Finite Group Databasebeta

← #19212235

Subgroups — #19212235

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#15675913C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic, complemented
3#15673154C211yesmaximal, characteristic, complemented
4#15671221C211yesmaximal, characteristic, complemented
5#15671219C211yesmaximal, characteristic, complemented
6#15671218C211yesmaximal, characteristic, complemented
7C23×#1270C211yesmaximal, characteristic, complemented
8C2×#10625109C411yescharacteristic
9C2×D4×Dic23C411yescharacteristic
10C2×(C22⋊D23)⋊C4—21no—
11C2×C42×D23C2211yescharacteristic
12C2×(C2×D23)⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14C2×C8×Dic23—21no—
15#13092315C2211yescharacteristic
16#13092311—21no—
17#13092293—21no—
18#13092274C411yescharacteristic
19C4⋊C4×Dic23C411yescharacteristic
20C22⋊C4×Dic23—21no—
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C22×C22⋊D23—21no—
29C23×Dic23—21no—
30C22×C4×D23C2×C411yescharacteristic
31C22×C4×D23D411yescharacteristic
32C22×C4×D23D411yescharacteristic
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—
40C2×C22⋊Dic23—21no—
41#10625109—22no—
42#10625109C814yescomplemented
43D4×Dic23—42no—
44C2×(C2×D23)⋊C4—21no—
45C2×C4⋊Dic23C2×C411yescharacteristic
46C2×C4⋊Dic23C2×C411yescharacteristic
47C2×Dic23⋊C4—21no—
48C2×C4×Dic23—21no—
49C2×C4×Dic23C2×C411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C2×C4×Dic23D411yescharacteristic
52C22×C23⋊C8—21no—
53C22×C23⋊C8—21no—
54(C22⋊D23)⋊C4—42no—
55(C22⋊D23)⋊C4—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—
63C24×C23—21no—
64C23×D23C22⋊C411yescharacteristic
65C2×D4×C23—21no—
66C2×D4×C23—41no—
67C2×D4×C23—41no—
68C2×D4×C23C2×C812yes—
69C22×C4×C23—21no—
70C22×C4×C23C22×C411yescharacteristic
71C22×C4×C23C2×D411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C2×C22⋊D23—24no—
74C2×C22⋊D23—42no—
75C2×C22⋊D23—42no—
76C22×Dic23—21no—
77C22×Dic23—21no—
78C22×Dic23—42no—
79C22×Dic23—42no—
80C22×Dic23—42no—
81C22×Dic23C22⋊C411yescharacteristic
82C22×Dic23C22⋊C411yescharacteristic
83C22×Dic23C22⋊C411yescharacteristic
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×C4×D23—21no—
87C2×C4×D23—21no—
88C2×C4×D23—22no—
89C2×C4×D23—22no—
90C2×C4×D23—41no—
91C2×C4×D23—41no—
92C2×C4×D23—41no—
93C2×C4×D23—41no—
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—41no—
103C22⋊C4×C23—41no—
104C22⋊C4×C23—41no—
105C22⋊C4×C23—41no—
106C22⋊C4×C23—41no—
107C42×C23—41no—
108C22⋊Dic23—24no—
109C22⋊Dic23—42no—
110(C2×D23)⋊C4—42no—
111C4⋊Dic23—21no—
112C4⋊Dic23—41no—
113C4⋊Dic23C2×C812yes—
114Dic23⋊C4—41no—
115Dic23⋊C4—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×C23—22no—
128C23×C23—41no—
129C23×C23—41no—
130C23×C23—41no—
131C23×C23—41no—
132C23×C23—41no—
133C23×C23—41no—
134C23×C23C2×C22⋊C411yescharacteristic
135C22×D23—21no—
136C22×D23—21no—
137C22×D23—21no—
138C22×D23—21no—
139C22×D23—21no—
140C22×D23—21no—
141C22×D23C22⋊C812yes—
142D4×C23—42no—
143D4×C23—42no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—41no—
151C2×C4×C23—41no—
152C2×C4×C23—41no—
153C2×C4×C23C22×C811yescharacteristic
154C2×C4×C23C2×M1611yescharacteristic
155C2×C4×C23#13511yescharacteristic
156C2×C4×C23#13511yescharacteristic
157C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
159C22⋊D23—48no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—22no—
167C2×Dic23—41no—
168C2×Dic23—41no—
169C2×Dic23—41no—
170C2×Dic23—41no—
171C2×Dic23—41no—
172C2×Dic23—84no—
173C2×Dic23C22⋊C812yes—
174C2×Dic23#9912yes—
175C2×Dic23#10412yes—
176C4×D23—42no—
177C4×D23—42no—
178C4×D23—42no—
179C4×D23—42no—
180C4×D23—42no—
181C4×D23—42no—
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#1271—231no—
191#1270—231no—
192#1270D2311yescharacteristic, complemented
193C22×C23—42no—
194C22×C23—42no—
195C22×C23—42no—
196C22×C23—81no—
197C22×C23—81no—
198C22×C23—81no—
199C22×C23—81no—
200C22×C23C2×C22⋊C811yescharacteristic
201C22×C23C2×#9911yescharacteristic
202C22×C23#41311yescharacteristic
203C22×C23#41611yescharacteristic
204C22×C23#41811yescharacteristic
205C22×C23C2×#10411yescharacteristic
206C22×C23#42111yescharacteristic
207C2×D23—22no—
208C2×D23—22no—
209C2×D23—22no—
210C2×D23—41no—
211C2×D23—41no—
212C2×D23—41no—
213C2×D23—41no—
214C4×C23—21no—
215C4×C23—21no—
216C4×C23—21no—
217C4×C23—21no—
218C4×C23—21no—
219C4×C23—21no—
220C4×C23—81no—
221Dic23—22no—
222Dic23—22no—
223Dic23—22no—
224Dic23—42no—
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#390C2×D2311yescharacteristic
234#389—231no—
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—82no—
246C2×C23#145911yescharacteristic
247C2×C23#147611yescharacteristic
248C2×C23#147811yescharacteristic
249C2×C23#150711yescharacteristic
250C2×C23#151611yescharacteristic
251C2×C23#152911yescharacteristic
252C2×C23#155311yescharacteristic
253D23—42no—
254C22×D4—461no—
255C22×D4C4×D2311yescharacteristic
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—231no—
270C2×C4⋊C4—231no—
271C2×C4⋊C4—461no—
272C2×C4⋊C4C4×D2311yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
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—461no—
288#95—461no—
289#95—461no—
290C23#758211yescharacteristic, complemented, Sylow
291C24—21no—
292C24—231no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—464no—
297C2×D4—922no—
298C2×D4—922no—
299C2×D4C8×D2312yes—
300C22×C4—21no—
301C22×C4—231no—
302C22×C4—231no—
303C22×C4—231no—
304C22×C4—232no—
305C22×C4—232no—
306C22×C4—462no—
307C22×C4—462no—
308C22×C4—461no—
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—41no—
337C4⋊C4—232no—
338C4⋊C4—461no—
339C4⋊C4—921no—
340C4⋊C4—921no—
341C4⋊C4—921no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—464no—
347C22⋊C4—922no—
348C22⋊C4—922no—
349C42—41no—
350C42—462no—
351C42—462no—
352C42—921no—
353C42—922no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—232no—
362C23—461no—
363C23—461no—
364C23—461no—
365C23—461no—
366C23—461no—
367C23—461no—
368C23C22⋊C4×D2311yescharacteristic
369D4—42no—
370D4—42no—
371D4—928no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—232no—
382C2×C4—232no—
383C2×C4—232no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—461no—
389C2×C4—461no—
390C2×C4—462no—
391C2×C4—922no—
392C2×C4—922no—
393C2×C4—922no—
394C2×C4—922no—
395C2×C4—922no—
396C2×C4—922no—
397C2×C4—921no—
398C2×C4—921no—
399C2×C4—921no—
400C2×C4—921no—
401C2×C4—921no—
402C2×C4—1844no—
403C2×C4C2×C8×D2311yescharacteristic
404C2×C4M16×D2311yescharacteristic
405C2×C4#1062508211yescharacteristic
406C2×C4#1062508311yescharacteristic
407C2×C4#1062508511yescharacteristic
408C2×C4#1062508711yescharacteristic
409C8—42no—
410C8—81no—
411C8—922no—
412C8—1841no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—462no—
421C22—462no—
422C22—462no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22C22⋊C8×D2311yescharacteristic
428C22#99×D2311yescharacteristic
429C22#1309239811yescharacteristic
430C22#1309241011yescharacteristic
431C22#1309242011yescharacteristic
432C22#104×D2311yescharacteristic
433C22#1309243211yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—462no—
442C4—462no—
443C4—462no—
444C4—922no—
445C4—1841no—
446C2—82no—
447C2—922no—
448C2#1567171211yescharacteristic
449C2#1567177611yescharacteristic
450C2#1567178611yescharacteristic
451C2#1567191111yescharacteristic
452C2#1567195011yescharacteristic
453C2#1567200111yescharacteristic
454C2#1567209911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7582
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. #15673464C2semidirect
3. #15673154C2semidirect
4. #15671221C2semidirect
5. #15671219C2semidirect
6. #15671218C2semidirect
7. C23×#1270C2semidirect
42. #10625109C8semidirect
192. #1270D23semidirect
290. C23#7582semidirect