Finite Group Databasebeta

← #49122320

Subgroups — #49122320

Order 36224.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#31827263C211yesmaximal, characteristic
2C2×#22583640C211yesmaximal, characteristic, complemented
3#31827041C211yesmaximal, characteristic, complemented
4#31826483C211yesmaximal, characteristic, complemented
5#31826473C211yesmaximal, characteristic, complemented
6#31826235C211yesmaximal, characteristic, complemented
7#410×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×Dic566C2211yescharacteristic
10#22583641—21no—
11#22583640—22no—
12#22583640—21no—
13#22583640—22no—
14#22583636—21no—
15#22583635—21no—
16#22583630—22no—
17C2×#17985382—21no—
18C2×#17985380—21no—
19C2×#17985376C2211yescharacteristic
20C2×#17985376C2211yescharacteristic
21#22583610—21no—
22#22583598—21no—
23#22583594—22no—
24#22583590—22no—
25#22583538—22no—
26#22583533—22no—
27C2×#41×C283C2211yescharacteristic
28#117×C283C2211yescharacteristic
29#117×C283C2211yescharacteristic
30#99×C283—22no—
31#17985392—21no—
32#17985392—21no—
33#17985392—21no—
34#17985392—21no—
35C2×Dic566—21no—
36C2×Dic566—21no—
37C2×Dic566—21no—
38C2×Dic566—21no—
39C2×Dic566—21no—
40C2×Dic566D412yes—
41C2×Dic566D411yescharacteristic
42C2×D1132D411yescharacteristic
43C2×C22⋊D283—21no—
44C22×Dic283—21no—
45C2×C4×D283—21no—
46#17985382—24no—
47#17985382—22no—
48#17985380—24no—
49#17985380—22no—
50#17985379—22no—
51#17985377—22no—
52#17985376—21no—
53#17985376—21no—
54#17985376—21no—
55#17985376D412yes—
56C2×C283⋊C8—21no—
57C2×C283⋊C8D412yes—
58C4⋊Dic283—24no—
59(C2×D283)⋊C4—24no—
60#41×C283—21no—
61#41×C283—21no—
62#41×C283—21no—
63#41×C283—21no—
64C2×Q8×C283D411yescharacteristic
65C2×D4×C283—21no—
66C2×D4×C283D411yescharacteristic
67C22×C4×C283—21no—
68C22×C4×C283C2311yescharacteristic
69C4⋊C4×C283—21no—
70C4⋊C4×C283—21no—
71C22⋊C4×C283—21no—
72C22⋊C4×C283D412yes—
73C42×C283—21no—
74C42×C283—21no—
75C22×D283—21no—
76Dic566—22no—
77Dic566—21no—
78Dic566—22no—
79Dic566—21no—
80Dic566—41no—
81Dic566—41no—
82D1132—21no—
83D1132—21no—
84C22⋊D283—41no—
85C22⋊D283—41no—
86C2×Dic283—22no—
87C2×Dic283—21no—
88C2×Dic283—41no—
89C2×Dic283—41no—
90C4×D283—41no—
91C4×D283—41no—
92C283⋊C8—22no—
93C283⋊C8—22no—
94C23×C283—21no—
95C23×C283C2×D411yescharacteristic
96Q8×C283—21no—
97Q8×C283—21no—
98D4×C283—21no—
99D4×C283—21no—
100D4×C283—41no—
101D4×C283—41no—
102C2×C4×C283—22no—
103C2×C4×C283—21no—
104C2×C4×C283—41no—
105C2×C4×C283—41no—
106C2×C4×C283—41no—
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2×D411yescharacteristic
112C2×C4×C283#4111yescharacteristic
113C22×C283—41no—
114C22×C283—41no—
115C22×C283—81no—
116C22×C283#12011yescharacteristic
117C22×C283#12111yescharacteristic
118C22×C283#12711yescharacteristic
119C2×D283—42no—
120C2×D283—41no—
121C4×C283—42no—
122C4×C283—41no—
123C4×C283—81no—
124C4×C283#12011yescharacteristic
125C4×C283#12011yescharacteristic
126C4×C283#12111yescharacteristic
127C4×C283#12111yescharacteristic
128Dic283—41no—
129Dic283—42no—
130C2×C283—21no—
131C2×C283—21no—
132C2×C283—21no—
133C2×C283—81no—
134C2×C283#39211yescharacteristic
135D283—81no—
136C283#200911yescharacteristic, complemented, Sylow
137#2009—2831nomaximal, Sylow
138#575—2831no—
139C2×#137—2831no—
140#536—2831no—
141#421—2831no—
142#419—2831no—
143#410D28311yescharacteristic, complemented
144#344—2831no—
145C2×#41—2831no—
146C2×#41C2×D28311yescharacteristic
147C22×Q8—2831no—
148#137—5662no—
149#137—5662no—
150#137—5661no—
151#137—5661no—
152AGL(1,ℤ/8)—5661no—
153AGL(1,ℤ/8)—5661no—
154#135—5662no—
155C2×Q16—5661no—
156C2×SD16—5661no—
157C2×M16—2831no—
158C2×M16—2831no—
159C4⋊Q8—5661no—
160#124—5661no—
161#123—5662no—
162C22⋊Q8—5662no—
163#117C2×D28311yescharacteristic
164#117C2×D28311yescharacteristic
165#104—5662no—
166#103—5662no—
167#99—22no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—5661no—
173#41—5661no—
174#41—5661no—
175#41—5661no—
176C2×Q8—2832no—
177C2×Q8—2831no—
178C2×Q8—5661no—
179C2×Q8—5661no—
180C2×Q8—5661no—
181C2×Q8—5661no—
182C2×Q8—5661no—
183C2×Q8D113211yescharacteristic
184C2×D4—21no—
185C2×D4—2831no—
186C2×D4—5661no—
187C2×D4D113211yescharacteristic
188C22×C4—21no—
189C22×C4—5661no—
190C22×C4—5661no—
191C22×C4C22×D28311yescharacteristic
192Q16—5664no—
193Q16—5662no—
194SD16—5664no—
195SD16—5662no—
196SD16—5662no—
197D8—5662no—
198M16—2832no—
199M16—5661no—
200M16—5661no—
201M16—5661no—
202C2×C8—2832no—
203C2×C8—5661no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—5664no—
207C22⋊C4—21no—
208C22⋊C4—5664no—
209C22⋊C4C22⋊D28312yes—
210C42—21no—
211C42—21no—
212C23—21no—
213C23—5661no—
214C23C2×C22⋊D28311yescharacteristic
215Q8—21no—
216Q8—21no—
217Q8—5662no—
218Q8—5661no—
219Q8—5662no—
220Q8—5661no—
221Q8—11321no—
222Q8—11321no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—5661no—
228D4—5661no—
229D4—11321no—
230D4—11321no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—5662no—
237C2×C4—5661no—
238C2×C4—11321no—
239C2×C4—11321no—
240C2×C4—11321no—
241C2×C4—11321no—
242C2×C4D4×D28311yescharacteristic
243C2×C4D4×D28311yescharacteristic
244C2×C4D4×D28311yescharacteristic
245C2×C4D4×D28311yescharacteristic
246C2×C4C2×D113211yescharacteristic
247C2×C4#1798539211yescharacteristic
248C8—5662no—
249C8—5662no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—11322no—
254C22—11321no—
255C22#2258357811yescharacteristic
256C22#2258358411yescharacteristic
257C22#2258360611yescharacteristic
258C4—42no—
259C4—41no—
260C4—81no—
261C4—11321no—
262C4—11322no—
263C4#2258358011yescharacteristic
264C4#2258358011yescharacteristic
265C4#2258358311yescharacteristic
266C4#2258358311yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—22641no—
272C2#3182637411yescharacteristic
subgroupG/H
centerC2#31826374
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#410×C283C2
socleC2×C283#392
prime radical#31827263C2
hypercenter#410D283
hypocenterC283#2009
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. C2×#22583640C2semidirect
3. #31827041C2semidirect
4. #31826483C2semidirect
5. #31826473C2semidirect
6. #31826235C2semidirect
7. #410×C283C2semidirect
136. C283#2009semidirect
143. #410D283semidirect

Maximal subgroups

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

subgroupindex
#318272632
C2×#225836402
#318270412
#318264832
#318264732
#318262352
#410×C2832
#2009283