Finite Group Databasebeta

← #49131716

Subgroups — #49131716

Order 36224.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583643C211yesmaximal, characteristic, complemented
2C2×#22583641C211yesmaximal, characteristic, complemented
3C2×#22583640C211yesmaximal, characteristic, complemented
4#31827011C211yesmaximal, characteristic
5C2×#22583608C211yesmaximal, characteristic, complemented
6#31826858C212yesmaximal, complemented
7#31826856C212yesmaximal, complemented
8#31826843C212yesmaximal, complemented
9#31826836C212yesmaximal, complemented
10M16×Dic283C211yesmaximal, characteristic, complemented
11C2×#137×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C22×Dic566C2211yescharacteristic
14#22583643—24no—
15#22583641—24no—
16#22583640—24no—
17C2×Dic1132C2212yes—
18C2×#17985382C2212yes—
19C2×#17985382C2212yes—
20C2×#17985381C2212yes—
21C2×#17985380C2212yes—
22C2×#17985379C2212yes—
23C2×#17985376C2211yescharacteristic
24#22583608—22no—
25#22583608C2212yes—
26#22583608C2212yes—
27#22583608C2211yescharacteristic
28#22583606C2211yescharacteristic
29#22583599C2211yescharacteristic
30#22583597C2211yescharacteristic
31#22583582—22no—
32C4×C22⋊D283—22no—
33C2×Dic283⋊C4—22no—
34C2×C4×Dic283C2211yescharacteristic
35#22583520C2212yes—
36C8×Dic283C2212yes—
37C2×#41×C283C2211yescharacteristic
38C22×Q8×C283C2211yescharacteristic
39#137×C283—24no—
40C2×Q16×C283C2212yes—
41C2×SD16×C283C2212yes—
42C2×M16×C283C2211yescharacteristic
43#17985392—22no—
44#17985392—22no—
45C2×Dic566—21no—
46C2×Dic566—22no—
47C2×Dic566—22no—
48C2×Dic566C2311yescharacteristic
49C2×Dic566C2312yes—
50C2×D1132C2311yescharacteristic
51C2×C22⋊D283—22no—
52C2×C22⋊D283—21no—
53C22×Dic283—21no—
54C22×Dic283D412yes—
55C2×C4×D283—21no—
56Dic1132—24no—
57#17985382—24no—
58#17985382—24no—
59#17985381—24no—
60#17985380—24no—
61#17985379—24no—
62#17985376D414yescomplemented
63C2×C283⋊C8C2312yes—
64Dic283⋊C4—24no—
65Dic283⋊C4—24no—
66Dic283⋊C4—22no—
67C22⋊Dic283—22no—
68(C2×D283)⋊C4—22no—
69C4×Dic283D412yes—
70C4×Dic283C2311yescharacteristic
71C4×Dic283C2311yescharacteristic
72#41×C283—22no—
73#41×C283—22no—
74C2×Q8×C283—21no—
75C2×Q8×C283—22no—
76C2×Q8×C283—22no—
77C2×Q8×C283C2311yescharacteristic
78C2×Q8×C283C2312yes—
79C2×D4×C283—21no—
80C2×D4×C283C2311yescharacteristic
81C22×C4×C283—21no—
82C22×C4×C283—21no—
83C22×C4×C283C2311yescharacteristic
84Q16×C283—24no—
85SD16×C283—24no—
86M16×C283D414yescomplemented
87C2×C8×C283C2312yes—
88C22×D283—21no—
89Dic566—22no—
90Dic566—22no—
91Dic566—21no—
92Dic566—21no—
93Dic566—42no—
94D1132—21no—
95D1132—21no—
96C22⋊D283—42no—
97C22⋊D283—44no—
98C2×Dic283—24no—
99C2×Dic283—21no—
100C2×Dic283—22no—
101C2×Dic283—42no—
102C2×Dic283C2×D412yes—
103C2×Dic283C2×D412yes—
104C4×D283—42no—
105C283⋊C8C2×D414yes—
106C23×C283—21no—
107C23×C283C2×D411yescharacteristic
108Q8×C283—22no—
109Q8×C283—21no—
110Q8×C283—22no—
111Q8×C283—21no—
112Q8×C283—42no—
113D4×C283—21no—
114D4×C283—21no—
115D4×C283—42no—
116C2×C4×C283—21no—
117C2×C4×C283—22no—
118C2×C4×C283—42no—
119C2×C4×C283—42no—
120C2×C4×C283C2×D411yescharacteristic
121C2×C4×C283C2×D412yes—
122C2×C4×C283C2×D412yes—
123C2×C4×C283C2411yescharacteristic
124C8×C283C2×D414yes—
125C22×C283—22no—
126C22×C283—41no—
127C22×C283—42no—
128C22×C283#12712yes—
129C22×C283C22×D411yescharacteristic
130C2×D283—41no—
131C2×D283—42no—
132C4×C283—41no—
133C4×C283—42no—
134C4×C283#12712yes—
135C4×C283C22×D411yescharacteristic
136C4×C283C22×D411yescharacteristic
137Dic283—22no—
138Dic283—41no—
139Dic283—42no—
140Dic283#13714yescomplemented
141C2×C283—22no—
142C2×C283—81no—
143C2×C283C2×#12711yescharacteristic
144C2×C283C2×#13712yes—
145D283—81no—
146C283#315211yescharacteristic, complemented, Sylow
147#3152—2831nomaximal, Sylow
148C2×#137—2831no—
149C2×#137—2831no—
150C2×#137—2831no—
151C2×#137D28311yescharacteristic, complemented
152#532—2831no—
153C2×C4⋊Q8—2831no—
154#497—2832no—
155#497—2832no—
156#494—2832no—
157#492—2832no—
158C4×M16—2831no—
159C2×#41—2831no—
160C2×#41C2×D28311yescharacteristic
161C22×Q8—2831no—
162C22×Q8C2×D28311yescharacteristic
163#137—24no—
164#137—5664no—
165#137—5664no—
166#137—5664no—
167C2×Q16—2832no—
168C2×Q16—2832no—
169C2×Q16—2832no—
170C2×Q16C2×D28312yes—
171C2×SD16—2832no—
172C2×SD16—2832no—
173C2×SD16—2832no—
174C2×SD16C2×D28312yes—
175C2×M16—2831no—
176C2×M16C2×D28311yescharacteristic
177C4⋊Q8—2832no—
178C4⋊Q8—2832no—
179C4⋊Q8—2831no—
180C4⋊Q8—5662no—
181#127—2831no—
182#124—2831no—
183#124—2831no—
184#121—5662no—
185C4×D4—5662no—
186C2×C4⋊C4—5662no—
187C2×C42—2831no—
188#97—2832no—
189C4×C8—2832no—
190#41—22no—
191#41—22no—
192#41—5662no—
193#41—5662no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—2831no—
198C2×Q8—2832no—
199C2×Q8—5661no—
200C2×Q8—5662no—
201C2×Q8—5662no—
202C2×Q8C22×D28311yescharacteristic
203C2×Q8C22×D28312yes—
204C2×D4—21no—
205C2×D4—2831no—
206C2×D4—5662no—
207C2×D4—5661no—
208C2×D4C22×D28311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—2832no—
212C22×C4—5661no—
213C22×C4—5661no—
214C22×C4C22×D28311yescharacteristic
215Q16—24no—
216Q16—5664no—
217Q16—5664no—
218Q16—5664no—
219SD16—24no—
220SD16—5664no—
221SD16—5664no—
222SD16—5664no—
223M16—2834no—
224M16C22⋊D28314yescomplemented
225C2×C8—2832no—
226C2×C8C22×D28312yes—
227C4⋊C4—5664no—
228C4⋊C4—5664no—
229C4⋊C4—5662no—
230C22⋊C4—5662no—
231C22⋊C4—5662no—
232C42—2832no—
233C42—2831no—
234C42—2831no—
235C23—21no—
236C23—5661no—
237C23D4×D28311yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—5662no—
244Q8—5661no—
245Q8—5662no—
246Q8—5661no—
247Q8—11322no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—5661no—
252D4—5661no—
253D4—11324no—
254D4—11322no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—2832no—
260C2×C4—2832no—
261C2×C4—5664no—
262C2×C4—5661no—
263C2×C4—5662no—
264C2×C4—11322no—
265C2×C4—11322no—
266C2×C4D4×D28311yescharacteristic
267C2×C4D4×D28312yes—
268C2×C4C2×C22⋊D28312yes—
269C2×C4C23×D28311yescharacteristic
270C8—2834no—
271C8C2×C22⋊D28314yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—11322no—
276C22—11321no—
277C22#2258360612yes—
278C22C2×D4×D28311yescharacteristic
279C4—41no—
280C4—42no—
281C4—2834no—
282C4—5662no—
283C4—11321no—
284C4—11322no—
285C4#2258360612yes—
286C4C2×D4×D28311yescharacteristic
287C4C22×C22⋊D28311yescharacteristic
288C2—22no—
289C2—81no—
290C2—22641no—
291C2C2×#2258360611yescharacteristic
292C2#137×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#137×C283C2
socleC22×C283C22×D4
prime radical#31827011C2
hypercenterC2×#137D283
hypocenterC283#3152
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#22583643C2semidirect
2. C2×#22583641C2semidirect
3. C2×#22583640C2semidirect
5. C2×#22583608C2semidirect
6. #31826858C2semidirect
7. #31826856C2semidirect
8. #31826843C2semidirect
9. #31826836C2semidirect
10. M16×Dic283C2semidirect
11. C2×#137×C283C2semidirect
62. #17985376D4semidirect
86. M16×C283D4semidirect
140. Dic283#137semidirect
146. C283#3152semidirect
151. C2×#137D283semidirect
224. M16C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C2×#225836412
C2×#225836402
#318270112
C2×#225836082
#318268582
#318268562
#318268432
#318268362
M16×Dic2832
C2×#137×C2832
#3152283