Finite Group Databasebeta

← #19212242

Subgroups — #19212242

Order 5888.

522 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#15675935C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic
3#15673154C211yesmaximal, characteristic
4#15671223C211yesmaximal, characteristic, complemented
5#15671221C211yesmaximal, characteristic, complemented
6#15671219C211yesmaximal, characteristic, complemented
7C23×#1272C211yesmaximal, characteristic, complemented
8C2×#10625117C411yescharacteristic
9C2×Q8×Dic23C411yescharacteristic
10C2×C42×D23C2211yescharacteristic
11C2×(C2×D23)⋊C8—21no—
12C2×(C2×D23)⋊C8—21no—
13C2×C8×Dic23—21no—
14#13092315C2211yescharacteristic
15#13092304—21no—
16#13092291—21no—
17#13092274C411yescharacteristic
18C4⋊C4×Dic23C411yescharacteristic
19#13092268—21no—
20#13092264—21no—
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#391C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×Q8×C23C2×C411yescharacteristic
28C22×C4×D23C2×C411yescharacteristic
29C22×C4×D23D411yescharacteristic
30C22×C4×D23D411yescharacteristic
31C22×C8×C23—21no—
32C22×C8×C23—21no—
33C2×C4⋊C4×C23C2×C411yescharacteristic
34C2×C42×C23C2311yescharacteristic
35#10625117—22no—
36#10625117C814yescomplemented
37Q8×Dic23—42no—
38C2×(C2×D23)⋊C4—21no—
39C2×(C2×D23)⋊C4—21no—
40C2×C4⋊Dic23—21no—
41C2×C4⋊Dic23C2×C411yescharacteristic
42C2×C4⋊Dic23C2×C411yescharacteristic
43C2×Dic23⋊C4—21no—
44C2×Dic23⋊C4—21no—
45C2×C4×Dic23—21no—
46C2×C4×Dic23—21no—
47C2×C4×Dic23C2×C411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C2×C4×Dic23D411yescharacteristic
50C22×C23⋊C8—21no—
51C22×C23⋊C8—21no—
52C42×D23—42no—
53C23×#95—21no—
54C23×#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58(C2×D23)⋊C8—24no—
59(C2×D23)⋊C8—42no—
60C8×Dic23—42no—
61C23×D23C22⋊C411yescharacteristic
62C2×Q8×C23—21no—
63C2×Q8×C23—41no—
64C2×Q8×C23—41no—
65C2×Q8×C23C2×C812yes—
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23C22×C411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C22×C4×C23C2×D411yescharacteristic
71C22×Dic23—21no—
72C22×Dic23—21no—
73C22×Dic23C22⋊C411yescharacteristic
74C22×Dic23C22⋊C411yescharacteristic
75C22×Dic23C22⋊C411yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23—22no—
81C2×C4×D23—22no—
82C2×C4×D23—41no—
83C2×C4×D23—41no—
84C2×C4×D23—41no—
85C2×C4×D23—41no—
86C2×C4×D23C2×C812yes—
87C2×C4×D23M1612yes—
88C2×C8×C23—22no—
89C2×C8×C23—41no—
90C2×C8×C23—41no—
91C2×C8×C23—41no—
92C2×C8×C23—41no—
93C2×C8×C23—41no—
94C4⋊C4×C23—41no—
95C42×C23—41no—
96(C2×D23)⋊C4—24no—
97(C2×D23)⋊C4—42no—
98C4⋊Dic23—21no—
99C4⋊Dic23—42no—
100C4⋊Dic23—41no—
101C4⋊Dic23C2×C812yes—
102Dic23⋊C4—24no—
103Dic23⋊C4—41no—
104Dic23⋊C4—41no—
105C4×Dic23—22no—
106C4×Dic23—22no—
107C4×Dic23—41no—
108C4×Dic23—42no—
109C4×Dic23—42no—
110C2×C23⋊C8—22no—
111C2×C23⋊C8—41no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115C2×C23⋊C8—41no—
116#7583—231nomaximal, Sylow
117C23×C23C2×C22⋊C411yescharacteristic
118C22×D23—21no—
119C22×D23—21no—
120C22×D23—21no—
121C22×D23—21no—
122C22×D23—21no—
123C22×D23—21no—
124C22×D23C22⋊C812yes—
125Q8×C23—42no—
126Q8×C23—42no—
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×C23#13711yescharacteristic
144C2×C4×C23#13711yescharacteristic
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—22no—
152C2×Dic23—41no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157C2×Dic23C22⋊C812yes—
158C2×Dic23#9912yes—
159C2×Dic23#10412yes—
160C4×D23—42no—
161C4×D23—42no—
162C4×D23—42no—
163C4×D23—42no—
164C4×D23—42no—
165C4×D23—42no—
166C8×C23—42no—
167C8×C23—81no—
168C23⋊C8—42no—
169C23⋊C8—81no—
170C4×C22⋊Q8—231no—
171#1817—231no—
172C4×C22⋊C8—231no—
173#1272—231no—
174#1272D2311yescharacteristic, complemented
175#1271—231no—
176#1271—231no—
177C22×C23C2×C22⋊C811yescharacteristic
178C22×C23C2×#9911yescharacteristic
179C22×C23#41311yescharacteristic
180C22×C23#41611yescharacteristic
181C22×C23#41911yescharacteristic
182C22×C23C2×#10411yescharacteristic
183C22×C23#42111yescharacteristic
184C2×D23—22no—
185C2×D23—22no—
186C2×D23—22no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—41no—
190C2×D23—41no—
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—22no—
202Dic23—42no—
203Dic23—81no—
204C2×C22⋊Q8—231no—
205C2×C4×Q8—231no—
206C22×C42—231no—
207C2×C22⋊C8—461no—
208C2×C22⋊C8—461no—
209C2×C4×C8—461no—
210#391C2×D2311yescharacteristic
211#389—231no—
212#387—461no—
213#385—461no—
214#380—231no—
215C4×C4⋊C4—231no—
216C4×C4⋊C4—461no—
217C4×C22⋊C4—461no—
218#336—231no—
219#336—231no—
220#336—461no—
221#336C2×D2311yescharacteristic
222#336C2×D2311yescharacteristic
223C2×C23#145911yescharacteristic
224C2×C23#147611yescharacteristic
225C2×C23#147911yescharacteristic
226C2×C23#150811yescharacteristic
227C2×C23#151611yescharacteristic
228C2×C23#152911yescharacteristic
229C2×C23#155411yescharacteristic
230D23—42no—
231C22×Q8C4×D2311yescharacteristic
232C23×C4—231no—
233C23×C4—231no—
234C23×C4—231no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—461no—
238C22×C8—461no—
239C22⋊Q8—234no—
240C22⋊Q8—462no—
241C4×Q8—922no—
242C2×C4⋊C4—231no—
243C2×C4⋊C4—231no—
244C2×C4⋊C4—461no—
245C2×C4⋊C4—461no—
246C2×C4⋊C4—461no—
247C2×C4⋊C4C4×D2311yescharacteristic
248C2×C22⋊C4—461no—
249C2×C22⋊C4—461no—
250C2×C42—231no—
251C2×C42—231no—
252C2×C42—231no—
253C2×C42—461no—
254C2×C42—461no—
255C2×C42—922no—
256C2×C42C22×D2311yescharacteristic
257C22⋊C8—464no—
258C22⋊C8—922no—
259C4×C8—922no—
260#95—21no—
261#95—21no—
262#95—461no—
263#95—461no—
264#95—461no—
265C23#758311yescharacteristic, complemented, Sylow
266C24—231no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8C8×D2312yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—231no—
274C22×C4—231no—
275C22×C4—231no—
276C22×C4—232no—
277C22×C4—232no—
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×C4—921no—
288C22×C4—921no—
289C22×C4—921no—
290C22×C4C2×C4×D2311yescharacteristic
291C22×C4D4×D2311yescharacteristic
292C22×C4D4×D2311yescharacteristic
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—462no—
300C2×C8—921no—
301C2×C8—921no—
302C2×C8—921no—
303C2×C8—921no—
304C2×C8—921no—
305C4⋊C4—41no—
306C4⋊C4—232no—
307C4⋊C4—464no—
308C4⋊C4—461no—
309C4⋊C4—921no—
310C4⋊C4—922no—
311C4⋊C4—921no—
312C4⋊C4—921no—
313C22⋊C4—464no—
314C22⋊C4—922no—
315C42—41no—
316C42—462no—
317C42—462no—
318C42—921no—
319C42—922no—
320C42—922no—
321C23—232no—
322C23—461no—
323C23—461no—
324C23—461no—
325C23—461no—
326C23—461no—
327C23—461no—
328C23C22⋊C4×D2311yescharacteristic
329Q8—42no—
330Q8—42no—
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—232no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—462no—
353C2×C4—922no—
354C2×C4—922no—
355C2×C4—922no—
356C2×C4—922no—
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#1062508611yescharacteristic
367C2×C4#1062508711yescharacteristic
368C2×C4#1062508911yescharacteristic
369C2×C4#1062509011yescharacteristic
370C8—42no—
371C8—81no—
372C8—922no—
373C8—1841no—
374C22—462no—
375C22—462no—
376C22—462no—
377C22—921no—
378C22—921no—
379C22—921no—
380C22—921no—
381C22C22⋊C8×D2311yescharacteristic
382C22#99×D2311yescharacteristic
383C22#1309239811yescharacteristic
384C22#1309241211yescharacteristic
385C22#1309242411yescharacteristic
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—462no—
399C4—922no—
400C4—1841no—
401C2—922no—
402C2#1567171211yescharacteristic
403C2#1567177811yescharacteristic
404C2#1567179011yescharacteristic
405C2#1567191511yescharacteristic
406C2#1567195211yescharacteristic
407C2#1567200111yescharacteristic
408C2#1567210611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7583
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #15671223C2semidirect
5. #15671221C2semidirect
6. #15671219C2semidirect
7. C23×#1272C2semidirect
36. #10625117C8semidirect
174. #1272D23semidirect
265. C23#7583semidirect