Finite Group Databasebeta

← #19212257

Subgroups — #19212257

Order 5888.

662 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675905C211yesmaximal, characteristic
2#15673376C211yesmaximal, characteristic, complemented
3D23×#336C211yesmaximal, characteristic, complemented
4#15671220C211yesmaximal, characteristic, complemented
5#15671217C211yesmaximal, characteristic, complemented
6#15671217C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D23—21no—
9C2×#10625066C411yescharacteristic
10C2×#10625064—21no—
11C2×#10625064C411yescharacteristic
12C2×C42×D23C2211yescharacteristic
13C2×Dic23⋊C8—21no—
14C2×(C2×D23)⋊C8—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—
51C2×C8×D23—24no—
52C2×C8×D23—42no—
53C2×C8×D23—42no—
54#10625066—22no—
55#10625066C814yescomplemented
56#10625064—42no—
57#10625064—42no—
58#10625064—42no—
59C42×D23—42no—
60C23×#95—21no—
61C23⋊#95—21no—
62C23⋊#95—21no—
63(C2×D23)⋊C8—42no—
64Dic23⋊C8—42no—
65C23×D23—21no—
66C23×D23C22⋊C411yescharacteristic
67C22×C4×C23—21no—
68C22×C4×C23—21no—
69C22×C4×C23C22×C411yescharacteristic
70C22×C4×C23C2×D411yescharacteristic
71C22×C4×C23C2×D411yescharacteristic
72C22×Dic23—21no—
73C22×Dic23C22⋊C411yescharacteristic
74C22×Dic23C22⋊C411yescharacteristic
75C22×Dic23C22⋊C411yescharacteristic
76C2×D92—24no—
77C2×D92—21no—
78C2×D92—41no—
79C2×D92—41no—
80C2×D92—42no—
81C2×D92—42no—
82C2×D92C2×C812yescomplemented
83C2×C4×D23—22no—
84C2×C4×D23—21no—
85C2×C4×D23—21no—
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×C4×D23D812yes—
97C2×C4×D23SD1612yes—
98C2×C8×C23—22no—
99C2×C8×C23—41no—
100C2×C8×C23—41no—
101C2×C8×C23—41no—
102C2×C8×C23—41no—
103C2×C8×C23—41no—
104C4⋊C4×C23—21no—
105C4⋊C4×C23—41no—
106C4⋊C4×C23—41no—
107C4⋊C4×C23—41no—
108C4⋊C4×C23C2×C812yescomplemented
109C42×C23—41no—
110(C2×D23)⋊C4—24no—
111(C2×D23)⋊C4—42no—
112(C2×D23)⋊C4—41no—
113(C2×D23)⋊C4—41no—
114(C2×D23)⋊C4—41no—
115(C2×D23)⋊C4—41no—
116(C2×D23)⋊C4—42no—
117C4⋊Dic23—41no—
118C4×Dic23—22no—
119C4×Dic23—22no—
120C4×Dic23—41no—
121C4×Dic23—42no—
122C2×C23⋊C8—22no—
123C2×C23⋊C8—41no—
124C2×C23⋊C8—41no—
125C2×C23⋊C8—41no—
126C2×C23⋊C8—41no—
127C2×C23⋊C8—41no—
128C8×D23—48no—
129#7586—231nomaximal, Sylow
130C23×C23C2×C22⋊C411yescharacteristic
131C22×D23—21no—
132C22×D23—21no—
133C22×D23—21no—
134C22×D23—21no—
135C22×D23—22no—
136C22×D23—41no—
137C22×D23—41no—
138C22×D23—41no—
139C22×D23—41no—
140C22×D23—41no—
141C22×D23—41no—
142C22×D23C22⋊C812yes—
143C22×D23#10212yes—
144C22×D23#10412yes—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—22no—
152C2×C4×C23—41no—
153C2×C4×C23—41no—
154C2×C4×C23—41no—
155C2×C4×C23—41no—
156C2×C4×C23—41no—
157C2×C4×C23C22×C811yescharacteristic
158C2×C4×C23C2×M1611yescharacteristic
159C2×C4×C23C2×D811yescharacteristic
160C2×C4×C23C2×SD1611yescharacteristic
161C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C23#13711yescharacteristic
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168C2×Dic23—21no—
169C2×Dic23—41no—
170C2×Dic23—41no—
171C2×Dic23—41no—
172C2×Dic23C22⋊C812yes—
173C2×Dic23#9912yes—
174C2×Dic23#10212yes—
175D92—42no—
176D92—42no—
177D92—48no—
178C4×D23—24no—
179C4×D23—24no—
180C4×D23—42no—
181C4×D23—42no—
182C4×D23—42no—
183C4×D23—42no—
184C4×D23—84no—
185C8×C23—42no—
186C8×C23—81no—
187C23⋊C8—42no—
188C23⋊C8—81no—
189C4×#121—231no—
190#1797—231no—
191C2×#336—231no—
192#1271—231no—
193#1271D2311yescharacteristic, complemented
194#1270—231no—
195#1270—231no—
196C22×C23C2×C22⋊C811yescharacteristic
197C22×C23C2×#9911yescharacteristic
198C22×C23#41311yescharacteristic
199C22×C23C2×#10211yescharacteristic
200C22×C23#41711yescharacteristic
201C22×C23C2×#10411yescharacteristic
202C22×C23#42111yescharacteristic
203C2×D23—22no—
204C2×D23—22no—
205C2×D23—22no—
206C2×D23—22no—
207C2×D23—22no—
208C2×D23—22no—
209C2×D23—42no—
210C2×D23—42no—
211C2×D23—42no—
212C2×D23—81no—
213C2×D23—81no—
214C2×D23—81no—
215C2×D23—81no—
216C2×D23D4⋊C814yes—
217C4×C23—21no—
218C4×C23—21no—
219C4×C23—21no—
220C4×C23—21no—
221C4×C23—21no—
222C4×C23—21no—
223C4×C23—42no—
224C4×C23—81no—
225Dic23—22no—
226Dic23—22no—
227Dic23—22no—
228Dic23—81no—
229C23×C8—461no—
230C2×#121—231no—
231C2×C4×D4—231no—
232C2×C4×D4—461no—
233C22×C42—231no—
234C2×C4⋊C8—461no—
235C2×C22⋊C8—461no—
236#390—231no—
237#389C2×D2311yescharacteristic
238#388—461no—
239#386—461no—
240#380—231no—
241C4×C4⋊C4—231no—
242C4×C22⋊C4—461no—
243#336—231no—
244#336—231no—
245#336—461no—
246#336C2×D2311yescharacteristic
247#336C2×D2311yescharacteristic
248C2×C23#145911yescharacteristic
249C2×C23C2×D4⋊C811yescharacteristic
250C2×C23#147711yescharacteristic
251C2×C23#150411yescharacteristic
252C2×C23#151911yescharacteristic
253C2×C23#153211yescharacteristic
254C2×C23#154711yescharacteristic
255D23—24no—
256D23—82no—
257C22×D4—231no—
258C22×D4—461no—
259C23×C4—231no—
260C23×C4—231no—
261C23×C4—231no—
262C23×C4—461no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—464no—
266C22×C8—461no—
267C22×C8—461no—
268C22×C8—922no—
269C22×C8—922no—
270#121—234no—
271#121—462no—
272C4×D4—922no—
273C4×D4—922no—
274C4×D4—922no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—231no—
277C2×C4⋊C4C4×D2311yescharacteristic
278C2×C4⋊C4C4×D2311yescharacteristic
279C2×C22⋊C4—461no—
280C2×C22⋊C4—461no—
281C2×C22⋊C4—461no—
282C2×C22⋊C4—461no—
283C2×C22⋊C4—461no—
284C2×C42—231no—
285C2×C42—231no—
286C2×C42—231no—
287C2×C42—461no—
288C2×C42—922no—
289C2×C42C22×D2311yescharacteristic
290C4⋊C8—922no—
291C22⋊C8—922no—
292#95—21no—
293#95—461no—
294#95—461no—
295C23#758611yescharacteristic, complemented, Sylow
296C24—231no—
297C24—461no—
298C2×D4—232no—
299C2×D4—464no—
300C2×D4—461no—
301C2×D4—921no—
302C2×D4—921no—
303C2×D4—922no—
304C2×D4—922no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—231no—
308C22×C4—231no—
309C22×C4—231no—
310C22×C4—232no—
311C22×C4—232no—
312C22×C4—232no—
313C22×C4—232no—
314C22×C4—462no—
315C22×C4—462no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4—461no—
319C22×C4—921no—
320C22×C4—921no—
321C22×C4—921no—
322C22×C4—921no—
323C22×C4—922no—
324C22×C4—922no—
325C22×C4—922no—
326C22×C4C2×C4×D2311yescharacteristic
327C22×C4D4×D2311yescharacteristic
328C22×C4D4×D2311yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—462no—
336C2×C8—928no—
337C2×C8—921no—
338C2×C8—921no—
339C2×C8—921no—
340C2×C8—921no—
341C2×C8—921no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—921no—
347C4⋊C4C8×D2312yescomplemented
348C22⋊C4—464no—
349C22⋊C4—922no—
350C22⋊C4—922no—
351C22⋊C4—921no—
352C22⋊C4—921no—
353C22⋊C4—921no—
354C22⋊C4—921no—
355C42—41no—
356C42—462no—
357C42—462no—
358C42—921no—
359C42—922no—
360C23—232no—
361C23—232no—
362C23—232no—
363C23—461no—
364C23—461no—
365C23—461no—
366C23—461no—
367C23—462no—
368C23—921no—
369C23—921no—
370C23—921no—
371C23—921no—
372C23—921no—
373C23—921no—
374C23C22⋊C4×D2311yescharacteristic
375D4—922no—
376D4—922no—
377D4—928no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—232no—
391C2×C4—232no—
392C2×C4—232no—
393C2×C4—464no—
394C2×C4—464no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—461no—
399C2×C4—461no—
400C2×C4—461no—
401C2×C4—922no—
402C2×C4—922no—
403C2×C4—922no—
404C2×C4—922no—
405C2×C4—921no—
406C2×C4—921no—
407C2×C4—921no—
408C2×C4—1844no—
409C2×C4C2×C8×D2311yescharacteristic
410C2×C4M16×D2311yescharacteristic
411C2×C4D8×D2311yescharacteristic
412C2×C4SD16×D2311yescharacteristic
413C2×C4#1062508511yescharacteristic
414C2×C4#1062508911yescharacteristic
415C8—42no—
416C8—81no—
417C8—922no—
418C8—1841no—
419C22—234no—
420C22—462no—
421C22—462no—
422C22—462no—
423C22—462no—
424C22—462no—
425C22—462no—
426C22—922no—
427C22—922no—
428C22—922no—
429C22—1841no—
430C22—1841no—
431C22—1841no—
432C22—1841no—
433C22C22⋊C8×D2311yescharacteristic
434C22#99×D2311yescharacteristic
435C22#1309240011yescharacteristic
436C22#102×D2311yescharacteristic
437C22#1309241711yescharacteristic
438C22#104×D2311yescharacteristic
439C22#1309243211yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—462no—
449C4—462no—
450C4—462no—
451C4—1841no—
452C2—464no—
453C2—1842no—
454C2#1567171411yescharacteristic
455C2D23×D4⋊C811yescharacteristic
456C2#1567178311yescharacteristic
457C2#1567190011yescharacteristic
458C2#1567196311yescharacteristic
459C2#1567201611yescharacteristic
460C2#1567207311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7586
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. #15673376C2semidirect
3. D23×#336C2semidirect
4. #15671220C2semidirect
5. #15671217C2semidirect
6. #15671217C2semidirect
7. C23×#1271C2semidirect
55. #10625066C8semidirect
82. C2×D92C2×C8semidirect
108. C4⋊C4×C23C2×C8semidirect
193. #1271D23semidirect
295. C23#7586semidirect
347. C4⋊C4C8×D23semidirect