Finite Group Databasebeta

← C23×#11903 #19159529

Subgroups — C23×#11903 #19159529

Order 5888.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C23×#2487C211yesmaximal, characteristic
2C23×#1800C211yesmaximal, characteristic
3C23×#1459C211yesmaximal, characteristic
4C23×#1353C214yesmaximal, complemented
5C2×C4×D4×C23C2211yescharacteristic
6C22×C4⋊C4×C23C411yescharacteristic
7C23×#423—21no—
8C2×C23×#100—21no—
9C2×C23×C22⋊C8—21no—
10C23×#400C2212yes—
11C23×#399C412yes—
12C23×#389—21no—
13C23×#386—21no—
14C23×#385—21no—
15C23×#380—21no—
16C23×#380C411yescharacteristic
17C23×#343C2212yes—
18C23×#324C2212yes—
19C23×#323—21no—
20C22×D4×C23D411yescharacteristic
21C23×C4×C23—21no—
22C23×C4×C23C2×C411yescharacteristic
23C23×C4×C23D411yescharacteristic
24C2×M16×C23—22no—
25C22×C8×C23—41no—
26C4×D4×C23—41no—
27C4×D4×C23—41no—
28C2×C4⋊C4×C23—21no—
29C2×C4⋊C4×C23—21no—
30C2×C4⋊C4×C23—22no—
31C2×C4⋊C4×C23—41no—
32C2×C4⋊C4×C23—41no—
33C2×C4⋊C4×C23C2×C412yes—
34C2×C4⋊C4×C23C2311yescharacteristic
35C2×C22⋊C4×C23—21no—
36C2×C22⋊C4×C23—22no—
37C2×C22⋊C4×C23C2×C411yescharacteristic
38C2×C22⋊C4×C23D411yescharacteristic
39C2×C42×C23D411yescharacteristic
40C23×C4⋊C8—41no—
41C23×C4⋊C8—41no—
42C23×#100—42no—
43C23×C22⋊C8—22no—
44C23×C22⋊C8—41no—
45C23×#95—22no—
46C23×#95—22no—
47C23×#95C2×C412yes—
48C24×C23C22⋊C411yescharacteristic
49C24×C23C22⋊C411yescharacteristic
50C2×D4×C23—41no—
51C2×D4×C23—41no—
52C2×D4×C23SD1612yes—
53C2×D4×C23Q1612yes—
54C22×C4×C23—21no—
55C22×C4×C23—21no—
56C22×C4×C23—21no—
57C22×C4×C23—21no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—42no—
61C22×C4×C23—42no—
62C22×C4×C23—42no—
63C22×C4×C23—82no—
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22×C411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69M16×C23—42no—
70M16×C23—42no—
71C2×C8×C23—42no—
72C2×C8×C23—42no—
73C2×C8×C23—82no—
74C4⋊C4×C23—41no—
75C4⋊C4×C23—42no—
76C4⋊C4×C23—42no—
77C4⋊C4×C23—41no—
78C4⋊C4×C23—41no—
79C4⋊C4×C23—82no—
80C22⋊C4×C23—41no—
81C22⋊C4×C23—41no—
82C22⋊C4×C23—42no—
83C22⋊C4×C23—82no—
84C42×C23—21no—
85C42×C23—21no—
86#11903C2311yesmaximal, characteristic, direct product factor, Sylow
87C23×C23—21no—
88C23×C23—21no—
89C23×C23—21no—
90C23×C23—21no—
91C23×C23—41no—
92C23×C23—41no—
93C23×C23—41no—
94C23×C23—41no—
95C23×C23#10312yes—
96C23×C23#10312yes—
97C23×C23C2×C22⋊C411yescharacteristic
98D4×C23—42no—
99D4×C23—42no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—22no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—42no—
107C2×C4×C23—42no—
108C2×C4×C23—42no—
109C2×C4×C23—41no—
110C2×C4×C23—41no—
111C2×C4×C23—41no—
112C2×C4×C23—42no—
113C2×C4×C23—42no—
114C2×C4×C23—42no—
115C2×C4×C23—42no—
116C2×C4×C23—42no—
117C2×C4×C23—42no—
118C2×C4×C23—81no—
119C2×C4×C23—84no—
120C2×C4×C23#9911yescharacteristic
121C2×C4×C23#9911yescharacteristic
122C2×C4×C23C2×SD1611yescharacteristic
123C2×C4×C23C2×Q1611yescharacteristic
124C8×C23—82no—
125C8×C23—82no—
126#2487C2×C2311yescharacteristic
127#1800C2×C2311yescharacteristic
128#1459C2×C2311yescharacteristic
129#1353C2×C2314yescomplemented
130C22×C23—21no—
131C22×C23—21no—
132C22×C23—22no—
133C22×C23—22no—
134C22×C23—42no—
135C22×C23—42no—
136C22×C23—42no—
137C22×C23—41no—
138C22×C23—41no—
139C22×C23—41no—
140C22×C23—41no—
141C22×C23—81no—
142C22×C23C2×#9911yescharacteristic
143C22×C23C2×#10311yescharacteristic
144C22×C23#42111yescharacteristic
145C4×C23—21no—
146C4×C23—21no—
147C4×C23—21no—
148C4×C23—41no—
149C4×C23—41no—
150C4×C23—41no—
151C4×C23—82no—
152C4×C23—82no—
153C4×C23#35212yes—
154C2×C4×D4C22×C2311yescharacteristic
155C22×C4⋊C4C4×C2311yescharacteristic
156#423—21no—
157C2×#100—21no—
158C2×C22⋊C8—21no—
159#400C22×C2312yes—
160#399C4×C2312yes—
161#389—21no—
162#386—21no—
163#385—21no—
164#380—21no—
165#380C4×C2311yescharacteristic
166#343C22×C2312yes—
167#324C22×C2312yes—
168#323—21no—
169C2×C23—21no—
170C2×C23—21no—
171C2×C23—42no—
172C2×C23—42no—
173C2×C23#152011yescharacteristic
174C2×C23C2×#35211yescharacteristic
175C2×C23#213411yescharacteristic
176C22×D4D4×C2311yescharacteristic
177C23×C4—21no—
178C23×C4C2×C4×C2311yescharacteristic
179C23×C4D4×C2311yescharacteristic
180C2×M16—22no—
181C22×C8—41no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4C2×C4×C2312yes—
190C2×C4⋊C4C23×C2311yescharacteristic
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4C2×C4×C2311yescharacteristic
194C2×C22⋊C4D4×C2311yescharacteristic
195C2×C42D4×C2311yescharacteristic
196C4⋊C8—41no—
197C4⋊C8—41no—
198#100—42no—
199C22⋊C8—22no—
200C22⋊C8—41no—
201#95—22no—
202#95—22no—
203#95C2×C4×C2312yes—
204C23#1190311yescharacteristic, direct product factor, Sylow
205C24C22⋊C4×C2311yescharacteristic
206C24C22⋊C4×C2311yescharacteristic
207C2×D4—41no—
208C2×D4—41no—
209C2×D4SD16×C2312yes—
210C2×D4Q16×C2312yes—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—82no—
221C22×C4C22⋊C4×C2311yescharacteristic
222C22×C4C22⋊C4×C2311yescharacteristic
223C22×C4C22×C4×C2311yescharacteristic
224C22×C4C2×D4×C2311yescharacteristic
225C22×C4C2×D4×C2311yescharacteristic
226M16—42no—
227M16—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—82no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—82no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—82no—
241C42—21no—
242C42—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23C23×#10312yes—
252C23C23×#10312yes—
253C23C2×C22⋊C4×C2311yescharacteristic
254D4—42no—
255D4—42no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—84no—
276C2×C4C23×#9911yescharacteristic
277C2×C4C23×#9911yescharacteristic
278C2×C4C2×SD16×C2311yescharacteristic
279C2×C4C2×Q16×C2311yescharacteristic
280C8—82no—
281C8—82no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22C2×C23×#9911yescharacteristic
295C22C2×C23×#10311yescharacteristic
296C22C23×#42111yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4C23×#35212yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—42no—
310C2C23×#152011yescharacteristic
311C2C2×C23×#35211yescharacteristic
312C2C23×#213411yescharacteristic
subgroupG/H
center, socleC22×C23C2×#99
commutatorC22×C4C22×C4×C23
Frattini, cosocleC2×C4⋊C4C23×C23
prime radicalC22×D4×C23D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C23×#1353C2semidirect
86. #11903C23direct (N × H)
129. #1353C2×C23semidirect
204. C23#11903direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#24872
C23×#18002
C23×#14592
C23×#13532
#1190323