Finite Group Databasebeta

← #19212260

Subgroups — #19212260

Order 5888.

646 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#15675961C211yesmaximal, characteristic
2#15673512C211yesmaximal, characteristic, complemented
3#15673141C211yesmaximal, characteristic, complemented
4#15671218C211yesmaximal, characteristic, complemented
5#15671217C211yesmaximal, characteristic, complemented
6#15671217C211yesmaximal, characteristic, complemented
7C23×#1270C211yesmaximal, characteristic, complemented
8C2×#10625111C411yescharacteristic
9C2×D4×Dic23C411yescharacteristic
10C2×#10625064C411yescharacteristic
11C2×(C22⋊D23)⋊C4—21no—
12C2×(C22⋊D23)⋊C4—21no—
13C2×Dic23⋊C8—21no—
14C2×C8×Dic23—21no—
15#13092319C2211yescharacteristic
16#13092317—21no—
17#13092317—21no—
18#13092286C411yescharacteristic
19C42×Dic23C2211yescharacteristic
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C22×C22⋊D23—21no—
29C22×C22⋊D23—21no—
30C23×Dic23—21no—
31C22×D92C2×C411yescharacteristic
32C22×C4×D23—21no—
33C22×C8×C23—21no—
34C22×C8×C23—21no—
35C2×C4⋊C4×C23C2×C411yescharacteristic
36C2×C22⋊C4×C23—21no—
37C2×C22⋊C4×C23—21no—
38C2×C42×C23C2311yescharacteristic
39C2×C22⋊Dic23—21no—
40#10625111—22no—
41#10625111C814yescomplemented
42D4×Dic23—42no—
43C2×(C2×D23)⋊C4—21no—
44C2×(C2×D23)⋊C4—21no—
45C2×(C2×D23)⋊C4—21no—
46C2×C4⋊Dic23C2×C411yescharacteristic
47C2×Dic23⋊C4—21no—
48C2×Dic23⋊C4—21no—
49C2×C4×Dic23C2×C411yescharacteristic
50C2×C4×Dic23C2×C411yescharacteristic
51C2×C4×Dic23D411yescharacteristic
52C2×C4×Dic23D411yescharacteristic
53C2×C4×Dic23D411yescharacteristic
54C2×C4×Dic23D411yescharacteristic
55C22×C23⋊C8—21no—
56C22×C23⋊C8—21no—
57#10625064—42no—
58(C22⋊D23)⋊C4—42no—
59(C22⋊D23)⋊C4—42no—
60(C22⋊D23)⋊C4—42no—
61(C22⋊D23)⋊C4—42no—
62Dic23⋊C8—42no—
63C8×Dic23—24no—
64C24×C23—21no—
65C23×D23—21no—
66C2×D4×C23—21no—
67C2×D4×C23—41no—
68C2×D4×C23—41no—
69C2×D4×C23C2×C812yes—
70C22×C4×C23—21no—
71C22×C4×C23C22×C411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C2×C22⋊D23—24no—
75C2×C22⋊D23—24no—
76C2×C22⋊D23—42no—
77C2×C22⋊D23—42no—
78C2×C22⋊D23—42no—
79C2×C22⋊D23—42no—
80C22×Dic23—21no—
81C22×Dic23—42no—
82C22×Dic23—42no—
83C22×Dic23—42no—
84C22×Dic23C22⋊C411yescharacteristic
85C22×Dic23C22⋊C411yescharacteristic
86C22×Dic23C22⋊C411yescharacteristic
87C22×Dic23C22⋊C411yescharacteristic
88C2×D92—21no—
89C2×D92—41no—
90C2×D92—41no—
91C2×D92C2×C812yes—
92C2×C4×D23—42no—
93C2×C4×D23—42no—
94C2×C4×D23—42no—
95C2×C8×C23—22no—
96C2×C8×C23—41no—
97C2×C8×C23—41no—
98C2×C8×C23—41no—
99C2×C8×C23—41no—
100C2×C8×C23—41no—
101C4⋊C4×C23—41no—
102C22⋊C4×C23—41no—
103C22⋊C4×C23—41no—
104C22⋊C4×C23—41no—
105C22⋊C4×C23—41no—
106C42×C23—41no—
107C22⋊Dic23—42no—
108(C2×D23)⋊C4—41no—
109(C2×D23)⋊C4—41no—
110(C2×D23)⋊C4—41no—
111(C2×D23)⋊C4—41no—
112(C2×D23)⋊C4—42no—
113C4⋊Dic23—41no—
114Dic23⋊C4—42no—
115Dic23⋊C4—42no—
116C4×Dic23—21no—
117C4×Dic23—21no—
118C4×Dic23—22no—
119C4×Dic23—22no—
120C4×Dic23—41no—
121C4×Dic23C2×C812yes—
122C4×Dic23M1612yes—
123C4×Dic23D812yes—
124C4×Dic23SD1612yes—
125C2×C23⋊C8—22no—
126C2×C23⋊C8—41no—
127C2×C23⋊C8—41no—
128C2×C23⋊C8—41no—
129C2×C23⋊C8—41no—
130C2×C23⋊C8—41no—
131#7587—231nomaximal, Sylow
132C23×C23—22no—
133C23×C23—41no—
134C23×C23—41no—
135C23×C23—41no—
136C23×C23—41no—
137C23×C23—41no—
138C23×C23—41no—
139C23×C23C2×C22⋊C411yescharacteristic
140C22×D23—22no—
141C22×D23—41no—
142C22×D23—41no—
143C22×D23—41no—
144C22×D23—41no—
145C22×D23—41no—
146C22×D23—41no—
147D4×C23—42no—
148D4×C23—42no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—41no—
156C2×C4×C23—41no—
157C2×C4×C23—41no—
158C2×C4×C23C22×C811yescharacteristic
159C2×C4×C23C2×M1611yescharacteristic
160C2×C4×C23C2×D811yescharacteristic
161C2×C4×C23C2×SD1611yescharacteristic
162C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
164C22⋊D23—48no—
165C22⋊D23—48no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168C2×Dic23—21no—
169C2×Dic23—21no—
170C2×Dic23—21no—
171C2×Dic23—21no—
172C2×Dic23—41no—
173C2×Dic23—41no—
174C2×Dic23—41no—
175C2×Dic23—84no—
176C2×Dic23C22⋊C812yes—
177C2×Dic23C22⋊C812yes—
178C2×Dic23#10012yes—
179C2×Dic23#10212yes—
180C2×Dic23#10212yes—
181C2×Dic23#10412yes—
182D92—42no—
183D92—42no—
184C4×D23—84no—
185C8×C23—42no—
186C8×C23—81no—
187C23⋊C8—42no—
188C23⋊C8—81no—
189C4×#127—231no—
190#1831—231no—
191#1744—231no—
192#1270—231no—
193#1270—231no—
194#1270—231no—
195#1270D2311yescharacteristic, complemented
196C22×C23—42no—
197C22×C23—42no—
198C22×C23—42no—
199C22×C23—81no—
200C22×C23—81no—
201C22×C23—81no—
202C22×C23—81no—
203C22×C23C2×C22⋊C811yescharacteristic
204C22×C23#41011yescharacteristic
205C22×C23C2×#10011yescharacteristic
206C22×C23C2×#10211yescharacteristic
207C22×C23#41811yescharacteristic
208C22×C23C2×#10411yescharacteristic
209C22×C23#42111yescharacteristic
210C2×D23—42no—
211C2×D23—42no—
212C2×D23—42no—
213C2×D23—81no—
214C2×D23—81no—
215C2×D23—81no—
216C2×D23—81no—
217C4×C23—21no—
218C4×C23—21no—
219C4×C23—21no—
220C4×C23—21no—
221C4×C23—21no—
222C4×C23—21no—
223C4×C23—81no—
224Dic23—22no—
225Dic23—22no—
226Dic23—22no—
227Dic23—81no—
228Dic23D4⋊C814yes—
229C2×#127—231no—
230C2×C4×D4—231no—
231C2×C4×D4—231no—
232C2×C4×D4—461no—
233C2×C4×D4—461no—
234C2×C4⋊C8—461no—
235C2×C4×C8—461no—
236#390—231no—
237#390—461no—
238#390—461no—
239#390C2×D2311yescharacteristic
240#384—231no—
241C43—231no—
242#336—231no—
243#336—231no—
244#336—461no—
245#336—461no—
246#336C2×D2311yescharacteristic
247#336C2×D2311yescharacteristic
248C2×C23—82no—
249C2×C23#146011yescharacteristic
250C2×C23C2×D4⋊C811yescharacteristic
251C2×C23#147811yescharacteristic
252C2×C23#150511yescharacteristic
253C2×C23#151711yescharacteristic
254C2×C23#153011yescharacteristic
255C2×C23#154511yescharacteristic
256D23—82no—
257C22×D4—231no—
258C22×D4—461no—
259C22×D4—461no—
260C22×D4C4×D2311yescharacteristic
261C23×C4—461no—
262C23×C4—461no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—461no—
266C22×C8—461no—
267#127—234no—
268#127—462no—
269C4×D4—922no—
270C4×D4—922no—
271C4×D4—922no—
272C4×D4—922no—
273C4×D4—922no—
274C4×D4—922no—
275C2×C4⋊C4—231no—
276C2×C4⋊C4—461no—
277C2×C4⋊C4—461no—
278C2×C4⋊C4C4×D2311yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—461no—
282C2×C22⋊C4—461no—
283C2×C22⋊C4—461no—
284C2×C22⋊C4—461no—
285C2×C42—231no—
286C2×C42—231no—
287C2×C42—231no—
288C2×C42—231no—
289C2×C42—231no—
290C2×C42—231no—
291C2×C42C22×D2311yescharacteristic
292C4⋊C8—922no—
293C4×C8—464no—
294C23#758711yescharacteristic, complemented, Sylow
295C24—21no—
296C24—461no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—232no—
301C2×D4—464no—
302C2×D4—464no—
303C2×D4—461no—
304C2×D4—921no—
305C2×D4—921no—
306C2×D4—922no—
307C2×D4—922no—
308C2×D4—922no—
309C2×D4—922no—
310C2×D4C8×D2312yes—
311C22×C4—21no—
312C22×C4—231no—
313C22×C4—231no—
314C22×C4—231no—
315C22×C4—231no—
316C22×C4—461no—
317C22×C4—922no—
318C22×C4—922no—
319C22×C4—922no—
320C22×C4—922no—
321C22×C4—922no—
322C22×C4—922no—
323C22×C4C2×C4×D2311yescharacteristic
324C22×C4D4×D2311yescharacteristic
325C22×C4D4×D2311yescharacteristic
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—462no—
333C2×C8—921no—
334C2×C8—921no—
335C2×C8—921no—
336C2×C8—921no—
337C2×C8—921no—
338C4⋊C4—41no—
339C4⋊C4—921no—
340C4⋊C4—922no—
341C4⋊C4—922no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—922no—
347C22⋊C4—922no—
348C22⋊C4—921no—
349C22⋊C4—921no—
350C22⋊C4—921no—
351C22⋊C4—921no—
352C42—41no—
353C42—232no—
354C42—232no—
355C42—232no—
356C42—232no—
357C42—462no—
358C42—462no—
359C42—461no—
360C42—461no—
361C42—921no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—462no—
370C23—921no—
371C23—921no—
372C23—921no—
373C23—921no—
374C23—921no—
375C23—921no—
376C23C22⋊C4×D2311yescharacteristic
377D4—42no—
378D4—42no—
379D4—922no—
380D4—922no—
381D4—928no—
382D4—928no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—232no—
393C2×C4—232no—
394C2×C4—232no—
395C2×C4—232no—
396C2×C4—232no—
397C2×C4—232no—
398C2×C4—461no—
399C2×C4—461no—
400C2×C4—461no—
401C2×C4—461no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—921no—
405C2×C4—921no—
406C2×C4—921no—
407C2×C4—1844no—
408C2×C4—1844no—
409C2×C4C2×C8×D2311yescharacteristic
410C2×C4M16×D2311yescharacteristic
411C2×C4D8×D2311yescharacteristic
412C2×C4#1062508211yescharacteristic
413C2×C4SD16×D2311yescharacteristic
414C2×C4#1062508511yescharacteristic
415C8—42no—
416C8—81no—
417C8—922no—
418C8—1841no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—922no—
427C22—922no—
428C22—922no—
429C22—1841no—
430C22—1841no—
431C22—1841no—
432C22—1841no—
433C22C22⋊C8×D2311yescharacteristic
434C22#1309238911yescharacteristic
435C22#100×D2311yescharacteristic
436C22#102×D2311yescharacteristic
437C22#1309242011yescharacteristic
438C22#104×D2311yescharacteristic
439C22#1309243211yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—234no—
448C4—462no—
449C4—462no—
450C4—462no—
451C4—1841no—
452C2—82no—
453C2—1842no—
454C2#1567171611yescharacteristic
455C2D23×D4⋊C811yescharacteristic
456C2#1567178611yescharacteristic
457C2#1567190311yescharacteristic
458C2#1567195511yescharacteristic
459C2#1567200611yescharacteristic
460C2#1567206311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7587
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673512C2semidirect
3. #15673141C2semidirect
4. #15671218C2semidirect
5. #15671217C2semidirect
6. #15671217C2semidirect
7. C23×#1270C2semidirect
41. #10625111C8semidirect
195. #1270D23semidirect
294. C23#7587semidirect