Finite Group Databasebeta

← #49094253

Subgroups — #49094253

Order 35968.

308 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824021C211yesmaximal, characteristic
2#31823602C211yesmaximal, characteristic, complemented
3#31823374C211yesmaximal, characteristic, complemented
4#31823198C211yesmaximal, characteristic, complemented
5#31823197C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic, complemented
7#448×C281C211yesmaximal, characteristic, complemented
8C2×D4×D281—21no—
9C2×#17985125—21no—
10#22582864—21no—
11#22582861—21no—
12#22582853C2211yescharacteristic
13#22582851—21no—
14#22582849—21no—
15#22582847—21no—
16C2×#17985115—21no—
17C2×#17985115C2211yescharacteristic
18#22582803—21no—
19C22⋊#14555886C2211yescharacteristic, complemented
20#22582786—21no—
21#22582786C2211yescharacteristic, complemented
22C22×Q8×C281C2211yescharacteristic, complemented
23C2×SD16×C281—21no—
24#121×C281C2211yescharacteristic
25#103×C281—21no—
26C22⋊C8×C281C2211yescharacteristic, complemented
27C23×D281—21no—
28C23×D281D411yescharacteristic
29C2×D1124—21no—
30C2×D1124D411yescharacteristic
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34D4×D281—42no—
35D4×D281—42no—
36C22×Dic281—21no—
37C22×Dic281D411yescharacteristic
38C2×C4×D281—21no—
39#17985125—42no—
40C2×#14555886—21no—
41C4⋊Dic281D411yescharacteristic
42#17985117—21no—
43C22⋊Dic281—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—42no—
49C2×Q8×C281—21no—
50C2×Q8×C281—21no—
51C2×Q8×C281—42no—
52C2×D4×C281—21no—
53C2×D4×C281D411yescharacteristic
54C22×C4×C281—21no—
55C22×C4×C281C2311yescharacteristic
56SD16×C281—42no—
57C2×C8×C281—21no—
58C4⋊C4×C281D411yescharacteristic
59C22⋊C4×C281—21no—
60C22×D281—21no—
61C22×D281—21no—
62C22×D281—21no—
63C22×D281—42no—
64C22×D281—41no—
65C22×D281—41no—
66C22×D281—81no—
67C22×D281—81no—
68C22×D281SD1612yescomplemented
69D1124—41no—
70D1124—42no—
71C22⋊D281—42no—
72C22⋊D281—41no—
73C22⋊D281—41no—
74C22⋊D281—81no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—41no—
78C2×Dic281—41no—
79C2×Dic281—41no—
80C2×Dic281—41no—
81C4×D281—42no—
82#14555886—41no—
83C23×C281—21no—
84C23×C281C2×D411yescharacteristic
85Q8×C281—22no—
86Q8×C281—22no—
87Q8×C281—41no—
88Q8×C281—41no—
89D4×C281—41no—
90D4×C281—41no—
91D4×C281—41no—
92C2×C4×C281—22no—
93C2×C4×C281—21no—
94C2×C4×C281—41no—
95C2×C4×C281—41no—
96C2×C4×C281—41no—
97C2×C4×C281C2×D411yescharacteristic
98C2×C4×C281C2×D411yescharacteristic
99C8×C281—41no—
100C22×C281—21no—
101C22×C281—21no—
102C22×C281—41no—
103C22×C281—41no—
104C22×C281—41no—
105C22×C281#12011yescharacteristic
106C22×C281C2×SD1611yescharacteristic
107C22×C281AGL(1,ℤ/8)11yescharacteristic
108C2×D281—22no—
109C2×D281—41no—
110C2×D281—41no—
111C2×D281—42no—
112C2×D281—41no—
113C2×D281—41no—
114C2×D281—41no—
115C2×D281—81no—
116C2×D281—84no—
117C4×C281—21no—
118C4×C281—21no—
119C4×C281—41no—
120C4×C281—42no—
121Dic281—41no—
122Dic281—41no—
123Dic281—81no—
124C2×C281—21no—
125C2×C281—21no—
126C2×C281—81no—
127C2×C281#45011yescharacteristic
128C2×C281#45511yescharacteristic
129C2×C281B(4,𝔽2)11yescharacteristic
130D281—42no—
131D281—81no—
132C281#160111yescharacteristic, complemented, Sylow
133#1601—2811nomaximal, Sylow
134#534—2811no—
135#448—2811no—
136#448D28111yescharacteristic, complemented
137#393—2811no—
138#327—2811no—
139#327—2811no—
140#323—2811no—
141C22×Q8C2×D28111yescharacteristic, complemented
142C22×D4—5621no—
143C2×SD16—21no—
144C2×SD16—5621no—
145#123—5621no—
146#123—5621no—
147#121—2811no—
148#121—5621no—
149#121C2×D28111yescharacteristic
150#120—5621no—
151#120—5621no—
152C2×C22⋊C4—2811no—
153C2×C22⋊C4—5621no—
154#103—21no—
155#103—5621no—
156C22⋊C8—2811no—
157C22⋊C8C2×D28111yescharacteristic, complemented
158#95—2811no—
159#95—5621no—
160C24—2811no—
161C24—5621no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—42no—
165C2×D4—21no—
166C2×D4—2811no—
167C2×D4—5621no—
168C2×D4—5621no—
169C2×D4—5621no—
170C2×D4—5621no—
171C2×D4—11242no—
172C2×D4—11242no—
173C2×D4C22⋊D28111yescharacteristic
174C22×C4—21no—
175C22×C4—2811no—
176C22×C4—5621no—
177C22×C4—5621no—
178C22×C4C22×D28111yescharacteristic
179SD16—42no—
180SD16—11242no—
181C2×C8—21no—
182C2×C8—5621no—
183C4⋊C4—2811no—
184C4⋊C4—5621no—
185C4⋊C4C22⋊D28111yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—5621no—
188C22⋊C4—5621no—
189C22⋊C4—5621no—
190C22⋊C4—5621no—
191C22⋊C4—5621no—
192C22⋊C4—11242no—
193C23—21no—
194C23—2812no—
195C23—5621no—
196C23—5621no—
197C23—5621no—
198C23—11241no—
199C23—11241no—
200C23—11242no—
201C23—22481no—
202C23—22481no—
203C23D4×D28111yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—11241no—
212D4—11242no—
213D4—11242no—
214D4—11241no—
215D4—11241no—
216D4—22481no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—5621no—
223C2×C4—5621no—
224C2×C4—11242no—
225C2×C4—11241no—
226C2×C4—11241no—
227C2×C4—11241no—
228C2×C4—11241no—
229C2×C4D4×D28111yescharacteristic
230C2×C4C2×C22⋊D28111yescharacteristic
231C8—41no—
232C8—11241no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—5622no—
239C22—11242no—
240C22—11241no—
241C22—11241no—
242C22—11241no—
243C22—11241no—
244C22—11241no—
245C22—22481no—
246C22—22484no—
247C22#2258284711yescharacteristic
248C22SD16×D28111yescharacteristic
249C22#2258290611yescharacteristic
250C4—21no—
251C4—21no—
252C4—42no—
253C4—41no—
254C4—11241no—
255C4—11241no—
256C4—22481no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—11242no—
261C2—22481no—
262C2#3182361211yescharacteristic
263C2#3182363911yescharacteristic
264C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#448×C281C2
socleC22×C281#120
prime radical#31824021C2
hypercenter#448D281
hypocenterC281#1601
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #31823602C2semidirect
3. #31823374C2semidirect
4. #31823198C2semidirect
5. #31823197C2semidirect
6. #31823186C2semidirect
7. #448×C281C2semidirect
19. C22⋊#14555886C22semidirect
21. #22582786C22semidirect
22. C22×Q8×C281C22semidirect
26. C22⋊C8×C281C22semidirect
68. C22×D281SD16semidirect
132. C281#1601semidirect
136. #448D281semidirect
141. C22×Q8C2×D281semidirect
157. C22⋊C8C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318240212
#318236022
#318233742
#318231982
#318231972
#318231862
#448×C2812
#1601281