Finite Group Databasebeta

← #1881×C233 #44447913

Subgroups — #1881×C233 #44447913

Order 29824.

310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 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#575×C233C211yesmaximal, characteristic
2#568×C233C211yesmaximal, characteristic, complemented
3#421×C233C211yesmaximal, characteristic, complemented
4#416×C233C211yesmaximal, characteristic, complemented
5#408×C233C211yesmaximal, characteristic, complemented
6#344×C233C211yesmaximal, characteristic, complemented
7#341×C233C211yesmaximal, characteristic, complemented
8C2×#41×C233C2211yescharacteristic
9C2×#41×C233C2211yescharacteristic
10#137×C233—21no—
11#137×C233C412yescomplemented
12AGL(1,ℤ/8)×C233—21no—
13AGL(1,ℤ/8)×C233C412yescomplemented
14#135×C233—22no—
15#131×C233—22no—
16#131×C233—22no—
17C2×M16×C233—22no—
18C2×M16×C233C2211yescharacteristic
19C2×M16×C233C2211yescharacteristic
20C2×M16×C233C2211yescharacteristic
21C22×C8×C233C2211yescharacteristic
22#117×C233C2211yescharacteristic
23#104×C233—22no—
24#103×C233—21no—
25#102×C233—21no—
26C22⋊C8×C233—22no—
27#41×C233—21no—
28#41×C233—21no—
29#41×C233—21no—
30#41×C233—21no—
31#41×C233—21no—
32#41×C233—21no—
33#41×C233C2×C412yes—
34#41×C233D412yes—
35C2×Q8×C233C2×C411yescharacteristic
36C2×Q8×C233D411yescharacteristic
37C2×D4×C233—21no—
38C2×D4×C233—21no—
39C2×D4×C233C2×C411yescharacteristic
40C2×D4×C233D411yescharacteristic
41C22×C4×C233—21no—
42C22×C4×C233—21no—
43C22×C4×C233C2311yescharacteristic
44Q16×C233—22no—
45SD16×C233—22no—
46SD16×C233—22no—
47D8×C233—22no—
48M16×C233—24no—
49M16×C233—21no—
50M16×C233—21no—
51M16×C233—21no—
52M16×C233—21no—
53M16×C233C2×C412yes—
54M16×C233D412yes—
55C2×C8×C233—24no—
56C2×C8×C233—21no—
57C2×C8×C233—21no—
58C2×C8×C233—21no—
59C2×C8×C233—21no—
60C2×C8×C233—21no—
61C2×C8×C233D412yes—
62C4⋊C4×C233—21no—
63C22⋊C4×C233—21no—
64C42×C233—21no—
65C23×C233—21no—
66C23×C233—21no—
67C23×C233#4111yescharacteristic
68Q8×C233—21no—
69Q8×C233—21no—
70Q8×C233—21no—
71Q8×C233C22⋊C412yes—
72D4×C233—22no—
73D4×C233—22no—
74D4×C233—21no—
75D4×C233—21no—
76D4×C233—21no—
77D4×C233—41no—
78D4×C233—41no—
79D4×C233C22⋊C412yes—
80C2×C4×C233—21no—
81C2×C4×C233—22no—
82C2×C4×C233—22no—
83C2×C4×C233—21no—
84C2×C4×C233—41no—
85C2×C4×C233—41no—
86C2×C4×C233—41no—
87C2×C4×C233C22×C411yescharacteristic
88C2×C4×C233C2×D411yescharacteristic
89C2×C4×C233C2×D411yescharacteristic
90C2×C4×C233C2×D411yescharacteristic
91C2×C4×C233C2×D411yescharacteristic
92C2×C4×C233#4111yescharacteristic
93C8×C233—22no—
94C8×C233—22no—
95C8×C233—22no—
96C8×C233—41no—
97C22×C233—22no—
98C22×C233—41no—
99C22×C233—42no—
100C22×C233—41no—
101C22×C233—81no—
102C22×C233C4×D411yescharacteristic
103C22×C233#12111yescharacteristic
104C22×C233#12311yescharacteristic
105C4×C233—22no—
106C4×C233—41no—
107C4×C233—81no—
108C4×C233C2×C22⋊C411yescharacteristic
109C4×C233C4×D411yescharacteristic
110C4×C233#12011yescharacteristic
111C4×C233#12111yescharacteristic
112C2×C233—21no—
113C2×C233—21no—
114C2×C233—21no—
115C2×C233—42no—
116C2×C233—81no—
117C2×C233#38611yescharacteristic
118C233#188111yescharacteristic, direct product factor, Sylow
119#1881C23311yesmaximal, characteristic, direct product factor, Sylow
120#575C2×C23311yescharacteristic
121#568C2×C23311yescharacteristic, complemented
122#421C2×C23311yescharacteristic, complemented
123#416C2×C23311yescharacteristic, complemented
124#408C2×C23311yescharacteristic, complemented
125#344C2×C23311yescharacteristic, complemented
126#341C2×C23311yescharacteristic, complemented
127C2×#41C22×C23311yescharacteristic
128C2×#41C22×C23311yescharacteristic
129#137—21no—
130#137C4×C23312yescomplemented
131AGL(1,ℤ/8)—21no—
132AGL(1,ℤ/8)C4×C23312yescomplemented
133#135—22no—
134#131—22no—
135#131—22no—
136C2×M16—22no—
137C2×M16C22×C23311yescharacteristic
138C2×M16C22×C23311yescharacteristic
139C2×M16C22×C23311yescharacteristic
140C22×C8C22×C23311yescharacteristic
141#117C22×C23311yescharacteristic
142#104—22no—
143#103—21no—
144#102—21no—
145C22⋊C8—22no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152#41C2×C4×C23312yes—
153#41D4×C23312yes—
154C2×Q8C2×C4×C23311yescharacteristic
155C2×Q8D4×C23311yescharacteristic
156C2×D4—21no—
157C2×D4—21no—
158C2×D4C2×C4×C23311yescharacteristic
159C2×D4D4×C23311yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4C23×C23311yescharacteristic
163Q16—22no—
164SD16—22no—
165SD16—22no—
166D8—22no—
167M16—24no—
168M16—21no—
169M16—21no—
170M16—21no—
171M16—21no—
172M16C2×C4×C23312yes—
173M16D4×C23312yes—
174C2×C8—24no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8D4×C23312yes—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—21no—
186C23#41×C23311yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—21no—
190Q8C22⋊C4×C23312yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—21no—
195D4—21no—
196D4—41no—
197D4—41no—
198D4C22⋊C4×C23312yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4C22×C4×C23311yescharacteristic
207C2×C4C2×D4×C23311yescharacteristic
208C2×C4C2×D4×C23311yescharacteristic
209C2×C4C2×D4×C23311yescharacteristic
210C2×C4C2×D4×C23311yescharacteristic
211C2×C4#41×C23311yescharacteristic
212C8—22no—
213C8—22no—
214C8—22no—
215C8—41no—
216C22—22no—
217C22—41no—
218C22—42no—
219C22—41no—
220C22—81no—
221C22C4×D4×C23311yescharacteristic
222C22#121×C23311yescharacteristic
223C22#123×C23311yescharacteristic
224C4—22no—
225C4—41no—
226C4—81no—
227C4C2×C22⋊C4×C23311yescharacteristic
228C4C4×D4×C23311yescharacteristic
229C4#120×C23311yescharacteristic
230C4#121×C23311yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—81no—
236C2#386×C23311yescharacteristic
subgroupG/H
centerC4×C233#120
commutatorC2×C4C22×C4×C233
Frattini, cosocleC22×C4C23×C233
socleC2×C233#386
prime radical#575×C233C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C233 ◁ C22×C4×C233 ◁ G

Complements

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

NH ≅ G/Ntype
2. #568×C233C2semidirect
3. #421×C233C2semidirect
4. #416×C233C2semidirect
5. #408×C233C2semidirect
6. #344×C233C2semidirect
7. #341×C233C2semidirect
11. #137×C233C4semidirect
13. AGL(1,ℤ/8)×C233C4semidirect
118. C233#1881direct (N × H)
119. #1881C233direct (N × H)
121. #568C2×C233semidirect
122. #421C2×C233semidirect
123. #416C2×C233semidirect
124. #408C2×C233semidirect
125. #344C2×C233semidirect
126. #341C2×C233semidirect
130. #137C4×C233semidirect
132. AGL(1,ℤ/8)C4×C233semidirect

Maximal subgroups

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

subgroupindex
#575×C2332
#568×C2332
#421×C2332
#416×C2332
#408×C2332
#344×C2332
#341×C2332
#1881233