Finite Group Databasebeta

← #19212222

Subgroups — #19212222

Order 5888.

568 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675878C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic
3D23×#336C211yesmaximal, characteristic
4#15671221C211yesmaximal, characteristic, complemented
5#15671220C211yesmaximal, characteristic, complemented
6#15671219C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D23—21no—
9C2×#10625063C411yescharacteristic
10C2×#10625063C411yescharacteristic
11C2×C42×D23C2211yescharacteristic
12C2×(C2×D23)⋊C8—21no—
13#13092316C411yescharacteristic
14#13092315C2211yescharacteristic
15#13092313C411yescharacteristic
16#13092291—21no—
17#13092288—21no—
18C4⋊C4×Dic23—21no—
19#13092268—21no—
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×C4×D23C2×C411yescharacteristic
28C22×C4×D23D411yescharacteristic
29C22×C4×D23D411yescharacteristic
30C22×C8×C23—21no—
31C22×C8×C23—21no—
32C2×C4⋊C4×C23—21no—
33C2×C4⋊C4×C23C2×C411yescharacteristic
34C2×C4⋊C4×C23C2×C411yescharacteristic
35C2×C42×C23C2311yescharacteristic
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×C4⋊Dic23—21no—
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C2×C4×Dic23—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C22×C23⋊C8—21no—
49C22×C23⋊C8—21no—
50C2×C8×D23—24no—
51C2×C8×D23—42no—
52C2×C8×D23—42no—
53#10625063—22no—
54#10625063—42no—
55#10625063C814yescomplemented
56C42×D23—42no—
57C23×#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60C23⋊#95—21no—
61(C2×D23)⋊C8—42no—
62C23×D23C22⋊C411yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23C22×C411yescharacteristic
66C22×C4×C23C2×D411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23C22⋊C411yescharacteristic
71C22×Dic23C22⋊C411yescharacteristic
72C22×Dic23C22⋊C411yescharacteristic
73C2×C4×D23—22no—
74C2×C4×D23—22no—
75C2×C4×D23—22no—
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23—22no—
79C2×C4×D23—22no—
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23—41no—
83C2×C4×D23C2×C812yes—
84C2×C4×D23M1612yes—
85C2×C8×C23—22no—
86C2×C8×C23—41no—
87C2×C8×C23—41no—
88C2×C8×C23—41no—
89C2×C8×C23—41no—
90C2×C8×C23—41no—
91C4⋊C4×C23—21no—
92C4⋊C4×C23—41no—
93C4⋊C4×C23—41no—
94C4⋊C4×C23—41no—
95C4⋊C4×C23C2×C812yescomplemented
96C42×C23—41no—
97(C2×D23)⋊C4—24no—
98(C2×D23)⋊C4—42no—
99C4⋊Dic23—21no—
100C4⋊Dic23—42no—
101C4⋊Dic23—41no—
102C4⋊Dic23C2×C812yescomplemented
103Dic23⋊C4—41no—
104Dic23⋊C4—41no—
105Dic23⋊C4—42no—
106C4×Dic23—24no—
107C4×Dic23—41no—
108C4×Dic23—41no—
109C4×Dic23—41no—
110C4×Dic23—42no—
111C2×C23⋊C8—22no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115C2×C23⋊C8—41no—
116C2×C23⋊C8—41no—
117C8×D23—48no—
118#7579—231nomaximal, Sylow
119C23×C23C2×C22⋊C411yescharacteristic
120C22×D23—21no—
121C22×D23—21no—
122C22×D23—21no—
123C22×D23—21no—
124C22×D23C22⋊C812yes—
125C22×D23#9912yes—
126C22×D23#10112yes—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—22no—
134C2×C4×C23—41no—
135C2×C4×C23—41no—
136C2×C4×C23—41no—
137C2×C4×C23—41no—
138C2×C4×C23—41no—
139C2×C4×C23C22×C811yescharacteristic
140C2×C4×C23C2×M1611yescharacteristic
141C2×C4×C23#13511yescharacteristic
142C2×C4×C23#13511yescharacteristic
143C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C23#13711yescharacteristic
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—22no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157C2×Dic23—41no—
158C2×Dic23C22⋊C812yes—
159C2×Dic23#10412yes—
160C4×D23—24no—
161C4×D23—24no—
162C4×D23—24no—
163C4×D23—24no—
164C4×D23—42no—
165C4×D23—42no—
166C8×C23—42no—
167C8×C23—81no—
168C23⋊C8—42no—
169C23⋊C8—81no—
170#2296—231no—
171#1817—231no—
172C2×#336—231no—
173#1271—231no—
174#1271—231no—
175#1271—231no—
176#1271D2311yescharacteristic, complemented
177C22×C23C2×C22⋊C811yescharacteristic
178C22×C23C2×#9911yescharacteristic
179C22×C23C2×#10111yescharacteristic
180C22×C23#41611yescharacteristic
181C22×C23#41711yescharacteristic
182C22×C23C2×#10411yescharacteristic
183C22×C23#42111yescharacteristic
184C2×D23—22no—
185C2×D23—22no—
186C2×D23—22no—
187C2×D23—22no—
188C2×D23—22no—
189C2×D23—22no—
190C2×D23#32414yes—
191C4×C23—21no—
192C4×C23—21no—
193C4×C23—21no—
194C4×C23—21no—
195C4×C23—21no—
196C4×C23—21no—
197C4×C23—42no—
198C4×C23—81no—
199Dic23—22no—
200Dic23—22no—
201Dic23—42no—
202Dic23—41no—
203Dic23—81no—
204C23×C8—461no—
205C2×#117—231no—
206C2×#117—231no—
207C22×C42—231no—
208C2×C22⋊C8—461no—
209#389—231no—
210#389—231no—
211#389—231no—
212#389C2×D2311yescharacteristic
213#385—461no—
214#385—461no—
215C4×C4⋊C4—461no—
216C4×C4⋊C4—461no—
217#336—231no—
218#336—231no—
219#336—461no—
220#336—461no—
221#336C2×D2311yescharacteristic
222#336C2×D2311yescharacteristic
223C2×C23C2×#32411yescharacteristic
224C2×C23#147611yescharacteristic
225C2×C23#147711yescharacteristic
226C2×C23#150411yescharacteristic
227C2×C23#151611yescharacteristic
228C2×C23#153111yescharacteristic
229C2×C23#155211yescharacteristic
230D23—24no—
231C23×C4—231no—
232C23×C4—231no—
233C23×C4—231no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—464no—
237C22×C8—461no—
238C22×C8—461no—
239C22×C8—922no—
240C22×C8—922no—
241#117—234no—
242#117—462no—
243#117—922no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—231no—
246C2×C4⋊C4—231no—
247C2×C4⋊C4—461no—
248C2×C4⋊C4—461no—
249C2×C4⋊C4—461no—
250C2×C4⋊C4C4×D2311yescharacteristic
251C2×C4⋊C4C4×D2311yescharacteristic
252C2×C22⋊C4—461no—
253C2×C22⋊C4—461no—
254C2×C42—231no—
255C2×C42—231no—
256C2×C42—231no—
257C2×C42—461no—
258C2×C42—461no—
259C2×C42—922no—
260C2×C42C22×D2311yescharacteristic
261C22⋊C8—922no—
262#95—21no—
263#95—461no—
264#95—461no—
265#95—461no—
266C23#757911yescharacteristic, complemented, Sylow
267C24—231no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—231no—
271C22×C4—231no—
272C22×C4—232no—
273C22×C4—232no—
274C22×C4—231no—
275C22×C4—462no—
276C22×C4—462no—
277C22×C4—462no—
278C22×C4—462no—
279C22×C4—462no—
280C22×C4—461no—
281C22×C4—461no—
282C22×C4—461no—
283C22×C4—461no—
284C22×C4—461no—
285C22×C4—461no—
286C22×C4—921no—
287C22×C4C2×C4×D2311yescharacteristic
288C22×C4D4×D2311yescharacteristic
289C22×C4D4×D2311yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—462no—
297C2×C8—928no—
298C2×C8—921no—
299C2×C8—921no—
300C2×C8—921no—
301C2×C8—921no—
302C2×C8—921no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—232no—
308C4⋊C4—461no—
309C4⋊C4—921no—
310C4⋊C4—922no—
311C4⋊C4—922no—
312C4⋊C4—921no—
313C4⋊C4—921no—
314C4⋊C4C8×D2312yescomplemented
315C22⋊C4—464no—
316C22⋊C4—922no—
317C42—41no—
318C42—464no—
319C42—921no—
320C42—921no—
321C42—921no—
322C42—922no—
323C23—232no—
324C23—232no—
325C23—232no—
326C23—461no—
327C23—461no—
328C23—461no—
329C23—461no—
330C23C22⋊C4×D2311yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—232no—
344C2×C4—232no—
345C2×C4—464no—
346C2×C4—464no—
347C2×C4—464no—
348C2×C4—464no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—461no—
353C2×C4—462no—
354C2×C4—461no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—922no—
358C2×C4—922no—
359C2×C4—921no—
360C2×C4—921no—
361C2×C4—921no—
362C2×C4—921no—
363C2×C4—921no—
364C2×C4C2×C8×D2311yescharacteristic
365C2×C4M16×D2311yescharacteristic
366C2×C4#1062508211yescharacteristic
367C2×C4#1062508611yescharacteristic
368C2×C4#1062508711yescharacteristic
369C2×C4#1062509011yescharacteristic
370C8—42no—
371C8—81no—
372C8—922no—
373C8—1841no—
374C22—234no—
375C22—462no—
376C22—462no—
377C22—462no—
378C22—462no—
379C22—462no—
380C22—462no—
381C22C22⋊C8×D2311yescharacteristic
382C22#99×D2311yescharacteristic
383C22#101×D2311yescharacteristic
384C22#1309241211yescharacteristic
385C22#1309241511yescharacteristic
386C22#104×D2311yescharacteristic
387C22#1309243211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—462no—
397C4—462no—
398C4—921no—
399C4—922no—
400C4—1841no—
401C2—464no—
402C2D23×#32411yescharacteristic
403C2#1567177811yescharacteristic
404C2#1567178111yescharacteristic
405C2#1567189811yescharacteristic
406C2#1567195211yescharacteristic
407C2#1567201011yescharacteristic
408C2#1567209611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7579
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #15671221C2semidirect
5. #15671220C2semidirect
6. #15671219C2semidirect
7. C23×#1271C2semidirect
55. #10625063C8semidirect
95. C4⋊C4×C23C2×C8semidirect
102. C4⋊Dic23C2×C8semidirect
176. #1271D23semidirect
266. C23#7579semidirect
314. C4⋊C4C8×D23semidirect