Finite Group Databasebeta

← #119189

Subgroups — #119189

Order 512.

524 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17751C211yesmaximal, characteristic
2#17749C211yesmaximal, characteristic
3C2×#1481C211yesmaximal, characteristic
4#8082C211yesmaximal, characteristic
5#8065C211yesmaximal, characteristic
6C2×#1292C211yesmaximal, characteristic
7#7934C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15#1561—22no—
16#1559—22no—
17#1552C414yes—
18#1550—22no—
19#1549—21no—
20#1548—21no—
21#1546—21no—
22#1546—21no—
23#1481—22no—
24#1481—22no—
25C2×Q8⋊C8—22no—
26#1301—22no—
27#1299—22no—
28#1292—22no—
29#1283—22no—
30C22×M16—21no—
31C22×M16—21no—
32C23×C8—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533C2×C412yes—
40#533D412yes—
41C2×C4⋊Q8D411yescharacteristic
42C2×C4⋊Q8D411yescharacteristic
43C2×#125—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×#117—21no—
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432C2×C412yes—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431D412yes—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423D412yes—
71#423D412yes—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8C2×C412yes—
82C2×C4⋊C8D412yes—
83#407—21no—
84#407—21no—
85C2×C22⋊C8—21no—
86C4×M16—21no—
87C4×M16—21no—
88C2×C4×C8—21no—
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—22no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—81no—
106C2×M16—81no—
107C2×M16—81no—
108C2×M16—81no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—82no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8C22⋊C412yes—
123C4⋊Q8C22⋊C412yes—
124#125—22no—
125#125—22no—
126#125—41no—
127#125—41no—
128C22⋊Q8—22no—
129C22⋊Q8—22no—
130C22⋊Q8—22no—
131C22⋊Q8—22no—
132C22⋊Q8—41no—
133C22⋊Q8—41no—
134C22⋊Q8—41no—
135C22⋊Q8—41no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144#117—22no—
145#117—22no—
146#117—41no—
147#117—41no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C42—41no—
156C2×C42C22×C411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192#97—22no—
193#97—41no—
194C4×C8—22no—
195C4×C8—41no—
196C4×C8—41no—
197C4×C8—41no—
198C24#12611yescharacteristic
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—82no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—81no—
217C22×C4#11711yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12311yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12411yescharacteristic
232C22×C4#12411yescharacteristic
233C22×C4#12611yescharacteristic
234C22×C4#12611yescharacteristic
235M16—42no—
236M16—42no—
237M16—82no—
238M16—82no—
239M16—81no—
240M16—81no—
241M16—81no—
242M16—81no—
243M16—82no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—82no—
251C2×C8—82no—
252C2×C8—82no—
253C2×C8—82no—
254C2×C8—82no—
255C2×C8—82no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42—42no—
271C42—42no—
272C42C2×C22⋊C411yescharacteristic
273C42#11711yescharacteristic
274C42C4×D411yescharacteristic
275C42C4×D411yescharacteristic
276C42#12011yescharacteristic
277C42#12011yescharacteristic
278C42#12111yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42#12111yescharacteristic
283C42#12311yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C42#12411yescharacteristic
287C42#12611yescharacteristic
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23#38811yescharacteristic
293C23#39711yescharacteristic
294C23#39711yescharacteristic
295Q8—42no—
296Q8—42no—
297Q8—82no—
298Q8—82no—
299Q8—81no—
300Q8—81no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4#38111yescharacteristic
330C2×C4#38611yescharacteristic
331C2×C4#38611yescharacteristic
332C2×C4#38811yescharacteristic
333C2×C4#38811yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#39411yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39711yescharacteristic
340C2×C4#39711yescharacteristic
341C2×C4#47111yescharacteristic
342C2×C4#47111yescharacteristic
343C2×C4#47112yes—
344C2×C4#47211yescharacteristic
345C2×C4#47311yescharacteristic
346C2×C4#47312yes—
347C8—82no—
348C8—82no—
349C8—82no—
350C8—82no—
351C8—82no—
352C8—82no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22#144011yescharacteristic
363C22#193012yes—
364C22#207811yescharacteristic
365C22#207911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—82no—
375C4—82no—
376C4#190711yescharacteristic
377C4#190811yescharacteristic
378C4#204611yescharacteristic
379C4#204711yescharacteristic
380C4#205111yescharacteristic
381C4#205212yes—
382C4#205211yescharacteristic
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2#1116411yescharacteristic
388C2#1117911yescharacteristic
389C2#1119211yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#177512
#177492
C2×#14812
#80822
#80652
C2×#12922
#79342