Finite Group Databasebeta

← #120886

Subgroups — #120886

Order 512.

547 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21943C211yesmaximal, characteristic
2#8102C211yesmaximal, characteristic
3#8100C211yesmaximal, characteristic
4#7982C211yesmaximal, characteristic
5#7982C211yesmaximal, characteristic
6#7946C211yesmaximal, characteristic
7#7927C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10#2280C2211yescharacteristic
11#2280C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14#2280C2211yescharacteristic
15#1854—22no—
16#1854—22no—
17#1809—22no—
18#1304—22no—
19#1304—22no—
20#1289—22no—
21#1289—22no—
22#1284C414yescomplemented
23#1282—22no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C23×C8Q811yescharacteristic
27C23×C8Q811yescharacteristic
28C2×#117—21no—
29C2×#117—21no—
30C2×#117—21no—
31C2×#117—21no—
32C2×#117—21no—
33C2×#107—22no—
34C2×#106—22no—
35#407—21no—
36#407—21no—
37#407C2×C412yes—
38#407Q812yes—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8D412yes—
47#381—21no—
48#381—21no—
49#381—21no—
50#381—21no—
51#381C2×C412yes—
52#380—21no—
53#380—21no—
54#380—21no—
55#380—21no—
56#380—21no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380D412yes—
61#380D412yes—
62#379—21no—
63#379—21no—
64#379—21no—
65#379—21no—
66#379D412yes—
67C4×C22⋊C4—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4—21no—
74C4×C22⋊C4—21no—
75C4×C22⋊C4—21no—
76C4×C22⋊C4C2×C412yes—
77#340—24no—
78C25C2×D411yescharacteristic
79C23×C4—81no—
80C23×C4—81no—
81C23×C4C22×C411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×Q811yescharacteristic
86C23×C4C2×Q811yescharacteristic
87C23×C4#4111yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C23×C4#4111yescharacteristic
95C2×M16—22no—
96C2×M16—22no—
97C2×M16—81no—
98C2×M16—81no—
99C22×C8—22no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—81no—
107C22×C8—81no—
108#117—81no—
109#117—81no—
110#117—81no—
111#117—81no—
112#117—81no—
113#117—81no—
114#117—81no—
115#117—81no—
116#117—81no—
117#117—81no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4—22no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—22no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C42—22no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143#107—82no—
144#106—82no—
145C22⋊C8—22no—
146C22⋊C8—22no—
147C22⋊C8—22no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8C4⋊C414yes—
153#95—22no—
154#95—22no—
155#95—22no—
156#95—22no—
157#95—22no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163C24—42no—
164C24—81no—
165C24—81no—
166C24C4×D411yescharacteristic
167C24#12111yescharacteristic
168C24#12111yescharacteristic
169C24#12111yescharacteristic
170C24#12311yescharacteristic
171C24#12311yescharacteristic
172C24C4⋊Q811yescharacteristic
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4C2×C4⋊C411yescharacteristic
200C22×C4#11711yescharacteristic
201C22×C4#11711yescharacteristic
202C22×C4C4×D411yescharacteristic
203C22×C4C4×D411yescharacteristic
204C22×C4C4×Q811yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4C22⋊Q811yescharacteristic
207C22×C4C22⋊Q811yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4C22⋊Q811yescharacteristic
210C22×C4C22⋊Q811yescharacteristic
211C22×C4#12311yescharacteristic
212C22×C4#12311yescharacteristic
213C22×C4#12311yescharacteristic
214C22×C4#12411yescharacteristic
215C22×C4#12411yescharacteristic
216C22×C4#12411yescharacteristic
217C22×C4#12411yescharacteristic
218C22×C4#12511yescharacteristic
219C22×C4#12511yescharacteristic
220C22×C4#12511yescharacteristic
221C22×C4#12511yescharacteristic
222C22×C4#12511yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4#12611yescharacteristic
225C22×C4#12611yescharacteristic
226C22×C4#12611yescharacteristic
227M16—82no—
228M16—82no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C2×C8—81no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4—82no—
249C22⋊C4—44no—
250C22⋊C4—82no—
251C22⋊C4—82no—
252C22⋊C4—82no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C22⋊C4—82no—
257C22⋊C4—82no—
258C22⋊C4—82no—
259C22⋊C4—82no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C22⋊C4—82no—
263C22⋊C4—82no—
264C42—81no—
265C42—81no—
266C42—82no—
267C42—82no—
268C42—82no—
269C42—82no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—88no—
292C23#38811yescharacteristic
293C23#38811yescharacteristic
294C23#38911yescharacteristic
295C23#39411yescharacteristic
296C23#39711yescharacteristic
297C23#39811yescharacteristic
298C23#39811yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4#38211yescharacteristic
350C2×C4#38511yescharacteristic
351C2×C4#38711yescharacteristic
352C2×C4#38711yescharacteristic
353C2×C4#39311yescharacteristic
354C2×C4#40011yescharacteristic
355C2×C4#40011yescharacteristic
356C2×C4#40011yescharacteristic
357C8—44no—
358C8—81no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22#144211yescharacteristic
388C22#205312yes—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—162no—
397C4—162no—
398C4—162no—
399C4—162no—
400C4—162no—
401C4#203211yescharacteristic
402C4#203211yescharacteristic
403C2—22no—
404C2—41no—
405C2—41no—
406C2—41no—
407C2—41no—
408C2—41no—
409C2—41no—
410C2#1127711yescharacteristic
411C2#1127911yescharacteristic
412C2#1128511yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
22. #1284C4semidirect

Maximal subgroups

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

subgroupindex
#219432
#81022
#81002
#79822
#79462
#79272