Finite Group Databasebeta

← #120845

Subgroups — #120845

Order 512.

545 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21941C211yesmaximal, characteristic
2#8104C211yesmaximal, characteristic
3C2×#1305C211yesmaximal, characteristic
4#8057C211yesmaximal, characteristic
5#7983C211yesmaximal, characteristic
6#7946C211yesmaximal, characteristic
7#7925C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14C2×#380C2211yescharacteristic
15#1854—22no—
16#1853—21no—
17#1852—21no—
18#1808—21no—
19#1807—21no—
20#1305—22no—
21#1305—21no—
22#1305—21no—
23#1298—21no—
24#1298—21no—
25#1289—22no—
26#1284—22no—
27#1282C414yescomplemented
28C24×C4C2311yescharacteristic
29C22×M16—21no—
30C22×M16—21no—
31C22×M16Q812yes—
32C23×C8—21no—
33C2×#117—21no—
34C2×#117—21no—
35C22×C4⋊C4—21no—
36C22×C22⋊C4—21no—
37C2×#107—22no—
38C2×#106—22no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407—21no—
48#407—21no—
49#407—21no—
50#407D412yes—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8C2×C412yes—
60C2×C22⋊C8C2×C412yes—
61C2×C22⋊C8D411yescharacteristic
62C2×C22⋊C8D411yescharacteristic
63C2×C22⋊C8Q812yes—
64#381—21no—
65#381—21no—
66#380—21no—
67#380—21no—
68#380—21no—
69#380—21no—
70#380—21no—
71#380—21no—
72#380D412yes—
73#380D411yescharacteristic
74#380D411yescharacteristic
75#379—21no—
76#379—21no—
77C4×C22⋊C4—21no—
78C4×C22⋊C4—21no—
79C4×C22⋊C4—21no—
80C4×C22⋊C4C2×C412yes—
81C2×#95—21no—
82#340—22no—
83#340—22no—
84C25#4111yescharacteristic
85C23×C4—41no—
86C23×C4—82no—
87C23×C4C22×C411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×Q811yescharacteristic
93C23×C4C2×Q811yescharacteristic
94C23×C4#4111yescharacteristic
95C23×C4#4111yescharacteristic
96C23×C4#4111yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—82no—
108C2×M16—82no—
109C2×M16—82no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—41no—
117C22×C8—82no—
118#117—82no—
119#117—82no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—82no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—82no—
136C2×C42—22no—
137C2×C42—41no—
138#107—82no—
139#106—82no—
140C22⋊C8—22no—
141C22⋊C8—22no—
142C22⋊C8—21no—
143C22⋊C8—21no—
144C22⋊C8—22no—
145C22⋊C8—22no—
146C22⋊C8—22no—
147C22⋊C8—22no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8C4⋊C412yes—
157C22⋊C8C4⋊C412yes—
158#95—22no—
159#95—21no—
160#95—21no—
161#95—22no—
162#95—41no—
163#95—41no—
164#95—41no—
165C24—41no—
166C24—41no—
167C24—42no—
168C24—81no—
169C24#11711yescharacteristic
170C24#12111yescharacteristic
171C24#12311yescharacteristic
172C24#12411yescharacteristic
173C24#12511yescharacteristic
174C24#12511yescharacteristic
175C24#12611yescharacteristic
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—42no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4—81no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4—82no—
195C22×C4—82no—
196C22×C4—82no—
197C22×C4C2×C4⋊C411yescharacteristic
198C22×C4#11711yescharacteristic
199C22×C4C4×D411yescharacteristic
200C22×C4C4×D411yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4C4×Q811yescharacteristic
203C22×C4#12011yescharacteristic
204C22×C4#12111yescharacteristic
205C22×C4#12111yescharacteristic
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#12311yescharacteristic
215C22×C4#12411yescharacteristic
216C22×C4#12411yescharacteristic
217C22×C4#12411yescharacteristic
218C22×C4#12511yescharacteristic
219C22×C4#12511yescharacteristic
220C22×C4#12511yescharacteristic
221C22×C4#12611yescharacteristic
222C22×C4#12611yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4C4⋊Q811yescharacteristic
225M16—82no—
226M16—82no—
227M16—82no—
228M16—82no—
229M16—82no—
230M16—82no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—82no—
239C2×C8—82no—
240C2×C8—82no—
241C2×C8—82no—
242C2×C8—82no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C22⋊C4—44no—
250C22⋊C4—82no—
251C22⋊C4—81no—
252C22⋊C4—81no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C22⋊C4—81no—
257C22⋊C4—81no—
258C22⋊C4—82no—
259C42—82no—
260C42—82no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—41no—
271C23—41no—
272C23—41no—
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—84no—
286C23—84no—
287C23#38211yescharacteristic
288C23#38711yescharacteristic
289C23#38811yescharacteristic
290C23#39411yescharacteristic
291C23#39811yescharacteristic
292C23#40011yescharacteristic
293C23#40011yescharacteristic
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
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—81no—
323C2×C4—81no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—164no—
335C2×C4#38511yescharacteristic
336C2×C4#38711yescharacteristic
337C2×C4#38811yescharacteristic
338C2×C4#38911yescharacteristic
339C2×C4#39311yescharacteristic
340C2×C4#39711yescharacteristic
341C2×C4#39811yescharacteristic
342C2×C4#40011yescharacteristic
343C8—42no—
344C8—42no—
345C8—82no—
346C8—82no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—82no—
377C22#144211yescharacteristic
378C22#183312yes—
379C22#204811yescharacteristic
380C22#204911yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—161no—
389C4—161no—
390C4—162no—
391C4—162no—
392C4#203212yes—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2#1126011yescharacteristic
402C2#1127411yescharacteristic
403C2#1127911yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25#41
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
27. #1282C4semidirect

Maximal subgroups

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

subgroupindex
#219412
#81042
C2×#13052
#80572
#79832
#79462
#79252