Finite Group Databasebeta

← #24919942

Subgroups — #24919942

Order 10624.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128397C211yesmaximal, characteristic
2#19128107C211yesmaximal, characteristic, complemented
3#19128039C211yesmaximal, characteristic, complemented
4#19128034C211yesmaximal, characteristic, complemented
5#19128019C211yesmaximal, characteristic, complemented
6#19128014C211yesmaximal, characteristic, complemented
7#19128008C211yesmaximal, characteristic, complemented
8#19127978C211yesmaximal, characteristic, complemented
9#19127949C211yesmaximal, characteristic, complemented
10#19127932C211yesmaximal, characteristic, complemented
11#19127799C211yesmaximal, characteristic, complemented
12#19127773C211yesmaximal, characteristic, complemented
13#19127741C211yesmaximal, characteristic, complemented
14C2×#14581725C211yesmaximal, characteristic, complemented
15#554×C83C211yesmaximal, characteristic, complemented
16C2×#13050577C2211yescharacteristic
17C2×#13050574C2211yescharacteristic
18C22×C83⋊C8C2211yescharacteristic
19#14581787—21no—
20#14581784C2211yescharacteristic
21#14581774—21no—
22#14581766C2211yescharacteristic
23#14581766C2211yescharacteristic
24#14581764—21no—
25C4×D332C2211yescharacteristic
26(C22⋊D83)⋊C4—21no—
27#14581751C2211yescharacteristic
28C2×C4⋊Dic83C2211yescharacteristic
29#14581725C2211yescharacteristic
30#14581725C2211yescharacteristic
31#14581725C2211yescharacteristic
32#14581725C2211yescharacteristic
33#14581725C2211yescharacteristic
34#14581725C2211yescharacteristic
35#14581723C2211yescharacteristic
36#14581723C2211yescharacteristic
37#14581723C2211yescharacteristic
38C4⋊(C83⋊C8)C2211yescharacteristic
39#14581716C2211yescharacteristic
40#14581716C2211yescharacteristic
41#14581716C2211yescharacteristic
42#14581712C2211yescharacteristic
43#14581712C2211yescharacteristic
44#14581712C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47#14581703C2211yescharacteristic
48C4⋊Q8×C83C2211yescharacteristic
49#125×C83—21no—
50C22⋊Q8×C83—21no—
51C22⋊Q8×C83—21no—
52C22⋊Q8×C83C2211yescharacteristic
53C22⋊Q8×C83C2211yescharacteristic
54C4×Q8×C83C2211yescharacteristic
55C4×D4×C83—21no—
56C4×D4×C83C2211yescharacteristic
57C2×C4⋊C4×C83C2211yescharacteristic
58C2×C4⋊C4×C83C2211yescharacteristic
59C2×D332C2311yescharacteristic
60C2×C22⋊D83—21no—
61C2×C22⋊D83—21no—
62C22×Dic83—21no—
63C2×C4×D83—21no—
64#13050577—22no—
65#13050574—22no—
66C2×C83⋊C8—22no—
67C2×C83⋊C8C2311yescharacteristic
68C2×C83⋊C8C2311yescharacteristic
69C2×C83⋊C8C2311yescharacteristic
70C2×C83⋊C8C2311yescharacteristic
71C4⋊Dic83—21no—
72C4⋊Dic83C2311yescharacteristic
73C4⋊Dic83C2311yescharacteristic
74C4⋊Dic83C2311yescharacteristic
75Dic83⋊C4—21no—
76Dic83⋊C4—21no—
77C22⋊Dic83—21no—
78(C2×D83)⋊C4—21no—
79(C2×D83)⋊C4—21no—
80(C2×D83)⋊C4—21no—
81C4×Dic83—21no—
82C2×Q8×C83—21no—
83C2×Q8×C83C2311yescharacteristic
84C2×D4×C83D411yescharacteristic
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83—21no—
93C4⋊C4×C83—21no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83D411yescharacteristic
96C4⋊C4×C83C2311yescharacteristic
97C4⋊C4×C83C2311yescharacteristic
98C4⋊C4×C83C2311yescharacteristic
99C22⋊C4×C83—21no—
100C22⋊C4×C83—21no—
101C22⋊C4×C83D411yescharacteristic
102C22⋊C4×C83D411yescharacteristic
103C42×C83—21no—
104C42×C83C2311yescharacteristic
105C23×C83C2×D411yescharacteristic
106C23×C83C2×D411yescharacteristic
107C22×D83—21no—
108Q8×C83—21no—
109Q8×C83—21no—
110Q8×C83—81no—
111D4×C83—22no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—81no—
121C2×C4×C83—81no—
122C2×C4×C83C2×D411yescharacteristic
123C2×C4×C83C2×D411yescharacteristic
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2×D411yescharacteristic
126C2×C4×C83C2411yescharacteristic
127C22⋊D83—42no—
128C22⋊D83—81no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—81no—
133D332—21no—
134D332—21no—
135C4×D83—81no—
136C83⋊C8—21no—
137C83⋊C8—21no—
138C83⋊C8—21no—
139C83⋊C8#4112yes—
140C22×C83—21no—
141C22×C83—21no—
142C22×C83—21no—
143C22×C83—21no—
144C22×C83—21no—
145C22×C83#13712yes—
146C22×C83C22×D411yescharacteristic
147C2×D83—41no—
148C2×D83—41no—
149C2×D83—41no—
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—41no—
155C4×C83—41no—
156C4×C83—41no—
157C4×C83—41no—
158C4×C83C2×#4111yescharacteristic
159C4×C832−1+411yescharacteristic
160Dic83—41no—
161Dic83—41no—
162Dic83—41no—
163C2×C83—22no—
164C2×C83—41no—
165C2×C83#54711yescharacteristic
166C2×C83C2×#13711yescharacteristic
167C2×C83#57611yescharacteristic
168D83—81no—
169#3346—831nomaximal, Sylow
170C83#334611yescharacteristic, complemented, Sylow
171#554D8311yescharacteristic, complemented
172#553—831no—
173#501—831no—
174#485—831no—
175#484—831no—
176#481—831no—
177#480—831no—
178#479—831no—
179#474—831no—
180#468—831no—
181#465—831no—
182#440—831no—
183#435—831no—
184#428—831no—
185C2×#107—831no—
186C2×SD16—831no—
187C2×M16—831no—
188C22×C8—831no—
189C4⋊Q8C2×D8311yescharacteristic
190#126—1661no—
191#125—21no—
192#125—831no—
193#123—1661no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D8311yescharacteristic
197C22⋊Q8C2×D8311yescharacteristic
198#121—831no—
199#121—831no—
200#121—1661no—
201C4×Q8C2×D8311yescharacteristic
202C4×D4—21no—
203C4×D4—831no—
204C4×D4—1661no—
205C4×D4C2×D8311yescharacteristic
206#117—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4C2×D8311yescharacteristic
209C2×C4⋊C4C2×D8311yescharacteristic
210#107—831no—
211#107—831no—
212#107—831no—
213#107—831no—
214#107—831no—
215#107—831no—
216#106—831no—
217#106—831no—
218#106—831no—
219C4⋊C8—831no—
220#103—831no—
221#103—831no—
222#103—831no—
223#102—831no—
224#102—831no—
225#102—831no—
226C22⋊C8—831no—
227C22⋊C8—831no—
228#97—831no—
229C2×Q8—21no—
230C2×Q8C22×D8311yescharacteristic
231C2×D4—831no—
232C2×D4—1661no—
233C2×D4—1661no—
234C2×D4C22⋊D8311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—1661no—
238C22×C4—1661no—
239C22×C4C22×D8311yescharacteristic
240C22×C4C22×D8311yescharacteristic
241SD16—1662no—
242M16—1662no—
243C2×C8—831no—
244C2×C8—831no—
245C2×C8—831no—
246C2×C8—831no—
247C2×C8—1662no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—831no—
255C4⋊C4—831no—
256C4⋊C4—831no—
257C4⋊C4—1661no—
258C4⋊C4—1661no—
259C4⋊C4—1661no—
260C4⋊C4C22⋊D8311yescharacteristic
261C4⋊C4C22×D8311yescharacteristic
262C4⋊C4C22×D8311yescharacteristic
263C4⋊C4C22×D8311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—1661no—
267C22⋊C4—1661no—
268C22⋊C4—1661no—
269C22⋊C4—1661no—
270C22⋊C4C22⋊D8311yescharacteristic
271C22⋊C4C22⋊D8311yescharacteristic
272C42—21no—
273C42—1661no—
274C42C22×D8311yescharacteristic
275C23—1661no—
276C23C2×C22⋊D8311yescharacteristic
277C23C2×C22⋊D8311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—3322no—
283D4—6641no—
284D4—1661no—
285D4—1661no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—6641no—
297C2×C4—6641no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4C2×C22⋊D8311yescharacteristic
302C2×C4C2×C22⋊D8311yescharacteristic
303C2×C4C2×C22⋊D8311yescharacteristic
304C2×C4C2×C22⋊D8311yescharacteristic
305C2×C4C23×D8311yescharacteristic
306C8—832no—
307C8—1661no—
308C8—1661no—
309C8—1661no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—3321no—
316C22—3321no—
317C22—3321no—
318C22#1458182312yes—
319C22C22×C22⋊D8311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—3321no—
329C4—3321no—
330C4—3321no—
331C4#41×D8311yescharacteristic
332C4#1458183911yescharacteristic
333C2—22no—
334C2—41no—
335C2—6641no—
336C2#1912835011yescharacteristic
337C2C2×#1458182311yescharacteristic
338C2#1912850411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#554×C83C2
socleC22×C83C22×D4
prime radical#19128397C2
hypercenter#554D83
hypocenterC83#3346
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19128107C2semidirect
3. #19128039C2semidirect
4. #19128034C2semidirect
5. #19128019C2semidirect
6. #19128014C2semidirect
7. #19128008C2semidirect
8. #19127978C2semidirect
9. #19127949C2semidirect
10. #19127932C2semidirect
11. #19127799C2semidirect
12. #19127773C2semidirect
13. #19127741C2semidirect
14. C2×#14581725C2semidirect
15. #554×C83C2semidirect
170. C83#3346semidirect
171. #554D83semidirect

Maximal subgroups

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

subgroupindex
#191283972
#191281072
#191280392
#191280342
#191280192
#191280142
#191280082
#191279782
#191279492
#191279322
#191277992
#191277732
#191277412
C2×#145817252
#554×C832
#334683