Finite Group Databasebeta

← #119183

Subgroups — #119183

Order 512.

506 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17718C211yesmaximal, characteristic
2#17715C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#8081C211yesmaximal, characteristic
5#8065C211yesmaximal, characteristic
6#7965C211yesmaximal, characteristic
7#7851C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×#423C2211yescharacteristic
15#1554—22no—
16#1552C414yes—
17#1549—21no—
18#1548—21no—
19#1546—21no—
20#1546—21no—
21#1544—22no—
22#1542—22no—
23#1493—22no—
24#1487—22no—
25#1481—22no—
26#1301—22no—
27#1299—22no—
28#1287—22no—
29#1273—22no—
30C22×M16—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533C2×C412yes—
38#533D412yes—
39C2×C4⋊Q8D411yescharacteristic
40C2×C4⋊Q8D411yescharacteristic
41C2×#125—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×#117—21no—
47C22×C42C2311yescharacteristic
48#432—21no—
49#432—21no—
50#432C2×C412yes—
51#432D412yes—
52#431—21no—
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#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423D412yes—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8C2×C412yes—
78C2×C4⋊C8D412yes—
79#407—21no—
80#407—21no—
81C2×C22⋊C8—21no—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C4×M16—21no—
85C4×M16—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8D412yes—
89#333—24no—
90#332—24no—
91#332—24no—
92#332—24no—
93Q8⋊C8—28no—
94C22×Q8—21no—
95C22×Q8—21no—
96C23×C4#4111yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—22no—
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—82no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8C22⋊C412yes—
115C4⋊Q8C22⋊C412yes—
116#125—22no—
117#125—22no—
118#125—41no—
119#125—41no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C22⋊Q8—22no—
124C22⋊Q8—41no—
125C22⋊Q8—41no—
126C22⋊Q8—41no—
127C22⋊Q8—41no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—41no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136#117—22no—
137#117—22no—
138#117—41no—
139#117—41no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C22⋊C4—41no—
147C2×C42—41no—
148C2×C42C22×C411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
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⋊C8—41no—
183C22⋊C8—41no—
184#97—22no—
185#97—22no—
186C4×C8—22no—
187C4×C8—22no—
188C4×C8—41no—
189C4×C8—41no—
190C4×C8—41no—
191C4×C8—41no—
192C4×C8—41no—
193C4×C8—41no—
194C24#12611yescharacteristic
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—82no—
200C2×Q8—82no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4#11711yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12311yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12411yescharacteristic
222C22×C4#12411yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4#12611yescharacteristic
225M16—82no—
226M16—82no—
227M16—82no—
228M16—82no—
229C2×C8—44no—
230C2×C8—44no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—82no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C42—42no—
255C42—42no—
256C42C2×C22⋊C411yescharacteristic
257C42#11711yescharacteristic
258C42C4×D411yescharacteristic
259C42C4×D411yescharacteristic
260C42#12011yescharacteristic
261C42#12011yescharacteristic
262C42#12111yescharacteristic
263C42#12111yescharacteristic
264C42#12111yescharacteristic
265C42#12111yescharacteristic
266C42#12111yescharacteristic
267C42#12311yescharacteristic
268C42#12311yescharacteristic
269C42#12311yescharacteristic
270C42#12411yescharacteristic
271C42#12611yescharacteristic
272C23—22no—
273C23—41no—
274C23—41no—
275C23#38811yescharacteristic
276C23#39711yescharacteristic
277C23#39711yescharacteristic
278Q8—44no—
279Q8—82no—
280Q8—82no—
281Q8—82no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4#38111yescharacteristic
306C2×C4#38611yescharacteristic
307C2×C4#38611yescharacteristic
308C2×C4#38811yescharacteristic
309C2×C4#38811yescharacteristic
310C2×C4#38811yescharacteristic
311C2×C4#39411yescharacteristic
312C2×C4#39411yescharacteristic
313C2×C4#39411yescharacteristic
314C2×C4#39411yescharacteristic
315C2×C4#39711yescharacteristic
316C2×C4#39711yescharacteristic
317C2×C4#47112yes—
318C2×C4#47312yes—
319C8—82no—
320C8—82no—
321C8—82no—
322C8—82no—
323C8—82no—
324C8—82no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—82no—
334C22#144011yescharacteristic
335C22#193012yes—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—82no—
346C4#188112yes—
347C4#204611yescharacteristic
348C4#204711yescharacteristic
349C4#205212yes—
350C4#208012yes—
351C2—22no—
352C2—41no—
353C2—41no—
354C2#1116411yescharacteristic
355C2#1117711yescharacteristic
356C2#1119411yescharacteristic
subgroupG/H
centerC2×C4#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1440
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#177182
#177152
#174862
#80812
#80652
#79652
#78512