Finite Group Databasebeta

← #19212171

Subgroups — #19212171

Order 5888.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625095C211yesmaximal, characteristic
2C2×#13092172C211yesmaximal, characteristic
3#15671222C212yesmaximal, complemented
4#15671221C212yesmaximal, complemented
5C4×C23×C22⋊C8C211yesmaximal, characteristic
6C23×C23⋊C8—21no—
7C2×#10625095C411yescharacteristic
8C2×C4×Dic46C411yescharacteristic
9#13092323C2211yescharacteristic
10#13092315C2211yescharacteristic
11#13092301—21no—
12#13092290—21no—
13#13092277C411yescharacteristic
14C4×Dic23⋊C4—21no—
15C4×C4⋊Dic23C411yescharacteristic
16C4×C22⋊Dic23—21no—
17#13092172—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C2×C4×C8×C23—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×Dic46C2×C411yescharacteristic
27C22×C8×C23—22no—
28C2×C42×C23—42no—
29C2×C42×C23C2×C411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×C22⋊Dic23—21no—
34C2×C22⋊Dic23—21no—
35C2×C4⋊Dic23C2×C411yescharacteristic
36C2×C4⋊Dic23C2×C411yescharacteristic
37C2×C4⋊Dic23C2×C411yescharacteristic
38#10625095—22no—
39#10625095C814yescomplemented
40C2×Dic23⋊C4—21no—
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C2×C4×Dic23—21no—
45C22×C23⋊C8—24no—
46C22×C23⋊C8—22no—
47C22×C23⋊C8—42no—
48C22×C23⋊C8—42no—
49C4×Dic46—42no—
50C23×C22⋊C8—24no—
51C4×C8×C23—42no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C24×C23C22⋊C411yescharacteristic
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—41no—
63C22×C4×C23—41no—
64C22×C4×C23—41no—
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C22⋊C411yescharacteristic
68C22×C4×C23C2×C812yes—
69C22×C4×C23M1612yes—
70C22×C4×C23SD1612yes—
71C22×C4×C23Q1612yes—
72C22×C4×C23C22×C411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C22×C4×C23C2×D411yescharacteristic
75C22×Dic23—21no—
76C22×Dic23—21no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79C2×Dic46—21no—
80C2×Dic46—41no—
81C2×Dic46—41no—
82C2×Dic46C2×C812yescomplemented
83C2×C8×C23—24no—
84C2×C8×C23—42no—
85C2×C8×C23—42no—
86C42×C23—22no—
87C42×C23—22no—
88C42×C23—41no—
89C42×C23—41no—
90C22⋊Dic23—24no—
91C22⋊Dic23—42no—
92C4⋊Dic23—21no—
93C4⋊Dic23—41no—
94C4⋊Dic23—41no—
95C4⋊Dic23C2×C812yescomplemented
96Dic23⋊C4—24no—
97Dic23⋊C4—42no—
98Dic23⋊C4—42no—
99C4×Dic23—42no—
100C4×Dic23—42no—
101C2×C23⋊C8—24no—
102C2×C23⋊C8—42no—
103C2×C23⋊C8—48no—
104C2×C23⋊C8—42no—
105#7566—231nomaximal, Sylow
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C22⋊C812yes—
111C23×C23#10312yes—
112C23×C23#10412yes—
113C23×C23C2×C22⋊C411yescharacteristic
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—24no—
123C2×C4×C23—24no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—42no—
128C2×C4×C23—42no—
129C2×C4×C23—44no—
130C2×C4×C23C22⋊C812yes—
131C2×C4×C23#9912yes—
132C2×C4×C23#10312yes—
133C2×C4×C23#10412yes—
134C2×C4×C23C22×C811yescharacteristic
135C2×C4×C23C2×M1611yescharacteristic
136C2×C4×C23C2×SD1611yescharacteristic
137C2×C4×C23C2×Q1611yescharacteristic
138C2×C4×C23#13512yes—
139C2×Dic23—22no—
140C2×Dic23—22no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23—41no—
145C2×Dic23—41no—
146C2×Dic23—41no—
147C2×Dic23—41no—
148C2×Dic23—41no—
149C2×Dic23—41no—
150C2×Dic23—41no—
151Dic46—42no—
152Dic46—42no—
153C8×C23—44no—
154C23⋊C8—44no—
155C4×C22⋊Q8—231no—
156C4×C22⋊C8D2311yescharacteristic
157C2×#336—231no—
158#1272—232no—
159#1271—232no—
160C22×C23—22no—
161C22×C23—22no—
162C22×C23—22no—
163C22×C23—22no—
164C22×C23—22no—
165C22×C23—22no—
166C22×C23Q8⋊C814yes—
167C22×C23C2×C22⋊C811yescharacteristic
168C22×C23C2×#9911yescharacteristic
169C22×C23#41311yescharacteristic
170C22×C23C2×#10311yescharacteristic
171C22×C23#41611yescharacteristic
172C22×C23C2×#10411yescharacteristic
173C22×C23C2×#10411yescharacteristic
174C4×C23—21no—
175C4×C23—21no—
176C4×C23—22no—
177C4×C23—21no—
178C4×C23—21no—
179C4×C23—22no—
180C4×C23—41no—
181C4×C23#32814yes—
182Dic23—42no—
183Dic23—42no—
184Dic23—81no—
185Dic23—81no—
186C23×C8—461no—
187C2×C22⋊Q8—231no—
188C2×C4×Q8—231no—
189C22×C42C2×D2311yescharacteristic
190C2×C22⋊C8—21no—
191C2×C4×C8—21no—
192#391—231no—
193#389—231no—
194#387—461no—
195#385—461no—
196#380—231no—
197C4×C4⋊C4—231no—
198C4×C4⋊C4—461no—
199C4×C22⋊C4—461no—
200#336—232no—
201#336—461no—
202#336C2×D2312yes—
203C2×C23—24no—
204C2×C23#145911yescharacteristic
205C2×C23C2×Q8⋊C811yescharacteristic
206C2×C23#147611yescharacteristic
207C2×C23C2×#32811yescharacteristic
208C2×C23#150111yescharacteristic
209C2×C23#152411yescharacteristic
210C2×C23#154211yescharacteristic
211C22×Q8—231no—
212C23×C4C4×D2311yescharacteristic
213C23×C4D9211yescharacteristic
214C23×C4C22⋊D2311yescharacteristic
215C22×C8—22no—
216C22×C8—464no—
217C22×C8—462no—
218C22×C8—922no—
219C22×C8—922no—
220C22⋊Q8—234no—
221C22⋊Q8—462no—
222C4×Q8—922no—
223C2×C4⋊C4—231no—
224C2×C4⋊C4—231no—
225C2×C4⋊C4—231no—
226C2×C4⋊C4—461no—
227C2×C4⋊C4—461no—
228C2×C4⋊C4—461no—
229C2×C22⋊C4—461no—
230C2×C22⋊C4—461no—
231C2×C42—42no—
232C2×C42—461no—
233C2×C42—461no—
234C2×C42C4×D2311yescharacteristic
235C2×C42D9211yescharacteristic
236C2×C42C22⋊D2311yescharacteristic
237C2×C42C22×D2311yescharacteristic
238C22⋊C8—24no—
239C4×C8—42no—
240#95—461no—
241#95—461no—
242#95—461no—
243#95—461no—
244#95—461no—
245C23#756611yescharacteristic, complemented, Sylow
246C24(C2×D23)⋊C411yescharacteristic
247C2×Q8—232no—
248C2×Q8—461no—
249C2×Q8—921no—
250C2×Q8—921no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—461no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C8×D2312yes—
263C22×C4#6726212yes—
264C22×C4#6726312yes—
265C22×C4Dic9212yes—
266C22×C4(C2×D23)⋊C411yescharacteristic
267C22×C4(C2×D23)⋊C411yescharacteristic
268C22×C4(C2×D23)⋊C411yescharacteristic
269C22×C4C2×C4×D2311yescharacteristic
270C22×C4C2×D9211yescharacteristic
271C22×C4C2×C22⋊D2311yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—464no—
276C2×C8—922no—
277C2×C8—928no—
278C2×C8—922no—
279C4⋊C4—232no—
280C4⋊C4—461no—
281C4⋊C4—464no—
282C4⋊C4—921no—
283C4⋊C4—921no—
284C4⋊C4—922no—
285C4⋊C4—922no—
286C22⋊C4—464no—
287C22⋊C4—922no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C42—922no—
293C42—922no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#1062498712yes—
299C23#1062499812yes—
300C23(C2×D23)⋊C812yes—
301C23C2×(C2×D23)⋊C411yescharacteristic
302Q8—922no—
303Q8—922no—
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—24no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—462no—
321C2×C4—462no—
322C2×C4—921no—
323C2×C4—921no—
324C2×C4—921no—
325C2×C4—921no—
326C2×C4—921no—
327C2×C4—921no—
328C2×C4—921no—
329C2×C4—921no—
330C2×C4—921no—
331C2×C4—921no—
332C2×C4#1062498812yes—
333C2×C4#1062499812yes—
334C2×C4(C2×D23)⋊C812yes—
335C2×C4#1062500712yes—
336C2×C4C2×C8×D2311yescharacteristic
337C2×C4C2×#6726211yescharacteristic
338C2×C4C2×#6726311yescharacteristic
339C2×C4C2×Dic9211yescharacteristic
340C2×C4#1062512112yes—
341C8—44no—
342C8—924no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22#1309214914yes—
350C22C2×(C2×D23)⋊C811yescharacteristic
351C22C2×#1062498811yescharacteristic
352C22#1309239911yescharacteristic
353C22C2×#1062499811yescharacteristic
354C22#1309241111yescharacteristic
355C22C2×#1062500711yescharacteristic
356C22C2×#1062498711yescharacteristic
357C4—21no—
358C4—21no—
359C4—22no—
360C4—21no—
361C4—21no—
362C4—22no—
363C4—41no—
364C4—922no—
365C4—922no—
366C4—1841no—
367C4—1841no—
368C4#1309215514yes—
369C2—24no—
370C2#1567171311yescharacteristic
371C2C2×#1309214911yescharacteristic
372C2#1567177711yescharacteristic
373C2C2×#1309215511yescharacteristic
374C2#1567188611yescharacteristic
375C2#1567198611yescharacteristic
376C2#1567205211yescharacteristic
subgroupG/H
centerC22×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC4×C23×C22⋊C8C2
socleC23×C23C2×C22⋊C4
hypercenterC4×C22⋊C8D23
hypocenterC23#7566
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #15671222C2semidirect
4. #15671221C2semidirect
39. #10625095C8semidirect
82. C2×Dic46C2×C8semidirect
95. C4⋊Dic23C2×C8semidirect
245. C23#7566semidirect