Finite Group Databasebeta

← #105913

Subgroups — #105913

Order 512.

830 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34059C211yesmaximal, characteristic
2#20741C211yesmaximal, characteristic
3#17449C211yesmaximal, characteristic
4#8071C211yesmaximal, characteristic
5#8052C211yesmaximal, characteristic
6#7949C211yesmaximal, characteristic
7#7940C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12#2320—22no—
13#2320—22no—
14#2316—21no—
15#2313—22no—
16#2310—21no—
17#2295—22no—
18#2295C414yescomplemented
19#2283—22no—
20#2283C2211yescharacteristic
21C4×#117C2211yescharacteristic
22C4×#117C2211yescharacteristic
23#1824—21no—
24#1805C414yescomplemented
25#1787—21no—
26#1763—22no—
27#1491C414yescomplemented
28#1487—22no—
29#1479—22no—
30#1300—22no—
31#1297—22no—
32#1285—22no—
33#1284—22no—
34C23×Q8D411yescharacteristic
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×Q8C2×C412yes—
42C2×C4×Q8C2×C412yes—
43C2×C4×Q8C2×C412yes—
44C2×C4×Q8D412yes—
45C2×C4×Q8D412yes—
46C2×C4×Q8Q812yes—
47C2×#117—21no—
48C2×#117—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4D411yescharacteristic
51C22×C42—21no—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432C2×C412yes—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#423—21no—
66#423—21no—
67C2×C4⋊C8C2×C412yes—
68C2×#103—24no—
69#407—21no—
70#407—21no—
71C2×C22⋊C8—21no—
72C4×M16—21no—
73C4×M16C2×C412yes—
74C2×#97—21no—
75#391—24no—
76#391—24no—
77#389—24no—
78#389—24no—
79#387—28no—
80#387—28no—
81#383—24no—
82#383—21no—
83#382—24no—
84#382C2×C412yes—
85#381—24no—
86#381—21no—
87#380—24no—
88#380—21no—
89C4×C4⋊C4—24no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C4⋊C4C2×C412yes—
94C4×C4⋊C4D412yes—
95C4×C22⋊C4—21no—
96C4×C22⋊C4—21no—
97C4×C22⋊C4—21no—
98C4×C22⋊C4D412yes—
99C4×C22⋊C4D412yes—
100#376—24no—
101#376—21no—
102#376—21no—
103#376D412yes—
104C43—21no—
105C43C2×C412yes—
106#340—24no—
107Q8⋊C8—28no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—44no—
112C22×Q8C22⋊C412yes—
113C22×Q8C22⋊C412yes—
114C22×Q8C4⋊C412yes—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C2×M16—22no—
121C2×M16—41no—
122C22×C8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8C4214yes—
136C4×Q8C22⋊C414yes—
137C4×Q8C4⋊C414yes—
138C4×Q8C4⋊C414yes—
139#117—44no—
140#117—44no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—28no—
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C22⋊C412yes—
156C2×C4⋊C4C4⋊C412yes—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—41no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—41no—
172C2×C42C22⋊C414yes—
173C2×C42C22×C411yescharacteristic
174C2×C42C22×C411yescharacteristic
175C2×C42C22×C411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×D411yescharacteristic
179C2×C42C2×D411yescharacteristic
180C2×C42C2×Q811yescharacteristic
181C2×C42#4111yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C2×C42#4111yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191#103—48no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#97—22no—
199#97—22no—
200#97—41no—
201#97—41no—
202C4×C8—22no—
203C4×C8—41no—
204#95—28no—
205#95—28no—
206#95—28no—
207#95—22no—
208#95—22no—
209#95—22no—
210#95—22no—
211#95—22no—
212#95—41no—
213#95—41no—
214#95C22⋊C414yes—
215C24#12011yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—24no—
220C2×Q8—24no—
221C2×Q8—44no—
222C2×Q8—44no—
223C2×Q8—44no—
224C2×Q8—44no—
225C2×Q8—44no—
226C2×Q8#9514yes—
227C22×C4—24no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—81no—
240C22×C4—82no—
241C22×C4C2×C22⋊C411yescharacteristic
242C22×C4C2×C22⋊C411yescharacteristic
243C22×C4C2×C22⋊C411yescharacteristic
244C22×C4C2×C22⋊C411yescharacteristic
245C22×C4C2×C4⋊C411yescharacteristic
246C22×C4C4×D411yescharacteristic
247C22×C4C4×D411yescharacteristic
248C22×C4C4×D411yescharacteristic
249C22×C4C4×D411yescharacteristic
250C22×C4#12011yescharacteristic
251C22×C4#12011yescharacteristic
252C22×C4#12011yescharacteristic
253C22×C4#12111yescharacteristic
254C22×C4#12111yescharacteristic
255C22×C4C22⋊Q811yescharacteristic
256C22×C4C22⋊Q811yescharacteristic
257C22×C4#12311yescharacteristic
258C22×C4#12311yescharacteristic
259M16—82no—
260M16—82no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—44no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—22no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—44no—
273C4⋊C4—44no—
274C4⋊C4—44no—
275C4⋊C4—88no—
276C4⋊C4#9514yes—
277C22⋊C4—44no—
278C22⋊C4—44no—
279C22⋊C4—82no—
280C42—24no—
281C42—24no—
282C42—24no—
283C42—24no—
284C42—44no—
285C42—44no—
286C42—44no—
287C42—44no—
288C42—82no—
289C42—82no—
290C42—82no—
291C42C2×C4211yescharacteristic
292C42C2×C22⋊C411yescharacteristic
293C42C2×C4⋊C411yescharacteristic
294C42C2×C4⋊C411yescharacteristic
295C42#11711yescharacteristic
296C42#11711yescharacteristic
297C42C4×D411yescharacteristic
298C42C4×D411yescharacteristic
299C42C4×D411yescharacteristic
300C42C4×D411yescharacteristic
301C42#12111yescharacteristic
302C42#12111yescharacteristic
303C42C22⋊Q811yescharacteristic
304C42C22⋊Q811yescharacteristic
305C42#12311yescharacteristic
306C42#12311yescharacteristic
307C23—22no—
308C23—22no—
309C23—41no—
310C23#37911yescharacteristic
311C23#38511yescharacteristic
312C23#38611yescharacteristic
313Q8—24no—
314Q8—24no—
315Q8—44no—
316Q8—44no—
317Q8—44no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4C2×#9511yescharacteristic
353C2×C4C4×C22⋊C411yescharacteristic
354C2×C4C4×C22⋊C411yescharacteristic
355C2×C4#38011yescharacteristic
356C2×C4#38011yescharacteristic
357C2×C4#38111yescharacteristic
358C2×C4#38511yescharacteristic
359C2×C4#38511yescharacteristic
360C2×C4#38511yescharacteristic
361C2×C4#38611yescharacteristic
362C2×C4#38611yescharacteristic
363C2×C4#38611yescharacteristic
364C2×C4#42114yes—
365C8—82no—
366C8—82no—
367C8—82no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—44no—
376C22C22⋊#9511yescharacteristic
377C22#179612yes—
378C22#189712yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—44no—
390C4—44no—
391C4—84no—
392C4—84no—
393C4—162no—
394C4#173312yes—
395C4#189712yes—
396C2—22no—
397C2—22no—
398C2—41no—
399C2#1072011yescharacteristic
400C2#1077711yescharacteristic
401C2#1079211yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ 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
18. #2295C4semidirect
24. #1805C4semidirect
27. #1491C4semidirect

Maximal subgroups

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

subgroupindex
#340592
#207412
#174492
#80712
#80522
#79492
#79402