Finite Group Databasebeta

← #19212237

Subgroups — #19212237

Order 5888.

606 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675905C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic, complemented
3#15673154C211yesmaximal, characteristic, complemented
4#15671220C211yesmaximal, characteristic, complemented
5#15671217C211yesmaximal, characteristic, complemented
6#15671217C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C2×#10625066C411yescharacteristic
9C2×#10625064—21no—
10C2×#10625064C411yescharacteristic
11C2×C42×D23C2211yescharacteristic
12C2×(C2×D23)⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14C2×C8×Dic23—21no—
15#13092319C2211yescharacteristic
16#13092307—21no—
17#13092295—21no—
18#13092274C411yescharacteristic
19C4⋊C4×Dic23C411yescharacteristic
20#13092264—21no—
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D92—21no—
28C22×D92C2×C411yescharacteristic
29C22×C4×D23—21no—
30C22×C4×D23C2×C411yescharacteristic
31C22×C4×D23D411yescharacteristic
32C22×C4×D23D411yescharacteristic
33C22×C8×C23—21no—
34C22×C8×C23—21no—
35C2×C4⋊C4×C23—21no—
36C2×C4⋊C4×C23C2×C411yescharacteristic
37C2×C4⋊C4×C23C2×C411yescharacteristic
38C2×C42×C23C2311yescharacteristic
39C2×(C2×D23)⋊C4—21no—
40C2×(C2×D23)⋊C4—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×(C2×D23)⋊C4—21no—
43C2×(C2×D23)⋊C4—21no—
44C2×C4⋊Dic23C2×C411yescharacteristic
45C2×C4×Dic23—21no—
46C2×C4×Dic23C2×C411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C22×C23⋊C8—21no—
50C22×C23⋊C8—21no—
51#10625066—22no—
52#10625066C814yescomplemented
53#10625064—42no—
54#10625064—42no—
55#10625064—42no—
56C42×D23—42no—
57C23×#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60(C2×D23)⋊C8—24no—
61(C2×D23)⋊C8—42no—
62C8×Dic23—42no—
63C23×D23—21no—
64C23×D23C22⋊C411yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23C22×C411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C22×Dic23—21no—
71C22×Dic23C22⋊C411yescharacteristic
72C22×Dic23C22⋊C411yescharacteristic
73C22×Dic23C22⋊C411yescharacteristic
74C2×D92—24no—
75C2×D92—21no—
76C2×D92—41no—
77C2×D92—41no—
78C2×D92—42no—
79C2×D92—42no—
80C2×D92C2×C812yes—
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23—21no—
84C2×C4×D23—21no—
85C2×C4×D23—22no—
86C2×C4×D23—22no—
87C2×C4×D23—41no—
88C2×C4×D23—41no—
89C2×C4×D23—41no—
90C2×C4×D23—41no—
91C2×C4×D23—42no—
92C2×C4×D23—42no—
93C2×C4×D23—42no—
94C2×C4×D23C2×C812yes—
95C2×C4×D23M1612yes—
96C2×C8×C23—22no—
97C2×C8×C23—41no—
98C2×C8×C23—41no—
99C2×C8×C23—41no—
100C2×C8×C23—41no—
101C2×C8×C23—41no—
102C4⋊C4×C23—21no—
103C4⋊C4×C23—41no—
104C4⋊C4×C23—41no—
105C4⋊C4×C23—41no—
106C4⋊C4×C23C2×C812yes—
107C42×C23—41no—
108(C2×D23)⋊C4—24no—
109(C2×D23)⋊C4—42no—
110(C2×D23)⋊C4—41no—
111(C2×D23)⋊C4—41no—
112(C2×D23)⋊C4—41no—
113(C2×D23)⋊C4—41no—
114(C2×D23)⋊C4—42no—
115C4⋊Dic23—41no—
116C4×Dic23—22no—
117C4×Dic23—22no—
118C4×Dic23—41no—
119C4×Dic23—42no—
120C2×C23⋊C8—22no—
121C2×C23⋊C8—41no—
122C2×C23⋊C8—41no—
123C2×C23⋊C8—41no—
124C2×C23⋊C8—41no—
125C2×C23⋊C8—41no—
126#7582—231nomaximal, Sylow
127C23×C23C2×C22⋊C411yescharacteristic
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23—21no—
132C22×D23—21no—
133C22×D23—21no—
134C22×D23—22no—
135C22×D23—41no—
136C22×D23—41no—
137C22×D23—41no—
138C22×D23—41no—
139C22×D23—41no—
140C22×D23—41no—
141C22×D23C22⋊C812yes—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—22no—
149C2×C4×C23—41no—
150C2×C4×C23—41no—
151C2×C4×C23—41no—
152C2×C4×C23—41no—
153C2×C4×C23—41no—
154C2×C4×C23C22×C811yescharacteristic
155C2×C4×C23C2×M1611yescharacteristic
156C2×C4×C23#13511yescharacteristic
157C2×C4×C23#13511yescharacteristic
158C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—41no—
167C2×Dic23—41no—
168C2×Dic23—41no—
169C2×Dic23C22⋊C812yes—
170C2×Dic23#9912yes—
171C2×Dic23#10412yes—
172D92—42no—
173D92—42no—
174D92—48no—
175C4×D23—42no—
176C4×D23—42no—
177C4×D23—42no—
178C4×D23—42no—
179C4×D23—42no—
180C4×D23—42no—
181C4×D23—84no—
182C8×C23—42no—
183C8×C23—81no—
184C23⋊C8—42no—
185C23⋊C8—81no—
186C4×#121—231no—
187#1817—231no—
188C4×C22⋊C8—231no—
189#1271—231no—
190#1271D2311yescharacteristic, complemented
191#1270—231no—
192#1270—231no—
193C22×C23C2×C22⋊C811yescharacteristic
194C22×C23C2×#9911yescharacteristic
195C22×C23#41311yescharacteristic
196C22×C23#41611yescharacteristic
197C22×C23#41811yescharacteristic
198C22×C23C2×#10411yescharacteristic
199C22×C23#42111yescharacteristic
200C2×D23—22no—
201C2×D23—22no—
202C2×D23—22no—
203C2×D23—41no—
204C2×D23—41no—
205C2×D23—41no—
206C2×D23—41no—
207C2×D23—42no—
208C2×D23—42no—
209C2×D23—42no—
210C2×D23—81no—
211C2×D23—81no—
212C2×D23—81no—
213C2×D23—81no—
214C4×C23—21no—
215C4×C23—21no—
216C4×C23—21no—
217C4×C23—21no—
218C4×C23—21no—
219C4×C23—21no—
220C4×C23—42no—
221C4×C23—81no—
222Dic23—22no—
223Dic23—22no—
224Dic23—22no—
225Dic23—81no—
226C2×#121—231no—
227C2×C4×D4—231no—
228C2×C4×D4—461no—
229C22×C42—231no—
230C2×C22⋊C8—461no—
231C2×C22⋊C8—461no—
232C2×C4×C8—461no—
233#390—231no—
234#389C2×D2311yescharacteristic
235#388—461no—
236#386—461no—
237#380—231no—
238C4×C4⋊C4—231no—
239C4×C22⋊C4—461no—
240#336—231no—
241#336—231no—
242#336—461no—
243#336C2×D2311yescharacteristic
244#336C2×D2311yescharacteristic
245C2×C23#145911yescharacteristic
246C2×C23#147611yescharacteristic
247C2×C23#147811yescharacteristic
248C2×C23#150711yescharacteristic
249C2×C23#151611yescharacteristic
250C2×C23#152911yescharacteristic
251C2×C23#155311yescharacteristic
252D23—42no—
253D23—82no—
254C22×D4—231no—
255C22×D4—461no—
256C23×C4—231no—
257C23×C4—231no—
258C23×C4—231no—
259C23×C4—461no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—461no—
263C22×C8—461no—
264#121—234no—
265#121—462no—
266C4×D4—922no—
267C4×D4—922no—
268C4×D4—922no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—231no—
271C2×C4⋊C4C4×D2311yescharacteristic
272C2×C4⋊C4C4×D2311yescharacteristic
273C2×C22⋊C4—461no—
274C2×C22⋊C4—461no—
275C2×C22⋊C4—461no—
276C2×C22⋊C4—461no—
277C2×C22⋊C4—461no—
278C2×C42—231no—
279C2×C42—231no—
280C2×C42—231no—
281C2×C42—461no—
282C2×C42—922no—
283C2×C42C22×D2311yescharacteristic
284C22⋊C8—464no—
285C22⋊C8—922no—
286C4×C8—922no—
287#95—21no—
288#95—461no—
289#95—461no—
290C23#758211yescharacteristic, complemented, Sylow
291C24—231no—
292C24—461no—
293C2×D4—232no—
294C2×D4—464no—
295C2×D4—461no—
296C2×D4—921no—
297C2×D4—921no—
298C2×D4—922no—
299C2×D4—922no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—231no—
303C22×C4—231no—
304C22×C4—231no—
305C22×C4—232no—
306C22×C4—232no—
307C22×C4—462no—
308C22×C4—462no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4—461no—
312C22×C4—461no—
313C22×C4—461no—
314C22×C4—921no—
315C22×C4—921no—
316C22×C4—921no—
317C22×C4—921no—
318C22×C4—922no—
319C22×C4—922no—
320C22×C4—922no—
321C22×C4C2×C4×D2311yescharacteristic
322C22×C4D4×D2311yescharacteristic
323C22×C4D4×D2311yescharacteristic
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—462no—
331C2×C8—921no—
332C2×C8—921no—
333C2×C8—921no—
334C2×C8—921no—
335C2×C8—921no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—921no—
341C4⋊C4C8×D2312yes—
342C22⋊C4—464no—
343C22⋊C4—922no—
344C22⋊C4—922no—
345C22⋊C4—921no—
346C22⋊C4—921no—
347C22⋊C4—921no—
348C22⋊C4—921no—
349C42—41no—
350C42—462no—
351C42—462no—
352C42—921no—
353C42—922no—
354C23—232no—
355C23—461no—
356C23—461no—
357C23—461no—
358C23—461no—
359C23—461no—
360C23—461no—
361C23—462no—
362C23—921no—
363C23—921no—
364C23—921no—
365C23—921no—
366C23—921no—
367C23—921no—
368C23C22⋊C4×D2311yescharacteristic
369D4—922no—
370D4—922no—
371D4—928no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—232no—
385C2×C4—232no—
386C2×C4—232no—
387C2×C4—461no—
388C2×C4—461no—
389C2×C4—461no—
390C2×C4—461no—
391C2×C4—461no—
392C2×C4—461no—
393C2×C4—922no—
394C2×C4—922no—
395C2×C4—922no—
396C2×C4—922no—
397C2×C4—922no—
398C2×C4—922no—
399C2×C4—921no—
400C2×C4—921no—
401C2×C4—921no—
402C2×C4—1844no—
403C2×C4C2×C8×D2311yescharacteristic
404C2×C4M16×D2311yescharacteristic
405C2×C4#1062508211yescharacteristic
406C2×C4#1062508511yescharacteristic
407C2×C4#1062508711yescharacteristic
408C2×C4#1062509011yescharacteristic
409C8—42no—
410C8—81no—
411C8—922no—
412C8—1841no—
413C22—462no—
414C22—462no—
415C22—462no—
416C22—921no—
417C22—921no—
418C22—921no—
419C22—921no—
420C22—922no—
421C22—922no—
422C22—922no—
423C22—1841no—
424C22—1841no—
425C22—1841no—
426C22—1841no—
427C22C22⋊C8×D2311yescharacteristic
428C22#99×D2311yescharacteristic
429C22#1309240011yescharacteristic
430C22#1309241211yescharacteristic
431C22#1309242011yescharacteristic
432C22#104×D2311yescharacteristic
433C22#1309243211yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—81no—
442C4—462no—
443C4—462no—
444C4—462no—
445C4—1841no—
446C2—922no—
447C2—1842no—
448C2#1567171411yescharacteristic
449C2#1567177811yescharacteristic
450C2#1567178611yescharacteristic
451C2#1567191111yescharacteristic
452C2#1567195211yescharacteristic
453C2#1567200311yescharacteristic
454C2#1567210111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7582
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
2. #15673464C2semidirect
3. #15673154C2semidirect
4. #15671220C2semidirect
5. #15671217C2semidirect
6. #15671217C2semidirect
7. C23×#1271C2semidirect
52. #10625066C8semidirect
190. #1271D23semidirect
290. C23#7582semidirect