Finite Group Databasebeta

← #118946

Subgroups — #118946

Order 512.

536 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21836C211yesmaximal, characteristic
2C2×#1998C211yesmaximal, characteristic
3#17667C211yesmaximal, characteristic
4#8081C211yesmaximal, characteristic
5#8074C211yesmaximal, characteristic
6#7962C211yesmaximal, characteristic
7#7883C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2283C2211yescharacteristic
15#1998—22no—
16#1998C414yescomplemented
17#1991—22no—
18#1989—22no—
19#1824—21no—
20#1823—21no—
21C2×#343—21no—
22C2×#343—21no—
23#1534—22no—
24#1528—22no—
25#1528—22no—
26#1301—22no—
27#1300—22no—
28#1286—22no—
29#1278—22no—
30C22×M16—21no—
31C22×M16—21no—
32C2×#125—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125C2×C412yes—
43C2×#125D412yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4D411yescharacteristic
47C22×C4⋊C4D411yescharacteristic
48C22×C42C2311yescharacteristic
49#432—21no—
50#432—21no—
51#432—21no—
52#432D412yes—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423C2×C412yes—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8D412yes—
70#407—21no—
71#407—21no—
72C2×C22⋊C8—21no—
73C4×M16—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16C2×C412yes—
78C4×M16D412yes—
79C2×#97—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82#383—21no—
83#382D412yes—
84#381—21no—
85#380—21no—
86C4×C4⋊C4—21no—
87C4×C22⋊C4—21no—
88#376—21no—
89#343—24no—
90#343—24no—
91#340—24no—
92#340—24no—
93#330—28no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—24no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—42no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—44no—
108C22×C8—22no—
109C22×C8—41no—
110C22×C8—41no—
111#125—22no—
112#125—22no—
113#125—22no—
114#125—22no—
115#125—22no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—41no—
120#125—41no—
121#125—41no—
122#125—41no—
123#125—41no—
124#125—41no—
125#125—41no—
126#125—41no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4C22⋊C412yes—
151C2×C4⋊C4C22⋊C412yes—
152C2×C22⋊C4—41no—
153C2×C42—41no—
154C2×C42C22×C411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C22⋊C8—22no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182#97—22no—
183#97—22no—
184#97—22no—
185#97—41no—
186C4×C8—22no—
187C4×C8—22no—
188C4×C8—41no—
189C4×C8—41no—
190C4×C8—41no—
191C4×C8—41no—
192#95—22no—
193#95—22no—
194#95—41no—
195#95—41no—
196C24#12311yescharacteristic
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—81no—
208C22×C4—82no—
209C22×C4—82no—
210C22×C4C2×C22⋊C411yescharacteristic
211C22×C4#11711yescharacteristic
212C22×C4#11711yescharacteristic
213C22×C4#12011yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4#12111yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12311yescharacteristic
223C22×C4#12311yescharacteristic
224C22×C4#12411yescharacteristic
225C22×C4#12411yescharacteristic
226C22×C4#12611yescharacteristic
227C22×C4#12611yescharacteristic
228M16—24no—
229M16—44no—
230M16—42no—
231M16—44no—
232M16—44no—
233M16—82no—
234M16—82no—
235C2×C8—44no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—82no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C22⋊C4—82no—
263C42—82no—
264C42C4×D411yescharacteristic
265C42C4×D411yescharacteristic
266C42C4×D411yescharacteristic
267C42C4×D411yescharacteristic
268C42#12011yescharacteristic
269C42#12111yescharacteristic
270C42#12111yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12311yescharacteristic
274C42#12311yescharacteristic
275C42#12311yescharacteristic
276C42#12411yescharacteristic
277C42#12411yescharacteristic
278C42#12611yescharacteristic
279C42#12611yescharacteristic
280C23—22no—
281C23—22no—
282C23—41no—
283C23#38111yescharacteristic
284C23#39411yescharacteristic
285C23#39711yescharacteristic
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4#38611yescharacteristic
317C2×C4#38611yescharacteristic
318C2×C4#38811yescharacteristic
319C2×C4#38811yescharacteristic
320C2×C4#38811yescharacteristic
321C2×C4#38811yescharacteristic
322C2×C4#39411yescharacteristic
323C2×C4#39411yescharacteristic
324C2×C4#39411yescharacteristic
325C2×C4#39711yescharacteristic
326C2×C4#39711yescharacteristic
327C2×C4#39711yescharacteristic
328C2×C4#45412yes—
329C2×C4#45612yes—
330C8—44no—
331C8—82no—
332C8—82no—
333C8—82no—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—44no—
343C22#144011yescharacteristic
344C22#203812yes—
345C22#208012yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—82no—
357C4—82no—
358C4—162no—
359C4#188611yescharacteristic
360C4#188811yescharacteristic
361C4#203812yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2#1115011yescharacteristic
366C2#1115311yescharacteristic
367C2#1116211yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ 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
16. #1998C4semidirect

Maximal subgroups

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

subgroupindex
#218362
C2×#19982
#176672
#80812
#80742
#79622
#78832