Finite Group Databasebeta

← #118134

Subgroups — #118134

Order 512.

629 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20735C211yesmaximal, characteristic
2#20727C211yesmaximal, characteristic
3#17806C211yesmaximal, characteristic
4C2×#1487C211yesmaximal, characteristic
5#8093C211yesmaximal, characteristic
6#8065C211yesmaximal, characteristic
7#7857C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14#2283C2211yescharacteristic
15#1823—21no—
16#1821—21no—
17#1805—22no—
18#1801—22no—
19#1787—21no—
20#1784—21no—
21C4×#103—22no—
22C4×#101—22no—
23#1574—22no—
24#1573—22no—
25#1564—22no—
26#1487—22no—
27#1487C414yescomplemented
28C2×Q8⋊C8—22no—
29#1303—22no—
30#1299—22no—
31#1274—22no—
32C23×Q8D411yescharacteristic
33C22×M16—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×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8C2×C412yes—
45C2×C4×Q8Q812yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4D411yescharacteristic
48C22×C42—21no—
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#431—21no—
55#431—21no—
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#431C2×C412yes—
65#431D412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423C2×C412yes—
71#423D412yes—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8D412yes—
76C2×#103—24no—
77C2×#101—24no—
78#407—21no—
79#407—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C4×M16—21no—
83C4×M16D412yes—
84C2×C4×C8—21no—
85C2×C4×C8D412yes—
86#383—21no—
87#382—21no—
88#381—21no—
89#380—21no—
90C4×C4⋊C4D412yes—
91C4×C22⋊C4—21no—
92#376—21no—
93#343—24no—
94#340—24no—
95#335—24no—
96#334—24no—
97Q8⋊C8—28no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—44no—
104C22×Q8C4⋊C412yes—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4C2×D411yescharacteristic
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—41no—
114C2×M16—82no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—41no—
118C4×Q8—22no—
119C4×Q8—22no—
120C4×Q8—22no—
121C4×Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4C4⋊C412yes—
147C2×C22⋊C4—41no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—41no—
152C2×C42—41no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42C22×C411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179#103—48no—
180#101—48no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189#97—22no—
190#97—41no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—41no—
194C4×C8—41no—
195C4×C8—41no—
196C4×C8C22⋊C414yes—
197#95—22no—
198#95—41no—
199#95—41no—
200#95—41no—
201C24#12311yescharacteristic
202C2×Q8—24no—
203C2×Q8—24no—
204C2×Q8—24no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—44no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—44no—
212C2×Q8—44no—
213C2×Q8—41no—
214C2×Q8—41no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—44no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—82no—
228C22×C4C2×C4⋊C411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12011yescharacteristic
232C22×C4#12011yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4#12311yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12411yescharacteristic
243C22×C4#12411yescharacteristic
244C22×C4#12611yescharacteristic
245C22×C4#12611yescharacteristic
246M16—44no—
247M16—44no—
248M16—82no—
249M16—82no—
250C2×C8—24no—
251C2×C8—44no—
252C2×C8—44no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—82no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—44no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C22⋊C4—82no—
268C42—42no—
269C42—42no—
270C42—42no—
271C42—42no—
272C42—42no—
273C42—42no—
274C42C2×C22⋊C411yescharacteristic
275C42#11711yescharacteristic
276C42C4×D411yescharacteristic
277C42C4×D411yescharacteristic
278C42#12011yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42#12111yescharacteristic
283C42C22⋊Q811yescharacteristic
284C42C22⋊Q811yescharacteristic
285C42C22⋊Q811yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42#12311yescharacteristic
288C42#12411yescharacteristic
289C42#12711yescharacteristic
290C23—22no—
291C23—22no—
292C23—41no—
293C23#38511yescharacteristic
294C23#39411yescharacteristic
295C23#39711yescharacteristic
296Q8—24no—
297Q8—24no—
298Q8—44no—
299Q8—42no—
300Q8—42no—
301Q8—44no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4#38011yescharacteristic
334C2×C4#38511yescharacteristic
335C2×C4#38611yescharacteristic
336C2×C4#38811yescharacteristic
337C2×C4#38811yescharacteristic
338C2×C4#39011yescharacteristic
339C2×C4#39211yescharacteristic
340C2×C4#39311yescharacteristic
341C2×C4#39411yescharacteristic
342C2×C4#39611yescharacteristic
343C2×C4#39611yescharacteristic
344C2×C4#39911yescharacteristic
345C2×C4#47112yes—
346C2×C4#47312yes—
347C8—44no—
348C8—82no—
349C8—82no—
350C8—82no—
351C8—82no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—44no—
360C22#143911yescharacteristic
361C22#205212yes—
362C22#208012yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—44no—
373C4—82no—
374C4—162no—
375C4#197711yescharacteristic
376C4#197911yescharacteristic
377C4#201012yes—
378C4#206412yes—
379C2—22no—
380C2—22no—
381C2—41no—
382C2#1108611yescharacteristic
383C2#1110011yescharacteristic
384C2#1112811yescharacteristic
subgroupG/H
centerC2×C4#390
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#123
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
27. #1487C4semidirect

Maximal subgroups

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

subgroupindex
#207352
#207272
#178062
C2×#14872
#80932
#80652
#78572