Finite Group Databasebeta

← #118448

Subgroups — #118448

Order 512.

621 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21370C211yesmaximal, characteristic
2#17449C211yesmaximal, characteristic
3C2×#1491C211yesmaximal, characteristic
4C2×#1461C211yesmaximal, characteristic
5#8090C211yesmaximal, characteristic
6#8060C211yesmaximal, characteristic
7#7966C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15#1950—22no—
16#1855—22no—
17C4×#108—22no—
18#1491—22no—
19#1491—22no—
20#1491—22no—
21#1487—22no—
22#1479—22no—
23C2×Q8⋊C8—22no—
24#1461—22no—
25#1461C414yes—
26C2×#324—22no—
27#1302—22no—
28#1299—22no—
29#1287—22no—
30C23×Q8Q811yescharacteristic
31C22×M16—21no—
32C2×C4×Q8—21no—
33C2×C4×Q8—21no—
34C2×C4×Q8—21no—
35C2×C4×Q8—21no—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8—21no—
42C2×C4×Q8C2×C412yes—
43C2×C4×Q8D412yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4Q811yescharacteristic
46C22×C42—21no—
47C22×C42C2311yescharacteristic
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432D412yes—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431C2×C412yes—
66#431C2×C412yes—
67#431D412yes—
68C2×#108—24no—
69#423—21no—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74#407—21no—
75#407—21no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8D412yes—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16D412yes—
84C4×M16D412yes—
85C2×#97—21no—
86C2×#97—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90#341—24no—
91Q8⋊C8—28no—
92Q8⋊C8—28no—
93#324—28no—
94C22×Q8—24no—
95C22×Q8—21no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—42no—
101C22×Q8C4⋊C412yes—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4C2×D411yescharacteristic
105C23×C4C2×Q811yescharacteristic
106C23×C4#4111yescharacteristic
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—22no—
110C2×M16—44no—
111C2×M16—41no—
112C22×C8—22no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C4×Q8—22no—
117C4×Q8—22no—
118C4×Q8—22no—
119C4×Q8—22no—
120C4×Q8—22no—
121C4×Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124C4×Q8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4C4⋊C412yes—
144C2×C42—22no—
145C2×C42—22no—
146C2×C42—41no—
147C2×C42—41no—
148C2×C42—41no—
149C2×C42—41no—
150C2×C42C22×C411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162#108—48no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8C22⋊C414yes—
183#97—22no—
184#97—22no—
185#97—22no—
186#97—41no—
187#97—41no—
188#97—41no—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—22no—
194C4×C8—41no—
195C4×C8—41no—
196C4×C8—41no—
197C24C22⋊Q811yescharacteristic
198C2×Q8—24no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C2×Q8—44no—
206C2×Q8—44no—
207C2×Q8—44no—
208C2×Q8—42no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#10814yescomplemented
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—82no—
225C22×C4C2×C22⋊C411yescharacteristic
226C22×C4C2×C4⋊C411yescharacteristic
227C22×C4#11711yescharacteristic
228C22×C4#12011yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12411yescharacteristic
240C22×C4#12411yescharacteristic
241C22×C4#12411yescharacteristic
242C22×C4#12711yescharacteristic
243M16—24no—
244M16—42no—
245M16—44no—
246M16—44no—
247M16—82no—
248C2×C8—24no—
249C2×C8—44no—
250C2×C8—44no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—82no—
257C2×C8—82no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C42—42no—
267C42—42no—
268C42—42no—
269C42—42no—
270C42C4×D411yescharacteristic
271C42C4×D411yescharacteristic
272C42C4×D411yescharacteristic
273C42C4×D411yescharacteristic
274C42#12011yescharacteristic
275C42#12011yescharacteristic
276C42#12111yescharacteristic
277C42#12111yescharacteristic
278C42#12111yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42#12311yescharacteristic
283C42#12311yescharacteristic
284C42#12611yescharacteristic
285C42#12611yescharacteristic
286C23—21no—
287C23—21no—
288C23—22no—
289C23—41no—
290C23#38011yescharacteristic
291C23#39311yescharacteristic
292C23#39911yescharacteristic
293Q8—24no—
294Q8—24no—
295Q8—44no—
296Q8—44no—
297Q8—42no—
298Q8—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4#38511yescharacteristic
327C2×C4#38511yescharacteristic
328C2×C4#38611yescharacteristic
329C2×C4#38811yescharacteristic
330C2×C4#38811yescharacteristic
331C2×C4#39011yescharacteristic
332C2×C4#39211yescharacteristic
333C2×C4#39411yescharacteristic
334C2×C4#39411yescharacteristic
335C2×C4#39611yescharacteristic
336C2×C4#39611yescharacteristic
337C2×C4#39711yescharacteristic
338C2×C4C2×#10812yes—
339C2×C4#43012yes—
340C8—44no—
341C8—44no—
342C8—82no—
343C8—82no—
344C8—82no—
345C8—82no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22#143911yescharacteristic
356C22#181011yescharacteristic
357C22#181111yescharacteristic
358C22#203112yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—82no—
370C4#185512yes—
371C4#185512yes—
372C4#204912yes—
373C2—21no—
374C2—21no—
375C2—22no—
376C2—41no—
377C2#1109111yescharacteristic
378C2#1109711yescharacteristic
379C2#1114311yescharacteristic
subgroupG/H
centerC2×C4#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
211. C2×Q8#108semidirect

Maximal subgroups

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

subgroupindex
#213702
#174492
C2×#14912
C2×#14612
#80902
#80602
#79662