Finite Group Databasebeta

← #19212326

Subgroups — #19212326

Order 5888.

608 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#10625045C211yesmaximal, characteristic
2#15673540C211yesmaximal, characteristic, complemented
3#15671217C214yesmaximal, complemented
4C23×#1839C211yesmaximal, characteristic, complemented
5C2×#10625045C411yescharacteristic
6C2×C4×D92—21no—
7C2×C4×D92—21no—
8C2×C4×D92C412yes—
9#13092319—21no—
10#13092319—21no—
11#13092319C2212yes—
12#13092287C411yescharacteristic
13#13092172—21no—
14#13092172—21no—
15#13092172C2212yes—
16C43×C23C2211yescharacteristic
17C23×#336—21no—
18C23×#336—21no—
19C23×#336C2212yes—
20C22×D92—21no—
21C22×D92—21no—
22C22×D92C2×C412yes—
23C22×C4×D23—22no—
24C22×C8×C23—22no—
25C2×C42×C23C2×C411yescharacteristic
26C2×C42×C23C2×C411yescharacteristic
27C2×C42×C23D411yescharacteristic
28C2×C42×C23D411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23C2311yescharacteristic
32C2×(C2×D23)⋊C4—22no—
33C2×(C2×D23)⋊C4—22no—
34C2×(C2×D23)⋊C4—22no—
35C2×C4⋊Dic23—21no—
36C2×C4⋊Dic23—21no—
37C2×C4⋊Dic23C2×C412yes—
38C22×C23⋊C8—22no—
39#10625045—22no—
40#10625045C814yescomplemented
41C4×D92—44no—
42C4×D92—44no—
43C4×D92—44no—
44C23×D23—22no—
45C22×C4×C23C22⋊C411yescharacteristic
46C22×C4×C23C22⋊C411yescharacteristic
47C22×C4×C23C22⋊C411yescharacteristic
48C22×C4×C23C22⋊C411yescharacteristic
49C22×C4×C23C22×C411yescharacteristic
50C22×C4×C23C2×D411yescharacteristic
51C22×C4×C23C2×D411yescharacteristic
52C22×Dic23—22no—
53C2×D92—24no—
54C2×D92—24no—
55C2×D92—22no—
56C2×D92—42no—
57C2×D92—42no—
58C2×D92—42no—
59C2×D92—42no—
60C2×D92—42no—
61C2×D92—42no—
62C2×D92C2×C814yes—
63C2×C4×D23—44no—
64C2×C4×D23—44no—
65C2×C4×D23—44no—
66C2×C8×C23—42no—
67C2×C8×C23—42no—
68C2×C8×C23—42no—
69C42×C23—22no—
70C42×C23—22no—
71C42×C23—22no—
72C42×C23—41no—
73C42×C23—41no—
74C42×C23—41no—
75C42×C23C2×C812yes—
76C42×C23M1612yes—
77(C2×D23)⋊C4—44no—
78(C2×D23)⋊C4—44no—
79(C2×D23)⋊C4—44no—
80C4⋊Dic23—42no—
81C4⋊Dic23—42no—
82C4⋊Dic23—42no—
83C2×C23⋊C8—42no—
84C2×C23⋊C8—42no—
85C2×C23⋊C8—42no—
86#7603—231nomaximal, Sylow
87C23×C23C2×C22⋊C411yescharacteristic
88C22×D23—24no—
89C22×D23—42no—
90C22×D23—42no—
91C22×D23—42no—
92C22×D23—42no—
93C22×D23—42no—
94C22×D23—42no—
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23C22⋊C812yes—
111C2×C4×C23C22⋊C812yes—
112C2×C4×C23#10012yes—
113C2×C4×C23C22×C811yescharacteristic
114C2×C4×C23C2×M1611yescharacteristic
115C2×C4×C23AGL(1,ℤ/8)12yes—
116C2×C4×C23AGL(1,ℤ/8)12yes—
117C2×Dic23—42no—
118C2×Dic23—42no—
119C2×Dic23—42no—
120D92—44no—
121D92—44no—
122D92—48no—
123D92—48no—
124C4×D23—88no—
125C8×C23—82no—
126C23⋊C8—82no—
127C4×#127—231no—
128#1839—231no—
129#1839D2311yescharacteristic, complemented
130#1270—234no—
131C22×C23C2×C22⋊C811yescharacteristic
132C22×C23#41011yescharacteristic
133C22×C23C2×#10011yescharacteristic
134C22×C23#41811yescharacteristic
135C22×C23#41811yescharacteristic
136C22×C23#42111yescharacteristic
137C22×C23#42111yescharacteristic
138C2×D23—44no—
139C2×D23—44no—
140C2×D23—44no—
141C2×D23—82no—
142C2×D23—82no—
143C2×D23—82no—
144C2×D23—82no—
145C4×C23—22no—
146C4×C23—21no—
147C4×C23—21no—
148C4×C23—22no—
149C4×C23—22no—
150C4×C23—22no—
151C4×C23—22no—
152C4×C23—41no—
153Dic23—82no—
154C2×#127—231no—
155C2×C4×D4—232no—
156C2×C4×D4—461no—
157C2×C4×D4—461no—
158#390—232no—
159#390—461no—
160#390—461no—
161#384—231no—
162C43C2×D2311yescharacteristic
163#336—21no—
164#336—21no—
165#336—232no—
166#336—461no—
167#336—461no—
168#336C2×D2312yes—
169C2×C23#146011yescharacteristic
170C2×C23#147811yescharacteristic
171C2×C23#147811yescharacteristic
172C2×C23#151411yescharacteristic
173C2×C23#151411yescharacteristic
174C2×C23#153611yescharacteristic
175C2×C23#155511yescharacteristic
176D23—84no—
177C22×D4—232no—
178C22×D4—461no—
179C22×D4—461no—
180C23×C4—462no—
181C22×C8—22no—
182C22×C8—462no—
183#127—234no—
184#127—462no—
185C4×D4—924no—
186C4×D4—924no—
187C4×D4—924no—
188C2×C4⋊C4—232no—
189C2×C4⋊C4—461no—
190C2×C4⋊C4—461no—
191C2×C22⋊C4—462no—
192C2×C22⋊C4—462no—
193C2×C22⋊C4—462no—
194C2×C42C4×D2311yescharacteristic
195C2×C42C4×D2311yescharacteristic
196C2×C42D9211yescharacteristic
197C2×C42D9211yescharacteristic
198C2×C42C22⋊D2311yescharacteristic
199C2×C42C22⋊D2311yescharacteristic
200C2×C42C22×D2311yescharacteristic
201C23#760311yescharacteristic, complemented, Sylow
202C24—462no—
203C2×D4—234no—
204C2×D4—462no—
205C2×D4—464no—
206C2×D4—464no—
207C2×D4—922no—
208C2×D4—922no—
209C2×D4—922no—
210C2×D4—922no—
211C2×D4—922no—
212C2×D4—922no—
213C22×C4—462no—
214C22×C4—924no—
215C22×C4—924no—
216C22×C4—924no—
217C22×C4(C2×D23)⋊C411yescharacteristic
218C22×C4(C2×D23)⋊C411yescharacteristic
219C22×C4(C2×D23)⋊C411yescharacteristic
220C22×C4(C2×D23)⋊C411yescharacteristic
221C22×C4C2×C4×D2311yescharacteristic
222C22×C4C2×D9211yescharacteristic
223C22×C4C2×C22⋊D2311yescharacteristic
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—922no—
228C2×C8—922no—
229C2×C8—922no—
230C4⋊C4—922no—
231C4⋊C4—922no—
232C4⋊C4—922no—
233C22⋊C4—924no—
234C22⋊C4—924no—
235C22⋊C4—924no—
236C42—22no—
237C42—22no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42C8×D2312yes—
243C42#6726212yes—
244C23—464no—
245C23—922no—
246C23—922no—
247C23—922no—
248C23—922no—
249C23—922no—
250C23—922no—
251C23C2×(C2×D23)⋊C411yescharacteristic
252D4—924no—
253D4—924no—
254D4—928no—
255D4—928no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—922no—
272C2×C4—922no—
273C2×C4—922no—
274C2×C4—1848no—
275C2×C4(C2×D23)⋊C812yes—
276C2×C4(C2×D23)⋊C812yes—
277C2×C4#1062500512yes—
278C2×C4C2×C8×D2311yescharacteristic
279C2×C4C2×#6726211yescharacteristic
280C2×C4#1062507912yes—
281C2×C4#1062512012yes—
282C8—82no—
283C8—1842no—
284C22—924no—
285C22—924no—
286C22—924no—
287C22—1842no—
288C22—1842no—
289C22—1842no—
290C22—1842no—
291C22C2×(C2×D23)⋊C811yescharacteristic
292C22#1309239011yescharacteristic
293C22C2×#1062500511yescharacteristic
294C22#1309242111yescharacteristic
295C22#1309242311yescharacteristic
296C22#1309243311yescharacteristic
297C22#1309243511yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—22no—
304C4—22no—
305C4—41no—
306C4—1842no—
307C2—1844no—
308C2#1567171711yescharacteristic
309C2#1567178711yescharacteristic
310C2#1567178911yescharacteristic
311C2#1567194311yescharacteristic
312C2#1567194511yescharacteristic
313C2#1567203111yescharacteristic
314C2#1567211011yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1839C2
socleC23×C23C2×C22⋊C4
hypercenter#1839D23
hypocenterC23#7603
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #15673540C2semidirect
3. #15671217C2semidirect
4. C23×#1839C2semidirect
40. #10625045C8semidirect
129. #1839D23semidirect
201. C23#7603semidirect