic
465C2#1257511yescharacteristic
subgroupG/H
center, socleC22C2×#342
commutatorC24C2×C42
Frattini, cosocleC22×C22⋊C4C23
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #1464C4semidirect
13. #1464C4semidirect
20. #1458C4semidirect
21. #1458C4semidirect

Maximal subgroups

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

subgroupindex
#173572
#139392
#73242