Finite Group Databasebeta

← #19212319

Subgroups — #19212319

Order 5888.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625046C211yesmaximal, characteristic
2#15673514C211yesmaximal, characteristic, complemented
3#15671222C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1831C211yesmaximal, characteristic, complemented
6C2×#10625046C411yescharacteristic
7C2×C4×Dic46C411yescharacteristic
8C2×C4×D92C411yescharacteristic
9C2×C4⋊(C23⋊C8)—21no—
10#13092323C2211yescharacteristic
11#13092319C2211yescharacteristic
12#13092308—21no—
13#13092308—21no—
14#13092283C411yescharacteristic
15C4×(C2×D23)⋊C4—21no—
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C2×C23×C4⋊C8—21no—
20C43×C23C2211yescharacteristic
21C23×#336—21no—
22C23×#336C2212yes—
23C22×D92C2×C411yescharacteristic
24C22×C4×D23—21no—
25C22×Dic46C2×C411yescharacteristic
26C22×C8×C23—22no—
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23C2×C411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23D411yescharacteristic
33C2×C42×C23C2311yescharacteristic
34C2×(C2×D23)⋊C4—21no—
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×(C2×D23)⋊C4—21no—
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×C4×Dic23—21no—
43C22×C23⋊C8—22no—
44#10625046—22no—
45#10625046C814yescomplemented
46C4×D92—42no—
47C4×Dic46—42no—
48C23×C4⋊C8—42no—
49C23⋊#95—21no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C4⋊(C23⋊C8)—42no—
54C23×D23—21no—
55C22×C4×C23C22⋊C411yescharacteristic
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C22⋊C411yescharacteristic
59C22×C4×C23C22×C411yescharacteristic
60C22×C4×C23C2×D411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×Dic23—21no—
63C22×Dic23—21no—
64C22×Dic23—21no—
65C2×D92—21no—
66C2×D92—41no—
67C2×D92—41no—
68C2×D92C2×C812yes—
69C2×C4×D23—42no—
70C2×C4×D23—42no—
71C2×C4×D23—42no—
72C2×Dic46—21no—
73C2×Dic46—41no—
74C2×Dic46—41no—
75C2×Dic46C2×C812yes—
76C2×C8×C23—42no—
77C2×C8×C23—42no—
78C2×C8×C23—42no—
79C42×C23—22no—
80C42×C23—21no—
81C42×C23—21no—
82C42×C23—21no—
83C42×C23—21no—
84C42×C23—41no—
85C42×C23—41no—
86C42×C23—41no—
87C42×C23C2×C812yes—
88C42×C23M1612yes—
89(C2×D23)⋊C4—24no—
90(C2×D23)⋊C4—24no—
91(C2×D23)⋊C4—42no—
92(C2×D23)⋊C4—41no—
93(C2×D23)⋊C4—41no—
94(C2×D23)⋊C4—41no—
95(C2×D23)⋊C4—41no—
96C4⋊Dic23—41no—
97C4⋊Dic23—41no—
98Dic23⋊C4—42no—
99C4×Dic23—42no—
100C2×C23⋊C8—42no—
101C2×C23⋊C8—42no—
102C2×C23⋊C8—42no—
103#7601—231nomaximal, Sylow
104C23×C23C2×C22⋊C411yescharacteristic
105C22×D23—22no—
106C22×D23—41no—
107C22×D23—41no—
108C22×D23—41no—
109C22×D23—41no—
110C22×D23—41no—
111C22×D23—41no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23C22⋊C812yes—
128C2×C4×C23C22⋊C812yes—
129C2×C4×C23#10012yes—
130C2×C4×C23C22×C811yescharacteristic
131C2×C4×C23C2×M1611yescharacteristic
132C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C23#13711yescharacteristic
135C2×C4×C23#13711yescharacteristic
136C2×Dic23—22no—
137C2×Dic23—41no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23—41no—
145D92—42no—
146D92—42no—
147C4×D23—84no—
148Dic46—42no—
149Dic46—42no—
150C8×C23—82no—
151C23⋊C8—82no—
152C4×#124—231no—
153#1831—231no—
154#1831D2311yescharacteristic, complemented
155#1272—232no—
156#1270—232no—
157C22×C23C2×C22⋊C811yescharacteristic
158C22×C23#41011yescharacteristic
159C22×C23C2×#10011yescharacteristic
160C22×C23#41711yescharacteristic
161C22×C23#41711yescharacteristic
162C22×C23#42111yescharacteristic
163C22×C23#42111yescharacteristic
164C2×D23—42no—
165C2×D23—42no—
166C2×D23—42no—
167C2×D23—81no—
168C2×D23—81no—
169C2×D23—81no—
170C2×D23—81no—
171C4×C23—21no—
172C4×C23—21no—
173C4×C23—22no—
174C4×C23—22no—
175C4×C23—21no—
176C4×C23—21no—
177C4×C23—21no—
178C4×C23—21no—
179C4×C23—22no—
180C4×C23—41no—
181Dic23—42no—
182Dic23—81no—
183Dic23—81no—
184C2×#124—231no—
185C2×C4×Q8—231no—
186C2×C4×D4—231no—
187C2×C4⋊C8—21no—
188C2×C4⋊C8—461no—
189#391—231no—
190#390—231no—
191#388—461no—
192#388—461no—
193#382—231no—
194C4×C22⋊C4—461no—
195C4×C22⋊C4—461no—
196C43C2×D2311yescharacteristic
197#336—21no—
198#336—232no—
199#336—461no—
200#336C2×D2312yes—
201C2×C23#146011yescharacteristic
202C2×C23#147711yescharacteristic
203C2×C23#147711yescharacteristic
204C2×C23#151211yescharacteristic
205C2×C23#151211yescharacteristic
206C2×C23#153311yescharacteristic
207C2×C23#156011yescharacteristic
208D23—82no—
209C22×Q8—231no—
210C22×D4—231no—
211C23×C4—461no—
212C22×C8—22no—
213C22×C8—462no—
214#124—234no—
215#124—462no—
216C4×Q8—922no—
217C4×D4—922no—
218C2×C4⋊C4—231no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—461no—
221C2×C22⋊C4—461no—
222C2×C22⋊C4—461no—
223C2×C22⋊C4—461no—
224C2×C22⋊C4—461no—
225C2×C22⋊C4—461no—
226C2×C42—461no—
227C2×C42C4×D2311yescharacteristic
228C2×C42C4×D2311yescharacteristic
229C2×C42D9211yescharacteristic
230C2×C42D9211yescharacteristic
231C2×C42C22⋊D2311yescharacteristic
232C2×C42C22⋊D2311yescharacteristic
233C2×C42C22×D2311yescharacteristic
234C4⋊C8—42no—
235C4⋊C8—922no—
236#95—461no—
237#95—461no—
238#95—461no—
239#95—461no—
240C23#760111yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—232no—
243C2×Q8—461no—
244C2×Q8—921no—
245C2×Q8—921no—
246C2×D4—232no—
247C2×D4—461no—
248C2×D4—921no—
249C2×D4—921no—
250C22×C4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—922no—
254C22×C4—922no—
255C22×C4—922no—
256C22×C4(C2×D23)⋊C411yescharacteristic
257C22×C4(C2×D23)⋊C411yescharacteristic
258C22×C4(C2×D23)⋊C411yescharacteristic
259C22×C4(C2×D23)⋊C411yescharacteristic
260C22×C4C2×C4×D2311yescharacteristic
261C22×C4C2×D9211yescharacteristic
262C22×C4C2×C22⋊D2311yescharacteristic
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—922no—
267C2×C8—922no—
268C2×C8—922no—
269C4⋊C4—921no—
270C4⋊C4—921no—
271C4⋊C4—922no—
272C22⋊C4—464no—
273C22⋊C4—464no—
274C22⋊C4—922no—
275C22⋊C4—921no—
276C22⋊C4—921no—
277C22⋊C4—921no—
278C22⋊C4—921no—
279C42—21no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—22no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—922no—
288C42C8×D2312yes—
289C42#6726212yes—
290C23—462no—
291C23—921no—
292C23—921no—
293C23—921no—
294C23—921no—
295C23—921no—
296C23—921no—
297C23C2×(C2×D23)⋊C411yescharacteristic
298Q8—922no—
299Q8—922no—
300D4—922no—
301D4—922no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—462no—
318C2×C4—921no—
319C2×C4—921no—
320C2×C4—921no—
321C2×C4—921no—
322C2×C4—921no—
323C2×C4—921no—
324C2×C4—921no—
325C2×C4—921no—
326C2×C4—1844no—
327C2×C4(C2×D23)⋊C812yes—
328C2×C4(C2×D23)⋊C812yes—
329C2×C4#1062500512yes—
330C2×C4C2×C8×D2311yescharacteristic
331C2×C4C2×#6726211yescharacteristic
332C2×C4#1062507911yescharacteristic
333C2×C4#1062508011yescharacteristic
334C2×C4#1062510311yescharacteristic
335C2×C4#1062511311yescharacteristic
336C8—82no—
337C8—1842no—
338C22—922no—
339C22—922no—
340C22—922no—
341C22—1841no—
342C22—1841no—
343C22—1841no—
344C22—1841no—
345C22C2×(C2×D23)⋊C811yescharacteristic
346C22#1309239011yescharacteristic
347C22C2×#1062500511yescharacteristic
348C22#1309241611yescharacteristic
349C22#1309241911yescharacteristic
350C22#1309243311yescharacteristic
351C22#1309243511yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—22no—
359C4—22no—
360C4—22no—
361C4—41no—
362C4—922no—
363C4—1841no—
364C4—1841no—
365C2—1842no—
366C2#1567171711yescharacteristic
367C2#1567178211yescharacteristic
368C2#1567178511yescharacteristic
369C2#1567193311yescharacteristic
370C2#1567193611yescharacteristic
371C2#1567202011yescharacteristic
372C2#1567213011yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1831C2
socleC23×C23C2×C22⋊C4
hypercenter#1831D23
hypocenterC23#7601
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #15673514C2semidirect
3. #15671222C2semidirect
5. C23×#1831C2semidirect
45. #10625046C8semidirect
154. #1831D23semidirect
240. C23#7601semidirect