Finite Group Databasebeta

← #121149

Subgroups — #121149

Order 512.

536 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#8107C211yesmaximal, characteristic
2#8107C211yesmaximal, characteristic
3#8057C211yesmaximal, characteristic
4#8015C211yesmaximal, characteristic
5#8015C211yesmaximal, characteristic
6C2×#1289C211yesmaximal, characteristic
7#7913C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12C2×#381C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×#380C2211yescharacteristic
15#1305—22no—
16#1305C414yescomplemented
17#1298—22no—
18#1294—21no—
19#1294—21no—
20#1294—21no—
21#1294—21no—
22#1289—22no—
23#1280—22no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C22×M16—21no—
27C22×M16—21no—
28C23×C8—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C22⋊C4—21no—
32C22×C22⋊C4—21no—
33C22×C22⋊C4—21no—
34#407—21no—
35#407—21no—
36#407—21no—
37#407—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407C2×C412yes—
44#407C2×C412yes—
45#407D412yes—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
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⋊C8D412yes—
58#381—21no—
59#381—21no—
60#381—21no—
61#381—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65#380—21no—
66#380—21no—
67#380—21no—
68#380C2×C412yes—
69#380Q812yes—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75C25#4111yescharacteristic
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—41no—
79C23×C4—41no—
80C23×C4—82no—
81C23×C4C22×C411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×Q811yescharacteristic
86C23×C4#4111yescharacteristic
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—22no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—82no—
102C2×M16—82no—
103C2×M16—82no—
104C22×C8—22no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—82no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—82no—
116C2×C4⋊C4—82no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—41no—
121C2×C22⋊C4—41no—
122C2×C22⋊C4—41no—
123C2×C22⋊C4—81no—
124C2×C22⋊C4—81no—
125C2×C22⋊C4—81no—
126C2×C22⋊C4—81no—
127C2×C22⋊C4—82no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—22no—
134C22⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144#95—22no—
145#95—22no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154C24—21no—
155C24—21no—
156C24—21no—
157C24—21no—
158C24—42no—
159C24—81no—
160C24#11711yescharacteristic
161C24#12111yescharacteristic
162C24C22⋊Q811yescharacteristic
163C24#12611yescharacteristic
164C24#12611yescharacteristic
165C24#12611yescharacteristic
166C24#12611yescharacteristic
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—82no—
190C22×C4—82no—
191C22×C4—82no—
192C22×C4—82no—
193C22×C4—82no—
194C22×C4—82no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4#11711yescharacteristic
200C22×C4#11711yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4C4×D411yescharacteristic
203C22×C4C4×D411yescharacteristic
204C22×C4C4×Q811yescharacteristic
205C22×C4#12111yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4C22⋊Q811yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4#12311yescharacteristic
210C22×C4#12311yescharacteristic
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×C4#12611yescharacteristic
225C22×C4#12611yescharacteristic
226C22×C4#12611yescharacteristic
227M16—82no—
228M16—82no—
229M16—82no—
230M16—82no—
231M16—82no—
232M16—82no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—82no—
238C2×C8—82no—
239C2×C8—82no—
240C2×C8—82no—
241C2×C8—82no—
242C2×C8—82no—
243C4⋊C4—82no—
244C4⋊C4—82no—
245C4⋊C4—82no—
246C4⋊C4—82no—
247C22⋊C4—82no—
248C22⋊C4—82no—
249C22⋊C4—81no—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C22⋊C4—81no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—82no—
282C23—82no—
283C23—82no—
284C23—82no—
285C23#38311yescharacteristic
286C23#38711yescharacteristic
287C23#38811yescharacteristic
288C23#39611yescharacteristic
289C23#39711yescharacteristic
290C23#40011yescharacteristic
291C23#40111yescharacteristic
292C23#47111yescharacteristic
293C23#47111yescharacteristic
294C23#47211yescharacteristic
295C23#47311yescharacteristic
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
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—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—164no—
337C2×C4—164no—
338C2×C4—161no—
339C2×C4—161no—
340C2×C4—161no—
341C2×C4—161no—
342C2×C4#38711yescharacteristic
343C2×C4#38711yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#38811yescharacteristic
346C2×C4#39711yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#40011yescharacteristic
349C2×C4#40011yescharacteristic
350C8—82no—
351C8—82no—
352C8—82no—
353C8—82no—
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—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22#144311yescharacteristic
388C22#193011yescharacteristic
389C22#193111yescharacteristic
390C22#206311yescharacteristic
391C22#206411yescharacteristic
392C22#207811yescharacteristic
393C22#207911yescharacteristic
394C22#210412yes—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—161no—
404C4—161no—
405C4—162no—
406C4—162no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—22no—
412C2—21no—
413C2—21no—
414C2—41no—
415C2—41no—
416C2—41no—
417C2#1130211yescharacteristic
418C2#1130311yescharacteristic
419C2#1131811yescharacteristic
subgroupG/H
center, socleC22#1443
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
16. #1305C4semidirect

Maximal subgroups

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

subgroupindex
#81072
#80572
#80152
C2×#12892
#79132